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by Copyright Mohammed Awad Al-Juaied 2004 The Dissertation Committee for Mohammed Awad Al-Juaied Certifies that this is the approved version of the following dissertation: Carbon Dioxide Removal from Natural Gas by Membranes in the Presence of Heavy Hydrocarbons and by Aqueous Diglycolamine /Morpholine Committee: __________________________ Gary T. Rochelle, Supervisor __________________________ William J. Koros, Co-Supervisor __________________________ Donald R Paul __________________________ Douglas R. Lloyd __________________________ R. Bruce Eldridge __________________________ Kamy Sepehrnoori Carbon Dioxide Removal from Natural Gas by Membranes in the Presence of Heavy Hydrocarbons and by Aqueous Diglycolamine /Morpholine by Mohammed Awad Al-Juaied, B.Sc.; M.S. Dissertation Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy The University of Texas at Austin May, 2004 Dedication To My Family Acknowledgements I would like to thank everyone who contributed to my education and experience throughout graduate school. I would like to express my gratitude to Professor Bill Koros and Professor Gary Rochelle for their guidance and support throughout this work. I am thankful for the chance to work for such professors. I would also like to acknowledge Saudi Aramco who financially supported me during my four years at UT. I would like to thank Dr.Paul for including me as part of his group from the time Dr.Koros left UT. I would like also to thank Dr. Sanchez and Dr.Peppas who provided me with the lab space. I would like also to thank my committee members, Dr. Eldridge, Sepehrnoori and Lloyd for their advice and suggestions. I want to thank Dr. Jim Critchfield of Huntsman Chemical who provided valuable feedback on my dissertation work. I want to express appreciation also for all the graduate students that worked in Dr. Rochelle s group and Dr. Koros s group during the time I spent at the University of Texas. Finally I would like to thank my parents and my wife who have been with me throughout my college years. v Carbon Dioxide Removal from Natural Gas by Membranes in the Presence of Heavy Hydrocarbons and by Aqueous Diglycolamine /Morpholine Publication No. ___________ Mohammed Al-Juaied, Ph.D. The University of Texas at Austin, 2004 Supervisors: Gary T. Rochelle and W.J. Koros Intrinsically defect-free asymmetric hollow fiber polyimide membrane modules were studied in the presence and absence of saturated and aromatic components. Results suggest that an essentially defect-free, non-nodular morphology offers advantages in stability under demanding operating conditions. Earlier work showed serious losses in performance of membranes comprised of similar materials, when the selective layer had a pronounced fused nodular nature as opposed to the intrinsically defect-free skin layers reported on here. Under some conditions for the ternary system, the permselectivity of the membrane is scarcely affected, while under other conditions, permselectivity is negatively affected by as much as 25%. In most cases, for the ternary feeds, significant depression in fluxes was observed due to competition between the CO2, CH4 and heavier hydrocarbons but the effect was even more pronounced for the toluene. In addition to steady state tests in the presence and absence of n-heptane and toluene, modules were conditioned for five days with ternary mixture of CO2, CH4 and one or the other of these heavy hydrocarbons. Following this conditioning process, the modules were studied with a simple binary 10% CO2 /90 % CH4 mixture. These conditioning studies provide insight into the fundamental effects induced in the membrane due to the long term exposure to the complex mixtures. Following exposure to the ternaries containing n-heptane, negligible CO2 permeance increase was seen, while significantly increased permeances were seen under some conditions following toluene exposure even at low pressures of the ternary toluene/CO2/CH4 vi conditioning gas mixture. Although a more protracted process occurs in the case of heptane/CO2/CH4 at 35 0C and 500 ppm, a serious loss in selectivity occurs in the actual ternary tests after exposure for five days. The problem caused by 300 ppm toluene at 35 0C is more immediately apparent, but the ultimate selectivity loss is similar. In addition to the selectivity, in the presence of toluene the permeability is also depressed significantly, presumably due to a greater capability to toluene to compete for added free volume elements introduced in the conditioning process. The permeation enhancement due to toluene exposure is lost slowly when the module downstream is put under vacuum and the gas no longer in contact with the module for up to three weeks. The conditioning treatment has negligible effect at 55 0C, suggesting that that the sorption affinity of toluene decreases with increasing temperature. It is seen from the sorption experiments that penetrant induced conditioning of toluene allows a significant increase in diffusivity than in solubility coefficients, thus allowing for higher permeability and lower selectivity. Solubility, rate of absorption and NMR data were obtained for carbon dioxide in aqueous morpholine (MOR), diglycolamine (DGA) and aqueous mixtures of MOR and DGA . Solubility and rate data were acquired in a wetted wall contactor. 23.5 wt%, 65 wt% DGA and 11 wt% MOR/53 wt% DGA concentrations were studied at 298K to 333K. MOR forms an unstable carbamate upon reaction with CO2 compared to DGA which forms a very stable carbamate. Morpholine at 11 wt% of the total amine increases the CO2 equilibrium partial pressure by a factor of 5 to 7 at high loading. The working capacity of 11 wt% MOR/53 wt% DGA was found to be 10% smaller compared to 65 wt% DGA under the conditions studied. The heat of reaction of 11 wt% MOR/53 wt% DGA was found to be comparable to the 65 wt% DGA. MOR was found also to be more volatile than DGA. The second order rate constant of DGA was found to increase linearly with loading by a factor of 5 over a loading range from 0 to 0.4. Experiments with 65 w% DGA, glycolic acid and potassium formate suggest that vii rate constant increases with loading in the same way as in 65 wt% DGA. The second order rate constant for MOR (k25C2=22000 L/mol s) is four times greater than DGA (k25C2=6600 L/mol s). The MOR reaction with CO2 was found to follow the zwitterion mechanism; DGA shows zwitterion mechanism in 25 wt% DGA and second order kinetics in 65 wt% DGA. Predictions made with a rigorous eddy diffusivity theory suggests that 11 wt% MOR/53 wt% DGA outperforms 65 wt% DGA of the same concentration by 50 % in terms of CO2 absorption rate. The CO2 enhancement decreases as CO2 loading increases. viii Table of Contents List of Tables ......................................................................................................... xii List of Figures ..................................................................................................... xviii Chapter 1: Introduction to Gas Treating & Research Objective...............................1 1.1 Current Technologies for CO2 Removal from Natural Gas ........................1 1.2 CO2 Removal with Membranes...................................................................3 1.3 CO2 Removal with Amines .........................................................................8 1.4 Natural Gas Sweetening with DGA ..........................................................13 1.5 DGA Reclaimer Operations ......................................................................15 1.6 Saudi Aramco Experience with DGA Units .............................................18 Chapter 2: The Effects of Aliphatic and Aromatic Component Conditioning on the Permeation Behavior of Hollow Fiber Asymmetric Membranes ........................20 2.1 Experimental Methods ..............................................................................21 2.1.1 Materials..........................................................................................23 2.1.1.1 Polymer ...............................................................................23 2.1.1.2 Permeants ............................................................................24 2.1.2 Module Housing ..............................................................................25 2.1.3 Pure Gas Permeation .......................................................................26 2.1.4 Mixed Gas Permeation ....................................................................28 2.1.5 Testing Procedure............................................................................32 2.2 Four Potential Deterioration Factors .........................................................34 2.2.1 Competition Effect ..........................................................................34 2.2.2 Plasticization ...................................................................................35 2.2.3 Swelling Induced Conditioning History Effect ...............................36 2.2.4 Compaction .....................................................................................38 2.3 Results and Discussion..............................................................................41 2.3.1 Comparison of Conditioning in Hollow Fiber Membranes at 200 psia before and after Exposure .......................................................41 2.3.2 Comparison of Conditioning in Hollow Fiber Membranes at 200 psia during Exposure ......................................................................50 2.3.3 Comparison of Conditioning in Hollow Fiber Membranes at 600 psia before and after Exposure .......................................................57 2.3.4 Comparison of Conditioning in Hollow Fiber Membranes at 600 psia during Exposure ......................................................................62 2.4 Defective vs. Defect-Free Fibers...............................................................66 2.5 Summary ...................................................................................................69 Chapter 3: Sorption Results and Permeation Behavior Modelling and Analysis ..74 ix 3.1 3.2 3.3 3.4 3.5 Background ...............................................................................................74 Gas Sorption Measurements......................................................................77 Results and Discussion..............................................................................80 Sorption and Permeation Data Analysis....................................................90 Conclusions .............................................................................................104 Chapter 4: Thermodynamics of Morpholine /Diglycolamine / Water / Carbon Dioxide...............................................................................................................106 4.1 Experimental Methods ............................................................................108 4.2 Model Description...................................................................................117 4.3 N2O Solubility of Carbon Dioxide in Aqueous Solution of DGA, MOR, and MOR/DGA .......................................................................................121 4.4 Solubility of Carbon Dioxide in Aqueous Solution of DGA, MOR, and MOR/DGA ..............................................................................................124 4.5 C13 NMR Data........................................................................................128 4.6 N2O Regression Results ..........................................................................140 4.7 Activity of Diglycolamine and Morpholine in Aqueous Mixtures ......141 4.8 Parameter Regression Results of CO2 Solubility and NMR Data...........146 4.8.1 DGA-CO2 system..........................................................................146 4.8.2 MOR-CO2 system..........................................................................151 4.8.3 MOR-DGA-CO2 system................................................................156 4.9 Solvent Working Capacity ......................................................................161 4.10 Regeneration Energy Requirements........................................................162 4.11 Solvent Vaporization losses ....................................................................165 4.12 Conclusions .............................................................................................166 Chapter 5: Absorption of Carbon Dioxide into Aqueous Diglycolamine .........168 5.1 Introduction .............................................................................................168 5.2 Experimental Methods ............................................................................171 5.3 Physical Properties ..................................................................................171 5.4 Model Description...................................................................................173 5.4.1 Rigorous model .............................................................................173 5.4.2 Pseudo first order models ..............................................................177 5.5 Results and Discussion............................................................................180 5.5.1 CO2 reactive absorption into low-loading aqueous DGA solutions.... .............................................................................................................. ........................................................................................................180 5.5.2 CO2 reactive absorption into partially loaded aqueous DGA solutions ........................................................................................192 5.5.3 The influence of ionic strength on the rate constant for the reaction of diglycolamine and CO2 .............................................................210 5.6 Conclusions .............................................................................................220 x Chapter 6: Absorption of CO2 in Aqueous MOR and MOR/DGA Blends .......222 6.1 Introduction .............................................................................................222 6.2 Physical Properties ..................................................................................223 6.3 CO2 Absorption in Aqueous MOR..........................................................224 6.4 Rate Results with 11 wt% MOR/53 wt% DGA ......................................230 6.5 Model Description...................................................................................231 6.6 Rate Model Predictions ...........................................................................238 6.7 Sensitivity to Model Parameters .............................................................241 6.8 Deviation from Approximate Solutions ..................................................242 6.9 Conclusions .............................................................................................244 Chapter 7: Conclusions and Recommendations ...................................................246 7.1 Effects of Heavy Hydrocarbon Impurities on Hollow Fiber Membranes Performance in Natural Gas Separation ..................................................246 7.2 Carbon Dioxide Absorption and Solution Equilibrium in Morpholine and Diglycolamine .........................................................................................251 Appendix A: Modeling of Asymmetric Hollow Fiber Membrane Modules used for High-Pressure Natural Gas Purification ............................................................255 A.1 Model Development ................................................................................258 A.2 Numerical Solution .................................................................................261 A.3 Simulations Results and Discussion........................................................266 A.4 Frame of Reference Model (FM) versus Diffusion Model (DM) ..........267 A.5 Effect of Feed Pressure ...........................................................................277 A.6 Effect of Membrane Thickness and Area................................................284 A.7 Effect of Permeate Pressure ....................................................................290 A.8 Diffusion and Frame of Reference Models Comparisons .......................293 A.9 Conclusions .............................................................................................298 Appendix B: Program Documentation .................................................................300 Appendix C: Experimental Reproducibility and Replication ...............................319 Appendix D: Equation for Compressibility Factors for Penetrants at 35 C ........327 Appendix E: Desorption Isotherm Sample Calculation........................................328 Appendix F: Working Equations for Sorption Isotherm Calculations .................330 Appendix G: Polynomial Fitting Parameters for Permeation and Sorption Results ..............................................................................................................................336 Appendix H: CO2 Solubility and Rate Data .........................................................339 Appendix I: Additional C13 NMR Data...............................................................369 Appendix J: 13C NMR Sample Calculation...........................................................377 Bibliography .........................................................................................................385 Vita........................................................................................................................398 xi List of Tables Table 1.1 Table 1.2 Table 2.1 Table 2.2 Table 2.3 Table 2.4 Table 3.1 Table 3.2 Table 3.3 Table 3.4 Table 4.1a Table 4.1b Table 4.1c Table 4.2 Table 4.3 Table 4.4 Table** 4.5 Table** 4.6 Comparison of amine and membrane CO2 removal systems (William, 2002).................................................................................2 Common conditions found in natural gas plants (Newman, 1985) 14 Reported gas permeabilites of Matrimid at 250C (Clausi and Koros, 2000; Clausi, 1998) .............................................................24 Pure gas permeation results for hollow fiber membranes used in this work at 250C. ..................................................................................40 Percent change in N2, O2 and He permeance in Matrimid asymmetric hollow fiber over 42 days of aging at room temperature (Punsalan, 2001). ............................................................................41 Permeability of CO2 in the 10/90 CO2/CH4, at 35 0C illustrating the hysteretic behavior before conditioning, after conditioning to the 10/90 CO2/CH4 +100 ppm toluene at 400 psia and after conditioning, followed by exposure to a vacuum source for 21 days. ........................................................................................................69 CH4 and CO2 / Matrimid dual mode sorption parameters in unconditioned and conditioned samples with 10/90 CO2/CH4 mixture at 600 psia and 35 0C.........................................................81 CH4 and CO2 / Matrimid dual mode sorption parameters in unconditioned and conditioned samples with 10/90 CO2/CH4 + 300 ppm toluene mixture at 600 psia and 35 0C ....................................84 CH4 and CO2 / Matrimid dual mode sorption parameters in unconditioned and conditioned samples with 10/90 CO2/CH4 + 500 ppm n-heptane mixture at 600 psia and 35 0C ................................87 Percent change in fractional free volume for CO2 and CH4 in conditioned samples with 10/90 CO2/CH4 + 300 ppm toluene mixture at 200 psia, 600 psia and 35 0C .......................................104 Default parameters for VLE program ...........................................119 Miscellaneous Constants for VLE program..................................120 Temperature dependent constants.................................................120 Temperature dependence of equilibrium constants, mole fraction based .............................................................................................121 Henry s constant for N 2O in water in kPa.L/mol-1 at 25 0C and 40 0 C ..................................................................................................122 N2O solubility data in unloaded amine solutions..........................122 CO2 Solubility in 65wt% DGA.....................................................125 CO2 Solubility in 23.5wt% MOR .................................................125 xii Table** 4.7 Table** 4.8 Table 4.9 Table 4.10 Table 4.11 Table 4.12 Table 4.13 Table 4.14 Table 4.15 Table 4.16 Table 4.17 Table 4.18 Table 4.19 Table 4.20 Table 4.21 Table 4.22. Table 4.23 Table 5.1 Table 5.2 Table 5.3 Table 5.4 Table 5.5 Table 5.6 Table 5.7 Table 5.8 Table 5.9 CO2 Solubility in 11wt% MOR/53wt% DGA (65wt% Amine) ...125 Heat of Absorption of CO2 at various loading for 23.5 wt% MOR, 65 wt% DGA and 11 wt% MOR//53 wt% DGA ..........................128 Detailed 13C NMR Results for 65 wt% DGA and 300K and loading 0.34 mol CO2/mol DGA...............................................................134 Detailed 13C NMR Results for 65 wt% DGA and 313K and loading of 0.40 mol CO2/mol MOR...........................................................135 Detailed 13C NMR Results for 23.5 wt% MOR/65 wt% DGA and 300K..............................................................................................135 C13 NMR in 65wt% DGA............................................................136 C13 NMR in 23.5wt% MOR ........................................................136 C13 NMR in 11wt% MOR/53wt% DGA .....................................137 Comparison of carbamate stability constants (Mole Fraction based*) ..........................................................................................139 Heat of reaction of carbamate for 65 wt% DGA and 23.5 wt% MOR. ............................................................................................140 Parameter Values of the Henry s C onstant...................................140 Excess heat of mixing at infinite dilution and 25oC .....................143 Fitted values of NRTL binary interaction parameters for MOR-H2O system. ..........................................................................................145 Non-Default parameters for the NRTL model..............................147 Non-Default parameters for the NRTL model..............................152 Non-Default parameters for DGA-MOR mixed amine parameters. ......................................................................................................157 Comparison of working capacities at 60 0C, PCO2, rich = 50 kPa, PCO2,lean = 10-3 kPa ........................................................................161 Van-Krevelen coefficients at 25 0C, 40 0C and 60 0C. .................172 Model Equations and Boundary Conditions.................................176 65 wt% DGA/water and 25 wt% DGA/water subset of the experimental rate measurements at zero loading. Total pressures from 0-28 psig...............................................................................182 Kinetic data for DGA....................................................................187 Analysis of importance of the kinetics at low and high loadings for 25 0C, 40 0C and 60 0C..................................................................198 Results for the regression of DDGA, Dp,r and k2. ............................201 Results for the fit of k2 as a function of . ...................................212 65wt%DGA/water-glycolic acid experimental rate measurements at zero loading. Total pressures from 15-42 psig .............................214 Measured values of Henry s constants and viscosities in glycolic acid-DGA solutions at 40 0C ........................................................216 xiii Table 5.10 Table 5.11 Table 5.12 Table 6.1 Table 6.2 Table 6.3 Table 6.4 Table 6.5 Table 6.6 Table A.1. Table A.2. Table C.1 Table C.2 Table C.3 Table C.4 Table C.5 Table C.6 Table C.7 65 wt%DGA/water- potassium formate subset of the experimental rate measurements. Total pressures from 10-18 psig ...................217 Measured values of Henry s constants and viscosities in potassium formate (CHKO2) solutions -DGA solutions................................218 Results for the fit of k2 as a function of for the results .............221 Rate of absorption data at zero loading into 23.5 wt% aqueous morpholine. Overall gas flowrates from 6.05 to 6.25 SLPM. Total pressures from 15-18 psig.............................................................225 Bronsted Correlation of Morpholine Kinetics at 25oC .................227 Rate Data for the Morpholine (Rochelle et al., 2000) ..................229 Rate of absorption into aqueous 11 wt% MOR/53 wt% DGA. Overall gas flowrates from 3.05 to 6.25 SLPM. Total pressures from 15-60 psig.............................................................................230 Model Equations and Boundary Conditions.................................233 Results for the regression of Equation 6.13. .................................237 Fugacity based dual-mode and partial immobilization parameters of CO2 and CH4 at 35 0C in 6FDA-TADPO polypyrrolone Kamaruddin and Koros, 1997)......................................................266 Default parameters for simulations...............................................267 Experimental data of conditioning by 10/90 CO2/CH4 mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 35 0C. Sample # 1 ...........................................................319 Experimental data of conditioning by 10/90 CO2/CH4 mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 35 0C. Sample # 2 ...........................................................319 Experimental data of conditioning by 10/90 CO2/CH4 + 500 ppm nheptane mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 35 0C. Sample # 1 ...............320 Experimental data of conditioning by 10/90 CO2/CH4 + 500 ppm nheptane mixture CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 35 0C. Sample # 2...............................320 Experimental data of conditioning by 10/90 CO2/CH4 + 300 ppm nheptane mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 400 psia and 35 0C. Sample # 1 ...............321 Experimental data of conditioning by 10/90 CO2/CH4 + 300 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 35 0C. Sample # 1 ...............321 Experimental data of conditioning by 10/90 CO2/CH4 + 300 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 35 0C. Sample # 2 ...............322 xiv Table C.8 Table C.9 Table C.10 Table C.11 Table C.12 Table C.13 Table C.14 Table C.15 Table C.16 Table E.1 Table E.2 Table E.3 Table F.1 Table F.2 Table F.3 Table F.4: Table G.1 Table G.2 Experimental data of conditioning by 10/90 CO2/CH4 + 300 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 600 psia and 35 0C. Sample # 1 ..............322 Experimental data of conditioning by 10/90 CO2/CH4 + 300 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 600 psia and 35 0C. Sample # 2 ..............323 Experimental data of conditioning by 10/90 CO2/CH4 + 500 ppm nheptane mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 600 psia and 35 0C. Sample # 1 ..............323 Experimental data of conditioning by 10/90 CO2/CH4 + 500 ppm nheptane mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 600 psia and 35 0C. Sample # 2 ..............324 Experimental data of conditioning by 10/90 CO2/CH4 mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 600 psia and 35 0C. Sample # 1 ...........................................................324 Experimental data of conditioning by 10/90 CO2/CH4 + 100 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 400 psia and 55 0C. Sample # 1 ...............325 Experimental data of conditioning by 10/90 CO2/CH4 + 300 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 55 0C. Sample # 1 ...............325 Experimental data of conditioning by 10/90 CO2/CH4 + 100 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 55 0C. Sample # 1 ...............326 Experimental data of conditioning by 10/90 CO2/CH4 + 500 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 55 0C. Sample # 1 ...............326 Voltage Measurements .................................................................328 Pressure and moles desorbed calculations ....................................328 Concentartion Calculation, polymer sample volume = 0.239 cc..329 Channel 1 Calibration ...................................................................331 Channel 2 Calibration ...................................................................332 Expansion No ball......................................................................334 Expansion with ball (VB = 0.719 cm3)......................................335 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 mixture at 200 psia and 35 0C.......................................................336 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 + 500 ppm n-heptane mixture at 200 psia and 35 0C .......................336 xv Table G.3 Table G.4 Table G.5 Table G.6 Table G.7 Table G.8 Table G.9 Table H.1 Table H.2 Table H.3 Table I.1 Table I.2 Table I.3 Table I.4 Table I.5 Table I.6 Table I.7 Table I.8 Table I.9 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 + 300 ppm toluene mixture at 200 psia and 35 0C ...........................336 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 mixture at 600 psia and 35 0C.......................................................337 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 + 500 ppm n-heptane mixture at 600 psia and 35 0C .......................337 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 + 300 ppm toluene mixture at 600 psia and 35 0C ...........................337 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 at 600 psia and 35 0C ........................................................................338 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 + 300 ppm toluene mixture at 600 psia and 35 0C. ..........................338 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 + 500 ppm n-heptane mixture at 600 psia and 35 0C .......................338 65 wt% DGA solubility and rate...................................................339 23.5 wt% MOR solubility and rate ...............................................353 11 wt% MOR/53 wt% DGA solubility and rate ...........................358 C13 NMR of 65 wt% DGA, Loading = 0.377 mol CO2/mol DGA, T=27 0C.........................................................................................369 C13 NMR of 65 wt% DGA, Loading = 0.525 mol CO2/mol DGA, T=27 0C.........................................................................................369 C13 NMR of 65 wt% DGA, Loading = 0.523 mol CO2/mol DGA, T=40 0C.........................................................................................370 C13 NMR of 65 wt% DGA, Loading = 0.332 mol CO2/mol DGA, T=60 0C.........................................................................................370 C13 NMR of 65 wt% DGA, Loading = 0.390 mol CO2/mol DGA, T=40 0C.........................................................................................371 C13 NMR of 65 wt% DGA, Loading = 0.385 mol CO2/mol DGA, T=60 0C.........................................................................................371 C13 NMR of 65 wt% DGA, Loading = 0.168 mol CO2/mol DGA, T=27 0C.........................................................................................372 C13 NMR of 65 wt% DGA, Loading = 0.180 mol CO2/mol DGA, T=60 0C.........................................................................................372 C13 NMR of 23.5 wt% MOR, Loading = 0.370 mol CO2/mol MOR, T=27 0C..............................................................................373 xvi Table I.10 Table I.11 Table I.12 Table I.13 Table I.14 Table I.15 Table I.16 Table I.17 Table I.18 Table I.19 Table I.20 Table I.21 Table I.22 Table I.23 Table I.24 Table I.25 Table I.26 Table I.27 C13 NMR of 23.5 wt% MOR, Loading = 0.569 mol CO2/mol MOR, T=27 0C..............................................................................373 C13 NMR of 23.5 wt% MOR, Loading = 0.478 mol CO2/mol MOR, T=27 0C..............................................................................373 C13 NMR of 23.5 wt% MOR, Loading = 0.258 mol CO2/mol MOR, T=27 0C..............................................................................374 C13 NMR of 23.5 wt% MOR, Loading = 0.427 mol CO2/mol MOR, T=27 0C..............................................................................374 C13 NMR of 23.5 wt% MOR, Loading = 0.325 mol CO2/mol MOR, T=27 0C..............................................................................374 C13 NMR of 23.5 wt% MOR, Loading = 0.392 mol CO2/mol MOR, T=40 0C..............................................................................374 C13 NMR of 23.5 wt% MOR, Loading = 0.370 mol CO2/mol MOR, T=40 0C..............................................................................375 C13 NMR of 23.5 wt% MOR, Loading = 0.569 mol CO2/mol MOR, T=40 0C..............................................................................375 C13 NMR of 23.5 wt% MOR, Loading = 0.478 mol CO2/mol MOR, T=40 0C..............................................................................375 C13 NMR of 23.5 wt% MOR, Loading = 0.258 mol CO2/mol MOR, T=40 0C..............................................................................376 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.364 mol CO2/mol MOR, T=27 0C ..............................................................376 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.271 mol CO2/mol MOR, T=27 0C ..............................................................377 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.521 mol CO2/mol MOR, T=40 0C ..............................................................377 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.374 mol CO2/mol MOR, T=40 0C ..............................................................378 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.285 mol CO2/mol MOR, T=40 0C ..............................................................379 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.522 mol CO2/mol MOR, T=60 0C ..............................................................379 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.285 mol CO2/mol MOR, T=60 0C ..............................................................380 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.374 mol CO2/mol MOR, T=60 0C ..............................................................381 xvii List of Figures Figure 1.1 Figure 1.2 Figure 1.3 Figure 1.4 Figure 1.5 Figure 1.6 Figure 1.7 Figure 2.1 Figure 2.2 Illustration of a membrane separation operation. .............................3 Schematic of hollow fiber membrane showing skin and Support (Gunaidi, 2000).................................................................................4 Relative Solubility of Some Typical Gas Components (Dortmundt, and Doshi, 1993; William, 2002)......................................................5 Hollow Fiber Membrane element (Dortmundt, and Doshi, 1993; William, 2002). .................................................................................6 Illustration of a absorption/stripping system for the removal of acid gases................................................................................................10 Structures of common amines used in gas treating.........................11 A typical process flow diagram of a DGA Agent reclaimer [Huntsman web site] .......................................................................16 Repeat unit of Matrimid 5218 polyimide. ...................................23 Scanning Electron Micrograph of cross section of a Matrimid asymmetric hollow fiber showing selective skin and porous support. The skin layer is shown in partially oblique view to illustrate its thin continuous nature (Gunaidi, 2000). .....................25 Shell-side feeding with the module construction............................26 Schematic diagram of pure gas permeation testing ........................27 Schematic of gas permeation apparatus for hollow fiber modules .29 Depiction of competition effect caused by a third component, C, in a membrane system. The symbols depict unrelaxed volume elements accessible to both components A and B in the glassy polymer in the absence of a strongly condensable (e.g. toluene or nheptane) component. During exposure to such C components, sorption and transport (i.e. permeation) pathways are precluded to A and B, thereby reducing their ternary gas permeation in comparison to binary feeds. ............................................................35 The effect of plasticizing: increase in the permeances of penetrants. In this case, besides any competition effects, additional swelling induced permeation pathways are made available to other components. The symbols depict unrelaxed volume elements accessible to both components A and B in the glassy polymer in the absence of a strongly condensable (e.g. toluene or n-heptane) component. The additional arrows shown in the during exposure case illustrates the hypothetically possible higher flux of both A and B during plasticization. ...................................................................36 The effect of conditioning is an increase in the permeances of penetrants. In this case, besides any competition effects, xviii Figure 2.3 Figure 2.4 Figure 2.5 Figure 2.6 Figure 2.7 Figure 2.8 Figure 2.9 Figure 2.10 Figure 2.11 Figure 2.12 Figure 2.13 Figure 2.14 Figure 2.15 Figure 2.16 Figure 2.17 Figure 2.18 Figure 2.19 Figure 2.20 additional swelling induced permeation pathways are made available to other components. The symbols depict unrelaxed volume elements accessible to both components A and B in the glassy polymer. The additional arrows show in the after exposure case illustrates the higher flux of both A and B due to conditioning. ........................................................................................................37 Depiction of the compaction effect.................................................39 Effect of conditioning of 10/90 CO2/CH4 mixture on a) the CO2 permeability, and b) the CO2/CH4 selectivity at ~200 psia and 35 0 C. Lines are drawn by eye . .........................................................43 Effect of conditioning of 10/90 CO2/CH4 + 500 ppm n-heptane mixture on a) the CO2 permeability, and b) the CO2/CH4 selectivity at 200 psia and 35 0C. Lines are drawn by eye . ..........................44 Effect of conditioning of 10/90 CO2/CH4 + 300 ppm toluene mixture on a) the CO2 permeability, and b) the CO2/CH4 selectivity at 200 psia and 35 0C. Lines are drawn by eye . ..........................46 CO2 and CH4 Arrhenius plots of 10/90 CO2/CH4 mixture at 200 psia ........................................................................................................48 Effect of conditioning of 10/90 CO2/CH4 + 300 ppm toluene mixture on the a) CO2 permeability, and b) CO2/CH4 selectivity at 200 psia and 55 0C. Lines are drawn by eye . ..............................49 Comparison of a) CO2 permeability, and b) CO2/CH4 selectivity during exposure at 200 psia, and 35 0C for 10/90 CO2/CH4 mixture , 10/90 CO2/CH4 + 300 ppm toluene mixture, and 10/90 CO2/CH4 + 500 ppm n-heptane mixture. ...........................................................51 Comparison of a) CO2 permeability, and b) CO2/CH4 selectivity during exposure at 200 psia, and 55 0C for 10/90 CO2/CH4 mixture , 10/90 CO2/CH4 + 300 ppm toluene mixture, and 10/90 CO2/CH4 + 500 ppm n-heptane mixture. ...........................................................53 Comparison of a) CO2 permeability, and b) CO2/CH4 selectivity during exposure at 200 psia, 35 0C and 55 0C for 10/90 CO2/CH4 + 100 ppm toluene mixture. ...............................................................55 Comparison of a) CO2 permeability, and b) CO2/CH4 selectivity during exposure at 400 psia, 35 0C and 55 0C for 10/90 CO2/CH4 + 100 ppm toluene mixture. ...............................................................56 Effect of conditioning of 10/90 CO2/CH4 mixture on a) the CO2 permeability, and b) the CO2/CH4 selectivity at 600 psia and 35 0C. Lines are drawn by eye . ...............................................................58 Effect of conditioning of 10/90 CO2/CH4 + 500 ppm n-heptane mixture on a) the CO2 permeability, and b) the CO2/CH4 selectivity at 600 psia and 35 0C. Lines are drawn by eye . ..........................60 xix Figure 2.21 Figure 2.22 Figure 2.23 Figure 2.24 Figure 2.25 Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6 Figure 3.7 Effect of conditioning of 10/90 CO2/CH4 + 300 ppm toluene mixture on a) the CO2 permeability, and b) the CO2/CH4 selectivity at 600 psia and 35 0C. Lines are drawn by eye . ..........................61 Comparison of a) CO2 permeability, and b) CO2/CH4 selectivity during exposure at 600 psia, 35 0C for 10/90 CO2/CH4 mixture, 10/90 CO2/CH4 + 300 ppm toluene mixture, and 10/90 CO2/CH4 + 500 ppm n-heptane mixture. ...........................................................63 Qualitative transport gap (free volume element) size distribution change after conditioning with 10/90 CO2/CH4 + 300 ppm toluene mixture. ...........................................................................................65 Hypothetical figure of the dense skin, and the defective morphology of an asymmetric hollow fiber. SEM of Matrimid asymmetric hollow fiber (taken by Seth Carruthers, 1999) ...............................66 Comparison of CO2/CH4 selectivity for defective and defect-free fibers during exposure at 35 0C for 10/90 CO2/CH4 + 300 ppm toluene mixture. ..............................................................................68 Schematic of pressure decay apparatus ..........................................78 Effects of 10/90 CO2/CH4 mixture exchange conditioning at 600 psia and 35 0C on a) CO2 sorption isotherms, and b) CH4 sorption isotherms for asymmetric hollow fibers of Matrimid conditioned. ........................................................................................................82 Effects of 10/90 CO2/CH4 + 300 ppm toluene mixture exchange conditioning at 600 psia and 35 0C on a) CO2 sorption isotherms, and b) CH4 sorption isotherms for asymmetric hollow fibers of Matrimid conditioned. .................................................................85 Effects of 10/90 CO2/CH4 + 500 ppm n-heptane mixture exchange conditioning at 600 psia and 35 0C on a) CO2 sorption isotherms, and b) CH4 sorption isotherms for asymmetric hollow fibers of Matrimid conditioned. .................................................................86 Solubility of CO2 and CH4 in conditioned samples with 10/90 CO2/CH4 , 10/90 CO2/CH4 + 300 ppm toluene and 10/90 CO2/CH4 + 500 ppm n-heptane at 600 psia and 35 0C. ..................................89 Change of a) CO2 local diffusion coefficient and b) CH4 local diffusion coefficient conditioned with 10/90 CO2/CH4 mixture, 10/90 CO2/CH4 + 500 ppm n-heptane mixture, and 10/90 CO2/CH4 + 300 ppm toluene mixture at 200 psia and 35 0C. Lines are drawn by eye ............................................................................................94 Change of a) CO2 local diffusion coefficient and b) CH4 local diffusion coefficient conditioned with 10/90 CO2/CH4 mixture, 10/90 CO2/CH4 + 500 ppm n-heptane mixture, and 10/90 CO2/CH4 + 300 ppm toluene mixture at 600 psia and 35 0C. Lines are drawn by eye ............................................................................................95 xx Figure 4.1 Figure 4.2 Figure 4.3 Figure 4.4 Figure 4.5 Figure 4.6 Figure 4.7 Figure 4.8 Figure 4.9 Figure 4.10 Figure 4.11 Figure 4.12 Figure 4.13 Figure 4.14 Figure 4.15 Figure 4.16 Figure 4.17 Figure 4.18 Figure 4.19 Figure 4.20 Figure 4.21 Figure 4.22 Figure 4.23 Figure 4.24 Detailed diagram of the wetted-wall column contactor................109 Flow diagram of the experimental setup.......................................110 Flux interpolation to determine equilibrium solubility. Data points for absorption into 11 wt% MOR/53 wt% DGA at CO2 loading of 0.13 mol/mol amine and a temperature of 40 0C. .........................113 Schematic diagram of the N2O experimental apparatus. ..............114 Solubility of nitrous oxide as a function of amine concentration. 124 Heat of Absorption of CO2 at various loading for 23.5 wt% MOR ......................................................................................................126 Heat of Absorption of CO2 at various loading for 65 wt% DGA .127 Heat of Absorption of CO2 at various loading for 23.5 wt% MOR/53 wt% DGA. .....................................................................127 13 C NMR spectrum of 65 wt% DGA at 300K and 0.34 loading. .130 13 C NMR spectrum of 23.5 wt% MOR at 313K and 0.40 loading. ......................................................................................................131 13 C NMR spectrum of 11 wt% MOR/53 wt% DGA at 300K and 0.52 loading. .................................................................................132 Expanded 13C NMR spectrum of 11 wt% MOR/53 wt% DGA at 300K and 0.52 loading..................................................................132 Expanded 13C NMR spectrum of 11 wt% MOR/53 wt% DGA at 300K and 0.52 loading..................................................................133 Proton, 13C and short range C-H correlation NMR spectra for 11 wt% MOR/53 wt% DGA at 300K and 0.52 moles/mol amine.....134 Apparent carbamate stability constant for the 23.5wt% MOR and the 65wt% DGA with 0.1 to 0.5 moles CO2/mol Amine..............139 Results of Nitrous Oxide data Regression in unloaded solutions. 141 Data of Huey et al. (1991) reinterpreted as activity coefficients for the water / MOR system at elevated temperature. ........................143 Results of regression of the equilibrium partial pressure of MOR in MOR-H2O mixture. Fitting the excess heat of mixing at 25 0C to 25 kJ/mol.......................................................................................145 Results of VLE and C13 NMR data regression of the DGA-CO2 system. ..........................................................................................147 Results of regression of the equilibrium partial pressure of CO2 in 65wt% DGA system obtained in this work. .................................148 Results of regression of C13 NMR data in 65wt % DGA system at 25 ..................................................................................................149 Results of regression of C13 NMR data in 65wt % DGA system at 40 0C. ............................................................................................149 Results of regression of C13 NMR data in 65wt % DGA system at 60 0C. ............................................................................................150 Predicted speciation of CO2 in 65 wt% DGA at 40 0C.................150 xxi Figure 4.25 Figure 4.26 Figure 4.27 Figure 4.28 Figure 4.29 Figure 4.30 Figure 4.31 Figure 4.32 Figure 4.33 Figure 4.34 Figure 4.35 Figure 4.36 Figure 4.37 Figure 4.38 Figure 4.39 Figure 4.40 Figure 5.1 Figure 5.2 Figure 5.3 Results of VLE and NMR data regression of the MOR-CO2 system Fixing CO2 solubility to the N2O Analogy. ..................................151 Results of regression of the equilibrium partial pressure of CO2 in 23.5wt% DGA system. .................................................................153 Results of regression of C13 NMR data in MOR-CO2 system at 25 0 C. .................................................................................................154 Results of regression of C13 NMR data in MOR-CO2 system at 40 0 C. .................................................................................................154 Results of regression of C13 NMR data in MOR-CO2 system at 60 0 C. .................................................................................................155 Predicted speciation of CO2 in 23.5 wt% MOR at 25 0C. ............155 Results of model prediction for VLE and NMR data regression with no parameter adjustments of the DGA-MOR-CO2 system...........156 Results of VLE and NMR data regression of the DGA-CO2 system. ......................................................................................................157 Results of VLE data regression of the 11 wt% MOR/53 wt% DGA system at 60 0C. ............................................................................158 Results of regression of C13 NMR data in DGA-MOR-CO2 system at 25 0C..........................................................................................159 Results of regression of C13 NMR data in DGA-MOR-CO2 system at 40 0C..........................................................................................159 Results of regression of C13 NMR data in the 11 wt% MOR/53 wt% DGA system at 60 0C............................................................160 Predicted speciation of CO2 in 11 wt% MOR/53 wt% DGA at 40 0 C. .................................................................................................160 CO2 partial pressure as a function of loading for the the 11 wt% MOR/53 wt% DGA system (solid lines) and 65 wt % DGA system (dashed lines) at 25 0C, 40 0C and 60 0C.......................................162 Heats of reaction of CO2 at various CO2 loading for 11 wt% MOR/53 wt% DGA (solid lines) and 65 wt % DGA (dashed lines) at 25 0C, 40 0C and 60 0C..............................................................164 Vapor pressure of MOR over 11 wt% MOR/53 wt% DGA, and CO2 loading of 0.01 mol CO2 / mol amine...........................................166 Straight line fit for rate of CO2 absorption into aqueous 65 wt% diglycolamine solutions at low solution loading ..........................182 Second-order rate constant for the reaction between CO2 and 65wt% DGA using the rigorous model, from data at zero loading. ......................................................................................................184 Comparison between the experimental and calculated interfacial fluxes of CO2 using the rigorous model for the 65 wt% DGA at zero loading. .........................................................................................185 xxii Figure 5.4 Second-order rate constant for the reaction between CO2 and 25wt% DGA. ................................................................................187 Figure 5.5 Second-order rate constant for the reaction between CO2 and DGA at zero loading...............................................................................188 Figure 5.6 Second-order rate constant for the reaction between CO2 and DGA. ......................................................................................................189 Figure 5.7 Comparison between the data obtained in this work for the 65 wt% and 25 wt% DGA solution and Pacheco et al., (2000) for the 50 wt% DGA solution at low loading. ...............................................190 Figure 5.8 Second-order rate constant for the reaction between CO2 and 65 wt% DGA.at 25 0C........................................................................193 Figure 5.9 Second-order rate constant for the reaction between CO2 and 65 wt% DGA.at 40 0C........................................................................193 Figure 5.10 Second-order rate constant for the reaction between CO2 and 65 wt% DGA.at 60 0C........................................................................194 Figure 5.11 Concentration gradients for absorption of carbon dioxide into 65 wt% DGA. Loading=0.115, kol=2.79E-3 m/s, Pi/P*=392.0, T=313K. ......................................................................................................196 Figure 5.12 Concentration gradients for absorption of carbon dioxide into 65 wt% DGA. Loading=0.385, kol=2.45E-3 m/s, Pi/P*=28.5, T=313K. ......................................................................................................196 Figure 5.13 Sensitivity of calculated CO2 flux to values of the diffusion coefficients of reactants and products and second order rate constant. 313 K, kol=2.74E-3 m/s, Pi=10P*. ................................199 Figure 5.14 Effect of CO2 loading on the second rate constant at 25 0C, 40 0C and 60 0C for the system DGA- water-CO2. Lines are model predictions.....................................................................................201 Figure 5.15 Comparison between the measured and calculated interfacial fluxes of CO2 for the 65 wt% DGA at various CO2 loading. ..................202 Figure 5.16 Predicted activity coefficients for 65 wt% DGA at 313K ............204 Figure 5.17 Predicted activity coefficients for 50 wt% DGA at 313K ............204 Figure 5.18 Predicted activity coefficients for 25 wt% DGA at 313K ............205 Figure 5.19 Effect of CO2 loading on the second rate constant calculated based on concentration and on activity at 40 0C for the system DGAwater-CO2. Lines are model predictions. ......................................207 Figure. 5.20 Normalized flux of 65wt% DGA and CO2 at low and high driving force at 313K. ...............................................................................208 Figure. 5.21 Normalized flux of 65wt% DGA and CO2 at low and high driving force at 298K. ...............................................................................209 Figure. 5.22 Normalized flux of 65wt% DGA and CO2 at low and high driving force at 313K. ...............................................................................209 xxiii Figure. 5.23 Normalized flux of 65wt% DGA and CO2 at low and high driving force at 333K. ...............................................................................210 Figure 5.24 Effect of ionic strength on the second rate constant at 25 0C, 40 0C and 60 0C for the system DGA- water-CO2 ..................................212 Figure 5.25 Normalized flux of 65wt% DGA and glycolic acid solvent at 40 0C. ......................................................................................................215 Figure 5.26 Effect of glycolic acid on the second rate constant at 40 0C for the system DGA- water-CO2 ..............................................................215 Figure 5.27 Normalized flux of fresh 65wt% DGA and potassium formate solutions. .......................................................................................218 Figure 5.28 Effect of potassium formate on the second rate constant at 25 0C and 40 0C for the system DGA- water-CO2 ..................................219 Figure 5.29 Effect of ionic strength on the second rate constant at 25 0C and 40 0 C for the system DGA-water-CO2, DGA-glycolic acid-water-CO2, and the system DGA-potassium formate-water-CO2....................220 Figure 6.1 Straight line fit for rate of CO2 absorption into aqueous 23.5 wt% MOR solutions at zero solution loading .......................................226 Figure 6.2 Second order rate constant of MOR and carbon dioxide..............227 Figure 6.3 Bronsted correlation of CO2 reaction rates with secondary amines at 25 0C. (Rochelle et al., 2000).......................................................228 Figure 6.4 Normalized flux of 11 wt% MOR/53 wt% DGA and CO2...........231 Figure 6.5 Comparison of predicted and experimental fluxes for absorption of carbon dioxide into 11 wt% MOR/53 wt% DGA.........................235 Figure 6.6 Third-order rate constant for the reaction between CO2 and 11 wt% MOR/53 wt% DGA using the rigorous model, from data at zero loading. .........................................................................................236 Figure 6.7 Rigorous model fit of all MOR/DGA absorption data. ................237 Figure 6.8 kMOR-DGA for absorption of carbon dioxide into 11 wt% MOR/53 wt% DGA at 25 0C, 40 0C and 60 0C. ...................................................238 Figure 6.9 Normalized flux of CO2 in 11 wt% MOR/53 wt% DGA and 65 wt% DGA at 25 0C, kol=1.77E-3 m/s, Pi=10P*.............................239 Figure 6.10 Normalized flux of CO2 in 11 wt% MOR/53 wt% DGA and 65 wt% DGA at 40 0C, kol=1.77E-3 m/s, Pi=10P*.............................240 Figure 6.11 Normalized flux of CO2 in 11 wt% MOR/53 wt% DGA and 65 wt% DGA at 60 0C, kol=1.77E-3 m/s, Pi=10P*.............................240 Figure 6.12 Sensitivity of calculated CO2 flux to values of the diffusion coefficients of reactants and products and rate constants, 40 0C, kol=1.77E-3 m/s, Pi=10P*............................................................241 Figure 6.13 Comparison of rigorous model and PFO model for CO2 absorption at 40 0C, kol=1.77E-3 m/s, Pi=10P*...............................................242 xxiv Figure 6.14 Figure A.1 Figure A.2 Figure A.3 Figure A.4 Figure A.5 Figure A.6 Figure A.7 Figure A.8 Figure A.9 Figure A.10 Figure A.11 Figure A.12 Figure A.13 Figure A.14 Comparison of rigorous model and PFO model for CO2 absorption rate at 40 0C, kol=2.74E-3 m/s, Pi=1.01P*.....................................243 Simplified block diagram of carbon dioxide/methane separation in a countercurrent hollow-fiber module. ............................................258 Effect of CO2 feed mole fraction on (a). r ; (b). CO 2 average concentration inside the membrane; (c). CH4 average concentration inside the membrane. ....................................................................270 Effect of CO2 feed mole fraction on (a). CO2 bulk flux contribution; (b). CH4 bulk flux contribution....................................................272 Simulation of CO2 permeance for (a) 10/90 CO2/CH4 feed (b) 50/50 CO2/CH4 feed (b) 90/10 CO2/CH4 feed as a function of axial position, considering the diffusion model (DM) and the frame of reference model (FM). ..................................................................274 Simulation of CH4 permeance for (a) 10/90 CO2/CH4 feed (b) 50/50 CO2/CH4 feed (b) 90/10 CO2/CH4 feed as a function of axial position, considering the diffusion model (DM) and the frame of reference model (FM). ..................................................................276 Effect of total feed pressure on (a) average CO2 concentration inside the membrane (b) average CH4 concentration inside the membrane as a function of axial position, for 50/50 CO2/CH4 feed considering the frame of reference model (FM)...............................................279 Simulation of average r , the mass flux ratio of CO 2 to CH4 in the membrane for (a) 10/90 CO2/CH4 feed (b) 50/50 CO2/CH4 feed (b) 90/10 CO2/CH4 feed as a function of axial position, considering the frame of reference model (FM). ...................................................282 Bulk flux contribution of (a) CO2 (b) CH4 in 10/90 CO2/CH4, 50/50 CO2/CH4 and 90/10 CO2/CH4 feed as a function of total feed pressure. ........................................................................................285 Effect of membrane area on bulk flux contribution of CO2 and CH4 in 50/50 CO2/CH4 feed. ................................................................286 Effect of membrane area on bulk flux contribution of CO2 and CH4 in 50/50 CO2/CH4 feed as a function of axial position. ................287 Effect of membrane thickness on bulk flux contribution of CO2 and CH4 in 50/50 CO2/CH4 feed..........................................................288 Effect of of membrane thickness on bulk flux contribution of CO2 and CH4 in 50/50 CO2/CH4 feed as a function of axial position. .289 Effect of permeate pressure on (a). r ; (b). CO 2 average concentration inside the membrane; (c). CH4 average concentration inside the membrane in 50/50 CO2/CH4 feed. ..............................292 Effect of permeate pressure on bulk flux contribution of CO2 and CH4 in 50/50 CO2/CH4 feed in a hollow-fiber module, operating in countercurrent. ..............................................................................293 xxv Figure A.15 Figure A.16 Figure A.17 Figure F.1 Figure F.2 Percent stage cut and percent error ([% stage cut FM - % stage cut DM]/ [% stage cut DM] x 100%) as a function of feed pressure for (a). 10/90 CO2/CH4 feed; (b). 50/50 CO2/CH4 feed; (c). 90/10 CO2/CH4 feed considering the frame of reference model (FM) and the diffusion model (DM). ..................................................................295 Simulation of CH4 recovery as a function of feed pressure, in a hollow-fiber module, operating in countercurrent, considering the frame of reference model (FM) and the diffusion model (DM) for 10/90 CO2/CH4 feed; 50/50 CO2/CH4 feed; and. 90/10 CO2/CH4 feed................................................................................................296 Simulation of CO2/CH4 selectivity as a function of feed pressure for different permeate pressures, in a hollow-fiber module, operating in countercurrent, considering the frame of reference model (FM) and the diffusion model (DM) for (a). 10/90 CO2/CH4 feed; and (b). 50/50 CO2/CH4 feed......................................................................297 Calibration curve for channel # 1 .................................................331 Calibration curve for channel # 2 .................................................332 xxvi Chapter 1: Introduction to Gas Treating & Research Objective Natural gas is a fuel that burns cleaner than many other traditional fossil fuels. It is used for heating, cooling, and production of electricity and it finds many uses in industry. Natural gas is more environmentally attractive than other fossil fuels because when burns it emits lower quantities of greenhouse gases than do other fossil fuels (Energy Information Administration, 2001). The composition of natural gas varies from one location to another. Common impurities in the natural gas streams include carbon dioxide, water vapor, hydrogen sulfide and nitrogen. These components are corrosive, and hydrogen sulfide is also toxic (Spillman, 1989); hence, removal of the contaminants is necessary to meet pipeline requirements. The pipeline specifications for these components are: <2% for CO2, <4 ppm for H2S, and <0.1 g/m3 for H2O (Spillman, 1984; Fournie and Agostini, 1987; Bhide and Stern, 1993). Removal of the contaminants also increases the heating value of the transported gas. 1.1 Current Technologies for CO2 Removal from Natural Gas Various processes are used to condition raw natural gas to pipeline quality. Carbon dioxide and/or hydrogen sulfide removal can be accomplished via amines, or membranes. The choice of technology is dependent upon the needs of the gas processor (Rojey et al., 1997). Although membranes have proven their usefulness, membrane technology has to compete with amine technology. Advantages of membranes are low capital investment, ease of operation, low energy consumption, cost effectiveness even at low gas volumes and good weight and space efficiency. However, amine treatment is still an efficient method, but the 1 amine units are large and heavy. Table 1.1 compares amines and membranes for CO2 removal systems. Despite all the advantages of membranes, it is still difficult to introduce membranes on a market where people are familiar with the conventional separation techniques. But given the number of commercial-scale membrane suppliers, there is a growing acceptance of membranes in industry. Table 1.1 2002). Comparison of amine and membrane CO2 removal systems (William, Amines Very familiar Very low Yes (ppm levels) Yes (<4 ppm) Moderate to high Moderate Low to moderate Relatively complex Moderate Product gas saturated Amines Long for large systems Long Low Not used Membranes Still considered new technology Losses depend upon conditions No (<2% economics are challenging) Sometimes Low, unless compression used Low to moderate Low, unless compression used Relatively simple Low Product gas dehydrated Membranes Modular construction is faster Short for skid-mounted equipment Low to moderate Use depends upon conditions Operating Issues User Comfort Level Hydrocarbon Losses Meets Low CO2 Spec. Meets Low H2S Spec. Energy Consumption Operating Cost Maintenance Cost Ease of Operation Environmental Impact Dehydration Capital Cost Issues Delivery Time On-Site Installation Time Pretreatment Costs Recycle Compression A nice review on the advantages and disadvantages of membranes and amines are given by William (2002). 2 1.2 CO2 Removal with Membranes Membranes, thin barriers that allow preferential passage of certain substances, are currently available for CO2 removal from natural gas streams. Figure 1.1 shows the simplest membrane operation. Feed in Residue Membrane/ Barrier Material Permeate Figure 1.1 Illustration of a membrane separation operation. The membrane materials that are currently available for natural gas conditioning are polymer based, for example, cellulose acetate, polyimides, polyamides, polysulfone, polycarbonates, and poly-etherimide. Polyimide has some potential in certain CO2 removal applications, but it has not received sufficient testing to be used in large applications. The most common types of membrane forms in use today for natural gas separation are of the spiral-wound type and the hollow-fiber type. The hollow fiber membranes consist of a very thin (0.1-1.0 micrometers, m), nonporous "skin" or surface layer, combined with a much thicker microporous backing (100 to 200 3 m). The separation of a gas mixture occurs in this skin, while the microporous substrate gives the membrane mechanical strength. Figure 1.2 shows the crosssection of hollow fiber membranes and the transition from the porous support to the dense-free skin. Figure 1.2 Schematic of hollow fiber membrane showing skin and Support (Gunaidi, 2000) In these membranes, CO2 dissolves into the thin surface layer and diffuses through the membrane more rapidly than methane or any of the other hydrocarbons present in natural gas. This is not a filtering type process; the gas molecules move through the membrane in a process based on solubility and diffusivity (Kesting and Fritzsche, 1993; Paul and Yampol'skii, 1994). Permeability is defined as the rate at which gases a nd vapors can pass through the membrane. Selectivity defines the ratio between the permeation rates between different components in the gas stream. Permeability and selectivity are important factors when it comes to select membranes for gas treating. Permeability and selectivity usually have inverse relationship; the higher the permeability, the less membrane area is required for a given separation and therefore the lower the membrane cost. The higher the selectivity is the lower the 4 losses of methane and therefore the higher the volume of the product that can be recovered. Permeation rate is dependent on the solubility of a given gas component, molecular size and the operating conditions (Porter, 1990; Ho and Sirkar, 1992; William, 2002). Figure 1.3 shows the relative permeability of the components most commonly found in natural gas streams. Water permeates faster than other components including CO2. This adds an advantage to membrane systems that can be used in gas dehydration while removing CO2. Figure 1.3 Relative Solubility of Some Typical Gas Components (Dortmundt, and Doshi, 1993; William, 2002) The hollow fibers are typically combined into a bundle similar to a shell and tube heat exchanger. Figure 1.4 illustrates the hollow fiber membrane element. In hollow-fiber elements, very fine hollow fibers are wrapped around a central tube in a highly dense pattern. In this wrapping pattern, both open ends of the fiber end up at a permeate pot on one side of the element. Feed gas which is high in CO2 concentration flows over and between the fibers, and the permeate stream which is 5 high in CO2 concentration flows into the fibers. The permeated CO2 then travels within the fibers until it reaches the permeate pot, where it mixes with CO2 permeates from other fibers. The total permeate exits the element through a permeate pipe. The components that do not permeate are called residual gas and are low in CO2 concentration (Dortmundt, and Doshi, 1993; William, 2002). Figure 1.4 Hollow Fiber Membrane element (Dortmundt, and Doshi, 1993; William, 2002). Membrane Pretreatment The use of membranes in the past have shown the need for pretreatment of the feed stream when processing natural gas. Membrane life was found to be too short. Natural gas can contain a wide variety of contaminants that quickly reduce membrane effectiveness and force premature replacement of the elements. Substances commonly found in natural gas streams that will lower the performance of CO2 removal membranes include: Liquids: Liquids cause swelling of the membranes and can destroy the membrane. 6 Heavy hydrocarbons, approximately > C15: Significant levels of these compounds slowly coat the membrane surface, thus decreasing permeation rate. In addition, as found in this study hydrocarbons can cause swelling and loss in selectivity under some conditions. Particulate material: Particles can block the membrane flow area. Certain corrosion inhibitors and well additives: Some corrosion inhibitors and well additives are destructive to the membrane systems. The pretreatment system must remove the above contaminants and must ensure that liquids do not form within the membrane. There are two cases where liquid hydrocarbons can form; in one case the gas cools down as a result of JouleThomson effect as CO2 permeates through the membrane. The second case is when the CO2 permeates and the gas becomes heavier in hydrocarbons and its dew point therefore increases through the membrane. To avoid condensation in the membrane sufficient heat must be applied. The pretreatment system must have a wide safety margin and be highly flexible to cope with unexpected circumstances. Heavy hydrocarbon content of a feed gas can vary widely from initial pre-start-up estimates and also from month to month during the plant s life. Large variations can happen between different wells in the same area. A reliable pretreatment system must take this variation into account and must be able to protect the membranes against a wide range of contaminants (Dortmundt and Doshi, 1993). The impact of heavy hydrocarbons on the membrane system has remained poorly understood due to the complexity of these components and the difficulty in characterizing their effects experimentally. This thesis consists of two parts including this introduction. The first part of the dissertation aims to understand and model the effect of heavy hydrocarbons on the performance of the membranes. Previous work on membrane formation has led to successful synthesis and 7 modeling of reliable membranes for CO2 removal from natural gas feeds. However, the tests performed in the laboratory on these membranes were contaminant free. In the actual field, membranes exhibit poorer performance. More work is needed to understand the key factors that undermine the gas separation ability of membranes in such applications. Therefore, the objectives of the first part of the dissertation are organized as follows; Chapter 2 presents the results and analysis of permeation experiments conducted with hollow fiber membranes which probe the glassy polymer environment with 10% CO2/ 90% CH4 feed gas and toluene and n-heptane molecules as a typical aromatic and parafinic hydrocarbons, respectively. Chapter 3 presents comparison of sorption behavior in asymmetric hollow fiber samples of Matrimid . Exchange conditioning experiments are conducted to observe the response of the various polymer samples to the introduction of additional sites for sorption due to the conditioning process. 1.3 Conclusions and recommendations are presented in Chapter 7. CO2 Removal with Amines The most widely used gas treating process for acid gas removal in the natural gas and petroleum processing industries is the chemical solvent process, using the various alkanolamines. These processes use a solvent, either an alkanolamine or an alkali-salt (hot carbonate processes) in an aqueous solution, which reacts with the acid gas (H2S and CO2) to form a complex or bond. This complex is subsequently reversed in the regenerator at elevated temperatures and reduced acid gas partial pressures releasing the acid gas and regenerating the solvent for reuse. These are well suited for low pressure applications where the acid gas partial pressures are low and low levels of acid gas are desired in the 8 residue gas since their acid gas removal capacity is relatively high and insensitive to acid gas partial pressures as compared to physical solvents. The chemical solvent processes are generally characterized by a relatively high heat of acid gas absorption and require a substantial amount of heat for regeneration. A simplified flow schematic of a typical gas treating operation using amine solvents is shown in Figure 1.5. A sour gas containing H2S and/or CO2 is introduced at the bottom of a high-pressure absorber where it rises and counter currently contacts an aqueous alkanolamine solution that is introduced at the top of the absorber. The CO2-rich amine solution that results is then pumped through heat exchangers where its temperature is raised. It is then introduced at the top of a stripper where it countercurrently contacts steam at an elevated temperature and reduced pressure. The steam strips the CO2 and H2S from solution and the lean alkanolamine solution is pumped through the heat exchanger, where it is cooled, and reintroduced at the top of absorber (LRGCC, 2003). 9 Treated Gas H2 S CO 2 H2 O Absorber HX Stripper Reboiler Sour Gas Rich Amine Lean Amine Figure 1.5 Illustration of a absorption/stripping system for the removal of acid gases. The alkanolamines most commonly used in industrial applications are monoethanolamine (MEA), diethanolamine (DEA), methyldiethanolamine (MDEA), and diglycolamine (DGA). For higher CO2 concentrations, physical solvents are employed that utilize a pressure-letdown to desorb the CO2 from the rich solvent. The alkanolamines are classified by the degree of substitution on the central nitrogen; a single substitution denoting a primary amine, a double substitution, a secondary amine, and a triple substitution, a tertiary amine. Each of the alkanolamines has at least one hydroxyl group and one amino group. In general, the hydroxyl group serves to reduce the vapor pressure and increase water solubility, while the amino group provides the necessary alkalinity in water solutions to promote the reaction with acid gases. It is readily apparent looking at the molecular structure that the non-fully substituted alkanolamines have hydrogen atoms at the non-substituted valent sites on the central nitrogen. This structural characteristic plays an important role in the acid gas removal capabilities of the various treating solvents. Figure 1.6 shows the commonly used alkanolamines in the gas treating industry (LRGCC, 2003; Kohl and Nielsen, 1997). 10 H HO-CH2-CH2-N H Monoethanolamine (MEA) -hydroxyaminoethyl ether Diglycolamine (DGA) HO-C2H4-O-C2H4-N H H HO-CH2-CH2 N-H HO-CH2-CH2 HO-CH2-CH2 HO-CH2-CH2 N-CH3 Diethanolamine (DEA) Methyldiethanolamine (MDEA) HO-CH2-CH2 HO-CH2-CH2 Triethanolamine (TEA) Piperazine (PZ) N-CH2-CH2-OH H-N N-H Figure 1.6 Structures of common amines used in gas treating. H2S and CO2 are acid gases because they dissociate to form a weak acidic solution when they come into contact with water or an aqueous medium. The amines are weak organic bases. The acid gases and the amine base will combine chemically to form an acid base complex or salt in the treating solution. In the absorber column the acid gas absorption of H2S is based only on acid -basereaction . Regardless of the structure of the amine, H 2S reacts instantaneously with the primary, secondary, or tertiary amine via a direct proton transfer reaction as shown in Equation.1.1 below to form the hydrosulfide (LRGCC, 2003): 11 H2S-reaction: Acid-base-reaction Relative kinetics: instantaneous H2S + [Amine] <=> HS- + [Amine]+ (1.1) For CO2 removal the basis of chemistry is a combination of indirect acid base reaction and direct carbama te reaction . The acid base reaction may occur with any of the alkanolamines regardless of the amine structure but it is kinetically slow because the carbonic acid dissociation step to the bicarbonate is relatively slow. The second reaction for CO2, which results in the formation of the carbamate, is called the carbamate formation reaction and may only occur with the primary and secondary amnies. CO2-reaction: Acid-base-reaction Relative kinetics: slow CO2 + H2O <=> H2CO3 (1.2) (1.3) H2CO3 + [Amine] <=> HCO3- + [Amine]+ CO2-reaction: Carbamate-reaction Relative kinetics: fast CO2 + 2 [Amine] <=> [Amine]+ + [Amine]COO- (1.4) The rate of CO2 absorption via the carbamate reaction is rapid, much faster than the CO2 hydrolysis reaction, but somewhat slower than the H2S absorption reaction. The stoichiometry of the carbamate reaction indicates that the capacity of the amine solution for CO2 is limited to 0.5 mole of CO2 per mole of amine if the only reaction product is the amine carbamate. However, the carbamate can undergo partial hydrolysis, as shown below in Equation 1.5, to form bicarbonate, regenerating free amine. Hence, CO2 loading greater than 0.5 is possible through the hydrolysis of the carbamate intermediate to bicarbonate. 12 [Amine]COO- + H2O <=> [Amine] + HCO3- (1.5) 1.4 Natural Gas Sweetening with DGA The Fluor Corporation patented the Diglycolamine process and DGA agent was commercialized in the late sixties by Fluor and Jefferson Chemical company, a predecessor to Texaco Chemical Company and Huntsman Corporation. DGA is a primary amine, and its low vapor permits its use in higher concentrations, typically 50 to 60 weight percent, resulting in significant lower circulation rates and energy requirements. The advantages of DGA agent include (LRGCC, 2003): Capital and operating cost savings due to lower circulation requirements Removal of COS and CS2 High reactivity. The H2S spec of grain can be generally obtained for applications with low operating pressures and high operating temperatures. Better mercaptan removal compared to other alkanolamines. Low freezing point; 50 wt% solution freezes at 30 0F, whereas 15 wt% MEA and 25wt% DEA solutions freeze at 25 and 21 0F, respectively. Some of the disadvantages of DGA are: Nonselective removal in mixed acid gas systems. Absorbs aromatic compounds from inlet gas which complicates the sulfur recovery unit design, and Higher solvent cost relative to MEA and DEA. Plants treating natural gas have DGA concentration ranging from 40 to 70 wt%. All of the natural gas sweetening plants are reducing H2S concentration to less than 0.25 grains of H2S/100 SCF. CO2 concentration can also be reduced to less than 100 ppmv in most medium and high-pressure applications. Lower levels of CO2 can be achieved when needed. Typical conditions found in natural gas plants are shown in Table 1.1 13 Table 1.2 Common conditions found in natural gas plants (Newman, 1985) Range of Feed Gas Composition: 0.5 25 Mole % CO2 0-33 Mole% H2S Range of Treating Pressures: 60-1150 psig Range of Feed Gas Temperatures: 65-120 0F Range of Treating Pressures: 60-1150 psig Typical Treated Gas Quality: Low pressure Medium ressure High pressure H2S, ppmv <4 <4 <4 CO2, ppmv >100 <100 <100 The acid gas loading of the rich DGA solution depends on three major factors; the DGA concentration, CO2/H2S ratio, and the material of construction. Plants treating natural gas with high CO2/H2S ratio generally operate with rich DGA acid gas loading of 0.35 to 0.40 moles of total acid gas/ mol DGA. Lean DGA loadings in these plants normally will be about 0.1 mol of acid gas/ mol DGA. Plants processing natural gas with low CO2/H2S ratios generally have loadings of 0.03 to 0.07 moles acid gas/mole DGA. Natural gas containing low CO2/H2S ratio is considered less corrosive to process in amine sweetening systems. DGA plants, treating this type gas, typically use higher acid gas loadings in the rich DGA which, in conjunction with lower lean solution loadings, results in a significant increase in the net acid gas pickup per mole of DGA. As is the case with loadings, the energy requirement to regenerate the DGA solution is also affected by the CO2/H2S ratio in the natural gas feeds. Plants operating with high CO2/H2S feed require less energy compared to feed with low CO2/H2S ratio. Plants operating with high CO2/H2S ratio may require 1.0 to 1.5 14 moles of water vapor per mole of acid gas in the regenerator overhead. Low CO2/H2S ratio of 0.2/1 may require 2.5 to 3.5 moles of water vapor per mole of total acid gas in the regenerator overhead. A reflux ratio of this magnitude is not unusual for low pressure treating plants which are required to produce natural gas with less than 0.25 grains of H2S/100 SCF (Newman, 1985). 1.5 DGA Reclaimer Operations The reclaimer is important in the operation of DGA plants. It reduces corrosion, foaming and fouling of the DGA solution in the plant. It regenerates the DGA solution by removing the high boiling point and non-volatile acids and iron products from the DGA solution, concentrating them in the reclaimer as well as converting the chemical degradation product BHEEU back to DGA. A typical process flow diagram of a DGA reclaimer is shown in Figure 1.7. The major chemical degradation product of DGA solution in gas treating plants is N,N'bis(hydroxyethoxyethyl)urea (BHEEU).The reaction of two moles of DGA with 1 mole of either CO2 or COS forms 1 mole of BUEEU. A second degradation product is thiourea or N,N'bis(hydroxyethoxyethyl)thiourea (BHEETU) which can also be formed by the reaction of 1 mole of either CS2 or COS. Experience have shown that the dominant reaction with COS will be to form BHEEU. The reactions between CO2, COS, or CS2 and DGA are reversible in the temperature range of 340 to 360 0F. These reactions are shown below: 15 Figure 1.7 A typical process flow diagram of a DGA Agent reclaimer [Huntsman web site] The rate of conversion of BHEEU to DGA increases by increasing the reclaiming temperatures. Below temperatures of 340 0F the reaction of BHEEU to DGA is slow and at temperatures of 360 to 380 0F the reaction increases to acceptable rates. In order to conserve energy, the hot lean DGA from the stripper reboiler is generally used as feed to the reclaimer. The reclaimer is filled with the hot lean amine solution until the heating tubes are fully immersed. A liquid level controller is used to maintain the liquid level above the heating tubes. A 250 psig saturated steam is used to bring up the kettle temperature to the operating temperature. Most of the overhead vapor initially at the start of each cycle will be water. As the cycle progresses, the amine will become more concentrated in the reclaimer bottoms and the amine concentration of the overhead stream will increase. As the solution becomes more concentrated in DGA, the temperature of the liquid in the reclaimer 16 will increase. Fresh make up feed are added via the level controller to maintain the liquid level above the heating tubes in the kettle. The amine concentration will increase until the vapor composition approximately equals the composition of the circulation solution. The flow to the reclaimer is set when equilibrium is reached. This flow is controlled by the heat flux flowing to the tube bundle. In this case, the reclaimer can be operated with little attendance, except for temperature check up on occasional times. In order to maintain the same level of regeneration in the stripping still, it may be necessary to reduce the heat input to the reboiler. A small packed column is used for removal of any entrained liquids in the flashed vapors. The reclaimer overhead stream is returned to the bottom of the regenerator column to recover the heat from the reclaiming operation. Solids, sludge, heat stable salts, decomposition and degradation products accumulate in the reclaimer bottoms until the end of the reclaimer cycle, after that they are dumped. The length of the reclaimer cycle depends on the degree of solution contamination. Normal reclaiming cycles can vary from a few weeks to as long as three months or more. Samples of lean solution and the reclaimer liquid are analyzed periodically for contaminants. The BHEEU level in the lean amine solution should be kept at less than 3-5 percent. Increases in contaminant level vary from plant to plant; therefore, a history of reclaiming operations should be maintained. [Huntsman web site] 17 1.6 Saudi Aramco Experience with DGA Units The largest gas plants which utilize DGA are located in Saudi Arabia. The choice of DGA as the sweetening agent for the Saudi gas plants was based on the following major criteria (Harruff, 1992): Removal of H2S to pipeline specifications, <10 ppmwt. Removal of CO2 to <300 ppmwt to facilitate ethane recovery. Be able to meet these specifications economically while operating with contactor pressures as low as 120-180 psig and inlet temperatures as high as 120-140 F. Be able to operate using air coolers alone with ambient temperatures as high as 126 F. Produce an acid gas stream capable of being used to make bright sulfur in downstream Claus units. Over the first few years of operation, two plants noted that the lean amine concentration of morpholine (MOR) was rising. One study (Harruff, 1992) showed that BHEEU can thermally degrade into MOR in the reclaimer. There is no information in the open literature about the sweetening power of DGA/MOR blends. No off gas specifications have been observed; however, it is not known what the effect of MOR is on the plant performance. In order to establish the performance of the DGA treating process in the presence of MOR, thorough knowledge is required on the thermodynamics and kinetics of the reaction of CO2 in DGA, MOR and DGA/MOR solutions. Therefore the objectives of the second part of the dissertation are organized as follows; Chapter 4 addresses the issues of MOR, DGA and MOR/DGA blend thermodynamics. Solubility data from the wetted wall column are combined with NMR data, physical solubility data and the electrolyte 18 NRTL model to predict the speciation of these solutions, the solvent working capacity, heat of reaction and solvent volatility. In Chapter 5, the aqueous DGA system is studied in a wetted wall column from 298K to 333K at loading from 0 to 0.4. Three models were used to model the absorption data; the rigorous mass transfer model developed by Bishnoi (2000), based on the eddy diffusivity theory, the pseudo first order (PFO) and interface pseudo first order (IPFO) approximations. The effect of ionic strength on the second order rate constant was also studied. In chapter 6, the kinetics of MOR are studied in a wetted wall column and found to be faster than DGA. The difference is attributed to MOR s cyclic nature. The behavior of rate enhancement for MOR/DGA blend is also shown. The rigorous model is shown to match absorption data from the wetted wall column. The model is also used to show what the important phenomena are at different operating conditions. Conclusions and recommendations are presented in Chapter 7. 19 Chapter 2: The Effects of Aliphatic and Aromatic Component Conditioning on the Permeation Behavior of Hollow Fiber Asymmetric Membranes Membranes are used to separate a wide variety of gases, and separation of CO2 from natural gas is one of the most important emerging applications of this technology. Most membrane-based gas separations are accomplished with asymmetric hollow fiber or spiral-wound modules, which provide a large amount of separation area per unit volume. Asymmetric fibers are comprised of a thin (500- 2000 A) separating skin layer, which is supported on a second porous layer that is usually 50-200 um thick. Ideally, the porous support has no effect on the permeation properties of the membrane (Spillman and Cooley, 1989; Kesting and Fritzsche, 1993; Porter, 1990; Ho and Sirkar, 1992; Paul and Yampol'skii1994). , Natural gas streams contain numerous heavy hydrocarbons. A topic of concern in designing a reliable membrane system for natural gas purification involves the impact of such heavy hydrocarbon on the membranes. Very heavy hydrocarbon contamination is believed to be the cause of most membrane failures and loss in performance even at low mass fractions. Because of this, it is very important to carefully consider the required pretreatment requirements for membrane systems. The impact of these hydrocarbons on the membrane system has remained poorly understood due to the complexity of the components present and the difficulty in characterizing their effects experimentally. This chapter aims to understand the effect of heavy hydrocarbons on the performance of such membranes. Previous work on membrane formation has led to successful formation and modeling of reliable membrane structures for CO2 removal for natural gas feeds (Clausi and Koros, 2000; Clausi, 1989; Thundyil, 1998); however, the tests performed in the laboratory on these membranes were 20 contaminant-free. In actual field tests, membranes often exhibit poorer performance. Cellulose acetate membranes tend to show relatively low intrinsic CO2/CH4 selectivity, but have fair-to-good tolerance (with no loss in flux or CO2/CH4 selectivity) for contaminants such as benzene, toluene, and xylene in natural gas streams (Schell et al., 1989; Lee et al., 1988). On the other hand, for glassy polymeric membranes with intrinsically high selectivities, one study cites harsh performance decline in the range of 50% reduction in CO2/CH4 selectivity for polyimide films due to saturated concentrations of toluene or hexane in mixed gas feeds of CO2/CH4 (White et al., 1995). For a state-of-the-art polyimide asymmetric hollow fiber, one study (Gunaidi, 2000) showed serious losses in performance when the selective layer had a pronounced fused nodular nature, as compared to a truly integral dense skin. Nodule-like structures with sizes ranging from 300-1000 A in diameter are often observed in conventional asymmetric membranes. These skin layers can be treated to fuse and plug defects in the nodular regime into an effectively defect free layer that is effective for gas separation in the absence of aggressive hydrocarbons such as considered here. More work is needed to understand the key factors that undermine the gas separation ability of membranes in such applications. The presence of hydrocarbons in the field, even in trace quantities, appears to be the culprit. Therefore, understanding the effect of heavy hydrocarbons is necessary for the development of more robust membranes for this application, and this study considers an intrinsically defect free skin that does not need defect-plugging treatment. Moreover, this study is the first of its kind to consider the effects of conditioning on defect-free asymmetric membranes. 2.1 Experimental Methods The performance of a membrane is mainly characterized by the selectivity and permeability, or permeance. The permeance, P/l, is simply the pressure 21 normalized flux and is the preferred productivity measure for asymmetric membranes where the actual thickness of the selective skin layer is not clearly measurable. Using these parameters, the membrane-based natural gas purification process can be examined, based on determination of CO2/CH4 selectivity and permeances. In order to understand the effect of the hydrocarbon s presence, one should compare the selectivity and permeances of the membranes from the same module. Testing with the same module minimizes the processing variability that could occur between modules. In addition, each fabricated module was only used at one state (one temperature and one hydrocarbon content) to avoid any hysteresis effect. Therefore, the experiments were completed by testing with two different sources of gases. The first source is a 10% CO2/90% CH4 tank without any hydrocarbons content. The second source has the same mixture of natural gas content, but with some hydrocarbons added as specified. Replicate runs were done by preparing multiple modules (usually 2) from each fiber state. See Appendix C. For each module, the binary gas feed was used to determine the base case of the permeances and selectivities of the membrane fibers. Then, the same module was subjected to conditioning with ternary feeds. The module was tested again with the binary gas that did not contain any hydrocarbons. The results of these experiments were then compared to understand the effect of hydrocarbons. For the permeation tests, the variables for the experiments are temperature, feed pressure and hydrocarbon concentration in 10% CO2/ 90% CH4 feed gas. The investigated operating temperatures were 350C and 550C. The hydrocarbon contents in the feed gas stream were 100 ppm and 300 ppm for toluene and 300 ppm and 500 ppm for n-heptane. These numbers simulate the concentration at a typical natural gas field. 22 2.1.1 Materials 2.1.1.1 Polymer Polyimides have been identified as materials with high selectivities and permeabilities for CO2/CH4 separation (Matsumoto and Xu, 1993; Kim et al., 1988; Kim et al., 1989; Tanaka et al., 1989; Stern et al., 1989; Coleman and Koros, 1990). In addition to high selectivities, polyimides possess high glass transition temperatures (Tg > 2000C). A polyimide that is available in the market is Matrimid 5218. Its permeation properties, combined with its processability (i.e., solubility in common solvents) make it an attractive candidate for gas separation applications. Furthermore, its mechanical strength and high glass transition temperature, better suit it for more rigorous working environments than other noncelluslosics such as polysulfone. Figure 2.1 shows the unit structure of this polyimide. H3C CH3 O O O N O O H3C N n Figure 2.1 Repeat unit of Matrimid 5218 polyimide. The density of Matrimid is 1.2 g/cm3. The polymer sample has a Tg at 3050C under differential scanning calorimetry (DSC-7, Perkin-Elmer) with a scan rate of 200C/min. Various gas permeabilities of this polymer at 250C are presented in Table 2.1. 23 Table 2.1 Reported gas permeabilites of Matrimid at 250C (Clausi and Koros, 2000; Clausi, 1998) Polymer P O2 (Barrer)* P N2 (Barrer)* P He (Barrer)* Matrimid 5218 1.32 0.183 22.5 cc( STP )cm *1 Barrer = 10 10 2 cm sec cmHg In the present study, these polymers are fabricated into asymmetric hollow fibers. The fibers were graciously provided by Dr. Seth Carruthers, Dr. David Wallace and Shabbir Husain. These hollow fiber membranes were produced in the laboratory using the phase-inversion method (Clausi and Koros, 2000; Clausi, 1998). Asymmetric membranes formed by this phase inversion techniques are generally said to be integrally skinned, since the porous substructure and skin layers are made from the same polymer in a single process. This particular process creates asymmetric membranes with a combination of adequate gas flux and excellent mechanical strength and essentially defect-free selective layers. Since the skin was formed in a defect-free condition, no post treatment was applied to these fibers. For this study, the fiber has an inner diameter (ID) of 100 m and outer diameter (OD) of 250 m. Figure 2.2 shows the scanning electron micrograph (SEM) of a fiber cross-section area. 2.1.1.2 Permeants The mixed gas used were certified mixtures of 10% CO2/ 90%CH4, 10% CO2/ 90%CH4 + 100 ppm toluene, 10% CO2/ 90%CH4 + 300 ppm toluene, 10% CO2/ 90%CH4 + 300 ppm n-heptane and 10% CO2/ 90%CH4 + 500 ppm nheptane. Gases were custom ordered through Air Liquide, Houston, TX. 24 Figure 2.2 Scanning Electron Micrograph of cross section of a Matrimid asymmetric hollow fiber showing selective skin and porous support. The skin layer is shown in partially oblique view to illustrate its thin continuous nature (Gunaidi, 2000). 2.1.2 Module Housing The module housing is constructed of brass and 316 stainless steel (316 SS) Swagelok and NPT fittings: two Swagelok union tees (316 SS), one port connector (316 SS), two adapters for NPT female to union tees (brass), two adapters for NPT male to tubing (brass). Figure 2.3 shows the schematic diagram of the module housing. The selection of the housing material was based on cost and reusability. To hold the fibers on the both ends at the NPT fittings, Stycast 2651 epoxy resin was mixed with Catalyst 9 (Emerson & Cuming). Before the Stycast was applied into the fitting, a PTFE tape is placed in between the fiber and the wall of the housing. The purpose of the PTFE tape was to prevent the epoxy from 25 dripping into the permeation area. Stycast has good properties for this module housing because its high-pressure resistance ability and its appropriate viscosity for flowing into the fibers interspace. The resulting module has an active length for permeation of approximately 10.5 cm. In the experiment, usually 10 fibers are potted in a module to produce an active permeation area of 8.2 cm2 per module. The module is designed to have a double-ended permeate flow. This design was to minimize the pressure drop effect that may occur in the permeate side (Thundyil et al., 1983). Shell side feeding is configured in the system to simulate the typical practice in the natural gas field. Feed Retentate Permeate Permeate Active membrane area Figure 2.3 Shell-side feeding with the module construction. 2.1.3 Pure Gas Permeation The skin integrity of the hollow fibers was confirmed by permeating oxygen, nitrogen and helium gases before testing with the natural gas components. The permeation technique utilized a bubble flow meter to measure the flux of the permeate. The equipment is shown schematically in Figure 2.4. 26 B R D D Figure 2.4 Schematic diagram of pure gas permeation testing For pure gas permeation testing, the retentate flow and one of the permeate side is capped. The flux of the gas is then measured at other end of the permeate side by connecting it to a bubble flow meter. The permeance, P/l, for the pure gas component is then calculated by 5.28x10 7 V P = l (T )( A)( p f p atm ) where: P/l = Permeance T = Temperature pf = Feed pressure [=] GPU [=] K [=] psia V = Permeate flow rate [=] cc(STP)/sec A = Membrane area [=]cm2 (2.1) 27 patm= Atmospheric pressure [=] psi 2.1.4 Mixed Gas Permeation The permeability of hollow fibers was measured under vacuum permeate conditions. Figure 2.5 shows the schematic diagram of the permeation apparatus. The system is stationed in a temperature-controlled water bath using a circulating water bath (Model W2 water bath, and Model E3 circulator, Haake Buchler Instrument Inc., Saddle Brook, NJ). The feed pressure is measured using an Ashcroft pressure gauge, which has 0 to 1000 psig pressure range (+0.2 psi). A coiled stainless steel tubing of three meters was placed after the entrance in the water bath to ensure that thermal equilibration was reached. The system uses stainless steel tubing of and 1/8 diameter with Swagelok fittings and was also rated for 1500 psia pressure. The downstream volume was measured using volume expansion method and was determined to be 1029 cm3 (Gunaidi, 2000). A two stage mechanical vacuum pump (Model E2M2, Edwards Vacuum, Crawley, Sussex, England) was used to maintain vacuum (<0.01 mmHg) on the downstream side. To ensure that the composition in the feed stream did not vary along the length, a stage cut (ratio of permeation rate to the retentate) of 1% was maintained. A Whitey (SS-31EF4) screwed bonnet needle valve was used to regulate the retentate flow rate. In order to determine the permeability and selectivity of permeants in mixed gas permeation, it was necessary to measure the composition of at least two streams from the feed, residue and permeate streams. The composition measurements were accomplished by the installed gas chromatograph (Model 5880A, Hewlett Packard, Atlanta, GA). 28 B GC R V1 A C D F M S E G V2 V4 V3 GC A: Supply Gas Cylinder F: Pressure Transducer B: Pressure Gauge G: Vacuum Pump C: Coiled Tubing V1-4: Valves D: Metering Valve M: Membrane E: Permeate Ballast Volume R: Pressure Regulator S: Gas Supply Figure 2.5 Schematic of gas permeation apparatus for hollow fiber modules 29 The selectivity is determined from the compositions of feed and permeate streams y x A B = A B y x B A (2.2) where y and x denote the mole fractions of components A and B in the permeate side and feed side, respectively. With mixed gas feeds, permeances were typically calculated using the component fluxes and the partial pressure (or fugacity) driving force (2.94 10 4 )(V )( )( (T )( A) p f x a dp p dt ) ya Pa = (2.3) where Pa = Permeability [=] 1 Barrer = 1 10 10 [=] torr/min cc( STP )cm cm 2 sec cmHg dp/dt = rate of permeate rise T = Temperature pf = Feed pressure = Film thickness [=] mils [=] Kelvin [=] cm2 [=] cmHg A = Membrane surface area ya = Feed composition of component a xa = Permeate composition of component a V= Downstream volume [=] 1029 cm3 Thundyil (1998) developed recently a rigorous mathematical model which takes into account variation in compositions in the shell and the tube sides. He approximated the pressure drop in the tube-side by the expression: 30 2 d pT 25.6 RT QT = dz d i4 22400 ( ) (2.4) where pi is the pressure in the tube-side, R is the ideal gas constant (8.3145 J mol1 K-1), T is absolute temperature (in K), is viscosity (in P), di is the inner diameter of the membrane fiber, and QT is the flow rate in the tube-side (in cm3 (STP)/s). To calculate the permeance of each component, a finite element analysis was performed on a spreadsheet, where each discrete axial element along the fiber had a separate pressure driving force and flow rate. From Equation (2.4), the pressure drop for element j along the single fiber was calculated by 25.6 RTQT ( j ) z 22400 d i4 pT ( j ) = 2 pT ( j 1) (2.5) where z is the differential length of each element. Since the exit permeate pressure was known, an iterative technique (e.g., Solver in Excel ) was used to determine the permeate pressure profile by varying the midpoint axial permeate pressure until the calculated exit permeate pressure agrees with the measured exit permeate pressure within the specified error tolerance (<0.01%). The permeances were also iterated and were used to calculate the flow rate of each element and the resulting permeate pressure for each element using Equation (2.5) above. Additionally, the component permeances were related by the known permselectivity from the gas chromatography analysis. Both the component permeances and midpoint permeate pressure were simultaneously iterated and used to calculate the flow rates and permeate pressures until convergence. The component viscosities were estimated by the Lucas correlation, and the mixture viscosity was estimated by the Wilke method. Further details on the full mathematical model are described by Thundyil (1998). The Excel spreadsheet and iterative technique used to calculate the component permeances of our 31 membrane fibers were adapted from this model. Calculation of component permeances with this model differed slightly (< 4%) from calculations using a simple mean pi in Equation (2.3). 2.1.5 Testing Procedure Before measurements were made, the module was placed under vacuum condition over night. The temperature of the circulating water bath is also adjusted to the desired setpoint. In this work, there are two sets of experiments depending on the conditioning pressure. The two sets are the 200 psia conditioning pressure series and the 600 psia conditioning pressure series. Conditioning pressure is defined as the pressure at which the membrane module is kept at by flowing a gas mixture for an extended period of time. In this work, the conditioning time in most cases is at least five days. The tests were then performed by starting the feed pressure at ~100 psia for the 200 psia conditioning pressure series and at ~200 psia for the 600 psia conditioning pressure series followed by, measuring the permeate pressure rise. To reduce the small variation in data among samples to a corresponding nondimensional form, plots of PCO2/PCO2ref against pressure or time were used. The permeances at ~100 psia and at ~200 psia for CO2 before exposure for the 200 psia conditioning pressure series and for the 600 psia conditioning pressure series respectively were used as reference values for normalization. Steady state was achieved in less than ten minutes for the thin selective layers. Once steady-state conditions were demonstrated, the vacuum pump valve (V2) was closed. This condition was verified by constancy of permeate flow rate and constancy of permeate composition for mixed gas feeds. The pressure increase in time, dp/dt, was then recorded by a SolTec chart recorder. The fact that the short period of time is needed to reach steady state is due to the extremely thin thickness of the skin. In this work, the GC sampling and the dp/dt measurements were taken 30 minutes to one hour after the steady state has been verified. After 32 the permeate pressure has risen to 50 torr, the permeate gas is sampled into the gas chromatograph. From the gas composition and the pressure increase in time, dp/dt, the permeability and selectivity can be calculated. Two to three measurements were taken for the gas composition and the dp/dt and the average value is reported on here. Following the injection, the permeate volume is then pulled to vacuum, while the feed pressure is increased to 150 psia, and 200 psia for the 200 psia conditioning series and to 400 psia, and 600 psia for the 600 psia conditioning series. The above steps for permeability and selectivity measurements were then repeated at each designated feed pressure. This procedure of increasing the pressure from 100 to 200 psia for the 200 psia conditioning series and from 200 to 600 psia for the 600 psia conditioning series is termed Pressurization . It should be remembered that the measurements of permeances of CO2 and CH4 and selectivity is performed with the 10/90 CO2/CH4 binary gas mixture; therefore, the pressurization step is termed also as Before exposure (meaning before exposure to the contaminant containing feed). At the conditioning pressure, 200 psia for the 200 psia conditioning pressure series and 600 psia for the 600 psia conditioning pressure series, the 10/90 CO2/CH4 gas mixture was exchanged with the 10/90 CO2/CH4 in the presence of the hydrocarbon impurity as specified. This exchange and the subsequent exposure are termed conditioning or During exposure in this study. Clearly, a base case of c onditioning corresponds to exposure of the fibers to only the binary mixture. The module was then subjected to conditioning for five days period at the conditioning feed condition. During the conditioning period, also termed as during exposure as noted earlier, the permeability and selectivity were measured as described above. After that, the ternary mixture was exchanged with the 10/90 CO2/CH4 and the permeability and selectivity were measured as described above to probe the effects caused by the heavy hydrocarbons. Feed pressures with 50 psia decreasing feed pressure decrements for the 200 psia 33 conditioning pressure series and with 200 psia decreasing feed pressure decrements for the 600 psia conditioning pressure series were then measured with the same method using the 10/90 CO2/CH4 binary mixture. Again, the CO2 permeance and gas composition measurements were taken 30 minutes to one hour after the steady state has been achieved. This was done because we wanted to probe the after effects of condition ing and not to monitor any slow further collapse of the membrane in the presence of the 10/90 CO2/CH4 feed. This procedure of pressure decreasing is termed Depressurization or After exposure . These sets of experiments compare the pressure -permeability before exposure to that after exposure without evacuation of the membrane, thereby providing insight into the effects caused by the heavy hydrocarbons during exposure. 2.2 Four Potential Deterioration Factors There are at least four possible non-ideal effects that the presence of hydrocarbons may cause in the selective skin layer of membrane used in natural gas purification processes. The four effects are: (i) competition, (ii) plasticization, (iii) conditioning and (iv) compaction. 2.2.1 Competition Effect The term competition effect will be used in this study to mean a specific response caused by the presence of a penetrant, that inhibits the transport of the other components. The dual mode sorption theory suggests the competition effect should be most apparent for highly condensable feed components, like toluene (Chern et al., 1999). If this effect is present and depresses the CO2/CH4 selectivity, the selectivity should return to the original value upon removal of the preferentially sorbing penetrant. Figure 2.6 illustrates a cartoon representation of the competition effect in the presence of a strongly competitive (highly sorbing) 34 component like toluene. In this connection, the term strong competitor is taken to mean components whose critical temperature, Tc, is greater than the measurement temperature. Before Exposure A B During Exposure A B After Exposure A B C C Figure 2.6 Depiction of competition effect caused by a third component, C, in a membrane system. The symbols depict unrelaxed volume elements accessible to both components A and B in the glassy polymer in the absence of a strongly condensable (e.g. toluene or n-heptane) component. During exposure to such C components, sorption and transport (i.e. permeation) pathways are precluded to A and B, thereby reducing their ternary gas permeation in comparison to binary feeds. 2.2.2 Plasticization Plasticization is said to occur when the presence of a given component in a polymer matrix causes the diffusion, and hence permeation, of other components to increase compared to the case without that component present due to a swelling-induced facilitation of a local segmental motion. A strongly sorbing component such as CO2 or toluene can cause plasticization even in the absence of other penetrants. Plasticization is apparent as non-constant, upwardly inflecting permeability or permeance as a function of CO2 or toluene feed pressure (Jordan and Koros, 1990; Jordan et al., 1990). The highly sorbing nature of toluene in aromatic polyimides was also expected to make it a potential plasticizing agent that would tend to increase the permeability or 35 permeance of both CO2 and CH4. Since CH4 is a larger molecule, facilitation of local segmental motions may promote its diffusion even more than it might assist the compact CO2; however, the effect has not been well documented. Figure 2.7 depicts the plasticization effect. Fortunately, as will be documented in the results section, no evidence for strong plasticization by either CO2 or toluene was seen over the range of conditions studied so far. Before Exposure A B During Exposure A B After Exposure A B C C Figure 2.7 The effect of plasticizing: increase in the permeances of penetrants. In this case, besides any competition effects, additional swelling induced permeation pathways are made available to other components. The symbols depict unrelaxed volume elements accessible to both components A and B in the glassy polymer in the absence of a strongly condensable (e.g. toluene or n-heptane) component. The additional arrows shown in the during exposure case illustrates the hypothetically possible higher flux of both A and B during plasticization. 2.2.3 Swelling Induced Conditioning History Effect Since glassy polymers are known to be nonequilibrium materials, the manner in which the samples have been treated can affect their sorption and transport properties. Previous studies have shown that exposure to a highly sorbing gas like CO2 at high pressures will cause an increase in sorption and dilation levels as compared to levels in an as-received or unconditioned sample (Jordan et al., 1990; Jordan and Koros, 1990). This phenomena has been explained in part by 36 attributing the increase in subsequent sorption and dilation levels to an increased number of subtle packing disruptions in the non-equilibrium polymer matrix, which makes it energetically easier for penetrant molecules to be sorbed and to diffuse. Figure 2.8 illustrates a cartoon representation of the conditioning effect in the presence of a strongly competitive (highly sorbing) component like toluene. Before Exposure A B During Exposure A B After Expos ure A B C C Figure 2.8 The effect of conditioning is an increase in the permeances of penetrants. In this case, besides any competition effects, additional swelling induced permeation pathways are made available to other components. The symbols depict unrelaxed volume elements accessible to both components A and B in the glassy polymer. The additional arrows show in the after exposure case illustrates the higher flux of both A and B due to conditioning. The swelling induced conditioning effect (SICE) is more pronounced if the secondary penetrant is introduced while the sample is still exposed to the conditioning agent, i.e. using a gas exchange protocol. Less dramatic effects are apparent upon exposing a glassy sample to a highly sorbing penetrant at a predetermined pressure; and then evacuating completely before exposure to the secondary penetrant since relaxation appears more facile in the absence of penetrant. Aromatic substances such as toluene are well known for their high condensability and therefore are suspected to act as potent SICE agents. Our 37 results show that, indeed, conditioning to toluene increases the transport properties of the membrane. 2.2.4 Compaction Under catastrophic conditions, plasticized glassy structures exposed to high transmembrane pressure can have reduced modulii and undergo significant rearrangements of the super-molecular morphology leading to a denser microstructure (Gunaidi, 2000). In an asymmetric hollow-fiber membrane, which is comprised of dense and porous regions, the compaction can lead to subtle densification of the finely porous transition region between the more or less dense skin region and the highly porous support layer. This results in added mass transfer resistance to the membrane. Since this added resistance is associated with a porous medium (e.g. Knudsen selective), the effective observed overall selectivity of the combined skin, transition region and formerly invisible support resistance is biased to reflect greater contribution with its lower selectivity porous Knudsen properties. Such a change tends, therefore, to reduce permeance of all components but to most negatively impact the highest permeability components, thereby also reducing selectivity. Hence, the effect of compaction will be a decrease in the flux and decrease in the selectivity. Once a membrane is compacted, it is visualized as being deformed as shown schematically in Figure 2.9. A dramatic drop in modulus can accompany strong swelling and plasticization effects (Mulder, 1991; Jonsson, 1978). It is possible that the onset of strong skin plasticization may accompany modulus drop in the transition layer as well, so catastrophic failure and the onset of strong skin layer plasticization may occur under similar feed conditions. Fortunately, our results, shows no evidence for strong plasticization or compaction by either CO2 or toluene as seen over the range of relatively aggressive conditions studied so far. 38 The asymmetric hollow fiber membranes used in this work are formed in a process known as dry wet phase inversion which is, in essence, a solvent nonsolvent quench (Clausi and Koros, 2000; Clausi, 1998). The resulting fibers consist of a thin selective layer over a nonselective porous support. Since membranes are formed very rapidly from solution, the dense selective layer is thought to consists of considerable excess free volume and is a highly out-ofequilibrium packing conformation. Therefore, there is a considerable driving force for densification of the selective layer of asymmetric membranes to an equilibrium packing density, which would result in a considerable loss in flux over time. Skin (Selective Layer) Transition Layer Porous Support Before Exposure During Exposure After Exposure Figure 2.9 Depiction of the compaction effect. 39 To better understand the effect of hydrocarbon conditioning on the transport properties of membrane, the fibers were aged for two months following the formation process to avoid scatter in the results due to second-order differences in the process of aging. The permeabilities and selectivities of the O2/N2, He/N2 gas pairs for the aged samples are shown in Table 2.2. There was little change in the permeabilities and permselectivities in the second two months. Therefore, the majority of the physical aging in the unconditioned fibers occurred in the first three months following the membrane formation process. These results were expected since the majority of the volume relaxation occurs within a very short time period during physical aging (Punsalan, 2001). The reduction in permeability with time was due primarily to the densification of the polymer matrix. Punsalan (2001) studied the change in permeance of defect-free Matrimid asymmetric hollow fiber over a 42-day period of aging time. Table 2.3 shows the change in permeance over time for oxygen, nitrogen and helium. Table 2.2 Pure gas permeation results for hollow fiber membranes used in this work at 250C. .O2/N2 .He/N2 P/lO2 (GPU)* P/lN2 (GPU)* P/lHe (GPU)* 7.1 126 3.1 0.448 57 *1 GPU = 10 6 2 cm seccmHg cc(STP) 40 Table 2.3 Percent change in N2, O2 and He permeance in Matrimid asymmetric hollow fiber over 42 days of aging at room temperature (Punsalan, 2001). P/l . Time, days 0 42 N2 0.96 0.70 O2 6.52 5.58 He 96.0 95.7 He/N2 100 137 O2/N2 6.8 8.0 Samples were stored at room temperature in a plastic bag, to guard against complications from humidity that need to be removed prior to testing; however, this was adequate to produce a representative sample. In order to conserve gas, only ten fibers were potted in each module. The results presented below represent the average values based on two replicates. 2.3 Results and Discussion 2.3.1 Comparison of Conditioning in Hollow Fiber Membranes at 200 psia before and after Exposure To establish a base case, the fibers were exposed to a simple binary 10/90 CO2/CH4 gas mixtures to show the conditioning effect of the CO2 and CH4 penetrants in hollow fiber membranes in the absence of toluene or n-heptane. The fibers were initially evacuated on the permeate side to remove any sorbed gases from the fibers. The feed pressure of the 10% CO2/ 90% CH4 was increased incrementally and the permeability was measured at each pressure increment. The feed was then maintained at the conditioning pressure for five days. After a five day period, the feed pressure of the conditioning mixture was reduced incrementally and the permeability measured at each pressure increment. An assumption in the measurement of conditioning effects has been that the hysteresis depends only on the maximum conditioning pressure. Therefore, the hysteresis was thought to be independent of the pathway used to reach the conditioning 41 pressure. Past studies have assumed that the extent of conditioning is strictly a function of the maximum exposure pressure for a specific polymer-penetrant pair (Coleman, 1990). Figure 2.10a shows the effect of conditioning of 10/90 CO2/CH4 at 200 psia and 35 0C on the CO2 permeability. A reduced or normalized permeability is used to compare the relative permeability enhancements resulting from conditioning treatments in different fibers. The reduced permeability is the ratio of the permeability at each pressure to the permeability in the unconditioned sample at 110 psia. Note (PCO2/l) at 110 psia used for normalization corresponds to the permeance at 110 psia before exposure. This was selected as a reasonable value that showed negligible time dependence over a period of five days after reaching Fickian steady state. As can be seen the maximum enhancement in CO2 permeability was 3% relative to the unconditioned sample. The maximum enhancement in permeability in the conditioned sample occurred at lower pressures. The permeability of CO2 and CH4 decreases with pressure, which is typical of the dual mode behavior in glassy polymers. The CO2 permeability enhancements following conditioning is probably a result of the loosening and reordering of the polymer matrix, which resulted in a slight increase in the CO2 permeability. The selectivity of CO2/CH4 following 10/90 CO2/CH4 conditioning is shown in figure 2.10b. The selectivity of CO2/CH4 was slightly higher in the conditioned sample than in the unconditioned sample. However, it should be remembered that this slight increase in selectivity and CO2 permeance is within the experimental error, and therefore the effects of conditioning at 200 psia with 10/90 CO2/CH4 on CO2 and CH4 permeances are negligible. Typical experimental results, illustrating the effect of n-heptane in a natural gas field stream, are shown in Figure 2.11a and 2.11b. Figures 2.11a and 2.11b show the experimental results of the permeability and selectivity, respectively, of the CO2/CH4 separation at 35oC. Between exposure and prior to the after 42 1.6 1.4 1.2 D epressu rizing w ith 10/90 C O /C H 2 4 (110 p sia) D uring exposure with 10/9 0 C O /C H for five days 2 4 CO2 CO2 /P 1 0.8 0.6 100 P re ssurizing with 10/90 C O /C H 2 4 P a 120 140 160 180 200 22 0 F eed P ressure (psia) 1.1 (110 psia) 1.0 5 1 C O 2/C H 4 P ressurizing w ith 10/90 CO /C H 2 4 0.9 5 0.9 0.8 5 0.8 0.7 5 0.7 100 D epre ssurizing with 1 0/90 C O /C H 2 4 / D uring exposure with 10/90 C O /C H fo r five days 2 4 C O 2/C H 4 b 120 140 160 180 200 220 Feed Pressure (psia) Figure 2.10 Effect of conditioning of 10/90 CO2/CH4 mixture on a) the CO2 permeability, and b) the CO2/CH4 selectivity at ~200 psia and 35 0C. Lines are drawn by e ye . 43 1 .6 E xchange condition the 10/90 C O /C H 2 4 (115 psia) 1 .4 1 .2 1 0 .8 with the 1 0/90 CO /C H + 500 ppm n-hep tane 2 4 for five days C O2 /P P ressu rizing with 10/90 C O /C H 2 4 C O2 D ep re ssurizing with 1 0/90 CO /C H 2 P 4 0 .6 10 0 a 12 0 14 0 16 0 180 200 22 0 Feed Pressure (psia) 1 .1 (115 psia) 1.0 5 1 CO 2/CH 4 P ressu rizing w ith 10/90 C O /C H 2 4 0.9 5 0 .9 0.8 5 0 .8 0.7 5 0 .7 10 0 D epressurizing with 10/9 0 CO /C H 2 4 / CO 2/CH 4 E xch ang e cond itio n th e 10/90 C O /C H 2 2 4 4 with th e 10/90 C O /C H + 500 pp m n -h eptan e for five days b 12 0 14 0 16 0 18 0 20 0 22 0 F eed P ressure (psia) Figure 2.11 Effect of conditioning of 10/90 CO2/CH4 + 500 ppm n-heptane mixture on a) the CO2 permeability, and b) the CO2/CH4 selectivity at 200 psia and 35 0C. Lines are drawn by eye . 44 exposure e xperiments, vacuum condition was applied on the permeate side of the membrane, (two to three hours), at the constant temperature of the experiment. The procedure is a method to remove the residual hydrocarbons that may be present in the membranes as a result of the exposure testing for five days. In order to understand which of the four potential effects, see section 2.2, that the n-heptane causes, one has to look upon the permeability responses as well as the selectivity responses. Permeation studies with 500 ppm n-heptane in the 10% CO2/ 90% CH4 mixed gas feed indicate approximately a 2% decrease in CO2 permeances with 23% loss in CO2/CH4 selectivity. After the n-heptane exposure, at 200 psia, the permeation behavior returned essentially to its original pattern. This recovery indicted that, the effect of n-heptane does not cause competition or major compaction or free volume plasticization induced facilitation of CH4 versus CO2 permeation. The small conditioning responses at 200 psia with the 300 ppm nheptane were also similar to those with the 500 ppm n-heptane. Both the 300 ppm and the 500 ppm feed gas mixtures showed negligible conditioning effects at 200 psia. In comparison to the n-heptane, one can see that the primary effect of exposure to toluene, is one of conditioning, (see section 2.2.3), since the permeance of CO2 exceeds the permeance before exposure as can be seen in figure 2.12a. Clearly, there is difference in the conditioning ability of the aromatic versus the aliphatic component. Toluene conditioning increased the permeability of both the CO2 and CH4 in the polymer. Moreover, toluene conditioning resulted in a decrease in the permselectivity of CO2/CH4 as shown in Figure 2.12b. This decrease in permselectivity was due presumably to a decrease in diffusivity selectivity caused by a loosening of the polymer matrix. The conditioning induced increase in permeability was a result of an increase in diffusivity caused by a 45 1 .6 (115 psia) 1 .4 D epressurizing with 10/90 CO /C H 2 4 Exchang e con ditio n th e 10/90 C O /C H 2 4 1 .2 1 0 .8 0 .6 10 0 with the 1 0/90 C O /C H + 300 ppm tolu ene 2 4 P C O2 /P C O2 for five days P ressurizin g with 1 0/90 C O /C H 2 4 a 12 0 14 0 16 0 180 200 22 0 F eed P ress ure (psia) 1.1 (115 psia) 1.0 5 1 CO 2/CH4 P ressurizing with 10/9 0 C O /C H 2 4 E xchang e condition th e 10/90 C O /C H 2 2 4 4 0.9 5 0.9 0.8 5 0.8 0.7 5 0.7 100 with the 1 0/90 C O /C H + 3 00 ppm toluen e for five days / CO 2/CH4 D ep ressurizin g with 10/90 C O /C H 2 4 b 120 14 0 16 0 18 0 200 22 0 Feed P ressure (psia) Figure 2.12 Effect of conditioning of 10/90 CO2/CH4 + 300 ppm toluene mixture on a) the CO2 permeability, and b) the CO2/CH4 selectivity at 200 psia and 35 0C. Lines are drawn by eye . 46 decrease in the intersegmental resistance to mobility of the polymer chain. The loosening of the polymer matrix presumably tends to increase the size and frequency of adequately large transient gaps available for diffusive jumps. Transport conditioning will preferentially increase the diffusivity of the larger penetrant, CH4 in this case, relative to the small penetrant, CO2 in this case, and should result in a decrease in the diffusivity selectivity. These findings are in line with the sorption results as will be discussed in the next chapter. Exchange conditioning of the 10/90 CO2/CH4 and 300 ppm toluene with 10/90 CO2/CH4 gas mixture at 200 psia led to 50-60% increase in the CO2 and CH4 permeability relative to the permeability of the unconditioned sample with a corresponding 13% loss in CO2/CH4 permselectivity. Mixed gas permeation experiments for the 10/90 CO2/CH4 were performed at 200 psia total feed pressure and 55 0C. As expected, with an increase in temperature an increase in permeability is observed, coupled with a decrease in selectivity, following the classical Arrhenius behavior. Since the temperature dependence of permeability is often modeled as an Arrhenius-type relationship, Arrhenius plots (log of permeance versus inverse absolute temperature) can be made and apparent activation energies for permeation can be obtained: Ep = 14.5 kJ/mol (for CO2) and Ep = 30.6 kJ/mol (for CH4). Figure 2.13 shows the Arrhenius plots for CO2 and CH4. The apparent activation energy for permeation is greater for CH4 compared to CO2, since apparent activation energy scales with penetrant diameter. This results in a declining selectivity with increasing temperature. The CO2 permeance and CO2/CH4 selectivity were 11.6 GPU and 34.3 at 35 0C compared to 16.4 GPU and 23.4 at 55 0C respectively. The effects of conditioning on the CO2 permeability and CO2/CH4 selectivity at 55 0C and 200 psia are shown in figure 2.14. Since the sorption level decreases with temperature, it is reasonable that the conditioning effect is lower at 55 0C as compared to 35 0C. The results in Figure 2.14a suggest that the 10/90 47 3 CO 2 2 1 LnP 0 -1 CH 4 -2 -3 3 10 3.1 1 0 -3 3.1 1 0 -3 3.1 1 0 -3 3.2 10 -3 3.2 1 0 -3 1/T (1/K ) Figure 2.13 CO2 and CH4 Arrhenius plots of 10/90 CO2/CH4 mixture at 200 psia CO2/CH4 and 300 ppm toluene conditioning is not an important factor at play. The maximum increase in permeability of CO2 was 2% at 100 psia for the conditioned sample relative to the unconditioned sample. The selectivity of CO2/CH4 shown in Figure 2.14b was slightly higher in the conditioned sample than for the unconditioned sample. Similar results have been seen for the 10/90 CO2/CH4 + 500 ppm n-heptane mixture. The reported results, however, represent the average of duplicate permeators for each state (temperature and toluene exposure), so the trends, are believed to be correct and meaningful. This important result shows that pretreatment may not be a problem at the 300 ppm level if the feed is simply heated to 55 0C; however, the CO2 flux is reduced during exposure as will be 48 1 .6 (100 psia) 1 .4 1 .2 1 P ressu rizin g with 10/90 C O /C H Exch ang e cond itio n th e 10/90 C O /C H 2 2 4 4 with the 1 0/90 C O /C H + 30 0 ppm tolu ene for five days C O2 D epressurizing with 10/90 CO /C H 2 P C O2 /P 4 0 .8 0 .6 2 4 a 80 100 12 0 14 0 160 18 0 20 0 22 0 F eed P ressure (psia) 1 .1 D epressurizing with 10/90 C O /C H (100 psia) 1.0 5 1 CO 2/C H4 2 4 P ressurizing with 10/90 C O /C H 2 4 0.9 5 0 .9 0.8 5 0 .8 0.7 5 0 .7 b 80 100 12 0 14 0 16 0 18 0 20 0 22 0 F eed Pressure (psia) E xchange condition the 10/90 C O /C H 2 2 4 / 4 with the 10/90 C O /C H + 3 00 pp m toluen e for five days Figure 2.14 Effect of conditioning of 10/90 CO2/CH4 + 300 ppm toluene mixture on the a) CO2 permeability, and b) CO2/CH4 selectivity at 200 psia and 55 0C. Lines are drawn by eye . 49 CO 2/C H4 discussed later due to competition effects. This problem can be alleviated by using more fibers while preserving the selectivity by operating at 55 0C. 2.3.2 Comparison of Conditioning in Hollow Fiber Membranes at 200 psia during Exposure As can be seen in Figure 2.15a, the CO2 permeance in the 10/90 CO2/CH4 + 500 ppm n-heptane decreased by 23%, when compared to the 10/90 CO2/CH4 binary mixture. The CO2 permeance in the 10/90 CO2/CH4 + 500 ppm n-heptane subsequently remains essentially constant during the five days period. The selectivity, as shown in figure 2.15b, decreased 5% during the five days of the experiment. Clearly, although possibly tolerable, pretreatment to remove even such paraffinic contaminants may be desirable if maximizing selectivity is crucial for a given application. On the other hand, the selectivity in the 10/90 CO2/CH4 + 300 ppm toluene decreased roughly 12% from the selectivity of the 10/90 CO2/CH4 base case. The permeance of CO2 decreased 40% on the first day and then increased steadily to 67% relative to the CO2 permeance of the 10/90 CO2/CH4. The small decrease of CO2 permeance here during exposure in the case of the 10/90 CO2/CH4 + 500 ppm n-heptane suggested that, unlike toluene, the nheptane does not compete strongly with the other components significantly to block transport through the membrane at the segmental scale. Toluene, on the other hand, appears to block permeation pathways such that the membranes are able to separate less efficiently. This may be due to competition with CO2 and CH4 for diffusion pathways and sorption sites in the gas mixture. Even at 300 ppm level, it appears that toluene has a sufficiently negative impact to make it necessary to reduce it to a lower level. The level required to render toluene no more problematic than n-heptane at 500 ppm would require more extensive study. Some investigation (discussed later) with 100 ppm toluene effectively is at this limit, but how 150, 200 or 250 ppm would behave cannot yet be predicted, since 50 1.1 [Before Exposure] 1 10 /90 CO 2/CH 4 + 500 ppm n-h epta ne 10/90 C O 2/CH 4 + 300 ppm T oluene 10 /90 CO 2/CH 4 0.9 C O2 /P 0.7 a 0 1 2 3 4 5 Tim e E lapsed (days) [Before Exposure] 1.15 10/90 CO 2/C H4 + 500 ppm n-heptane 10/90 CO 2/C H4 + 300 ppm T o luen e 10/90 C O 2/C H4 P 0.6 1.1 1.05 CO 2/C H 4 C O2 0.8 1 CO 2/C H 4 / 0.95 b 5 0.9 0 1 2 3 4 Tim e Elapsed (d ays) Figure 2.15 Comparison of a) CO2 permeability, and b) CO2/CH4 selectivity during exposure at 200 psia, and 35 0C for 10/90 CO2/CH4 mixture , 10/90 CO2/CH4 + 300 ppm toluene mixture, and 10/90 CO2/CH4 + 500 ppm n-heptane mixture. 51 the operative phenomena are not well understood yet. Synergistically, negative effects of operating with different levels of theses two penetrants also should be investigated, but this is an even more complex problem and was not a problem that was considered in the present work. The reduced conditioning effect in the membranes is probably a result of the lower solubility level of n-heptane than the toluene at similar weight fractions. The decrease in selectivity was presumably due to a decrease in diffusivity selectivity caused by a loosening of the polymer matrix. There was 3% increase in selectivity after the exposure in the 10/90 CO2/CH4 mixtures with no significant changes in CO2 permeability during the five-day period as can be seen in Figure 2.10a, so in the absence of hydrocarbons impurities, the binary CO2/CH4 feed does not have any negative impact on performance properties at the 200 psia feed pressure. At 35 0C, the reduced permeability , PCO2/PCO2ref , was 5% smaller than at 55 0C at the same pressure for the 10/90 CO2/CH4 + 500 ppm n-heptane mixture relative to the 10/90 CO2/CH4 as shown in Figures 2.15a and 2.16a. Similar results are seen for the 10/90 CO2/CH4 + 300 ppm toluene mixture. The solubility of toluene exceeds that of n-heptane and causes a 12 % decrease in CO2 permeability in 10/90 CO2/CH4 + 300 ppm toluene relative to the 10/90 CO2/CH4 + 500 ppm nheptane mixture at 550C. The CO2 permeability in 10/90 CO2/CH4 + 300 ppm toluene at 35 0C had a slightly lower CO2 permeability than the 10/90 CO2/CH4 + 300 ppm toluene at 55 0C in the first two days as can be seen from Figures 2.15a and 2.16a. However, during the last three days, moderate increases in the CO2 permeance (10%) were observed. More prolonged exposure (>5 days) to a pressurized feed gas with and without hydrocarbon impurities was not pursued; however, this type of study would be interesting, although it is beyond the scope of this work. In any case, the lack of significant changes in this period of time in the permselectivity of CO2/CH4 and CO2 permeability for the 10/90 CO2/CH4 mixture 52 1.1 [Before Exposure] 1 10/90 C O 2/C H 4 + 300 ppm T oluene 10/90 CO 2 /C H4 + 500 ppm n-heptane 10/90 C O2 /C H4 0.9 C O2 /P 0.7 a 0 1 2 3 4 5 Tim e Elapsed (days) [B efore E xposure] 1.1 5 P 0.6 1 .1 10/90 CO 2/CH4 + 500 ppm n -he ptan e 10/90 C O 2/C H4 + 300 ppm T olue ne 10/90 C O 2/CH4 C O2 C O 2/CH 4 0.8 1.0 5 1 C O 2/CH 4 / 0.9 5 b 0 1 2 3 4 5 Tim e Elapsed (days) 0 .9 Figure 2.16 Comparison of a) CO2 permeability, and b) CO2/CH4 selectivity during exposure at 200 psia, and 55 0C for 10/90 CO2/CH4 mixture , 10/90 CO2/CH4 + 300 ppm toluene mixture, and 10/90 CO2/CH4 + 500 ppm n-heptane mixture. 53 validates the characterization results of the membranes for these short term testing conditions. The selectivity of CO2/CH4 in the 10/90 CO2/CH4 + 300 ppm toluene at 55 0 C was 11% higher than in the 10/90 CO2/CH4 at the same temperature as can be seen in figure 2.16b. Increases in gas selectivity preclude notions that reductions in permeance are a result of the collapse of the substructure or that plasticization is a dominant feature. Collapse of the substructure would result in an additional resistance for mass transfer which is non-selective for gases since the mechanism for mass transfer is Knudsen instead of solution-diffusion. Ultimately, this would lead to an observed decline in gas selectivity (which was not observed in fact). The selectivity increase in the 10/90 CO2/CH4 + 300 ppm toluene is postulated to be caused by the anti -plasticization of toluene at high temperatures. The high temperature in the presence of toluene appears to strengthen the anti-plasticization characteristics of hollow fibers. In comparison to the toluene, the presence of nheptane does not increase the selectivity, and currently the effects are not yet understood fundamentally; however, they are believed to be real and outside the experimental uncertainty. Experiments with 10/90 CO2/CH4 + 100 ppm toluene were performed at 200 and 400 psia and at 35 oC and 55 0C to confirm the above results. Figures 2.17 and 2.18 show CO2 permeance and CO2/CH4 selectivity during conditioning to the ternary mixture 10/90 CO2/CH4 + 100 ppm toluene at 200 psia, and 400 psia respectively. As can be seen in Figure 2.17a and 2.18a, at 35 0C the decrease in CO2 permeance is larger than at 55 0C at the same toluene concentration, which is again consistent with expected lower sorption level of toluene with higher temperature. In addition, CO2 permeability at 35 0C and 400 psia in the presence of 100 ppm toluene shows minimal creep indicating minimal if any permeation plasticization. It can also be seen from Figures 2.16a and 2.17a that the decrease in the CO2 permeances at 300 ppm is larger than at 100 ppm, which is consistent 54 1 .1 [B efore E xp osu re] 1 10 /90 CO 2/C H4 + 100 ppm T oluene (5 5C) 10 /90 CO 2/C H4 + 100 ppm T oluene (3 5C) 0 .9 CO2 /P 0 .7 a 0 1 2 3 4 5 6 Tim e E laps ed (days) [B efore E xposure] 1.1 5 10/90 CO 2/C H4 + 100 ppm T olu ene (55 C) 10/90 CO 2/C H4 + 100 ppm T olu ene (35 C) P 0 .6 1 .1 1.0 5 C O 2/CH 4 CO2 0 .8 1 C O 2/CH 4 / 0.9 5 b 0 1 2 3 4 5 6 Tim e E laps ed (days) 0 .9 Figure 2.17 Comparison of a) CO2 permeability, and b) CO2/CH4 selectivity during exposure at 200 psia, 35 0C and 55 0C for 10/90 CO2/CH4 + 100 ppm toluene mixture. 55 1 .1 [B e fore E xpo sure] 1 10/90 CO 2/CH 4 + 100 ppm T oluen e (35C ) 10/90 CO 2/CH 4 + 100 ppm T oluen e (55C ) 0 .9 C O2 /P 0 .7 a 0 1 2 3 4 5 Tim e E lapsed (days) 6 7 P 0 .6 [B efore E xposure] 1.1 5 10/90 CO 2/C H4 + 100 ppm T olue ne (35C ) 10/90 CO 2/C H4 + 100 ppm T olue ne (55C ) C O2 C O 2/C H4 0 .8 1 .1 1.0 5 1 C O 2/C H4 / 0.9 5 b 0 1 2 3 4 5 Tim e E laps ed (days) 6 7 0 .9 Figure 2.18 Comparison of a) CO2 permeability, and b) CO2/CH4 selectivity during exposure at 400 psia, 35 0C and 55 0C for 10/90 CO2/CH4 + 100 ppm toluene mixture. 56 with the depressed CO2 and CH4 permeances at higher toluene concentrations due to expected competition between toluene for sorption and transport environments available to all three penetrants. Similar to the 10/90 CO2/CH4 + 300 ppm toluene results at 55 0C, the permselectivity of CO2/CH4 in the 10/90 CO2/CH4 + 100 ppm toluene at 200 psia, 400 psia and 55 0C increased approximately 5% relative the 10/90 CO2/CH4 base case. This, presumably, again reflects an effective anti -plasticization effect induced by the presence of toluene. 2.3.3 Comparison of Conditioning in Hollow Fiber Membranes at 600 psia before and after Exposure In the previous sections, the effect on the transport properties for CO2 and CH4 caused by conditioning to 10/90 CO2/CH4 at 200 psia were discussed. The swelling conditioning effect of 10/90 CO2/CH4 on the transport properties on the hollow fiber membranes increased with increasing conditioning pressure as can be clearly seen by comparing Figures 2.10a and 2.19a. The increased permeability enhancements at 600 psia conditioning pressure compared to conditioning at 200 psia reflect an increase in sorption and penetrant induced swelling. At 200 psia conditioning pressure, the CO2 partial pressure was too low to cause large swelling; however, at 600 psia exposure, the conditioning effects become much more apparent. The maximum increase in permeability of the conditioned sample in the 10/90 CO2/CH4 occurred at low pressures in both figures. In Figure 2.19a, the conditioning effect of 10/90 CO2/CH4 is reflected in 25% increase in the CO2 permeance at 200 psia following depressurization. This increase in CO2 permeance resulted in a 3 to 5% decrease in selectivity relative to the unconditioned sample as shown in Figure 2.19b. More importantly, however, is the dramatically larger negative impact on post exposure performance for the 600 psia conditioning. This is not completely surprising, since at the same temperature and weight fraction, the partial pressure of each respective hydrocarbon is three times higher at 600 psia 57 2 1.8 (200 psia) 1.6 D urin g expo sure with 10/90 C O /C H fo r five d ays 1.4 1.2 1 0.8 2 4 C O2 D ep re ssurizin g with 1 0/90 C O /C H 2 4 P C O2 /P P ressu rizin g with 10/90 C O /C H 2 4 0.6 100 1 .1 (200 psia) 1.05 1 CO 2/CH4 a 600 70 0 20 0 30 0 40 0 50 0 Feed P res sure (psia) P ressurizin g with 1 0/90 C O /C H 2 4 0.95 0 .9 0.85 0 .8 0.75 0 .7 10 0 20 0 30 0 40 0 50 0 F eed P ressure (psia) 600 70 0 D uring exposure with 10/90 CO /C H for five days 2 4 Figure 2.19 Effect of conditioning of 10/90 CO2/CH4 mixture on a) the CO2 permeability, and b) the CO2/CH4 selectivity at 600 psia and 35 0C. Lines are drawn by eye . 58 CO 2/CH4 / D ep ressurizin g with 1 0/90 C O /C H 2 4 versus 200 psia during the exposure conditioning process. Again, however, it is not possible yet to predict or model the observed effects due to the three times higher respective hydrocarbons partial pressures. Specifically CO2 permeability changes after exposure to n-heptane do not show additional swelling induced conditioning as measured by CO2 permeation in the membrane compared to that seen only with the 10/90 CO2/CH4 binary (Figure 2.19). Nevertheless, significant effects are seen at 600 psia that are not apparent at 200 psia. Even, though CO2 is affected like it was with no heavy hydrocarbons at 600 psia, the selectivity at 600 psia is much more negatively impacted. This suggests that CH4 detects any subtle conditioning effect more sensitively than CO2 does and makes CH4 a sensitive probe of changes in the glass that are induced by conditioning. Permeation studies with 500 ppm n-heptane at 600 psia conditioning pressure in the 10% CO2/ 90% CH4 mixed gas feed indicate approximately 19% increase in CO2 permeance with 11% loss in CO2/CH4 selectivity at 200 psia compared to the unconditioned sample as can be seen in Figures 2.20a and 2.20b respectively. Figure 2.21a compares the CO2 permeability, following conditioning with 10/90 CO2/CH4 + 300 ppm toluene, to the CO2 permeability before the 10/90 CO2/CH4 + 300 ppm toluene exposure. While only CH4 senses the subtle changes brought by exposure to heptane/CO2/CH4, CO2 also shows a dramatic increase following exposure to toluene/CO2/CH4. Since the selectivity of the sample after exposure is not greatly different in either figure 2.21b or 2.20b, both CO2 and CH4 appear to be increased by roughly the same large extent. Exchange conditioning of the 10/90 CO2/CH4 + 300 ppm toluene with the 10/90 CO2/CH4 at 600 psia led to 116% increase in the CO2 permeability relative to the permeability of the unconditioned sample with a corresponding 13% loss in CO2/CH4 permselectivity at 600 psia compared to the unconditioned sample. This increase in permeability was attributed to the increase in the subtle packing disruptions in 59 2 1.8 (200 psia) E xch ang e cond itio n th e 10/90 C O /C H 1.6 1.4 1.2 1 0.8 0.6 100 1 .1 2 4 with the 10/90 C O /C H + 500 p pm n-heptan e 2 4 for five days De pressu rizing w ith 10/90 C O /C H 2 C O2 4 P C O2 /P P ressu rizing with 10/90 C O /C H 2 4 a 600 70 0 20 0 30 0 40 0 50 0 Feed P ressure (psia) P ress urizing w ith 10/90 C O /C H 2 (200 psia) 1.0 5 1 CO 2/C H 4 4 0.9 5 0 .9 0.8 5 0 .8 0.7 5 E xc hang e condition th e 10/90 C O /C H 2 2 4 4 w ith the 10/90 C O /C H + 500 p pm n-heptane for five days CO 2/C H 4 / D epressu rizing with 10/90 C O /C H 2 4 0 .7 20 0 b 30 0 400 500 600 70 0 F eed Pressure (psia) Figure 2.20 Effect of conditioning of 10/90 CO2/CH4 + 500 ppm n-heptane mixture on a) the CO2 permeability, and b) the CO2/CH4 selectivity at 600 psia and 35 0C. Lines are drawn by eye . 60 1 .6 D e pressurizing with 10/90 C O /C H 2 4 (200 psia) 1 .4 1 .2 1 0 .8 0 .6 100 1 .1 E xchange co ndition the 10/90 C O /C H 2 2 4 4 w ith th e 10/90 C O /C H + 3 00 pp m toluen e for five days C O2 /P C O2 P ressu rizing with 10/90 C O /C H 2 4 P a 20 0 30 0 40 0 50 0 600 70 0 F eed P res sure (psia) (200 psia) 1.0 5 1 CO 2/CH4 P ressurizing with 10/90 C O /C H 2 4 0.9 5 0 .9 E xch ange condition the 1 0/90 C O /C H 2 2 4 4 / CO 2/CH4 0.8 5 0 .8 with the 10/90 C O /C H + 300 ppm toluene for five days 0.7 5 D epressurizing w ith 10/90 C O /C H 0 .7 10 0 2 4 b 600 70 0 20 0 30 0 40 0 500 Feed P ress ure (psia) Figure 2.21 Effect of conditioning of 10/90 CO2/CH4 + 300 ppm toluene mixture on a) the CO2 permeability, and b) the CO2/CH4 selectivity at 600 psia and 35 0C. Lines are drawn by eye . 61 the polymer caused by toluene swelling at 600 psia. The selectivity was also lower at 600 psia than at 200 psia. Unfortunately, the hollow fiber membranes failed at 600 psia and 55 0C possibly due to stresses induced by the large swelling of the polymer matrix. 2.3.4 Comparison of Conditioning in Hollow Fiber Membranes at 600 psia during Exposure Figure 2.22 shows CO2 permeability and CO2/CH4 selectivity behavior during the exposure conditioning as a function of time. The reported experimental data in Figure 2.22 as well as other conditioning experiments did reflect steady state permeation properties of the hollow fiber membranes. The CO2 permeability in the 10/90 CO2/CH4 mixture (in the absence of toluene or n-heptane) increased in the first day roughly by 10% relative to the CO2 permeability at time zero and then leveled off with an increase between 10% and 15%. There was a slight increase in selectivity because CO2 was being more selectively permeated by the membrane; presumably due to a favorable competition by CO2 for any small addition of free volume. The results of Figure 2.22 indicates the absence of short term nonselective plasticization, but there is a longer term relaxation controlled creep that produces an increased CO2 and CH4 permeances at higher pressures. Both CO2 and CH4 permeabilities increased up to 15 % and 10% respectively at 600 psia following conditioning; however, CO2 showed the largest increase. Therefore, the selectivity increased approximately 4% relative to the unconditioned sample. The CO2 permeance in the 10/90 CO2/CH4 + 500 ppm n-heptane shows a 10% decrease from the CO2 permeance of the 10/90 CO2/CH4 conditioned sample. Compared to the unconditioned sample, CO2 shows essentially no increases. This suggests that both n-heptane and CO2 compete for the increased free volume introduced by n-heptane. Moreover, since CO2 permeation in figure 2.20 increases by 20 % after removing n-heptane, the introduced free volume is definitely 62 1 .2 [B efore E xposure] 1 .1 1 0 .9 0 .8 0 .7 0 .6 a 0 1 2 3 4 5 6 Tim e Elapsed (days) [B efo re E xposure] 1.0 5 1 0.9 5 0 .9 0.8 5 0 .8 0.7 5 b 0 1 2 3 4 5 6 Tim e Elaps ed (days) 10 /90 CO 2/CH 4 + 500 ppm n-h epta ne (35C ) 10 /90 CO 2/C H 4 + 300 ppm T oluene (35 C ) 10 /90 C O 2/C H 4 (35C ) 10/90 CO 2/C H4 + 500 ppm n-hep tane (35C ) 10/90 CO 2/C H4 + 300 ppm T oluen e (35C ) 10/90 CO 2/C H4 (35 C) P Figure 2.22 Comparison of a) CO2 permeability, and b) CO2/CH4 selectivity during exposure at 600 psia, 35 0C for 10/90 CO2/CH4 mixture, 10/90 CO2/CH4 + 300 ppm toluene mixture, and 10/90 CO2/CH4 + 500 ppm n-heptane mixture. 63 C O 2/C H 4 / C O 2/C H 4 C O2 /P C O2 significant . This surprising result in figure 2.22b, however, is that CH4, (perhaps due to its high partial pressure) competes even more successfully, with heptane and CO2, thereby reducing selectivity in a steady downward creep process. For the toluene containing stream during conditioning, the CO2 permeance in the 10/90 CO2/CH4 + 300 ppm toluene shows a marked 40% decrease relative to the CO2 permeance of the 10/90 CO2/CH4 conditioned sample. This suggests that neither the n-heptane nor the toluene ultimately compete strongly with CH4; however, toluene appears to block permeation opportunities available to CO2 such that the membranes are able to separate less efficiently. The abrupt drop in CO2 permeance in the 10/90 CO2/CH4 + 300 ppm toluene at the beginning (< 1 day) may reflect the high affinity of the toluene to the membrane compared to n-heptane. A full explanation of the extremely complex processes at play in these conditioning phenomena will clearly need more studies. This increase in CH4 permeability was accompanied by a considerable gradual decrease in permselectivity. The selectivity decreased by 15% at the end of the five days relative to the selectivity in the unconditioned sample and appears to be approaching the same level as for toluene. A shift in free volume, caused by sorbing n-heptane facilitates, leads to an increase in the diffusion coefficient of CH4 and only a moderate increase in CO2 diffusion coefficient. Assuming a shift in the free volume distribution to high intersegmental spacings leads to lower selectivity. Normally, this would be expected to result in an increase in the diffusion coefficient and a decrease in the diffusivity selectivity. The corresponding type of change believed to reflect the behavior seen for the reduced permselectivity of CO2/CH4 in figure 2.21a and 2.21b which was conditioned with the 10/90 CO2/CH4 + 300 ppm toluene at 600 psia is illustrated in Figure 2.23. Conditioning was found to result in 20% decreases in the CO2/CH4 permselectivities relative to the unconditioned sample. This decrease in selectivity can be attributed to increases in the subtle packing disruptions in the polymer as 64 CO2 f (#/sec) CH4 swollen transient gap size Figure 2.23 Qualitative transport gap (free volume element) size distribution change after conditioning with 10/90 CO2/CH4 + 300 ppm toluene mixture. well as to a decrease in the diffusivity selectivity caused by toluene swelling. This decrease in selectivity does suggest a change in the free volume distribution as opposed to the n-heptane conditioning. In general, this is true since it shows a large increases in CO2 opportunities , but a much larger percent increase in CH opportunities . In the presence of the hydrocarbons, it is believed that the decrease in selectivity after exposure to n-heptane and toluene at 600 psia conditioning pressure is because CH4 is at its high partial pressure. As a result, this may out compete CO2 as well as toluene or n-heptane. After removal of the conditioning hydrocarbon, the high CH4 partial pressure makes the sorption level of CH4 in the 4 65 high energy sites so large that CH4 out compete CO2 for jump opportunities and thus the selectivity decreases as seen in figures 2.22b. 2.4 Defective vs. Defect-Free Fibers Figure 2.24 depicts simplified schematic morphologies and SEM of a defective nodular and defect free non-nodular asymmetric hollow fiber membrane skin layer. In practice, actual defects caulked using a variety of methods; however, the basic nodular morphology persists. Skin Defect-Free Support layer Skin Defective Support layer Figure 2.24 Hypothetical figure of the dense skin, and the defective morphology of an asymmetric hollow fiber. SEM of Matrimid asymmetric hollow fiber (taken by Seth Carruthers, 1999) Although the nodules are depicted for simplicity as being spherical, they have poorly-defined shape and the nodules are thought to be interconnected by polymer chains that will be referred to as tie chains (Jordan et al., 1990). The tie chains are envisioned as keeping adjacent nodules fused together, with 66 negligible viscous flow through the volume between nodules. The gas molecules diffuse through the complex morphology occupied by the polymer chains in the nodules. The toluene presumably causes some swelling of the glassy matrix within the nodules, and might cause the nodules (or the internodular tie chain region) to become highly dilated. If such a hypothetical picture is valid, during exposure to a swelling agent, tie chains between the nodules may induce a variety of complex responses. If the toluene sorption level is high, many of the chains could presumably actually sufficiently swell and even disengage, thereby enabling viscous flow in the inter-nodular volume when 10/90 CO2/CH4 + 300 ppm toluene mixture is applied. The hypothetical morphology of the defect-free dense skin is also shown in Figure 2.25. Although it is probably denser in structure than the defective structure, it is believed that the technique we used in the asymmetric membrane formation produces selective layers that may still contain discontinuous nanoscale pores during the phase separation (Carruthers, 2001). However, this structure is hypothesized to be capable of maintaining resistivity of the conditioning effect caused by toluene plasticization. The swelling of the polymer matrix may result in permeability enhancement as discussed earlier, but no catastrophic selectivity losses as typical of the inter-nodular failures mentioned above. Using this concept, many of the anomalous results obtained for the module conditioning studies between the defective and defect free fibers can be rationalized. The data indicated in Figure 2.25 suggest that an essentially defectfree, non-nodular morphology offers advantages in stability under demanding operating conditions. Earlier work (Gunaidi, 2000) showed serious losses in performance of membranes comprised of the same polymer, when the selective layer had a pronounced fused nodular nature as opposed to the intrinsically defectfree skin layers reported on here. 67 [B e fore E xpo su re] 1 G unaidi (20 00), sho rt term e xp osure < i h our 0.95 0 .9 0.85 CO 2/C H 4 T his work, Lon g term expo sure ~ 5 da ys 0 .8 0.75 0 .7 0.65 CO 2/C H 4 / 0 10 0 20 0 30 0 400 50 0 F e ed P re ss ure [psia] 60 0 70 0 Figure 2.25 Comparison of CO2/CH4 selectivity for defective and defect-free fibers during exposure at 35 0C for 10/90 CO2/CH4 + 300 ppm toluene mixture. When the module is depressurized and exposed to vacuum, the hypothetical excess volume introduced during conditioning can collapse to their unconditioned state as shown in Table 2.4. Admittedly, it would be expected that packing defects induced by conditioning would be readily relaxed out of the fibers since there is both a short diffusional path of voids to the surface and a large driving force for volume recovery since the fibers are under vacuum. Hence, the defect-free fibers are able to recover by diffusion, and the permeability approaches its original level (95% to 100% recovery) when the fibers are depressurized and the downstream is put under vacuum. 68 Table 2.4 Permeability of CO2 in the 10/90 CO2/CH4, at 35 0C illustrating the hysteretic behavior before conditioning, after conditioning to the 10/90 CO2/CH4 +100 ppm toluene at 400 psia and after conditioning, followed by exposure to a vacuum source for 21 days. % change in CO2 % change in selectivity* permeance* After Exposure with +42.3 -7.8 10/90 CO2/CH4 +100 ppm toluene After Exposure with +3.8 -1.8 10/90 CO2/CH4 +100 ppm toluene and 21 days under vacuum *Original values of CO2 permeance and selectivity are 11.1 GPU and 35.5 respectively. 2.5 Summary Under the range of conditions studied here, our permeation results suggest the absence of strong plasticization or compaction of the asymmetric morphology by either CO2 or toluene. The results suggest also the presence of competition consistent with dual mode theory. The competition effect is more pronounced for toluene compared to n-heptane. The permeation flux for CO2 and CH4 increased significantly following conditioning as high as 115% and 155% respectively. Heptane causes a slow and a more subtle set of changes; however, the ultimate loss in selectivity is similarly serious as toluene for 35 0C, 500 ppm level and 600 psia feed. Conditioning with 10/90 CO2/CH4 at 200 psia and 35 0C; CO2 permeance increased 3% relative to the unconditioned sample. The increase in CO2 permeance after conditioning is a direct result of the loosening and reordering of the polymer matrix. The selectivity of CO2/CH4 following conditioning was slightly higher by 2-3% in the conditioned sample than in The following conclusions can be made about the permeation experiments; 69 the unconditioned sample. These results showed that the conditioning effects of 10/90 CO2CH4 mixture at 200 psia and 35 0C are negligible. Conditioning with 10/90 CO2/CH4 at 600 psia and 35 0C; The CO2 permeance after conditioning with 10/90 CO2/CH4 gas mixture at 35 0C and 600 psia were higher by 10 to 25 % than before conditioning. The reason for this increase in CO2 permeances is believed to be an increase in the number of hypothetical gaps due to an increase in the conditioning pressure. The selectivity is essentially unchanged. This is a surprising result, since the high CH4 partial pressure enables CH4 to effectively compete for newly introduced free volume due to large hydrocarbons like n-heptane and toluene. It appears that simple CO2 conditioning does not introduce such large additional free volume packets as with the larger hydrocarbons. In this case, perhaps the intrinsic polymer affinity constants for CO2 and CH4 are still applicable. For the larger hydrocarbon conditioned cases, the larger packing defects may have lower affinity constants for CO2 and even CH4. Nevertheless, the large partial pressure of the CH4 in the feed appears to still allow a large enough sorption in the langmuir sites to enable CH4 to compete with CO2 and the heavier hydrocarbons for newly introduced free volume. Conditioning with 10/90 CO2/CH4 + 500 ppm n-heptane at 200 psia and 35 0 C; Conditioning the fibers with 10/90 CO2/CH4 + 500 ppm n-heptane at 200 psia does not change the transport properties of the membrane appreciably. The selectivity and permeability following conditioning remained essentially constant at their original values before conditioning. This shows that n-heptane does not cause compaction or free volume plasticization at this low level of exposure. Conditioning with 10/90 CO2/CH4 + 500 ppm n-heptane at 600 psia and 35 0 C; Conditioning with 10/90 CO2/CH4 + 500 ppm n-heptane at 600 psia 70 and 35 showed 10 to 20% increase in CO2 permeance following conditioning. The selectivity also decreased 10 to 20% compared to the unconditioned sample. Conditioning with 10/90 CO2/CH4 + 300 ppm toluene at 200 psia and 35 0 C; Following conditioning with 10/90 CO2/CH4 + 300 ppm toluene at 200 psia and 35 showed large increases in CO2 and CH4 permeances compared to the original values before conditioning. The CO2 permeance increased 60 to 80% following conditioning and selectivity decreased 12 to 15% relative to the unconditioned samples. Conditioning with 10/90 CO2/CH4 + 300 ppm toluene at 600 psia and 35 0 C; Conditioning with 10/90 CO2/CH4 + 300 ppm toluene at 600 psia and 35 0C showed the maximum increase in CO2 permeance in all the conditioning experiments considered. The conditioning treatment increased the CO2 permeance 110% to 120%, CH4 permeance 150% to 160% and decreased the selectivity 10% to 25% relative to the unconditioned samples. Toluene compared to n-heptane clearly swells the membrane. Because of toluene swelling the steric hindrance to chain motions is reduced, and therefore the size and the jumps frequency for CO2 and CH4 are increased. Conditioning with 10/90 CO2/CH4 + 300 ppm toluene at 200 psia and 55 0 C; The conditioning experiments at 55 0C with the 10/90 CO2/CH4 + 300 ppm toluene at 200 psia showed negligible conditioning effects on the CO2 permeance and selectivity suggesting the decrease in toluene sorption level with temperature. Conditioning with 10/90 CO2/CH4 + 300 ppm toluene at 600 psia and 55 0 C; The membrane fails under these conditions and presumably due to stresses in the membrane and high CO2 partial pressure. 71 During Conditioning with 10/90 CO2/CH4 , 10/90 CO2/CH4 + 500 ppm nheptane, and 10/90 CO2/CH4 + 300 ppm toluene 35 0C; The results showed that the presence of a third component (toluene or n-heptane) depresses the permeances of CO2 and CH4 and this is consistent with the dual mode theory. At 600 psia, the CO2 permeance in the 10/90 CO2/CH4 + 500 ppm n-heptane decreased 10% and the CO2 permeance in the 10/90 CO2/CH4 + 300 ppm toluene decreased 40% relative to the CO2 permeance of the 10/90 CO2/CH4 conditioned sample. On the other hand, at 200 psia the CO2 permeance decreased 15% to 20% in the the 10/90 CO2/CH4 + 500 ppm nheptane and 35% to 40% in the the 10/90 CO2/CH4 + 300 ppm toluene. At 200 psia and 55 0C, the decrease in CO2 permeance is 10% to 15% and 25% to 30% in the the 10/90 CO2/CH4 + 500 ppm n-heptane and the 10/90 CO2/CH4 + 300 ppm toluene mixtures respectively. This suggests the high affinity of membrane to toluene and that n-heptane does not strongly compete as toluene for sorption sites and permeation pathways. During conditioning to the 10/90 CO2/CH4 + 500 ppm n-heptane at 35 0C and 55 0 C, the selectivity is depressed almost at the same level relative to the selectivity of the 10/90 CO2/CH4. However, during conditioning to the 10/90 CO2/CH4 + 300 ppm toluene the selectivity is increased at 55 0C while it decreased at 35 0C relative to the selectivity of the 10/90 CO2/CH4 base case. The hollow fiber membranes used in this work are defect free and showed distinct advantages compared to the defective fibers in terms of stability and separation efficiency under demanding conditions. The structure of theses fibers is denser than the defective fibers. This structure showed stronger conditioning resistivity. In this work, the toluene caused swelling in the polymer matrix resulting in large permeability enhancements but no 72 catastrophic failures in performance were observed as seen in the defective fibers. The defect free membrane is able to return to its original values of permeability and selectivity after depressurizing and when the module was put under vacuum for an adequate time to relax out excess free volume introduced during the hydrocarbon exposure conditioning. 73 Chapter 3: Sorption Results and Permeation Behavior Modelling and Analysis In the preceding chapter, it was shown that the asymmetric hollow fiber membrane modules conditioned with 10/90 CO2/CH4 + 300 ppm toluene gas mixture have significantly enhanced CO2 and CH4 permeation rates as compared to their unconditioned values. Permeation increases as high as 116% and 154% are reported for CO2 and CH4 respectively for modules conditioned for five days at 600 psia with 10/90 CO2/CH4 + 300 ppm toluene gas mixture. On the other hand, the conditioning treatment with 10/90 CO2/CH4 + 500 ppm n-heptane gas mixture had negligible effect on the CO2 and CH4 permeation rates. The conditioning treatment caused reductions in permselectivity of 2-25% relative to the as-received samples for mixed gas feed streams of 10/90 CO2/CH4 + 300 ppm toluene and 10/90 CO2/CH4 + 500 ppm n-heptane, under the conditions studied. In this chapter, the sorption data are reported and analyzed along with the permeation data obtained in the previous chapter. 3.1 Background The solubility of gases in glassy materials is usually described by the dualmode sorption model (Chan et al., 1978; Vieth et al., 1976). This model idealizes sorption as occurring in two different environments, the dense well-packed region (as described by Henry s Law mode) as well as in non -equilibrium packing defects or macrovoids (as described by Langmuir mode). Total sorption can be defined as: C A = C DA + C H A (3.1) 74 Where C D A = k DA p A is also known as Henry s Law, and C H A = ' C H bA p A A 1 + bA p A models the Langmuir sorption. The parameter k D A is the Henry s Law constant that characterize the sorption tendency in the normally densified regions of the glassy matrix, p A is the partial pressure of component A, while b A , characterizes the ' affinity of the penetrant for the Langmuir sites and C H A is the Langmuir capacity constant. It is generally accepted that penetrant-induced conditioning effects for glassy polymers give rise to added sorptive capacity compared to solubilities which may be anticipated in the first exposure of a glassy polymer to a high pressure gas. This phenomenon has been explained in the framework of dual mode sorption as an increased Langmuir sorption. It has also been found that the Langmuir capacity depends on prior gas exposure of the material (Jordan and Koros; 1990; Jordan, Koros and Fleming, 1990; Jordan, Henson and Koros, 1990). The results of these effects on sorption isotherms will be discussed in more detail ' later in terms of increases in a base case Langmuir capacity, C H . Inherent in the dual mode model is the assumption that only the fraction of the total sorption attributed to dissolution into the polymer, CD, is associated with the separation of chain segments to accommodate penetrant (Fleming and Koros, 1990; Koros and Hellums; 1990). It is also hypothesized that conditioning principally affects the Langmuir capacity parameter with little change in kD or b. Previous studies considered CO2 conditioning effects for pressures as high as 900 psia at 35 0C (Fleming, 1988). Lasting effects of high pressure CO2 exposure have been studied by Fleming (1988), Jordan (1990) and Pope (1991). It has been found that pre-exposure of high pressure CO2 leads to subsequently higher gas sorption and permeation. The current explanation of this phenomenon, which has been termed co nditioning, is that highly sorbing species can cause 75 disruptions in the chain packing conformations in the polymer matrix. These disruptions may act as additional excess free volume sites, which can also accommodate penetrant molecules. It was further found that if a polymer sample is probed with sorption measurements while the sample is still swollen, in a procedure called exchange conditioning , even greater increases in solubility are observed. By comparing these results to the conventionally conditio ned (evacuation of the sample in between preexposure and subsequent sorption probing) results, it can be inferred that although CO2 conditioning results in semipermanent increases in sorptive capacity, some additional excess free volume is lost when the conditioning agent is removed. While this analysis is useful in understanding the sorption of mixtures and swelling properties of CO2, it also provides a means to observe the addition of excess free volume in glassy polymers, which is directly relevant to hydrocarbon conditioning in this study. While some work has been conducted on observing the conditioning effect of CO2 on gas solubility in glassy polymers (Fleming, 1988; Jordan, 1990; Pope, 1991), no literature has been found to date on the effect of conditioning of heavy hydrocarbons on penetrant sorption and also the effects on apparent mobility. Therefore, an objective of this chapter is to evaluate the conditioning effects of toluene and n-heptane on CO2 and CH4 gas sorption in hollow fiber membranes and to determine the magnitude of these effects. An additional objective is to connect the changes in sorption to changes in diffusivity of each penetrant and of one penetrant versus the others (e.g., DCO2/DCH4). All fibers used in the measurements were from the same batch and were stored in a plastic bag + desiccant to prevent excessive moisture uptake. Each sorption isotherm represents a run conducted on a virgin sample, which has not previously exposed to high pressure gas. Sorption measurements have been made for 10/90 CO2/CH4 with and without the heavy hydrocarbons exposure to hollow fiber membranes at pressures as high as 600 psia at 35 0C. Therefore, at these 76 conditions the toluene or n-heptane activity approaches activity levels as high as those used in the permeation studies. The samples are tested at aging times of at least two months. Based on prior work in our group and elsewhere (Punsalan, 2001) is believed that aged samples have a much more stable morphology. By combining the sorption and permeability measurements as will be discussed later in this chapter, one can determine the change on the gas diffusivity for the gas/polymer system. Analysis of such data provides a substantially improved understanding of the rather complex interactions in gas/hydrocarbon/polymer systems. 3.2 Gas Sorption Measurements Sorption measurements were measured by the pressure decay method (Koros and Paul, 1976). A schematic of a two-transducer pressure decay cell is shown in Figure 3.1. This design has been described in the literature and was successfully modified by adding a new valve (valve C in Figure 3.1) in order to be able to do exchange conditioning procedure without evacuation of the sample between exposure and subsequent sorption probing. The sorption system was equipped with two 0-1000 psia temperature compensated pressure transducers (Model PA822-1M-16553, Schlumberger Statham, Oxnard, CA), the fittings were Nupro SS-4H-V13 bellows valves. The transducers were excited by a 10V DC power supply (Model LCS-A-10, Lambda Group of Unitech, Melville, NY). The power supply and transducer output voltages were measured using a digital multimeter (Model 195A, Keithley, Cleveland, OH) with 100 point data logging used to take the average voltage reading at any given time. Measurements were made at 350C by keeping the cells immersed in a circulation bath (Model W26 water bath and Model E3 circulator, Haake Buchler Instruments Inc., Saddle Brook, NJ). It is essential that the water level be maintained at exactly the same 77 level, as slight variations in temperature and pressure can cause variation in the transducer output. pressure transducers valve C gas in volume A volume B gas out valve A valve B polymer containing chamber Figure 3.1 Schematic of pressure decay apparatus The gas sorption measurement with this device is based on a rigorous mole balance. Initially, volumes A and B are evacuated and valves A, B and C are closed. An amount of CO2/CH4 gas mixture is injected into volume A and the pressure is monitored by the pressure transducer. Knowing the volume of chamber A, along with the compressibility, temperature, and pressure of the gas, the number of moles of gas in volume A is calculated. The gas is then introduced to the polymer in volume B by opening valve B. The pressure of volume B is monitored until no further change is seen. The number of moles remaining in volume B is calculated the same manner as for volume A. Then knowing the total number of moles of gas initially injected into the system, along with the number of remaining moles of gas in volume A and B, the amount of gas sorbed into the polymer is calculated. The reservoir and cell volumes were determined by the procedure shown in Appendix F. Statham pressure transducers (model PA822-1M- 78 16653) are used to measure the pressure and are powered by a Lauda 10DCV power source (Model LCS-A-1). The signal is measured with a Keithley 2000 Digital Multi-meter (DMM). The DMM is interfaced with a personal computer running National Instruments LabViewTM software, which allows for visualization of the pressure decay and equilibrium and also for data collection. The resolution of the measurement is approximately 0.005 cc(STP) (Punsalan, 2001). After the sorption measurement for the probe gas (CO2 or CH4) is performed, volumes A and B are evacuated and the mixed gas mixture is introduced. This work uses the following gas mixtures for conditioning experiments; 10/90 CO2/CH4, 10/90 CO2/CH4 + 500 ppm n-heptane and 10/90 CO2/CH4 + 300 ppm toluene. The fibers were then conditioned for five days at the conditioning pressure used in the permeation experiments by closing valve B. Following conditioning, the probe gas is introduced through valves A and B at the same gas fugacity as in the gas mixture and by slowly opening valve C. The fugacity of CO2 and CH4 were calculated using the virial equation of state truncated after the second term (Smith and Van Ness, 1975). The gas compressibility is calculated from the equation of state shown in Appendix D. The probe gas is kept flowing for 15 to 30 minutes until all the components of the gas mixtures are displaced and then valves B and C are closed. The probe gas (CO2 or CH4) solubility is tested again. The gas in volume B is then introduced to volume A by opening valve B. It should be noted that the probe gas was depressurized gradually of approximately 10 psi and 50 psi increments for CO2 and CH4 sorption respectively. This is done to prevent "foaming" of the polymer, which is known to happen if a highly swelling penetrant is removed too quickly from a polymer sample (Fleming, 1988; Pope, 1991). The desorption steps are repeated until the pressure in volume B is close to zero. The total number of moles of gas sorbed following conditioning is then calculated. A sample calculation of the total number of moles is shown in Appendix E. From the total number of moles and the number 79 of moles desorbed in each single step, the desorption curve can be constructed. The sorption and desorption are then compared to see the effect of conditioning with CO2/CH4 mixture in the presence and absence of toluene and n-heptane. The sorption system was initially tested for leaks after pressurizing to 900 psia CO2 for more than five days. If the pressure deteriorates more than 5 psi, a leak exists and corrective action, such as tightening all fittings, is necessary. If no leaks are observed, the sorption system is presumed to have no detectable leaks as applicable and therefore it can be used for testing. 3.3 Results and Discussion Since the magnitude of the conditioning effect was expected to be directly related to the level of the preswelling agent (toluene or n-heptane) in the 10/90 CO2/CH4 gas mixture used to condition the hollow fiber membranes, it was important to run the 10/90 CO2/CH4 case with no hydrocarbons (the base case). Shown in Figure 3.2 are CH4 and CO2 sorption isotherms for Matrimid the hollow fiber membranes. As is evident in both gases, the sorption isotherms increased only slightly over the 5 days base case conditioning period for either component. The higher pressure regime of the sorption isotherm for the conditioned sample appears to be shifted a little bit upward compared to the unconditioned sample while sharing a similar slope. These trends are consistent with the dual mode sorption understanding of conditioning and suggest presumably an increase in the Langmuir capacity with negligible change in the Henry s law constant as a result of gas conditioning. Table 3.1 shows the DMS model parameters determined for the experimental data from Figure 3.2. 80 Table 3.1 CH4 and CO2 / Matrimid dual mode sorption parameters in unconditioned and conditioned samples with 10/90 CO2/CH4 mixture at 600 psia and 35 0C Dual Mode Model Parameters CO2 CH4 Unconditioned Conditioned Unconditioned Conditioned kd [cc(STP)/cc psia] (x 10) b [psia-1] (x 102) CH [cc(STP)/cc] 2, R2 0.17 (fixed) 0.07 (fixed) 17.8 0.19 0.87,0.99 0.17 (fixed) 0.07 (fixed) 18.6 0.41 4.17,0.99 0.02 (fixed) 0.01 (fixed) 26.9 0.13 0.68,0.999 0.02 (fixed) 0.01 (fixed) 27.5 0.19 1.58,0.99 To simplify interpretation of results, an unconstrained non-linear least squares fit to the DMS model is applied to all sorption data for a particular polymer-gas pair. Then an average of resulting Henry s law constants and the affinity constant are used for all data and are used as fixed parameter. This methodology is rationalized by the theory of dual mode sorption which postulates that kD and b are intrinsic polymer/penetrant parameters and the relatively subtle effects studied here comply with the range of their applicability. 81 25 c[c c (STP) CO /cc polym er] 20 15 B efore E xposu re A fter Exposure 2 10 5 a 0 10 20 30 40 50 60 P ressure [psia] 30 0 c[cc (STP) C H /cc polym er] 25 20 15 10 5 0 b 0 100 200 300 400 500 Pressure [p sia] Before Exposu re After Exposure Figure 3.2 Effects of 10/90 CO2/CH4 mixture exchange conditioning at 600 psia and 35 0C on a) CO2 sorption isotherms, and b) CH4 sorption isotherms for asymmetric hollow fibers of Matrimid conditioned. 4 82 Despite the added constraint on parameter determination, the resulting values for R2 are remarkably close to unity and the Chi-squared values are sufficiently low (Press et al., 1988) which suggests that the assumption of equal kD s and b s for conditioned and unconditioned samples is statistically reasonable. As reported in the above table, the increase in the Langmuir capacity constant is roughly only 1 cc(STP)/cc polymer for either gas; illustrating the minor effect of conditioning on sorption in the absence of the heavy hydrocarbons. It was thought that conditioning the sample with the 10/90 CO2/CH4 with either toluene or n-heptane would give rise to a more swelled matrix, thus increasing the effects of conditioning. Therefore, it was expected that the sorption difference between the unconditioned and conditioned samples would be more, and in addition the total sorption isotherms would shift more upward due to an increase in unrelaxed volume. To test this hypothesis - samples were conditioned with 10/90 CO2/CH4 + 300 ppm toluene over a period of five days, and then probed with CO2 and CH4 gases. The sorption results of these samples are shown in Figure 3.3 and the corresponding DMS parameters shown in Table 3.2. As ' expected, the increase in C H due to gas conditioning in these samples is slightly ' higher; however, the change in C H of 2.2 cc(STP)/cc polymer due to the five days conditioning hydrocarbon period was smaller than might be expected based on the large conditioning. CH 4 increases seen in chapter 2 for the permeability of each component after The results in Table 3.2 show also that C ' H CO 2 < C ' H since p CO 2 >> p CH 4 due to the fact that CO2 is being closer to its critical point. This shows that expectation of filling up holes may be too simplistic. 83 Table 3.2 CH4 and CO2 / Matrimid dual mode sorption parameters in unconditioned and conditioned samples with 10/90 CO2/CH4 + 300 ppm toluene mixture at 600 psia and 35 0C Dual Mode Model Parameters CO2 CH4 Unconditioned Conditioned Unconditioned Conditioned kd [cc(STP)/cc psia] (x 10) b [psia-1] (x 102) CH [cc(STP)/cc] 2, R2 0.11 (fixed) 0.03 (fixed) 27.1 0.25 0.88,0.99 0.11 (fixed) 0.03 (fixed) 28.1 0.49 3.22,0.99 0.03 (fixed) 0.007 (fixed) 14.0 0.63 1.27,0.99 0.03 (fixed) 0.007 (fixed) 16.2 0.38 8.42,0.99 The samples conditioned with the 10/90 CO2/CH4 + 500 ppm n-heptane behaved similarly as the samples conditioned with the 10/90 CO2/CH4 + 300 ppm toluene. The results are shown in Figure 3.4 and the resulting dual mode parameters are reported in Table 3.3. The resulting values for R2 are remarkably close to unity and the Chi-squared values are sufficiently low. Conditioning caused a slight increase in sorption capacity for both samples and, furthermore, this effect seems more pronounced in the 10/90 CO2/CH4 + 300 ppm toluene conditioned samples than the 10/90 CO2/CH4 + 500 ppm n-heptane conditioned samples. However, it should be noted that the uncertainty associated for that particular set of data is rather high with an error for CH of 1.5 cc(STP)/cc polymer. 84 25 c[c c (S T P) CO /cc p olym er] 20 15 2 10 B efo re E xp osu re A fte r E xp osu re 5 a 0 10 20 30 40 50 60 P ressure [psia] 30 0 c[cc (S TP ) C H /cc polym er] 25 20 15 10 5 0 0 10 0 20 0 30 0 400 P re ss ure [p sia] 500 b 60 0 B efore E xp osu re A fter E xp osure Figure 3.3 Effects of 10/90 CO2/CH4 + 300 ppm toluene mixture exchange conditioning at 600 psia and 35 0C on a) CO2 sorption isotherms, and b) CH4 sorption isotherms for asymmetric hollow fibers of Matrimid conditioned. 4 85 25 c[c c (S TP ) CO /cc po lym er] 20 15 B efore E xposure A fter E xp osu re 2 10 5 a 0 10 20 30 40 P re ssure [psia] 50 60 0 30 c[c c (S TP ) C H /cc polym er] 25 20 15 10 5 0 0 10 0 20 0 30 0 40 0 Pre ss ure [psia] 500 b 60 0 B efore E xposure A fte r E xp osu re Figure 3.4 Effects of 10/90 CO2/CH4 + 500 ppm n-heptane mixture exchange conditioning at 600 psia and 35 0C on a) CO2 sorption isotherms, and b) CH4 sorption isotherms for asymmetric hollow fibers of Matrimid conditioned. 4 86 Table 3.3 CH4 and CO2 / Matrimid dual mode sorption parameters in unconditioned and conditioned samples with 10/90 CO2/CH4 + 500 ppm n-heptane mixture at 600 psia and 35 0C Dual Mode Model Parameters CO2 CH4 Unconditioned Conditioned Unconditioned Conditioned kd [cc(STP)/cc psia] (x 10) b [psia-1] (x 102) CH [cc(STP)/cc] 2, R2 0.05 (fixed) 0.04 (fixed) 30.6 0.27 1.03,0.99 0.05 (fixed) 0.04 (fixed) 31.4 0.49 3.22,0.99 0.03 (fixed) 0.007 (fixed) 17.2 0.19 2.08,0.99 0.03 (fixed) 0.007 (fixed) 18.8 0.21 2.33,0.99 This unusually high error is more than likely associated with the constraint that has been placed on the value of k d and b . Therefore, it is difficult to draw a conclusion as if there is a large increase in the Langmuir sorptive capacity due to gas conditioning as a result of the 300 ppm toluene or the 500 ppm n-heptane in the 10/90 CO2/CH4 gas mixture. In any case, the absolute value of the solubility coefficients for CO2 and CH4 as a function of pressure suggest that the gas conditioning affect the diffusion and diffusion selectivity much more than the solubility and solubility selectivity. The solubility coefficient of a particular penetrant gas is equal to the concentration of gas penetrant in the polymer divided by its partial pressure in the gas phase; Si = C i / p i (3.1) The above sorption results after conditioning with 10/90 CO2/CH4, 10/90 CO2/CH4 + 500 ppm n-heptane and 10/90 CO2/CH4 + 300 ppm toluene can be reinterpreted in terms of Equation 3.1. Figure 3.5 and 3.6 shows the solubility 87 curve of CO2 and CH4 as a function of partial pressure at 35 & 7KH UHVXOWV DJDLQ show that the solubility coefficient of CO2 and CH4 calculated using raw data are nearly close. The separation factor of a membrane, if the downstream is held constant, for component i versus j , ij is defined by (Fleming, 1988); ij = Pi / Pj = [Di / D j ][S i / S j ] selectivity to have two parts, a solubility S i / S j (3.2) As indicated in equation 3.2, one can conveniently consider the overall [ ] coefficients and a mobility contribution Di / D j . This ratio, also called the ideal separation factor, is equal to the ratio of pure component permeabilities when external phase solution nonidealities are negligible and polymer phase plasticizing effects due to process stream components are not present. [ ] 88 CO s olu bility [cc (S TP )/cc po lym er.p sia ] 1 .4 1 .2 10/90 C O 2/C H 4 10/90 C O 2/C H 4 + 30 0 ppm toluen e 10/90 CO 2/C H4 + 50 0 ppm n-heptane 1 0 .8 0 .6 a 0 10 20 2 2 0 .4 30 40 50 60 CO P ress ure (psia) C H solubility [c c (S TP )/cc p olym er.psia] 0.1 8 0.1 6 0.1 4 0.1 2 0.1 0.0 8 0.0 6 0.0 4 0 100 20 0 30 0 40 0 C H P ressure (psia) 4 10/9 0 C O 2 /C H 4 10/9 0 C O 2 /C H 4 + 30 0 ppm to lue ne 10/9 0 C O 2 /C H4 + 500 ppm n-hep tane 4 b 500 60 0 Figure 3.5 Solubility of CO2 and CH4 in conditioned samples with 10/90 CO2/CH4 , 10/90 CO2/CH4 + 300 ppm toluene and 10/90 CO2/CH4 + 500 ppm nheptane at 600 psia and 35 0C. 89 While these constraints seem restrictive, for many cases, they are often obeyed to a first approximation, and the data discussed in the following section have been collected in this way, so the data can be interpreted unambiguously in terms of equation 3.2. 3.4 Sorption and Permeation Data Analysis Permeation through hollow fiber membranes can be described in terms of a simple one-dimensional diffusion model. The local flux of component i through the skin layer is given by the following expression (Crank, 1975): N i = Deff (C t ) dC i dx (3.3) where Ci is the concentration of component i, Deff is the diffusion coefficient of component i and is a function of the total concentration, C t and temperature. In this work, the total concentration is the sum of the concentration of CO2 and CH4. The permeability can be defined as shown in equation 3.4 in terms of the steady state permeation flux through a membrane of thickness P= N p / (3.4) . where N is the steady state flux, cc(STP/(cm3.sec), and P is the pressure difference between the upstream and downstream membrane faces (cm Hg). Substituting the expression for the flux given in equation 3.3 into equation 3.4 yields the permeability as a function of the local concentration gradient: P = Deff (C ) dC 1 dx P (3.5) 90 Equation 3.5 can be rearranged and integrated for the appropriate boundary condition used in most of the experiments in this study: C = C 2 at x = 0 membrane): P dx = 0 C2 Deff (C )dC C 2 = SD C2 p2 0 where S and D are the average solubility and diffusivity coefficients (Koros, 1977). The local diffusion coefficient can also be evaluated using equation 3.6, which allows analysis of permeability and solubility data to directly determine this coefficient at an arbitrarily selected upstream pressure p 2 , assuming the downstream pressure p1 is negligible. Equation 3.7 is derived by applying the Liebnitz rule for differentiation under an integral sign to equation 3.6. Deff (C t ) = P + dP p dp dp dC p2 In state-of-the-art asymmetric membranes, the skin layer, , may be on the order of 1000 Angstroms thick and is thus difficult to reliably measure. Therefore, for the purpose of this calculation it is assumed that skin layer is 1000 Angstroms thick. We could also have assumed 1 cm instead. This should not greatly affect our conclusions since we are particularly interested in relative diffusion coefficient changes before and after conditioning and not in the absolute value of the diffusion coefficient. Since we are using permeance instead of permeability in equation 3.7, we multiply equation 3.7 by the skin thickness 91 (upstream face of the membrane) and C = 0 at x = (downstream face of the (3.6) (3.7) p2 to obtain the diffusion coefficient. Moreover, since we are dealing with virtually identical starting fibers, points here regarding changes in fundamental materials properties. Figures 2.11-2.12 and Figures 2.20-2.21 show the CO2 and CH4 permeance results at 200 and at 600 psia and at 35 0C before and after conditioning to the 10/90 CO2/CH4, the 10/90 CO2/CH4 + 500 ppm n-heptane, and the 10/90 CO2/CH4 + 300 ppm toluene. A reduced permeability was used in the previous chapter to compare the relative permeability enhancements resulting from conditioning treatments in different fibers. In this chapter we use the actual CO2 and CH4 permeance results as a function of partial pressure of CO2 and CH4 in order to calculate dP . dp the analysis in terms of D / could also be done, but this will not change the key As can be seen in Figures 2.10-2.11 and Figures 2.19-2.20 for CO2 and CH4 before conditioning and after conditioning with the 10/90 CO2/CH4 and 10/90 CO2/CH4 + 500 ppm n-heptane, the permeance decreases with increasing pressure, which is typical of the dual mode behavior in glassy polymers. On the other hand after gas conditioning with the 10/90 CO2/CH4 + 300 ppm toluene mixture as can be seen in figures 2.12 and 2.21, the permeance is relatively independent of pressure. Although it is clear that the nature of the glassy polymer has been altered by the conditioning process, the reason for this difference in permeance slopes is not clear. For this reason, the permeance results were fitted with a polynomial equation in pressure instead of fitting the data to the dual mode-model. This approach avoids imposing model dependent constraints on the interpretation. The polynomial equation has the following form; P = A + Bp + Cp 2 + Dp 3 (3.8) 92 where A, B, C and D are the fitting parameters. Appendix G shows a summary of the fitting parameters for the CO2 and CH4 permeances at 35 0C before and after conditioning to the 10/90 CO2/CH4, the 10/90 CO2/CH4 + 500 ppm n-heptane, and the 10/90 CO2/CH4 + 300 ppm toluene at 200pisa and 600 psia. The sorption results were also fitted with a four-term polynomial equation in pressure. C = A + Bp + Cp 2 + Dp 3 (3.9) The fitting parameters are also summarized in Appendix G. Using equation 3.9 and the fitting parameters for the sorption results, dC/dP can be calculated at each penetrant pressure. The permeance, P, and the tangent slope of the permeance versus the upstream pressure, dP/dp can be calculated readily from equation 3.8. Thus, we can now use equation 3.7 to get D(c) versus c . Figures 3.6-3.7 show the percent change in the effective local diffusion coefficient of CO2 and CH4 at 35 0C conditioned with 10/90 CO2/CH4 mixture, 10/90 CO2/CH4 + 500 ppm n-heptane mixture, and 10/90 CO2/CH4 + 300 ppm toluene mixture relative to the diffusion coefficient before conditioning. 93 20 0 Before C onditioning 10/9 0 C O 2/C H 4 10/9 0 C O 2/C H 4 + 5 00 p pm n-heptane 10/9 0 C O2/CH 4 + 3 00 p pm to luene a CO2 (% ) C han ge in D 15 0 10 0 50 0 -5 0 100 200 B efo re Co nditio ning 10/90 C O 2/CH 4 10/90 C O 2/CH 4 + 500 ppm n-h epta ne 1 0/90 C O 2/CH 4 + 30 0 pp m toluene 12 0 14 0 16 0 18 0 Pre ssure [psia] 200 22 0 b 150 C H4 (% ) C han ge in D 100 50 0 -50 100 12 0 14 0 16 0 18 0 Pre ssure [psia] 200 22 0 Figure 3.6 Change of a) CO2 local diffusion coefficient and b) CH4 local diffusion coefficient conditioned with 10/90 CO2/CH4 mixture, 10/90 CO2/CH4 + 500 ppm n-heptane mixture, and 10/90 CO2/CH4 + 300 ppm toluene mixture at 200 psia and 35 0C. Lines are drawn by eye 94 20 0 a 15 0 C O2 (% ) 10 0 C hange in D Before Conditioning 10/9 0 C O 2/C H4 10/9 0 C O 2/C H4 + 5 00 p pm n-heptane 10/9 0 C O2/CH 4 + 3 00 p pm toluene 50 0 -5 0 10 0 200 200 30 0 40 0 50 0 Pressure [psia] 600 70 0 150 (% ) B efo re Co ndition ing 10 /90 CO 2/CH 4 10 /90 CO 2/CH 4 + 500 ppm n-h epta ne 10 /90 C O 2/CH 4 + 300 ppm toluene C H4 C han ge in D 100 50 0 -50 100 20 0 30 0 40 0 50 0 Pre ssure [psia] 600 70 0 Figure 3.7 Change of a) CO2 local diffusion coefficient and b) CH4 local diffusion coefficient conditioned with 10/90 CO2/CH4 mixture, 10/90 CO2/CH4 + 500 ppm n-heptane mixture, and 10/90 CO2/CH4 + 300 ppm toluene mixture at 600 psia and 35 0C. Lines are drawn by eye 95 As noted earlier in the previous chapter, the 10/90 CO2/CH4 gas mixtures do not have the ability to produce a conditioning effect at 200 psia to the hollow fiber membranes compared to the 10/90 CO2/CH4 gas mixture in the presence of toluene. The permeabilities of both penetrants show virtually no increase after conditioning. The solubility selectivity of conditioned sample was essentially unchanged compared to the unconditioned samples. Since the permeability and the solubility selectivity is unaltered, changes in segmental packing and motion caused by the conditioning treatment of the 10/90 CO2/CH4 gas mixture at 35 0C and 200 psia are believed not to have affected the mobility selectivity of the conditioned matrix as can be seen in figures 3.6 for the CO2 and CH4. For the case of conditioning with the 10/90 CO2/CH4 gas mixture at 35 0C and 600 psia, reported earlier, the mixed gas permeabilities values of CO2 and CH4 after conditioning were higher than values before conditioning. This increase in the mixed gas values was discussed and explained earlier in the previous chapter in terms of an increase in the number of hypothetical gaps due to an increase in the conditioning pressure. Therefore, the larger increase in CO2 and CH4 permeabilities following the conditioning with the 10/90 CO2/CH4 gas mixtures for the hollow fiber membrane samples at 600 psia versus 200 psia seems reasonable. On the other hand, the overall selectivity is effectively constant. In addition, the conditioning treatment with the 10/90 CO2/CH4 causes no significant change in the solubility of either penetrant in the conditioned fibers. This suggests that the solubility selectivity should indeed remain essentially constant before and after conditioning. Therefore, since the solubility of both penetrants is not greatly affected after conditioning, and because diffusivity selectivity is the only other selectivity mechanism, the diffusivity selectivity is expected to increase. This result is shown in Figure 3.7a and 3.7b. The sorption and permeation measurements have shown that the major effect of the CO2 conditioning treatment is to introduce residual packing disruptions in the matrix, without significantly 96 increasing the number of Langmuir sites present in the polymer. These subtle packing disruptions act as a source of locally available volume that reduces the amount by which the penetrant needs to dilate the matrix during sorption in order to be accommodated. This important conclusion shows that the idealized dual mode sorption vision of conditioning primarily affecting the Langmuir capacity constant, and hence K j constant calculated by the following equation; ' C Hj b j (3.10) k Dj is simply not adequate to understand the full range of permeation and diffusion ' behavior. The C Hj in equation 3.10 is the Langmuir capacity constant, k Dj is the Kj = Henry s law constant of component j which characterizes the sorption in the dense region of the polymer matrix; b j is a constant that is a measure of the affinity of the penetrant to the Langmuir sites Based on the preceding discussion, a natural question arises concerning the behavior of the CO2 and CH4 components in the 10/90 CO2/CH4, following a conditioning treatment with the 10/90 CO2/CH4 + 500 ppm n-heptane mixture at 200 psia and 600 psia. This issue was treated earlier in chapter 2. It was shown that the increase in CO2 permeability was essentially negligible in the presence of nheptane at 200 and 600 psia. In fact, CO2 permeability is slightly lowered by the presence of n-heptane. In addition, the conditioning treatment resulted in tolerable losses in permselectivity as discussed in chapter 2. The net effect of the conditioning treatment is to produce small selectivity losses of 3% and 14% for conditioning pressure of 200 psia and 600 psia, respectively. Figure 3.6 and 3.7 show the hysteretic results of the CO2 and CH4 diffusion coefficient before and after conditioning for fibers that were conditioned with 10/90 CO2/CH4 + 500 ppm n-heptane mixture, at 200 psia and 600 psia for 5 days. A higher CH4 diffusion coefficient was observed at 600 psia in the conditioned sample compared with that 97 in the unconditioned sample. Methane, itself cannot produce a hysteresis in permeability, but it can maintain a state of increased permeability in a film that has been conditioned by 10/90 CO2/CH4 + 500 ppm n-heptane at 600 psia. Similar to the methane, n-heptane does not have the ability to produce a similar conditioning effect by itself as the CO2 does as can be seen by comparing the CO2 diffusion coefficients results in Figure 3.7a after conditioning with 10/90 CO2/CH4 and 10/90 CO2/CH4 + 500 ppm n-heptane. Presumably, the conditioning effect caused by 10/90 CO2/CH4 + 500 ppm n-heptane was not completely lost, as the solubility of CH4, was still high enough to prevent total consolidation of the matrix. It is hypothesized that there is shift in the free volume distribution, as discussed in chapter 2, caused by sorbing n-heptane. This shift in free volume is more important in facilitating an increase in the diffusion coefficient of CH4 and only a moderate increased CO2 diffusion coefficient. Assuming a shift in the free volume distribution to high chains spacings leads to low selectivity. This is reasonable, since disruptions of the packing presumably make it easier to insert CH4 between segments in a molecularly dissolved state. Normally, this would be expected to result in an increase in the diffusion coefficient of CH4 and a decrease in the diffusivity selectivity. The solubility CO2 and CH4 of the conditioned sample increased slightly compared to the unconditioned samples as discussed in the previous section. The magnitude of this change is not much beyond the experimental accuracy of the equipment, so it is hard to say how significant this increase in solubility is. We currently believe that solubility of CO2 and CH4 is not greatly affected by the conditioning treatment in all three conditioning experiments with; 10/90 CO2/CH4 mixture, 10/90 CO2/CH4 + 500 ppm n-heptane mixture and 10/90 CO2/CH4 + 300 ppm toluene mixture. Therefore, the increased CO2 and CH4 permeability observed at 600 psia is believed to be due to increases in the value of the diffusion coefficients. 98 As discussed in chapter 2, the 10/90 CO2/CH4 + 300 ppm toluene mixture conditioning increases the permeability of CO2 and CH4 in exchange experiments with a 10/90 CO2/CH4, mixed gas feed. Unlike the 10/90 CO2/CH4 + 500 ppm nheptane mixture, marked differences were seen for the CO2 and CH4 permeabilities after conditioning with the 10/90 CO2/CH4 + 300 ppm toluene. We currently believe that the ability of toluene, to induce and maintain conditioning in the glassy matrix is due primarily to its much higher solubility coefficient compared with n-heptane; however, additional more subtle penetrant polymer interaction and even shape factors of the flat toluene versus the linear n-heptane may be at play. Even the qualitative dependence of CO2 and CH4 permeabilities after conditioning is clearly different for the 10/90 CO2/CH4 + 300 ppm toluene as compared to the 10/90 CO2/CH4 + 500 ppm n-heptane conditioning which show typical dual-mode behavior in the conditioned samples. This qualitative difference, which is suggestive of conditioning enhanced increases in CO2 and CH4 permeabilities is clearly not apparent for either the 10/90 CO2/CH4 or 10/90 CO2/CH4 + 500 ppm n-heptane mixtures. As discussed above in the context of the 10/90 CO2/CH4 and the 10/90 CO2/CH4 + 500 ppm n-heptane conditioning, the solubility is presumably unchanged. While the increase in the solubility of CO2 and CH4 following conditioning was qualitatively similar between the three gas conditioning mixtures, the relative increases are somewhat different. Within the experimental accuracy, the increases in the gas solubility of CO2 and CH4 for the three cases studied, are identical. Therefore, the CO2 and CH4 permeabilities enhancements are largely due to increases in the average diffusion coefficients. If one considers the CO2 and CH4, 300 ppm toluene exchange conditioned permeability data for the 200 psia conditioning pressure, the CO2 and CH4 diffusion coefficients calculated using equation 3.7 are higher by 75% and 87% for the CO2 and CH4 materials compared to the unconditioned, asreceived samples (or the 500 ppm n-heptane conditioned samples ) as shown in 99 Figure 3.5. These changes are significant, since conditioning of the samples at 200 psia with 10/90 CO2/CH4 or 10/90 CO2/CH4 + 500 ppm n-heptane has essentially no ability to condition the fibers. In addition, fibers were exchange conditioned at 600 psia for five days with the 500 ppm n-heptane or 300 ppm toluene. Then, the 10/90 CO2/CH4 + 300 ppm toluene or 500 ppm n-heptane was completely replaced by 10/90 CO2/CH4 at 600 psia, and the fibers were maintained at this pressure for 1-2 hours to ensure that steady state had been reached. The results for the diffusion coefficient at 600 conditioning pressure are shown in Figs. 3.7. The conditioning treatment results in a 150% increase in CO2 diffusion coefficient, and a 177% increase in CH4 diffusion coefficient. The mobility selectivity is slightly decreased. As was the case at 200 psia, the conditioning treatment allows significant enhancement of the permeability at 600 psia without sacrificing selectivity. The latter fact, that selectivity is maintained suggests that CO2 and CH4 must somehow compete for additional jumps opportunities. This highly surprising result suggests that the simplistic arguments based on Figures 3.6 and 3.7 are not valid in actual mixed gas situations. The CO2 and CH4 average diffusion coefficients enhancements are largely due to increases in the excess free volume generated during the conditioning treatment. Since the three samples were conditioned at a similar pressure, it is believed that the amount of free volume added to each of the matrices should be different. The increase in free volume for the samples conditioned with either the 10/90 CO2/CH4 or the 10/90 CO2/CH4 + 500 ppm n-heptane gas mixtures is significantly smaller than the free volume added for the sample conditioned with the 10/90 CO2/CH4 + 300 ppm toluene gas mixture. On the other hand, introduction of actual penetrant-scale defects is not suggested here since this ' mechanism will lead to increases in C H , which was not seen in our sorption 100 results. We are tempted by this view, since the membrane is not apparently damaged and with only slight loss in selectivity. A useful way of interpreting the above results can also be seen in terms of the following expression for the effective local diffusion coefficient in systems that obey the dual mode model (Fleming, 1988): Deff = DD 1 + FK / (1 + C D b / k D ) [1 + K /(1 + C [ 2 D b / kD ) 2 ] ] (3.11) ' After conditioning, presumably C H remains constant from the sorption experiments, and hence K in equation 3.11. It is also hypothesized that conditioning does not affect k D or b as discussed above. C D , is the fraction of the total sorption attributed to dissolution into the polymer. The value of F = DH / DD , is typically small (< 0.1) for CO2 and CH4. In the high pressure region, where C D b / k D , is large compared to unity, increases in Deff is mainly due to increase in DD as shown below in equation 3.12; Deff = DD (3.12) At low pressures, C D b / k D , is small compared to unity and equation 3.11 reduces to equation 3.13: Deff = DD [1 + FK ] (3.13) [1 + K ] So increased values of DD cause an increase in the local diffusion coefficient, since the other quantities remains constant. Therefore, the increased permeabilities after conditioning with the 10/90 CO2/CH4 subtle disruption or loosening of the equilibrium packing is what causing the diffusivity referred to 101 as DD , in equation 3.13 to increase by facilitating movement through the more ' open matrix. This is can be understood, since the increase in C H or unrelaxed volume is presumably negligible. This appears more descriptive of what actually happening, since the selectivity is essentially not much affected. Nevertheless, the number of jump opportunities increased for both CO2 and CH4, so DD increased. The addition of toluene mostly involves filling up holes and reorganizing small holes to accommodate penetrants in low energy sites. The actual making of dissolved sorption sites will presumably not lead to huge holes after the toluene is removed. As a result, it is probable that all that happens is for the effective packing to slightly disturbed and few large (high energy) new gaps persists. The large enhancements in the permeability of CO2 and CH4 following conditioning with the 10/90 CO2/CH4 +300 ppm toluene can be also rationalized by examining the free volume changes of the polymer. The free volume approach has proved particularly useful for a description of the effect of various factors on DD in polymers above Tg through the corresponding changes in fractional free volume. In this work, the change in free volume will be reflected by a change in DD since the toluene induced swelling effects are weak on the excess free volume of the polymer. According to Fujita (Fujita et al., 1961), the diffusion coefficient can be given by the expression for CO2 and CH4: * CO2 CO2 DCO2 = RTAd exp Bd /v f * CH4 CH4 DCH4 = RTAd exp Bd /v f ( ) ) (3.14a) (3.14b) ( where R is the universal gas constant; T is the absolute temperature; v f is the volume fraction of the free volume, i.e., the fractional free volume of the system CO CH CO2 CH4 comprised of penetrant and amporphous polymer; Ad , Ad , Bd 2 and Bd 4 are 102 characteristic parameters which depend on the size and shape of the penetrant molecules CO2 and CH4. The four parameters are taken to be independent of temperature and penetrant concentration. It is further assumed that the dependence of Ad and Bd on conditioning is negligible. Clearly, changes in the effective distribution of free volume shown speculatively in figure 2.23 may call this ze ro order assumption into question, but it still is a useful starting point for any such analysis. Denoting the diffusion coefficient before conditioning by Du and the diffusion coefficient after conditioning by Dc , we can write the following; v fc v fu v fc v fu D = ln c / Bd (3.15) Du With the further assumption that B d = 1, the increase in the fractional volume can be calculated. Again, the last assumption is only a rather crude approximation for strongly interacting penetrants. B d according to a more rigorous and complex treatment (Vrentas and Duda, 1977) depends on the size of the polymer jumping unit. Tables 3.4 show the percent increase in diffusion coefficient of CO2 and CH4 and the percent increase in the fractional free volume for samples conditioned with 10/90 CO2/CH4 + 300 ppm toluene at 200 psia, 600 psia and 35 0C. The results in Table 3.4 enable us to draw some conclusions. The tendency of the DD to increase with pressure or concentration (swelling effect) is interpreted on the basis of the higher fractional free volume of the liquid penetrant relative to the pure polymer (assuming additivitiy of volumes upon mixing). It follows that, in the 10/90 CO2/CH4 + 300 ppm toluene mixture, mutual enhancements of diffusion rates can be expected according to the relation; vf = vfo + C6H6CH3vC6H6CH + CO2 vCO2 + CH4 vCH4 (3.16) 103 where vfo is the fractional free volume of the pure polymer at some reference temperature Ts and pressure ps . Furthermore, on the basis of the relative changes in the diffusivity suggests an increase in DD for a given gas with the concentration of toluene in the polymer. If these phenomena can be merged with the traditional dual mode sorption and transport model for glassy polymers, modelling of conditioning and complex phenomena will be feasible. This would be a valuable focus for future work. Table 3.4 Percent change in fractional free volume for CO2 and CH4 in conditioned samples with 10/90 CO2/CH4 + 300 ppm toluene mixture at 200 psia, 600 psia and 35 0C Conditioning Component % Change in % Change in Pressure, psia diffusivity fractional free volume CO2 75 432 200 CH4 87 447 CO2 150 501 600 CH4 177 518 3.5 Conclusions The solubility results indicate negligible increases in the solubility after conditioning with the three conditioning gas mixtures; 10/90 CO2/CH4, 10/90 CO2/CH4 + 500 ppm n-heptane, and 10/90 CO2/CH4 + 300 ppm toluene gas mixtures. These changes are within the experimental accuracy of the sorption equipment. Therefore, it is hard to draw a conclusion about the effect of conditioning on the solubility selectivity. It is believed that under the conditions studied, the solubility of CO2 and CH4 are not much affected by the conditioning treatment, so that the major contribution to the increased permeability following conditioning is an increase in diffusivity. The following conclusions can be made about the sorption experiments; 104 Conditioning treatments had negligible effects on the Langmuir capacity constant, and therefore it affects diffusion in the dense matrix much more than in the free volume sites. The relative changes in the diffusion coefficient before and after conditioning for CO2 and CH4 have been found to be dependent on the conditioning pressure. The increases in diffusivity following conditioning with 10/90 CO2/CH4, and 10/90 CO2/CH4 + 500 ppm n-heptane were found to be negligible due to the weak conditioning effects on permeability. Conditioning increased the diffusion coefficients 115% and 155% for CO2 and CH4 respectively following conditioning with 10/90 CO2/CH4 + 300 ppm toluene at 35 0C and 600 psia. Similarly for samples conditioned with 10/90 CO2/CH4 + 300 ppm toluene at 35 0C and 200 psia, the diffusion coefficients increased 60% and 80% for CO2 and CH4 respectively. The largest increase in CO2 and CH4 permeabilities, at a given conditioning level, observed for samples conditioned with 10/90 CO2/CH4 + 300 ppm toluene is due to large increases in the fractional free volume at given conditioning pressure as compared to samples conditioned with 10/90 CO2/CH4 and 10/90 CO2/CH4 + 500 ppm n-heptane gas mixtures. 105 Chapter 4: Thermodynamics of Morpholine /Diglycolamine / Water / Carbon Dioxide The removal of acid gases by the amine process is accomplished by a chemical reaction. The alkanolamines most commonly used in industrial applications are monoethanolamine (MEA), diethanolamine (DEA), methyldiethanolamine (MDEA), and diglycolamine (DGA). DGA is a primary amine, and its low vapor pressures permits its use in higher concentrations, typically 50 to 60 weight percent, resulting in significantly lower circulation rates and energy requirements (LRGCC, 2003). DGA systems are normally installed with reclaimers to maintain solvent quality by reducing corrosion, foaming and degradation of the solvent. Research and experience have shown that DGA can thermally degrade in reclaimers to produce MOR (Harruff, 1992). The main objective of the present study is to determine thermodynamic characteristics of MOR/DGA/H2O, MOR/H2O and DGA/H2O. This chapter explains how thermodynamics affects the performance of the CO2 absorption process using DGA. Thermodynamics of aqueous amine systems are crucial to understanding their industrial use to remove acid gas from process gas streams. The equilibrium partial pressure of acid gas above a solution of the amine defines pinch conditions for the absorber and stripper. Speciation of the amine and reaction products define the driving force for the forward and reverse reactions with CO2. An understanding of this is important since the reactions are usually rate controlling. Furthermore, a consistent thermodynamic model can quantify the energy required for regenerating the solvent and solvent losses due to amine volatility. 106 Amine vaporization losses have become an important factor in operating gas plants due to increased chemical costs. Amine vaporization losses can be calculated based on vapor pressure data of the specific amine and the gas stream temperature and pressure. Using a consistent thermodynamic model, an estimate of amine losses can be obtained for the absorber, flash vent tanks and stripper. These are the three areas of vapor losses in alkanolamine treating systems. The thermodynamic model provides information on the heats of absorption. Solvents with higher reactivity as indicated by higher forward reaction rate constants tend generally to have higher heats of absorption and therefore they may require more energy for regeneration and may be more difficult to regenerate. The amine reactivity of MOR, DGA and their blends is the subject of chapters 5 and 6. The thermodynamic model can also provide information on the solvent capacity. The solvent capacity establishes the solvent circulation rate, which has a major impact on both plant investment and operating cost of the systems. The solvent circulation rate has a direct impact on the size of the absorber tower, piping system, circulation pumps, and size of the regenerator facilities. In general, 50 to 70% of the plant investment is directly associated with the magnitude of the solvent circulation rate. A good amine solvent is the one that has higher CO2 absorption capacity, faster CO2 absorption rates, and lower vapor pressure. Therefore, these three most important cost factors working capacity, regeneration energy duty and amine losses will be discussed and estimated in this chapter. Blended amine solvents have been studied by several researchers. Austgen (1989) studied the thermodynamics of MDEA blends with MEA, DEA and DGA using the electrolyte NRTL model. Posey (1996) improved the models by studying the activity coefficient of the amines at infinite dilution. 107 Pacheco et al. (2000) studied the absorption of CO2 into aqueous DGA/MDEA blends. Glasscock (1990) and Critchfield (1988) have studied blends of DEA and MEA/MDEA. Littel et al. (1992 I&II) as well as many others have studied a variety of tertiary amines promoted by primary or secondary amines. Specifically, this work will use the thermodynamic frameworks presented by Bishnoi and Rochelle (2000), Austgen et al. (1989) and Posey and Rochelle (1997). VLE data acquired by Martin et al. (1998) and Dingman et al. (1999) for the DGA system will be also used. The N2O data obtained by Versteeg and Van Swajj (1988) for the DGA and MOR systems will also be used in this work. A wetted wall column was used to measure CO2 solubility. The solubility of N2O in amine aqueous solutions was measured by using a solubility apparatus, similar to those presented by Al-Ghawas et al. (1989) and Haimour et al. (1984). The N2O apparatus has been built in this work. The C13 NMR experiments were run on a Varian INOVA-500 machine. Parameters of the electrolyte NRTL model were adjusted in order to match the CO2 solubility data, C13 NMR data, and the N2O solubility data. The fitted model was then used to estimate the solvent working capacity, heat of reaction and vaporization losses for the DGA and the MOR/DGA blend systems. 4.1 Experimental Methods Wetted Wall Column: Solubility of carbon dioxide was determined using a wetted-wall column (Figure 4.1). This contactor was designed and constructed by Mshewa (1995), then modified by Pacheco (1998). This apparatus was also used by Dang (2001), and Cullinane (2002). The column was constructed from a stainless-steel tube of 1.26 cm outside diameter with an exposed length of 9.1 cm. The interfacial area for mass transfer was 38.52 cm2. 108 Paraffin Oil Out to Bath Gas Out Gas Out Reaction Chamber Amine Solution to Bath Circulating Paraffin Oil Gas In Paraffin Oil From Bath Amine Solution From Bath Figure 4.1 Detailed diagram of the wetted-wall column contactor. Figure 4.2 represents the overall flow diagram of the experimental set up. The amine solution was contained in a 1000 cm3 stainless-steel reservoir in a heating bath at the temperature of the experiment. The gas stream fed to the contactor was either pure CO2 or a mixture of N2 and CO2. This gas stream was presaturated with water at the temperature of the experiment. CO2 gas concentration was determined continuously by two infrared analyzers (HORIBA model PIR- 2000) in series with ranges of 0-1 and 0-25% CO2. The gas from the reactor was cooled by ice water to remove water from the gas phase to protect the CO2 analyzer. The contactor was operated at a total pressure from 1 to 9 atm. The chemical solvent was circulated by a Cole-Parmer micropump. 109 Dilution Nitrogen Water Condenser IR CO2 Analyzer Nitrogen Saturator Amine Circulation Figure 4.2 Flow diagram of the experimental setup. The liquid flow rate was controlled at 2-3 cm3/s to maintain a smooth liquid film. The liquid level at the bottom of the reactor was maintained at approximately the same point where the gas is fed. A small amount amine solution was added or withdrawn from the sample plot in order to keep the liquid level in the wetted wall column constant. J-type thermocouples were used in the solution inlet and outlet lines to the reactor for temperature measurement. Measurements of both CO2 absorption and desorption were made with a continuously changing solution loading. Every 10-15 min the output of the analyzers, total pressure, and temperatures were recorded and a liquid sample was obtained to determine the CO2 loading. The amount of total CO2 (free CO2 plus chemically combined) in the liquid phase was determined using a total carbon analyzer, model 525 from Paraffin Oil Circulation Contactor Flow Control Carbon Dioxide 110 Oceanography International Corporation. The CO2 was carried by a nitrogen stream which bubbles through the acid solution to an infrared analyzer HORIBA model PIR-2000 with a range of 0-0.25% CO2. This analyzer was calibrated using a standard solution of 7 mM sodium carbonate. Commercial grade DGA and MOR with a purity of not less than 99% were used in the experimental work. In this work, at any given loading, both absorption and desorption rates were measured by variation of CO2 partial pressure around the equilibrium partial pressure. When the flux is equal to zero, the partial pressure of CO2 will be the equilibrium partial pressure of CO2 at that loading. This point can be found by bracketing the absorption and desorption rates. Figure 4.3 gives an example with 11 wt% MOR/53 wt% DGA at CO2 loading of 0.13 mol/mol amine and 40 0C. In figure 4.3, the interfacial pressure of CO2, PCO 2, int , was calculated by; PCO 2,int = PCO 2,b flux / k g (4.1) where, PCO 2,b is the log mean CO2 partial pressure in the gas phase, k g is the gas film mass transfer coefficient. The gas film coefficient was determined by the absorption of sulfur dioxide into sodium hydroxide solutions (Bishnoi, 2002). The gas film mass transfer coefficient is given by: 0.85 d Sh = 1.075 Re Sc h (4.2) where d is the hydraulic diameter of the annulus (0.44 cm), h is the length of the column (9.1 cm), Sh is Sherwood number, Re is Reynolds number and Sc is Schmidt number. Appendix H tabulates the detailed CO2 solubility experimental data. While inferring the equilibrium partial pressure, only measurements close to equilibrium were considered. By applying the same method to every loading, CO2 equilibrium partial pressure can be determined at a number of solution loading. The liquid film mass transfer coefficient of the wetted wall column was measured by Mshewa (1995) and Pacheco (1998) by carbon dioxide desorption 111 from water and ethylene glycol mixtures. The model solves momentum balance equations (Bird et al., 1960) for a falling film to determine the film thickness ( ) and surface velocity (usurf) where W is the wetted perimeter length. /=3 u surf 2= 3 4 !J: !J/ 2 = 2 l (4.3) (4.4) (4.5) u surf The mass transfer coefficient is given as a function of =D / 2, where is the surface contact time, and l is the length of the contactor (l=9.1cm). The contact area between liquid and gas phases is 38 cm2. L [A]iL [A]o ,out = L [A]iL [A]o ,in = 0.7857 exp( 5.121 ) + 0.1001exp( 39.21 ) + ; for >0.01 (4.6) 0.036 exp( 105.6 ) + 0.0181exp( 204.7 ) = [A ]L [A ]L ,out i o L [A ]i [A ]L ,in o = 1 3 ; for <0.01 (4.7) o k L,A = QL (1 ) a (4.8) 112 1.5 10 -8 1 10 -8 Flux (m ol/cm .s) 5 10 2 -9 0 -5 10 -9 -1 10 -8 0 10 2 20 30 40 50 60 C O interfacial partial pressure (P a) Figure 4.3 Flux interpolation to determine equilibrium solubility. Data points for absorption into 11 wt% MOR/53 wt% DGA at CO2 loading of 0.13 mol/mol amine and a temperature of 40 0C. NMR experiments were performed at UT s Department of Chemistry and Biochemistry NMR laboratory. 13 C experiments were performed using D2O solvent. All experiments were run at 27oC, 40 oC, and 60 oC on a Varian INOVA500 machine. After the sample preparation step, small volume samples (< 5 mL) were sparged with CO2 for ~ 15 minutes through a fine teflon line placed directly in the sample to almost the sample bottom. The NMR tubes were then flame sealed to prevent CO2 from escaping the glass tube. The NMR spectrums were acquired with a relaxation delay of 5T1 to ensure quantitative signals. T1 is the relaxation time. 113 The N2O solubility apparatus: The experimental apparatus used in the N2O measurements is shown in figure 4.4. Nitrous oxide purge out Mercury Burette stem Syringe Skin Thermostat Water jacket 25. 0 Bubbles Movable Barometric leg Equilibrium cell Magnetic stirrer Constant temperature Figure 4.4 Schematic diagram of the N2O experimental apparatus. The principal of the operation of the apparatus is to displace a measured volume of gas into a liquid. The apparatus consists of a thick walled mercury reservoir (15 cm tall with a 5 cm ID) connected to Tygon tubing (1/4 inch ID), which was in turn connected to a glass tube open to the atmosphere, an inverted burette (graduated +/- 0.2 ml), and a second glass tube which is connected to the absorption flask via 9mm flange. The reservoir is open to the atmosphere and was attached to a 2 feet stand with clamp (2) and could be moved up and down the entire length of the stand to ensure that the pressure in the burette is always 114 atmospheric. The absorption flask was a 100 ml round bottom, with three necks of 24/40 Pyrex neck size. The middle neck allows for sample injection through a septum by a hypodermic syringe, one side neck has a water saturator maintained at the experiment temperature and allows for the N2O gas flows to the system. The second side neck is connected to the displacement section by a flange and a rubber seal. The absorption flask is connected through plastic tubing to a second water saturator. The whole apparatus is kept at constant temperature inside a temperature-controlled water bath. The displacement section is jacketed using water as the circulating liquid. The accuracy of the temperature of the system is estimated to be +/-0.5 0C. Testing procedure: The following steps should give a detailed procedure on how to operate this apparatus: Prior to the testing of a sample, the apparatus was purged with water saturated nitrous oxide for about 10 minutes. Both taps were then closed so that the nitrous oxide was sealed inside the apparatus. The movable barometric leg was adjusted to produce equal mercury levels in the two glass legs. By doing this, the pressure inside the apparatus was made equal to the surrounding atmospheric pressure. Solubility measurements are sensitive to air dissolved in the solution because as gas is absorbed, it displaces dissolved air. Since the method used measures the change in volume of the gas, concomitant desorption of air would introduce sizable error. To overcome this, all samples were vacuum degassed. Sample degassing should be done quickly to ensure that carbon dioxide removal from loaded solutions was minimal. 115 A 20 mL sample was taken by syringe and weighed on an analytical balance. The sample was injected through the septum into the absorption flask while atmospheric pressure was maintained inside the system by adjustment of the movable leg. An important criteria of running this apparatus is deciding when equilibrium has been reached. This is done by taking gas volume measurements during the course of the experiment. Equilibrium was said to have been achieved when three identical gas volume measurements were in agreement to within 0.1 mL. The solubility is calculated in terms of the Henry's law constant as follows: H N 2O = PN 2O / C * 2O N (4.9) where C* 2O is the equilibrium concentration of N2O, which can be calculated from N the total moles of gas absorbed in a volume of absorbing liquid. The partial pressure of N2O in the absorption apparatus can be calculated using Raoult's law as follows; PN 2O = Ptotal x H 2 O PH 2O x MOR PMOR x DGA PDGA (4.10) where Ptotal is the total system pressure, x H 2 O , x MOR and x DGA are the mole fraction of H2O, MOR and DGA respectively. PH 2 O , PMOR and PDGA are the vapor pressure of H2O, MOR and DGA respectively. The vapor pressure of water was calculated using the following equation (Al-Ghawas et al, 1989): PH 2O = 1.33567 10 6 exp ( 5243.04/T) where PH 2O is in bars, and T is in Kelvin. (4.11) 116 7KH DWLYLW\ FRHIILFLHQW F shown in the following equation; N2O, is calculated by normalizing the N2O solubility in the aqueous alkanolamine with the Henry s constant H N2O,H2O , as N 2O = C * N 2O PN 2O .H N 2 O,H 2O (4.12) The Henry s constant of N 2O in water is given by the following equation (Versteeg and van Swaaij, 1988); H N 2 O,H 2 O = 8.5470 10 6 exp ( 2284 /T) where H N 2 O,H 2 O is in kPa.m3.kmol-1, and T is in Kelvin. 4.2 Model Description (4.13) A flexible Fortran code for the solution and phase equilibrium of acid gas systems was developed by Austgen (1989). This code was modified to model MOR, DGA, and MOR/DGA blends. The model uses the Smith and Missen (1988) non-stoichiometric algorithm to speciate the liquid solution. Equilibrium constants were used to calculate the standard state chemical potentials using the method described by Austgen (1989). The following reactions and species are considered. CO 2 (aq) + 2H 2 O HCO3 + H 3 O + (4.14) (4.15) (4.16) HCO + H 2 O CO + + 3 2 3 + H 3O + 2H 2 O H 3 O + OH MORH + H 2 O MOR + H 3 O + (4.17) (4.18) (4.19) (4.20) MOR + CO 2 + H 2 O MORCOO + H 3 O + DGA + CO 2 + H 2 O DGACOO + H 3 O + DGAH + + H 2 O DGA + H 3 O + The total amount of water, carbon dioxide, MOR and DGA present in the liquid phase are specified. Equilibrium is first calculated in the liquid phase and 117 then vapor/liquid equilibrium is calculated for all molecular species (MOR, DGA, H2O, CO2). Gas phase non-idealities are calculated using the SRK equation of state (Soave, 1972). Liquid phase non-idealities are calculated using the electrolyte NRTL model (Chen and Evans, 1986; Chen et al., 1982, Mock et al., 1986). The use of the electrolyte NRTL model in amine / acid gas systems has been described previously by Austgen (1989), Posey (1996) and Bishnoi and Rochelle (2000). This work most closely resembles that of Bishnoi and Rochelle (2000) with CO2 referenced to infinite dilution in water. All ions are also referenced to infinite dilution in water. The MOR, DGA and H2O are all referenced to the respective pure components at the system temperature. The reader is referred to Bishnoi and Rochelle (2000) for a more detailed description of the gas and liquid phase models used to account for non-ideality. Tau parameters are defined in order to be consistent with the work of Bishnoi and Rochelle (2000). Tau parameters for molecule / molecule interactions are defined as: B (4.21) T Tau parameters for salt pair / molecule and molecule / salt pair are defined =A+ as: 1 1 = A + B T T ave Here, T is temperature in Kelvin and Tave is 353.15K. Default parameters consistent with Aspen PlusTM version 8.5 were used in this work. This is consistent with the work of Austgen (1989), Posey (1996) and Bishnoi and Rochelle (2000). A description of these defaults are given in Table 4.1a. (4.22) 118 Table 4.1a Default parameters for VLE program Parameter A molecule / molecule 0 water / salt pair 8.0 salt pair / water -4.0 all molecule (other than 15.0 water) / salt pair all salt pair / molecule -8.0 (other than water) B 0 0 0 0 0 . 0.2 0.2 0.2 0.1 0.1 Critical constants used by the SRK equation of state and the accentric factor were taken from the DIPPR database (Rowley et al., 1994). The Henry s law constant for CO2 was fit by Chen et al. (1979). Brevli-O Connell parameters used in this work were obtained from the original work of Brelvi and O Connell (1972). Critical compressibilities used in the Rackett model were obtained from the DIPPR database. The dielectric constant of MOR was assumed to be the same as MEA. Although this is purely an assumption, the mole fraction of MOR is so small that it will have a negligible effect on the calculated results. The Antoine equation for MOR was obtained from Stephenson and Malanowski (1987). Values of all these constants are documented in Tables 4.1b and 4.1c. 119 Table 4.1b Miscellaneous Constants for VLE program Constant Carbon Water DGA Dioxide Critical T (K) 304.2 647.3 699.0 Critical P (kPa) 7376 22090 4360 Critical V 9.4E-2 5.7E-2 0.33 (m3/mol) Accentric Factor 0.23 0.34 0.9693 Rackett ZRA 0.27 0.24 0.19 Brelvi-O Connell 9.6E-2 - MOR 618.0 5340 0.2760 0.3552 0.20 - Table 4.1c Temperature dependent constants Henry s Law Constant (Pa / Mole Fraction) : Ln H x = A + B/T + Cln(T) + DT Carbon Dioxide A B C D 170.7126 -8477.711 -21.95743 0.005781 Dielectric Constant : D = A + B[1/T 1/273.15] A B H2O 88.36 33030 DGA 24.76 8989 MOR (as MEA) 36.76 14836 Antoine Equation (Pa) : ln PSAT=A + B/T + C ln T + D TE A B C D E H2O 72.55 -7206.7 -7.1385 4.04E-6 2.0 DGA 131.58 -14878 -14.614 6.1463E-18 6.0 MOR 87.958 -7860.7 -9.6344 5.676E -6 2.0 Equilibrium constants for reactions 4.14, 4.15, 4.16, 4.17 and 4.20 are documented in Table 4.2 along with their sources. The first and second dissociation constants of CO2, the DGA protonation and water dissociation constants are unchanged from the work of Austgen (1989). The dissociation equilibrium constant for MOR is reported in Vistad et al. (2003) work and is based on molality scale. It is modified in this work in section 4.7 in order to treat MOR as a solvent rather than as a solute and also to change the equilibrium constant from the molality scale to the mole fraction scale. 120 Table 4.2 Temperature dependence of equilibrium constants, mole fraction based *Ln (Kx) = A + B/T + Cln T + DT Eq No. 14 15 16 17 18 19 20 Equilibrium Constant A 231.4 216.0 132.9 -4.06 + B -12092 -12432 -13446 -6445 -823 5141 -8431.653 C -36.78 -35.48 -22.48 0.0 0.0 0.0 0.0 D 0.0 0.0 0.0 0.0 0.0 0.0 -0.50369E2 a HCO 3 a H 3O + a CO 2a 2 2 O H a H 3O + a CO 3= a HCO 3 a H 2 O a H 3O + a OH a 2 2O H a MOR a H 3O + Value at 313 K 8.55E-9 1.04E-12 9.15E-18 1.97E-11 -10.5 -8.5 2.25E-12 Source Posey (1996) Posey (1996) Posey (1996) Vistad et al. (2003) This work This work Austgen (1989) a H 2 O a MORH a MORCOO a H 3O + -7.9 -24.9 1.69569 a MOR a CO 2 a H 2 O a DGACOO a H 3O + a DGA a CO 2 a H 2 O a DGA a H 3O + a H 2 O a DGAH + 4.3 N2O Solubility of Carbon Dioxide in Aqueous Solution of DGA, MOR, To validate the solubility apparatus and the experimental procedure, the and MOR/DGA solubility of N2O in water was measured. The measured solubility of N2O in water was 4260 and 5140 kPa m3 kmol-1 for 25 0C and 40 0C, respectively. Data at 60 0C were obtained but were not reproducible. Previously published data at 60 0C show also some discrepancy. In Table 4.3, the comparison between the literature values for the solubility of N2O in water and the values obtained in this study at 25 0C and at 40 0C is shown. As shown in Table 4.3, the measured solubility of N2O in water is in good agreement with the literature values. 121 Table 4.3 Henry s constant for N 2O in water in kPa.L/mol-1 at 25 0C and 40 0C source 25 0C 40 0C Joosten and Danckwerts (1972) 4151 Browning and Weiland (1972) 4169 Sada et al. (1994) 4116 Markham and Kobe (1941) 4209 Haimour and Sandall (1984) 4167 Versteeg and van Swaaij, (1988) 4073 6136 Li and Lai (1995) 5725 Al-Ghawas et al. (1989) 3909 5020 This work 4260 32 5140 45 Versteeg and Van Swajj (1988) studied the solubility of nitrous oxide at DGA concentrations from 0 to 60 wt% at 298 to 318 K. They also studied the solubility of nitrous oxide in MOR solutions. Experiments were performed at concentrations from 0 to 30 wt% at 303 K. The effect of amine concentration is seen to lower the solubility of nitrous oxide in aqueous solutions. This may be seen in figure 4.5 where the solubility is plotted as the activity coefficient of nitrous oxide with a reference state of infinite dilution in water. The results are also summarized in Table 4.4. Table 4.4 DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA Amine N2O solubility data in unloaded amine solutions Conc, mol/L 0.19 0.40 0.80 1.63 2.28 3.25 3.26 0.21 0.41 0.81 1.61 2.44 3.24 4.67 T, 0C 303 303 303 303 303 303 303 298 298 298 298 298 298 298 HN2O, L-atm/gmol 47.8 46.9 46.3 49.8 50.2 54.0 55.4 40.6 41.9 42.5 43.6 46.6 49.8 53.3 Reference Versteeg et al (1986) Versteeg et al (1986) Versteeg et al (1986) Versteeg et al (1986) Versteeg et al (1986) Versteeg et al (1986) Versteeg et al (1986) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) 122 DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA DGA MOR MOR MOR MOR MOR MOR MOR 6.13 6.14 0.19 0.40 0.79 1.63 2.28 3.25 3.26 0.20 0.36 0.91 1.83 2.58 3.59 3.64 0.20 0.41 0.80 1.71 2.32 2.49 3.25 3.54 0.20 0.48 0.78 1.59 2.19 3.11 3.24 298 298 303 303 303 303 303 303 303 318 318 318 318 318 318 318 333 333 333 333 333 333 333 333 303 303 303 303 303 303 303 60.8 59.2 48.6 47.7 47.1 50.6 51.1 54.9 56.4 69.2 70.3 68.9 69.2 72.3 75.4 74.1 90.8 88.7 89.9 91.4 89.6 92.3 86.5 85.7 47.2 47.8 48.6 46.2 46.1 48.3 46.9 Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) Littel (1992) 123 1 .6 1 .5 1 .4 1 .3 1 .2 1 .1 1 0 .9 0 Ve rste e g a n d Van Sw a aij (D G A , 2 5 C ) Ve rste e g a n d Van Sw a aij (D G A , 3 0 C ) Ve rste e g a n d Van Sw a aij (D G A , 3 0 C ) Ve rste e g a n d Van Sw a aij (D G A , 4 5 C ) V erste e g a n d Va n Sw a aij (M O R , 3 0 C ) 0 0 0 0 0 A ctivity C oefficient of N O 2 10 20 30 40 50 A m ine C o nce ntration, wt% 60 70 Figure 4.5 Solubility of nitrous oxide as a function of amine concentration. 4.4 Solubility of Carbon Dioxide in Aqueous Solution of DGA, MOR, and Data for CO2 solubility in DGA/H2O, MOR/H2O, and MOR/DGA/H2O solutions were obtained in this work. Data in 23.5wt% MOR, 65wt% DGA, and 11wt% MOR/53wt% DGA at 298, 313 and 333 K are given in Tables 4.5, 4.6, and 4.7. Throughout this work, loading is represented as moles CO2/mole amine where the total concentration of amine is equal to the concentration of DGA plus the concentration of MOR. MOR/DGA 124 Table** 4.5 CO2 Solubility in 65wt% DGA T Loading P*CO2 T Loading 0 0 C (Pa) C 24.2 0.23 15 41.2 0.10 23.8 0.43 735 39.5 0.23 38.9 0.42 Table** 4.6 CO2 Solubility in 23.5wt% MOR T Loading P*CO2 T Loading 0 0 C (Pa) C 24.4 0.08 10 39.8 0.08 35 39.8 0.21 60.0 0.08 250 59.5 0.21 P*CO2 (Pa) 10 75 2120 P*CO2 (Pa) 1175 6150 T C 58.5 60.2 59.6 0 Loading 0.11 0.24 0.42 Loading 0.32 0.32 P*CO2 (Pa) 145 795 14750 P*CO2 (Pa) 9540 53700 T C 24.0 40.1 0 Table** 4.7 CO2 Solubility in 11wt% MOR/53wt% DGA (65wt% Amine) T Loading P*CO2 T Loading P*CO2 T Loading 0 0 0 C (Pa) C (Pa) C 25.7 0.16 5 24.7 0.27 25 24.7 0.36 40.7 0.16 20 40.8 0.27 285 40.2 0.36 58.7 0.16 515 61.7 0.27 1180 58.1 0.36 25.2 0.45 41.4 0.45 ** Numbers are rounded to the nearest five P*CO2 (Pa) 150 725 6700 3775 16190 The addition of roughly 11 wt% MOR to a 53wt% aqueous DGA solution increases the equilibrium partial pressure of CO2 by a factor of 5 to 7 at high loading. The data of DGA/MOR converges with the equilibrium partial pressure of DGA at CO2 loading below 0.2. Martin et al. (1978) obtained solubility data for CO2 in solutions of 60 wt% DGA solutions at 50 0C and 100 0C. The data were collected for regions of high acid gas partial pressures. Their data are very helpful in studying the high loading region since our experimental data was not acquired in this region. Dingman et al. (1983) obtained a large amount of data in solutions of 65wt% DGA down to low levels of acid gas loadings. Again, their CO2 solubility data complements the data taken in this work. 125 The heat of absorption, + abs , of 23.5 wt % MOR, 65 wt % DGA and 23.5 wt % MOR/53 wt% DGA solutions was determined at various loadings at three different temperatures using the VLE data above. Using the Clayperon equation (Smith and Van Ness, 1975), + abs can be calculated as; * d ln PCO 2 + abs = d(1/T ) R ( ) (4.23) Results are displayed graphically in figure 4.6, 4.7 and 4.8. The results are also given in Table 4.8. 12 H a bs ldg=0.32, =19.7 kcal/m ol 10 (P a) ldg= 0.21, =17.3 k cal/m ol 8 H * a bs ln P CO2 6 H a bs ldg=0.08, = 19.1 kcal/m ol 4 60 C 2 0.00 3 0 40 C 0 25 C 0 0 .003 2 0 .0034 1/T (1/K ) Figure 4.6 Heat of Absorption of CO2 at various loading for 23.5 wt% MOR 126 10 H a bs ldg=0.42, = 18.3 kcal/m ol 8 (Pa) ldg=0.23, =2 2.1 kcal/m ol 6 H a bs * ln P CO2 4 H ldg=0.10, =34.6 k cal/m ol 2 a bs 0 0 .002 9 0.00 3 0 .003 1 0 .003 2 1/T (1/K) 0 .003 3 0.0034 Figure 4.7 Heat of Absorption of CO2 at various loading for 65 wt% DGA 10 H a bs ldg=0.45, = 16.8 kca l/m ol 8 H (Pa) a bs ldg= 0.35, = 22.3 kca l/m ol 6 H ldg=0.13, = 29.1 kcal/m ol H ldg=0.26, = 20.9 kca l/m ol * ln P CO2 4 a bs a bs 2 60 C 0.00 3 0 0 0.0029 40 C 0 .003 1 0 .003 2 1/T (1/K) 0 25 C 0.0033 0.0034 0 Figure 4.8 Heat of Absorption of CO2 at various loading for 23.5 wt% MOR/53 wt% DGA. 127 Table** 4.8 Heat of Absorption of CO2 at various loading for 23.5 wt% MOR, 65 wt% DGA and 11 wt% MOR//53 wt% DGA Solvent Heat of absorption, Loading, mol CO2/mol kcal/mol amine 23.5 wt% MOR 0.08 19.1 23.5 wt% MOR 0.21 17.3 23.5 wt% MOR 0.32 19.7 65 wt% DGA 0.10 34.6 65 wt% DGA 0.23 22.1 65 wt% DGA 0.42 18.3 11 wt% MOR/53 wt% 0.13 29.1 DGA 11 wt% MOR/53 wt% 0.26 20.9 DGA 11 wt% MOR/53 wt% 0.35 22.3 DGA 11 wt% MOR/53 wt% 0.45 16.8 DGA 4.5 C13 NMR Data The speciation of loaded solutions plays a critical role in determining the rate of CO2 absorption and the solution capacity especially with primary and secondary amines. The more bicarbonate ions form in equilibrium CO2alkanolamine-H2O solutions, the more free amines exist, and these free amines are able to react with CO2 molecules again, which finally leads to a remarkable enhancement in the solution capacity. The overall reaction stoichiometry indicates that 2 mols of amine are required per mole of CO2 reacted for the carbamate anion, whereas a one-to-one ratio is required for the bicarbonate ion. The degree of hydrolysis of the carbamate anion is determined by reaction parameters such as the amine concentration, solution pH, and chemical stability of the carbamate anion. Equation 4.24 represent the carbamate hydrolysis; RNHCOO- + H2O RNH2 + HCO3- (4.24) 128 In a rich amine solution the concentration of unreacted amine depends on the carbamate stability constant. Typically the value of the carbamate stability constant is determined by regressing data on overall CO2 solubility. Values have been determined this way for MEA, DEA, and DGA. The solution speciation has been measured more directly by C13 NMR. These measurements have been reported for MEA and a number of moderately hindered amines. In primary and secondary amines the carbamate stability constant is given by the following relationship; K carb = [R NH CO ] [HCO ][R NH] 2 3 2 2 (4.25) In this work, the solution speciation in the aqueous 23.5wt% MOR/H2O, 65wt% DGA/H2O, and 11% MOR/53% DGA/H2O solutions was measured by C13 NMR at 300K, 313K, and 333K and at CO2 loading ranging from 0 to 0.5. Figures 4.9 to 4.14 show typical 13C NMR spectrum of 23.5wt% MOR/H2O, 65wt% DGA/H2O, and 11wt% MOR/53wt% DGA/H2O solutions. Additional NMR data from this work can be found in Appendix I. Tables 4.9, 4.10 and 4.11 give the detailed NMR results of the spectrums in figures 4.9, 4.11 and 4.12. Tables 4.12, 4.13 and 4.14 also give the ratio of carbamate anion to bicarbonate ions peak areas as a function of CO2 loading and temperature for all the NMR specta acquired in this work. 129 1+5+9 HO-3-1-O-2-4-N-H2 HO-7-5-O-6-8-N-H3+ HO-11-9-O-10-12-N-H-13-OO13 3+7+11 2+6 4+8 HCO3- 10 12 Figure 4.9 13 C NMR spectrum of 65 wt% DGA at 300K and 0.34 loading. 130 2 O 1 N-H 6 O 5 N-H-7-OO- 7 2 4 O 1 3 N-H2+ 6 5 4 3 2+4 HCO31+3 6 5 Figure 4.10 13 C NMR spectrum of 23.5 wt% MOR at 313K and 0.40 loading. 131 15 HO-3-1-O-2-4-N-H2 HO-7-5-O-6-8-N-H3+ HO-11-9-O-10-12-N-H-13-OO 17 O 16 N-H2+ 17 16 6 O - 14 N-H O 19 18 15 14 N-H-20-OO19 18 Figure 4.11 loading. 13 C NMR spectrum of 11 wt% MOR/53 wt% DGA at 300K and 0.52 13 20 HCO3- Figure 4.12 Expanded 300K and 0.52 loading. 13 C NMR spectrum of 11 wt% MOR/53 wt% DGA at 132 1+5+9 2+6+19 10 3+7+11 14+16+18 15+17 12 4+8 Figure 4.13 Expanded 300K and 0.52 loading. 13 C NMR spectrum of 11 wt% MOR/53 wt% DGA at 133 Figure 4.14 Proton, 13C and short range C-H correlation NMR spectra for 11 wt% MOR/53 wt% DGA at 300K and 0.52 moles/mol amine. . Table 4.9 Detailed 13C NMR Results for 65 wt% DGA and 300K and loading 0.34 mol CO2/mol DGA. Species (ppm) Methylene C s adjacent to nitrogen in DGA/ Protonated DGA Methylene C s adjacent to nitrogen in DGA carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side Methylene C s adjacent to oxygen in DGA carbamate on carbamate side Area 39.2 40.6 59.9 68.8 69.8 132.7 67.6 206.1 131.9 66.7 134 Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side DGA carbamate Carbonate / Bicarbonate 71.3 163.5 160.9 205.2 6451 53 Table 4.10 Detailed 13C NMR Results for 65 wt% DGA and 313K and loading of 0.40 mol CO2/mol MOR. Species Carbamate ring C s adjacent to carbamate side Carbamate ring C s adjacent to non carbamate side MOR / Protonated MOR on carbamate side MOR / Protonated MOR on noncarbamate side MOR carbamate Carbonate / Bicarbonate 13 (ppm) 44.2 66.4 43.4 64.6 162.8 160.4 Area 3.8 3.8 7.6 7.7 100.0 21.9 Table 4.11 Detailed 300K. C NMR Results for 23.5 wt% MOR/65 wt% DGA and (ppm) 38.6 40.5 59.9 66.3 69.8 71.4 163.5 159.8 43.9 66.3 42.8 63.8 162.1 Area 23.6 17.7 46.1 22.3 17.4 41.9 1000 170.4 12.5 12.5 9.2 9.2 329.2 Species Methylene C s adjacent to nitrogen in DGA/ Protonated DGA Methylene C s adjacent to nitrogen in DGA carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side Methylene C s adjacent to oxygen in DGA carbamate on carbamate side Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side DGA carbamate Carbonate / Bicarbonate Carbamate ring C s adjacent to carbamate side Carbamate ring C s adjacent to n on carbamate side MOR / Protonated MOR on carbamate side MOR / Protonated MOR on noncarbamate side MOR carbamate 135 Table 4.12 C13 NMR in 65wt% DGA T, oC Loading 27 0.167 60 0.179 27 0.337 60 0.326 27 0.362 40 0.384 60 0.382 27 0.468 40 0.481 60 0.475 DGACOO-/HCO3193.1 78.7 102.4 42.9 59.5 52.9 32.6 6.6 6.1 5.8 Kcarb 56.5 25.0 61.2 25.0 38.5 37.8 22.2 63.1 39.3 25.5 Kcarb 6.8 3.8 2.8 6.9 4.1 2.1 4.4 3.1 1.8 7.2 4.5 5.0 8.3 5.7 4.1 11.0 8.0 4.6 12.6 8.7 4.7 Table 4.13 C13 NMR in 23.5wt% MOR T, oC Loading MORCOO-/HCO327 0.478 2.76 40 0.478 1.87 60 0.478 1.51 27 0.405 4.57 40 0.392 3.12 60 0.392 1.79 27 0.370 3.75 40 0.370 2.76 60 0.370 1.72 27 0.569 1.46 40 0.569 1.18 60 0.569 1.24 27 0.428 4.60 40 0.428 3.37 60 0.428 2.62 27 0.325 10.9 40 0.325 8.01 60 0.325 4.77 27 0.258 16.7 40 0.258 11.6 60 0.258 6.31 136 Table 4.14 C13 NMR in 11wt% MOR/53wt% DGA T, oC Loading 27 40 60 27 40 60 27 40 60 0.524 0.524 0.524 0.364 0.374 0.374 0.271 0.285 0.285 [DGACOO-+MORCOO]/HCO37.80 7.18 6.50 54.74 37.67 24.00 127.1 73.00 52.11 To estimate the carbamate stability constant, the solution speciation in aqueous MOR, DGA and MOR/DGA solutions was measured. In particular, two important species in the CO2-amine-H2O solutions, namely, bicarbonate ion and carbamate anion, were identified by 13C NMR spectroscopy. To assign protonated amine and free amine in the equilibrated CO2-amine-H2O solutions, the NMR spectroscopic results of the aqueous amine solutions without any dissolved CO2 were compared with those of the CO2-amine-H2O solutions. The chemical shifts were found nearly identical in the two 13C NMR spectra in the three amine solutions. For chemical shifts of 25-100 ppm, carbon peaks of protonated/free amine (AMH+, AM) were observed, and hence, the remaining peaks could be identified with the carbamate form of the amines (AMCO2-). The carbon peaks of carbamate anion (AM13CO2-) and bicarbonate ion (H13CO3-) appeared at 150-175 ppm. Bicarbonate ions of the CO2-MOR-H2O, CO2-DGA-H2O, and CO2-MORDGA-H2O solutions showed similar chemical shifts at the same carbon dioxide absorbing conditions. The quantitative analysis of bicarbonate ion (H13CO3-) was made by considering the ratio of the peak areas of the carbons in the carbamate form of the amine and the carbons in the carbamate anion. The formation of carbonate ions is not likely to occur because the basicities of amine solutions are 137 low enough (pH = 7-10) to guarantee that the carbonate-bicarbonate equilibrium is shifted more toward the bicarbonate side at various CO2 loadings. The CO2 loading can also be calculated from the peak areas of protonated/free amine, bicarbonate ion and carbamate anion peak areas. It should be noted that the peak area of the carbon attached to nitrogen and the four methylenes carbons of the carbamate have different intensities. Figures 4.9 through 4.14 give the detailed identification of the peaks. Sample calculation is also given in Appendix J of loading and species mole fractions. After identifying the peaks, the carbamate stability constant can then be calculated using equation 4.25. Table 4.15 is a summary of the apparent carbamate stability constants obtained in the present study. Literature values of the apparent carbamate stability constants of MOR and DGA are also listed in this Table, as a reference. It is clear that the carbamate stability constant in the 65wt % aqueous DGA is greater than that of MOR. This suggests that MOR forms a very unstable carbamate upon reaction with CO2 and requires one amine molecule for each CO2 molecule reacted. However, the reaction of DGA with CO2 to form very stable carbamate, which could not be converted to bicarbonate and remained in the solution, resulted in the conversion of two amine molecules for each reacted CO2 molecule. This phenomenon might be due to the difference in the molecular structures of DGA and MOR. The van't Hoff equation(Smith and Van Ness, 1975) can be used to estimate the temperature dependence of the carbamate stability constant for DGA and MOR. ln K carb = + r n /RT + B (4.26) The results are given in Table 4.16 and figure 4.16. It is clear that the heat of reaction for DGA is higher than that of MOR since DGA carbamate is more stable compared to MOR carbamate. 138 Table 4.15 Comparison of carbamate stability constants (Molarity based*) Amine T (0C) reference Kcarb MOR 10 Caplow, 1968 8 27 This work 8.2 40 5.4 60 3.6 DGA 25 Austgen, 1989 calc 12 27 This work 61.0 40 38.6 60 24.4 x AMCOO * K CARB = x AM x HCO 3 10 0 65 wt% DG A A pparen t K carb 10 2 3.5 wt% M OR 1 0 .002 9 60 C 0.003 0 40 C 0 27 C 0 .003 4 0 0 .003 1 0.0032 0.0033 -1 Te m peratu re (K ) Figure 4.15 Apparent carbamate stability constant for the 23.5wt% MOR and the 65wt% DGA with 0.1 to 0.5 moles CO2/mol Amine. 139 Table 4.16 Heat of reaction of carbamate for 65 wt% DGA and 23.5 wt% MOR. Solvent Heat of reaction (kJ/mol CO2) 65 wt% DGA 22.9 23.5 wt% MOR 20.9 x AMCOO * K CARB = x AM x HCO 3 4.6 N2O Regression Results As can be seen in figure 4.5, the data of Versteeg and Van Swajj data showed slightly higher activity values compared to one at zero DGA concentration. Therefore, the Henry s constant of CO 2 in water was adjusted so that it is a function of amine strength. In this way, we introduced the decrease in solubility with increasing amine strength. N2O solubility data in unloaded DGA and MOR solutions was then regressed. Parameters obtained for the Henry s constant are summarized in Table 4.17 along with their standard deviation. Parameters where the standard deviation is not listed were not regressed. The results of the regression for the DGA and MOR solutions are shown in figure 4.16 as a parity plot. Table 4.17 Parameter Values of the Henry s Constant Ln Hx = A + B/T + Cln(T) + DT A 170.7 B -8477 C -22.0 D 0.00578 9.40E-05 140 V erste eg a nd V an Swajj (DG A , 298 K ) 1 .3 V erste eg a nd V an Swajj (DG A , 303 K ) V erste eg a nd V an Swajj (DG A , 313 K ) V erste eg a nd V an Swajj (DG A , 333 K ) 1 .2 c alc Verste eg a nd V an Sw ajj (M O R, 30 3 K ) exp/H H C O2 C O2 1 .1 1 0 .9 0 .8 20 30 40 50 60 70 A m ine C oncentra tion (wt% ) Figure 4.16 Results of Nitrous Oxide data Regression in unloaded solutions. 4.7 Activity of Diglycolamine and Morpholine in Aqueous Mixtures Huey et al. (1991) have measured vapor liquid equilibrium for MOR/H2O system at 75 oC and 95 oC. Appendix A.X gives the VLE data for MOR/H2O system at 75 0C and 95 0C. From the VLE data for MOR/H2O system, the activity coefficients of MOR and H2O can be calculated assuming ideal gas conditions since the total pressure is less than 1 atm; 0 10 i = yi P x i p sat i (4.27) where i is the activity coefficient of component i, x i and y i are the mole fractions in the liquid and the gas phase respectively, P is the system pressure, and 141 p sat is the saturation pressure of component i. Figure 4.17 shows the activity i coefficients for the MOR/H2O system. Analysis of activity coefficients at the two temperatures they studied and equation 4.28 yields an excess heat of mixing at infinite dilution of -16.7 kJ/mol for liquid MOR. ln (2)MOR (1)MOR P,x h Ex = 2 1 1 (2) R T T(1) (4.28) The absolute value of the activity coefficients should not be compared with those at temperatures of 25oC since the data of Huey et al. (1991) are at 75 to 95 0 C. A comparison of the excess heat of mixing at infinite dilution is provided in Table 4.18. The value for amines is consistently negative and seems to be related to the amino group. This value of -16.7 kJ/mol is lower than the standard value of 25 kJ/mol at 25 0C. The former value is obtained by extrapolation from the high temperature data. Extrapolation is risky and should be performed with caution. The reason for us to extrapolate is because our data were obtained over the temperature range of 25 0C to 60 0C. In addition, Huey et al. (1991) have pointed out that the predictive UNIFAC model with parameters reported in the literature results in poor predictions for the MOR/H2O mixture. They hypothesized that the cyclic secondary amine group in MOR should be considered a different functional group from the noncyclic secondary amine group. Therefore, an attempt to use the UNIFAC model to calculate the excess heat of mixing was not pursued. 142 1 .4 1 .2 A ctivity coeffic ient 1 0 .8 M O R - 75 C 0 0 0 .6 H 2O - 75 C M O R - 95 C H 2O - 95 C 0 0 0 .4 0 0.2 0 .4 0 .6 0 .8 M orph oline M ole F ractio n 1 Figure 4.17 Data of Huey et al. (1991) reinterpreted as activity coefficients for the water / MOR system at elevated temperature. Table 4.18 Excess heat of mixing at infinite dilution and 25oC Species hEX, AM (KJ/mol) Source Piperazine -59 Dortmund Modified UNIFAC Piperazine -38 Wilson and Wilding (1994) Piperidine -26 Dohnal et al. (1994) Morpholine -25 Dohnal et al. (1994) Cyclohexylamine -23 Dohnal et al. (1994) *All species listed are liquids in their pure state at ambient conditions except PZ **Reference state of most components in Dortmund UNIFAC database is liquid As noted previously, MOR is referenced to the pure component at the system temperature; therefore, the activity coefficient of MOR must be normalized in the same way that the activity coefficient of water and DGA are normalized so that 143 Am 1 as x Am 1 (4.29) This is the normalization convention adopted for alkanolamines in this work. Using the following equation (Austgen, 1989) to relate K ' and K x ; x where is the symmetrically normalized activity coefficient of MOR at ininite Am dilution in water, K x is the dissociation constant expressed on the mole fraction, K' = Kx x Am (4.30) K 'is the new dissociation constant after adopting the above normalization x convention. The value of can then be obtained from the VLE data for the Am binary MOR-H2O mixture and the fact that the excess heat of mixing at infinite dilution is -25 kJ/mol. Vistad et al. (2003) determined the dissociation constant of MOR as a function of temperature by potentiometric pH measurement of a MOR-H2O solution (2.1:60 ratio) while varying the temperature within the range 0-50 0C. The determined temperature dependence of pKa is the following; pK a = 1560/T + 3.52 (4.31) The above dissociation constant is reported on the molality scale. The pKa is the negative logarithm (base 10) of K m and can be converted to K x using the following equation (Austgen, 1989); 1000 ln K x = ln K m ln M s (4.32) where M s is the molecular weight of water. The NRTL parameters for MOR/H2O and H2O/MOR are then fit to the infinite dilution activity coefficient values calculated by the fit to the VLE data and the excess heat of reaction at 25 0C. These parameters are reported in Table 4.19. Accurate prediction of the MOR activity coefficient is useful in two ways. It helps predict the volatility and losses 144 of the amine as well as correcting the equilibria that involve MOR for the effect of DGA. The results of the regression are shown in figure 4.18 and Table 4.19. 1 10 75 C 95 C 0 0 MOR (calc) (exp)/P P 10 -1 MOR 10 0 0 0 .2 0 .4 0.6 0 .8 M orpholine M ole F ra ction 1 Figure 4.18 Results of regression of the equilibrium partial pressure of MOR in MOR-H2O mixture. Fitting the excess heat of mixing at 25 0C to -25 kJ/mol Table 4.19 Fitted values of NRTL binary interaction parameters for MOR-H2O system. Molecule Pair A B (K) H2O-MOR 4.62 0.23 0.00* * MOR-H2O 0.000 -960 1.65 ** DGA-H2O 1.99 0.35 0.00** H2O-DGA 0.000** -770 62.2 ** Parameters were fitted in earlier work of Austgen (1989). * Parameters fixed at zero, could not be estimated with statistical significance Using the NRTL model parameters shown in Table 4.19, the activity coefficient for MOR at infinite dilution can then be calculated into the common temperature form used for the equilibrium constants; 145 ln = 8.06 2853/T (4.33) MOR From equations 4.30, 4.31 and 4.32, the protonation equilibrium constant (mole fraction based) for MOR can be calculated as; ln K x = -4.06 6445/T (4.34) 4.8 Parameter Regression Results of CO2 Solubility and NMR Data The electrolyte-NRTL parameters and the carbamate equilibrium constant for the DGA-CO2 system were regressed to two VLE data sets and VLE and NMR data set from this work. The four data sets were simultaneously regressed and the resulting parameters are given in Table 5.20. In this work, only the partial pressure for the VLE data and the ratio of the carbamate to the bicarbonate mole fractions for the NMR data were adjusted and therefore it reflects all the error. As can be seen from figure 5.20 the ratios of experimental to calculated are well distributed about a value of unity, suggesting that the scatter is due to experimental error rather than a lack of fit by the model. In general, the model appears to represent the experimental data, as a whole, well. This is especially true in view of the fact that the VLE data used to estimate parameters vary over extremely wide ranges of CO2 pressure and loading. 4.8.1 DGA-CO2 system 146 10 1 D ingm an et al. (1 983) - 65 w t% DG A M artin et al. (1978 ) - 60 wt% D G A T his work - VLE T his work - NM R [P R E D ] [D G A C OO /H CO ] [D G A C O O /H CO ] CO2 [E XP ]/P 10 0 - - 3 PR E D 3 E XP - CO2 / P 10 -1 0 .1 0 .2 0.3 0 .4 0 .5 0.6 0 .7 CO loading, m ol CO /m ol DG A 2 2 0 .8 Figure 4.19 Results of VLE and C13 NMR data regression of the DGA-CO2 system. Table 4.20 Parameter Non-Default parameters for the NRTL model. A B 40 Default ln Kx @ 40oC This Austgen, work 1989 (IH2O,IDGAH,IHCO3) (IH2O,IDGAH,IDGACOO) (IDGAH,IHCO3, IH2O) (IDGAH,IDGACOO, IH2O) ln Kx carbamate 1 1 = A + B T T ave B ln K = A + T 8.5 0.11 787 297 8.8 8 10.4 0.12 -5221 1189 8.6 8 -3.7* -1713* -4.4 -4 -5.3* 2395 443 -4.5 -4 -7.9* -823 77 for salt pair / molecule and molecule / salt pair -10.5 -8.0 * Parameters could not be estimated with statistical significance 147 The binary interaction parameters of DGA-H2O and H2O-DGA used in this work are the same as the ones used by Austgen (1989). Most of the parameters are well predicted as indicated by the low standard deviation. The regressed value obtained in this work does not deviate far from the default value. This places some confidence in their absolute value. Figure 4.20 compare partial pressure predictions from the current model to the VLE data obtained in this work. Figures 4.21, 4.22, 4.23 and 4.24 give the predicted speciation at 25 0C, 40 0C and 60 0C. 3 10 CO ) 10 2 o 2 */[loading] (kPa.mol DGA/mol 10 1 60 C 2 2 P CO2 10 0 2 40 C o 10 -1 25 C o 10 -2 0.1 0.2 0.3 0.4 0.5 CO Loading, m ol CO /m ol DGA 2 2 0.6 Figure 4.20 Results of regression of the equilibrium partial pressure of CO2 in 65wt% DGA system obtained in this work. 148 1 D G AH F raction of Total DG A + DGACOO - 0 .1 DGA 0.0 1 0 0 .1 0 .2 0 .3 0.4 0.5 C O Lo adin g, m ol C O /m ol D G A 2 2 0 .6 Figure 4.21 Results of regression of C13 NMR data in 65wt % DGA system at 25 0 C. 10 0 DGAH Frac tion of To tal DG A + DGACOO - 10 -1 DGA 10 -2 0 0 .1 0 .2 0 .3 0 .4 0.5 C O Loading, m ol C O /m ol D G A 2 2 0 .6 Figure 4.22 Results of regression of C13 NMR data in 65wt % DGA system at 40 0 C. 149 10 0 DGAH F raction of Total D G A + DGACOO - 10 -1 DGA 10 -2 0 0 .1 0 .2 0 .3 0.4 0.5 C O Lo adin g, m ol C O /m ol DG A 2 2 0 .6 Figure 4.23 Results of regression of C13 NMR data in 65wt % DGA system at 60 0 C. 10 0 DGA 10 Mole fra ctio n -1 DGAH + DG A C O O - 10 -2 H CO 10 -3 3 10 -4 0 0.1 0 .2 0 .3 0 .4 0.5 CO lo a din g, m ol CO /m o l DG A 2 2 0 .6 Figure 4.24 Predicted speciation of CO2 in 65 wt% DGA at 40 0C. 150 4.8.2 MOR-CO2 system The electrolyte-NRTL parameters and the carbamate equilibrium constant for the MOR-CO2 system were regressed to the VLE and C13 NMR data. The two data sets were simultaneously regressed and the resulting parameters are given in figure 4.25 and Table 4.21. 10 1 This w ork - VLE This wo rk - N MR [P R E D ] [MO R C O O /H CO ] [MO R C OO /H CO ] C O2 [E XP ]/P 10 0 - - 3 PR ED 3 E XP - P C O2 / 10 -1 0 0 .1 0 .2 0.3 0.4 0 .5 CO lo ading, m ol CO /m o l M OR 2 2 0 .6 Figure 4.25 Results of VLE and NMR data regression of the MOR-CO2 system Fixing CO2 solubility to the N2O Analogy. 151 Table 4.21 Non-Default parameters for the NRTL model. Parameter A B 40 Default 8 8 -4 -4 This work ln Kx @ 40oC * = A + B T T ave B ln K = A + T (IH2O,IMORH,IHCO3) 20.1 1.8 - 27204* 10.3 (IH2O,IMORH,IMORCOO) 3.91 0.12 - 39885* -10.5 (IMORH,IHCO3, IH2O) -8.71 0.92 12722* -4.1 (IMORH,IMORCOO, IH2O) -5.41 0.22 -964* -5.8 ln Kx carbamate -24.9 0.61 5141* 1 1 for salt pair / molecule and molecule / salt pair -8.5 Parameters could not be estimated with statistical significance The binary interaction parameters of MOR-H2O and H2O-MOR obtained in the previous section were fixed during the regression of the VLE and C13 NMR data. The regressed value obtained in this work does not deviate far from the default value as can be seen in Table 4.21. This places some confidence in their absolute value. Figure 4.25 compare partial pressure predictions from the current model to the VLE data obtained in this work. Figures 4.26, 4.27, 4.28 and 4.29 give the predicted speciation at 25 0C, 40 0C and 60 0C. 152 10 CO 2 ) 2 4 10 3 */[loading] MOR/mol 2 10 2 CO2 (kPa.mol 40 C 10 1 P 2 0 25 C 10 0 0 0 0.1 0.2 0.3 0.4 CO loading, mol CO /mol MOR 2 2 0.5 Figure 4.26 Results of regression of the equilibrium partial pressure of CO2 in 23.5wt% DGA system. 153 1 MOR Fra ctio n of Tota l M O R MORH + MORCOO - 0 .1 0 0 .1 0 .2 0 .3 0 .4 0.5 Lo ading, m ol C O /m o l M O R 2 0 .6 Figure 4.27 Results of regression of C13 NMR data in MOR-CO2 system at 25 0 C. 1 MOR Fra ction of Tota l M O R MORH + MO R C O O 0 .1 - 0 0 .1 0 .2 0 .3 0 .4 0.5 Lo ading, m ol C O /m o l M OR 2 0 .6 Figure 4.28 Results of regression of C13 NMR data in MOR-CO2 system at 40 0 C. 154 1 MOR Frac tio n of Tota l M OR MORH + MORCOO 0.1 - 0 0 .1 0 .2 0.3 0.4 0 .5 Loa din g, m ol C O /m o l M O R 2 0 .6 Figure 4.29 Results of regression of C13 NMR data in MOR-CO2 system at 60 0 C. 10 -1 MOR MORH + Mole fra ction 10 -2 MO R C O O - HCO 3 10 -3 0 0 .1 0 .2 0 .3 0.4 0.5 CO lo adin g, m ol CO /m o l M O R 2 2 0 .6 Figure 4.30 Predicted speciation of CO2 in 23.5 wt% MOR at 25 0C. 155 4.8.3 MOR-DGA-CO2 system The parameters obtained in the single amine systems (see Tables 4.20 and 4.21) were used in the MOR-DGA-CO2 system. Similarities can be seen in the two amine tau values. Initial model prediction of the VLE and NMR data shows a reasonably good fit. Figure 4.31 shows that the model has done a fairly good job in fitting the data considering no parameters were regressed upon this data. Parameters for the water mixed amine interactions were then regressed to improve the fit. Figure 4.32 shows the improvement in the data fitting. Table 4.22 lists the parameter values that have been used to represent interaction in the DGA-MOR systems. 10 CO2 (PR E D ) P C O2 (EXP )/P 1 T his w ork - C 13 N M R This w ork - V LE 0 .1 0.1 5 0 .2 0.2 5 0 .3 0.3 5 0 .4 0.45 0 .5 Loa din g, m ol CO /m ol A m in e 2 0.55 Figure 4.31 Results of model prediction for VLE and NMR data regression with no parameter adjustments of the DGA-MOR-CO2 system. 156 10 This work - C 13 N MR This w ork - VLE CO2 (PR E D ) P 0 .1 0.15 0 .2 0.2 5 0.3 0.35 0 .4 0.45 0 .5 Loading, m ol C O /m ol Am in e 2 C O2 (E XP )/P 1 0.55 Figure 4.32 Results of VLE and NMR data regression of the DGA-CO2 system. Table 4.22. Non-Default parameters for DGA-MOR mixed amine parameters. Parameter A B 40 Default (IH2O,IMORH,IDGACOO) -4.0 -24095 -12.7 8 (IH2O,IDGAH,IMORCOO) 11.0 -24044 2.3 8 (IMORH,IDGACOO, IH2O) -3.7 -960 -4.0 -4 (IDGAH,IMORCOO, IH2O) -0.81 -1019 -1.2 -4 1 1 for salt pair / molecule and molecule / salt pair = A + B T T ave Figure 4.33 compares partial pressure predictions from the current model to the VLE data obtained in this work. Figures 4.34, 4.35, 4.36 and 4.37 give the predicted speciation at 25 0C, 40 0C and 60 0C. 157 10 CO ) 2 2 4 10 3 */[loading] Amine/mol 2 10 2 0 60 C 10 1 CO2 (kPa.mol 2 40 C 10 0 P 0 25 C 0 10 -1 0.1 0.2 0.3 0.4 0.5 CO Loading, mol CO /mol Amine 2 2 0.6 Figure 4.33 Results of VLE data regression of the 11 wt% MOR/53 wt% DGA system at 60 0C. 158 10 0 M O R H +D G A H + + Frac tion of T otal Am in e D G AC OO - MORCOO 10 -1 MOR+DGA 10 -2 0 0 .2 0 .4 0.6 0 .8 C O lo ading, m ol C O /m ol A m in e 2 2 1 Figure 4.34 Results of regression of C13 NMR data in DGA-MOR-CO2 system at 25 0C. 10 0 M O R H +D G A H Frac tion of T otal Am in e + + M O R C OO 10 -1 - D G AC O O - M O R+ D G A -2 10 0 0 .2 0.4 0 .6 0 .8 C O loading, m ol C O /m ol A m in e 2 2 1 Figure 4.35 Results of regression of C13 NMR data in DGA-MOR-CO2 system at 40 0C. 159 10 0 M O R + DG A M O R H +D G A H + + Frac tion of T otal A m in e DGACOO - 10 -1 MORCOO - 10 -2 0 0 .2 0.4 0 .6 0 .8 C O loading, m ol C O /m ol A m in e 2 2 1 Figure 4.36 Results of regression of C13 NMR data in the 11 wt% MOR/53 wt% DGA system at 60 0C. 0 .2 DGAH 0.1 5 M ole fraction DGA 3 + HCO 0 .1 D G A C OO 0.0 5 MOR - MORCOO MORH + - 0 0 0.2 0 .4 0 .6 0 .8 C O loa din g, m ol C O /m ol Am ine 2 2 1 Figure 4.37 Predicted speciation of CO2 in 11 wt% MOR/53 wt% DGA at 40 0C. 160 4.9 Solvent Working Capacity Figure 4.38 shows the equilibrium CO2 loading of the 65wt% DGA and 11wt% MOR/53 wt% DGA solutions at 25 0C, 40 0C and 60 0C. At Shedgum gas plant, the natural gas stream contains 10.3% CO2 and is contacted with 50 wt% solvent DGA in an absorber at a total pressure of 1500 kPa and 40 to 60 0C. The corresponding CO2 partial pressure is 155 kPa. In order to achieve maximum capacity of each volume of solution circulated, the circulation rate is set so that the maximum recommended loading can be achieved. Typically the maximum loading is represented as an approach to equilibrium set by the VLE data. Assuming that the approach to equilibrium at the bottom of the absorber is 30%, and the equilibrium partial pressure of CO2 under regeneration conditions is 10-3 kPa, the solvent working capacity can then be calculated. As can be seen in figure 4.33 the blend solution shows steeper slope compared to the 65 wt% DGA. The 65 wt% DGA provides the highest equilibrium loading compared to blend mixture. The 11 wt% MOR reduces the working capacity by 11% compared to the 65 wt% DGA working capacity at 60 0C. From solvent capacity point of view, the 65 wt% DGA solution is better than the 11 wt% MOR/53 wt% DGA solution requiring a lower solvent circulation rate. Table 4.23 gives the results of the calculations at 60 0C. Table 4.23 Comparison of working capacities at 60 0C, PCO2, rich = 50 kPa, PCO2,lean = 10-3 kPa . Solvent Lean loading Rich loading Working capacity (mol/mol) (mol/mol) (mol/mol) 65 wt% DGA ~0.01 0.51 0.51 11 wt% MOR/53 ~0.01 0.46 0.45 wt% DGA 161 C O E quilib rium Partial P re ss ure (kP a) 10 10 10 10 10 10 10 3 2 1 0 60 C 0 -1 40 C 0 -2 -3 25 C 0 .2 0 .3 0.4 0.5 C O Loa din g, m ol C O /m ol A m in e 2 2 0 2 0 .1 0 .6 Figure 4.38 CO2 partial pressure as a function of loading for the the 11 wt% MOR/53 wt% DGA system (solid lines) and 65 wt % DGA system (dashed lines) at 25 0C, 40 0C and 60 0C. 4.10 Regeneration Energy Requirements The main source of energy consumption in an amine process is the regeneration step. As much as 80% of the total energy is consumed during solvent regeneration. The total energy required to regenerate a CO2 loaded solvent can be expressed as follows: Total Energy = Heat of Reaction + Sensible Heat + Latent Heat of Vaporization of Water In the regeneration step, first the rich solvent temperature must be raised to the stripper temperature by sensible heat transfer. The amount of heat required for 162 this process is dictated by the specific heat capacity of the solvent, which does not vary much among the various solvents. In addition, the water component of the solvent must also be vaporized to generate the stripping vapor. While the specific heat capacity and the latent heat of vaporization of water remains the same for all solvents, the energy required for this step depends on the proportion of water present in a given solvent. Therefore, the energy required for the vaporization of water in the 65wt% DGA and the 11 wt% MOR/53 wt% DGA (65wt% total Amine) solutions will be the same. Finally, sufficient heat must be provided to break up the CO2-solvent complex formed during the absorption process. This can be accounted for by the heat of reaction. The heat of reaction, + abs , of 65 wt% DGA and 11 wt% MOR/53 wt% DGA solutions was determined at various loadings at 25 0C, 40 0C and 60 0C. Using the Clayperon equation, equation 5.16, the + abs can be calculated. Results are displayed graphically in figure 4.39. For the 65 wt% DGA and 11 wt% MOR/53 wt% DGA, the heat of absorption is about the same. Note that loading has a significant effect on the heat of absorption, increasing the loading decreases the heat of reaction. 163 -20 2 Heat of Absorption, kJ/mol CO -40 -60 -80 -100 -120 25 C -140 0 0.1 0.2 0.3 0.4 CO loading, mol CO /mol Amine 2 2 0 60 C 0 0 40 C 0.5 Figure 4.39 Heats of reaction of CO2 at various CO2 loading for 11 wt% MOR/53 wt% DGA (solid lines) and 65 wt % DGA (dashed lines) at 25 0C, 40 0C, and 60 0 C. As can be seen in figure 4.39, the 65wt% DGA heat of reaction is slightly higher than that of the 11 wt% MOR/53 wt% DGA. As a result more energy must be provided to regenerate DGA than the mixed amine solution. It should be noted that the experiental results in figures 4.7and 4.8 suggest that the heat of reaction in the blend and the 65 wt% DGA are comparable. Based on the heats of reaction, it is clear that 11 wt% MOR/53 wt% DGA solution would have slight less energy requirements than 65wt% DGA. However, the problem is that the mixed amine solution capacity is lower than that of the 164 DGA solution as discussed above in section 4.9. The mass transfer rate of MOR and DGA is the subject of Chapter 5 and 6. 4.11 Solvent Vaporization losses Amine plant losses stem from vaporization, solubility, mechanical, degradation and entrainment. Vaporization losses are a direct result of alkanolamine vapor pressure in the treating solution on the contacted gas stream. Parameters that govern the amount of vaporized amine are temperature, pressure and amine concentration. These parameters establish equilibrium between the amine vapor pressure in solution and the partial pressure of amine in the gas stream. As temperature increases and / or pressure decreases, the amount of gas phase amine increases due to higher vapor pressure exerted by the alkanolamine on the gas. Because treated gas is continuously being replaced by new gas moving up the absorber, additional amine must move into the gas phase via vaporization to maintain equilibrium. Vaporization estimates of MOR in the 11 wt% MOR/53 wt% DGA solutions are presented in figure 4.40. Since total pressures and gas phase compositions vary widely in industrial absorbers, results are presented as the vapor side fugacity of MOR. Since the gas leaving the absorber is in contact with the lean amine solution entering the top of the column, all calculations are done at a lean loading of 0.01. MOR is seen to be very volatile compared to DGA. 165 V apor S ide Equilibrium Fugacity (P a) 10 3 10 2 MOR 10 1 10 0 DG A 10 -1 10 -2 290 300 31 0 32 0 330 Tem p eratu re (K ) 340 35 0 Figure 4.40 Vapor pressure of MOR over 11 wt% MOR/53 wt% DGA, and CO2 loading of 0.01 mol CO2 / mol amine. 4.12 Conclusions 1. Equilibrium partial pressure: The experimental solubility of CO2 and model predictions presented in this work suggest that the 23.5 wt % MOR gives a higher CO2 equilibrium partial pressure compared to the 65 wt% DGA and 11 wt % MOR/53 wt% DGA solutions. In addition, 11 wt%MOR/53 wt% DGA blend shows a higher equilibrium partial pressure of CO2 at high loading by a factor of 5 to 7 than 65 wt% DGA. This is due to the low carbamate stability constant of MOR compared to DGA. Partial pressures at low loading (<0.1) in 166 the blend are, however, seen to be simialr to those in 65 wt% DGA. This is due to the carbamate stability each of of the DGA and MOR. 2. Solvent working capacity: the 65 wt% DGA solution gives ~ 10% higher working capacity compared to the blend solution under the condition studied so far. Therefore, for a given column, the 65 wt% DGA solution will require less solvent circulation rate to achieve the separation compared to the blend solution. 3. MOR losses due to volatility: The volatility of MOR is higher than DGA. MOR vapor pressure is ~ 100 times greater than DGA vapor pressure at 313 K to 333 K. The MOR vaporization losses can be reduced by using a water-wash system. The water wash has a low concentration of MOR and a low MOR vapor pressure. The MOR partial pressure in the gas phase establishes a new equilibrium by forcing MOR into the water phase. 4. Regeneration energy requirements: the 11 wt% MOR/53 wt% DGA solution will probably require less energy to regenerate compared to the 65wt% DGA. 5. NMR has proven to be a useful technique in quantifying speciation. 6. Reaction products at different conditions: The most prevalent reaction product at high loading (>0.5 at high loading) is MOR carbamate. The existence of the protonated DGA have the effect of stabilizing the overall MOR carbamate formation 7. At loading greater than 0.4, free DGA approximately equals free MOR, therefore reaction rates in rich solutions will be dominated by MOR. 8. The carbamate species of MOR is very unstable compared to the carbamate of DGA by a factor 7 to 10 from 27 0C to 60 0C. 167 Chapter 5: Absorption of Carbon Dioxide into Aqueous Diglycolamine 5.1 Introduction The most widely employed gas treating process for acid gas removal in the natural gas and petroleum processing industries is the chemical solvent process, using the various alkanolamines. These processes use a solvent, either an alkanolamine or an alkali-salt (hot carbonate processes) in an aqueous solution, which reacts with the acid gas (H2S and CO2) to form a complex or bond. This complex is subsequently reversed in the regenerator at elevated temperatures and reduced acid gas partial pressures releasing the acid gas and regenerating the solvent for reuse. The alkanolamines most commonly used in industrial applications are monoethanolamine (MEA), diethanolamine (DEA), methyldiethanolamine (MDEA), and diglycolamine (DGA). The use of DGA for the purpose of acid gas removal was patented by Blohm and Riesenfeld (1960) and DGA agent was commercialized in the late sixties by Fluor and Jefferson Chemical company. DGA is a primary amine, and its low vapor pressures permits its use in higher concentrations, typically 50 to 60 weight percent, resulting in significantly lower circulation rates and energy requirements. The equilibrium partial pressure of CO2 over aqueous DGA solutions is significantly lower than that over MEA solutions, which would create more favorable driving force for mass transfer for DGA (Martin et al., 1978). For the reaction of CO2 with primary and secondary amines the zwitterion reaction mechanism, originally proposed by Caplow (1968) and reintroduced by Danckwerts (1979), is generally accepted as the reaction mechanism; 168 k1 CO2 + R2NH k-1 kb R2NH+COO- + B k-b This mechanism comprises two steps: formation of the CO2-amine zwitterion (reaction 1), followed by base-catalyzed deprotonation of this zwitterion (reaction 2). This mechanism leads to the following expression for CO2; R2NCOO- + BH+ (5.2) R2NH+COO(5.1) R CO 2 = k 2 [R 2 NH ][CO 2 ] (5.3) k 1 1+ k b [B] where k b [B] is the contribution to the removal of the proton by all bases present in the solution. For two asymptotic cases Eq. (5.3) can be simplified if, The second term in the denominator is much less than one. This results in simple second order kinetic expression R CO 2 = k 2 [R 2 NH ][CO 2 ] (5.4) The second term in the denominator is much greater than one. This results in the following third order kinetic expression R CO 2 = Although the reaction of CO2 with primary and secondary amines has been studied extensively only limited information is available for the reaction between CO2 and DGA. The reaction kinetics of DGA has been studied by Pacheco (1998), Pacheco et al. (2000), Littel et al. (1991), Alper (1990), and Hikita et al. (1977). In k2 [R 2 NH][CO 2 ] k b [B] (5.5) k 1 169 most cases, there is general agreement as to the order and rate of reaction with respect to DGA in the temperature range of 250C to 400C. However, there is disagreement on the rate data at 600C. Hikita et al. (1977) studied the CO2 kinetics in DGA solutions up to 400C and at very low amine concentrations in a stopped flow reactor. Alper (1990) studied the reaction rate with 0.1 and 0.2 M DGA and at 250C in a stopped flow reactor, and found that his results compared very well with Hikita et al. (1977). Littel et al. (1991) have extended the temperature and the concentration range by studying kinetics up to 600C and over the concentration range of 0 to 5 M in a stirred cell reactor. Littel et al. (1991) found a value of two for the overall reaction order at temperatures below 400C and a higher value at 600C for the overall reaction order, and therefore used the zwitterion mechanism to explain the CO2/DGA kinetics. They concluded that their data showed good agreement with previous authors. Overall it can be concluded that below 400C the kinetics of DGA are well established. Recently, Pacheco (1998) and Pacheco et al. (2000) have studied DGA-CO2 kinetics in a wetted-wall column, and their results are comparable to those of previous investigators at temperatures below 400C; however, the activation energy was found to be higher than previously published values. In this chapter, the work of Pacheco (1998) is reviewed and it has been extended to include more data at 65wt% DGA concentration from 250C to 600C at 0 to 0.4 moles CO2/mole DGA. Unfortunately, it was not possible to evaluate the data of previous researchers because they did not publish the values of the Henry s constant and diffusivity. This work also uses the mass transfer model developed by Bishnoi (2000), based on the eddy diffusivity theory. The use of mass transfer models becomes more important especially at conditions where it is possible to significantly deplete the amine at the gas liquid interface. The rate model depends on the speciation from the VLE model. This has been verified in chapter 4 using C13 NMR measurements. Speciation is critical especially at high loading. The pseudo first order (PFO) and interface pseudo first order (IPFO) approximation 170 models were also compared to the rigorous model. The effect of ionic strength on the second order rate constant was also studied in this chapter. Glycolic acid and potassium formate were used to modify the ionic strength of the DGA solution. 5.2 Experimental Methods The absorption rate of carbon dioxide was determined in a wetted wall column. The use of this apparatus to provide data for CO2 absorption in amine solutions has been described in detail in chapter 4. Solution flowed down the outside of a stainless steel tube that was 9.1 cm long with a contact area of 38.52 cm2. The column operated at 1 to 8 atm with gas rates of 4 to 6 L/min. Loaded amine solution was recirculated at 2 cm3/s from reservoirs of 1L volume. The absorption rate was determined from continuous infrared analysis of the gas leaving the system. The reported CO2 partial pressure is the log mean average of the gas entering and leaving the contactor. The liquid film mass-transfer coefficient was determined by CO2 desorption from water and ethylene glycol mixtures. The gas film coefficient was determined by the absorption of sulfur dioxide into sodium hydroxide solutions (Bishnoi, 2002). 5.3 Physical Properties The Henry s law constant for CO 2 (HCO2) is obtained using the N2O analogy with the solubility of N2O measured by Versteeg and van Swaaij (1988) in 65 wt% DGA solution at 25 0C. H CO 2 = H CO 2, H 2 O H N 2O , H 2 O H N 2 O (5.6) Pacheco (1998) correlated the Henry s Law constant for carbon dioxide in pure water measured by Versteeg and van Swaaij. (1988) and reported by AlGhawas et al. (1989): 171 HoCO2 (atm cm3 / mol) = 1.7107E+07 exp {-1886.1 / T (K)}(5.7) The Henry's constant for N in loaded DGA solutions is given by 2O Danckwerts (1979); H log * = (k ' + k ' + k ')I + g H (5.8) ' ' The parameters k + , k , and k 'g (van-Krevelen coefficients) are specific to the cations, the anions, and the gas, respectively, and are assumed to be ion concentration independent and I i is the partial ionic strength of each ion, given as 1 I i = c i z i2 (5.9) 2 where ci is the ion concentration and zi the ion charge. The superscript * refers to solubility in unloaded solution. ' ' Table 5.1 give the values of k + , k , and k 'g at 25 0C, 40 0C and 60 0C. Table 5.1 Van-Krevelen coefficients at 25 0C, 40 0C and 60 0C. Parameter 25 0C 40 0C 0.043 0.043 k' k k + ' ' g 60 0C 0.043 0.047 -0.016 0.047 -0.019 0.047 -0.026 For applying the model equations, the ionic strength of the solution as a function of the composition must be calculated. The liquid composition can be calculated as a function of the CO2 loading, using the equilibrium model developed in the previous chapter. 172 The diffusivity of CO2 in DGA solutions was estimated using the modified Stokes-Einstein equation to correct the diffusivity of CO2 in pure water for the change in viscosity with the addition of DGA as follows: D CO 2 = D o CO 2 L 0.6 (5.10) o where DCO 2 is the diffusivity of CO2 in pure water, DCO 2 is the diffusivity of CO2 in DGA solutions, 0 is the viscosity of pure water and L is the viscosity of the DGA solution. For diffusivity of CO2 in aqueous DGA solutions, the following equation was obtained from the data reported by Hikita et al. (1981): D DGA = 2.868 10 8 0.449 T L (5.11) where DDGA in cm2/s and T in K. Diffusion coefficients of all ions are arbitrarily set at the same value as DGA. Here, the solution viscosity is calculated using the data by Jefferson (1970). The solution density is also calculated using the data by Jefferson (1970). Viscosity of DGA/glycolic acid and DGA/potassium formate solutions were measured using the Cannon-Fenske procedures for viscosity measurement. A size 150 viscometer was used to measure the viscosity of the DGA/glycolic acid and DGA/potassium formate solutions. 5.4 Model Description 5.4.1 Rigorous model The model developed by Bishnoi (2000), based on the eddy diffusivity theory, was used in this work. The advantage of the eddy diffusivity theory over other theories, like surface renewal and penetration theory, is that it predicts the correct dependence of the mass transfer coefficient on the diffusion coefficient without introducing time as a variable. Glasscock and Rochelle (1989) have shown 173 that the absorption predictions from eddy theory are comparable to surface renewal and penetration theory within 5%. For a second order reaction, Glasscock and Rochelle showed that film theory deviates by 30% at enhancement factors of about 100. For this reason, the eddy diffusivity theory will be used for all rigorous modeling in this work. A full description of the model equations can be found in Bishnoi (2000). For absorption of CO2 into a reactive solvent, Bishnoi used the following expression to represent the material balance equation D i + x 2 [i ] = i (5.12) where i is a component to be included in the model, is the mass transfer coefficient parameter, i is the overall rate of the reaction of species i , and is the derivative operator with respect to the space variable x, where x represents the liquid depth away from the gas-liquid interface. This can be simplified further as (( ) ) 2 [i] = i (5.13) where 2 can be considered the Eddy Diffusivity operator. A proper understanding of the model used in this work begins with a discussion of all species and reactions used. The following two reactions are assumed to be kinetically controlled and reversible CO 2 + OH HCO 3 (5.14) DGA : H 2 O + CO 2 DGACOO + H 3 O + (5.15) For example, the rate of DGA reaction with CO2 is given by: DGACOO H 3 O + [DGA ][CO 2 ] r = k DGA K [ ][ ] (5.16) where k DGA is given by 174 H a 1 1 k DGA = k 25 C . exp R T 298.15 O (5.17) and the equilibrium constant K15 = [DGACOO ][H O ] [DGA][CO2 ] 3 + (5.18) is calculated by the ratio of the species in the bulk solution. The rate constant for reaction 5.14 is the expression presented by Pinsent et al. (1956). The rate constant, kDGA, for reaction 5.15 is fit to match absorption data into loaded and unloaded solutions. Note that water is left out of the kinetic and equilibrium expressions since it is considered to be constant across the boundary layer and, therefore, can be lumped with the apparent rate and equilibrium constants. In order to avoid having H3O+ as a species in the model, rates of reaction for carbamate formation are described as: Kw (5.19) R 15 = k DGA [DGA ][CO 2 ] DGACOO K 15 OH DGACOO H 3 O + + where K w = H 3 O OH and K 15 = [DGA][CO 2 ] [ [ ][ ] ] [ [ ] ][ ] Reactions involving only a proton transfer are always considered to be in equilibrium. All equilibrium constants are calculated directly from the ratio of products and reactants in the bulk solution. The bulk solution is speciated using the electrolyte NRTL model described in chapter 4. These reactions are DGA : H 2 O DGAH + + OH = HCO 3 + OH CO 3 + H 2 O (5.20) (5.21) The equations to be solved are presented in Table 5.2. Along with these seven equations, we define boundary conditions at the interface and in the bulk solution. We use the condition that all concentrations are equal to the equilibrium 175 concentrations as liquid depth approaches infinity. We also assume phase equilibrium of CO2 at the interface leading to a known concentration of CO2 at the interface for a given interfacial partial pressure of CO2. The concentration of species which undergo proton exchange are defined by the combined buffer system flux being zero at the interface and chemical equilibrium between the two species involved in the proton exchange. Electroneutrality is also assumed at the interface. Table 5.2 documents also the boundary conditions used in this work. Table 5.2 Model Equations and Boundary Conditions Conservation Equations at Each Node Overall Species Material Balance 2[DGA] + 2[DGACOO-] + 2[DGAH+] = 0 2[CO2] + 2[HCO3-] + 2[CO3=] + 2[DGACOO-] = 0 Equilibrium Relationships K 20 K 21 [DGAH ][OH ] = + [CO ] = [HCO ][OH ] = 3 3 [DGA] Material Balance for Molecular CO2 2[CO2]-(R1 + R2) = 0 Carbamate Balance 2[DGACOO-] + R2 = 0 Electroneutrality [DGAH+] = [HCO3-] + 2[CO3=] + [OH-] + [DGACOO-] Boundary Conditions At x=0 [CO2]=[CO2]I 176 DHCO3- [HCO3-] + DCO3= [CO3=] = 0 DDGA [DGA] + DDGAH+ [DGAH+] = 0 [DGACOO-] = 0 K[HCO3-][OH-] [CO3=] = 0 K[DGA] [DGAH+][OH-] = 0 [DGAH+] = [HCO3-] + 2[CO3=] + [OH-] + [DGACOO-] At x = [i] = [i]o For all species i in solution 5.4.2 Pseudo first order models The rigorous solution of mass transfer with chemical reaction is more complicated as seen in the last section. It requires the solution of many simultaneous equations. There are certain situations when it is not necessary to deal with a complicated large system of equations, if a few simplifying assumptions are satisfied. Assumptions 1 and 2 listed below lead to the pseudo first order (PFO) and interface pseudo first order (IPFO) approximations. Assumption 1: The liquid phase driving force (PCO2,interface -P*CO2,bulk) is very small. This means that the flux is so small that the PCO2,interface P*CO2,bulk. and that [DGA]interface [DGA]bulk Assumption 2: The reaction of CO2+DGA is fast enough that CO2 reaches equilibrium with the rest of the solution, near the inteface. The IPFO approximation requires assumption 2; the PFO approximation requires assumption 1. In assumption 1 P*CO2,bulk is the partial pressure of CO2 that would be in equilibrium with the bulk composition at the bulk temperature and loading. Small liquid phase driving force means that the DGA is not significantly depleted at the interface and there is no accumulation of reaction products at the interface. This assumption implies that the concentrations of every component in solution, except CO2, can be considered constant in the liquid boundary layer at their bulk values. The assumption of small driving force is relative to the loading; at low loading there is a large amount of free DGA in solution, and a high driving 177 force is necessary to break the validity of the assumption; at high loading there is little free DGA in solution: a very small driving force is required for the PFO assumption to be valid. Assumption 2 (IPFO) implies that all the reaction of CO2 occurs in a small fraction of the boundary layer (that can be called reaction sub-layer), so that the CO2 reaches equilibrium with the rest of the solution before the DGA and the other species in solution change significantly their concentrations from their values at the interface (CO2 reaches an asymptote in this layer). The reaction sub-layer is controlled by the kinetics. In the diffusion region the DGA and the ions diffuse from and to the bulk; the CO2 concentration changes, because it remains at equilibrium with all the other species. Both the IPFO and PFO approximations assume that the concentration profiles of all the species in the reaction sub-layer, except CO2, are constant. The IPFO differs from the PFO approximation in that the profiles are assumed constant at their interface value, different from the bulk value. The advantage of PFO and IPFO models is that the flux of CO2 can be derived from the analytical solution of equation 5.11, when the two following boundary conditions are applied. [CO2] = [CO2]i @ x=0 for PFO and IPFO [CO2] = [CO2]*bulk for PFO or (5.23) [CO2] = [CO2]*i as x , for IPFO The x coordinate goes from the interface into the liquid bulk. The analytical solutions for the CO2 flux are equations 5.23 and 5.24, as shown by Freguia (2002), for PFO and IPFO respectively. In equations 5.23 and 5.24 the CO2+OH- reaction was neglected. (5.22) N CO 2 = k 2,DGA[DGA]bulk D CO 2 (P CO 2 ,i * PCO 2,bulk ) H CO 2 (5.24) 178 N CO 2 = k 2,DGA[DGA]i D CO 2 (P CO 2 ,i * PCO 2,i ) H CO 2 (5.25) P*CO2,i is the partial pressure of CO2 that would be in equilibrium with the composition at the interface. The results are often reported as normalized flux kG , defined by equation 5.26. k' = G (P N CO 2 * PCO 2, bulk CO 2 ,i ) (5.26) It is clear that equation 5.24 can be applied explicitly to calculate the flux, because [DGA]bulk can be calculated with the equilibrium model described in chapter 4. Equation 5.25 presents the problem that the concentration of DGA at the interface, [DGA]int, is not known a priori. Diffusion of reactants and products needs to be accounted for with mass transfer coefficients for those species. The * calculation of [DGA]int and PCO 2,i is performed using the equilibrium model in chapter 5 and knowing also the CO2 loading at the interface, ldg int , which can be calculated using the following equation; where k ,prod is the liquid mass transfer coefficient of the DGA products. Generally; k ,prod =k where D prod is the diffusion coefficient of products and is set at the same value as DGA. It should be noted that the CO2 flux in equation 5.27 is calculated using equation 5.25. In order to make the CO2 flux continuous across the interface, the 179 ldg int = N CO 2 + ldg bulk k ,prod [DGA ]T (5.27) D prod ,CO 2 D CO 2 (5.28) solution for the flux is iterated between equation 5.25 and equation 5.26 until convergence is achieved. The experimental flux can be used as an initial guess in this case. The convergence criterion is that the change in the flux from one iteration to the next is less than 10-5 moles/cm2.sec. The same iterative procedure is also applied when using the rigorous model. 5.5 Results and Discussion The mass transfer rates of CO2 measured in the wetted wall column contactor were interpreted using the rigorous model described above unless otherwise noted. The model was coupled to a Generalized REGression package, GREG (Caracotsios, 1986) to estimate parameter values and confidence intervals. Reaction rate constants and diffusion coefficients of reactants and products were extracted from the experimental measurements. 5.5.1 CO2 reactive absorption into low-loading aqueous DGA solutions Since the reaction rate between CO2 and DGA is very fast, the contribution of the gas-side resistance becomes more important. In order to extract the CO2 kinetics with DGA, the interfacial mass transfer rates of CO2 in 65 wt% DGA were measured near atmospheric pressure. High vapor flow rates, approximately 5 SLPM, were used in order to decrease the contribution of the gas-side resistance. The overall gas phase resistance was 20 to 40% for data collected in this work. Also lower CO2 partial pressures were used to achieve lower CO2 loading and avoid significant deviations from the kinetic controlled regime and pseudo-first order mechanism. At low CO2 loading, the equilibrium partial pressure will approach zero. The enhancement factor will also be much greater than one. Therefore, from equation 5.24 we can see that a plot of the flux versus interfacial partial pressure will yield a straight line. Figure 5.21 shows the results of several temperatures, 180 and partial pressures. The data fits a straight line with a y-intercept of approximately zero as predicted by equation 5.24. Table 5.3 presents a subset of the absorption data in 65 wt% and 25 wt% DGA obtained in this work at zero solution loading. The data analysis of the results of the 25 wt% will be discussed later in this section. The complete sets of the rate data are given in Appendix K. The second order rate constant was extracted by taking the best fit straight line of each series represented in Figure 5.1 and correcting the slope for the diffusion coefficient and Henry s law constant for carbon dioxide. Temperature dependence of the rate constant is shown in Figure 5.2 as an Arrhenius plot. For this system the second order rate constant for the reaction between CO2 and DGA was extracted from the experimental measurements of the interfacial mass transfer rates of CO2. m3 1 E 1 = k 2 (T =298K) exp a k DGA (5.29) kmol.s R T 298K m3 k 2 ( 298K) = 1.8E + 04 kmol.s kJ E a = 49.1 mol 181 2.5 1 0 -6 25 C o o o 2 10 F lu x (m ole s/c m .s) 2 -6 40 C 60 C 1.5 1 0 -6 1 10 -6 5 10 -7 0 300 0 400 0 5000 600 0 P in t (P a) Figure 5.1 Straight line fit for rate of CO2 absorption into aqueous 65 wt% diglycolamine solutions at low solution loading Table 5.3 65 wt% DGA/water and 25 wt% DGA/water subset of the experimental rate measurements at zero loading. Total pressures from 0-28 psig. [DGA]T T POUTCO2 *103 Flux *106 kgo*1010 klo*105 PICO2*103 o C Pa m/s Pa kmol kmol kmol 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 m3 0 1000 200 0 24.5 24.5 24.5 24.6 24.9 40.2 40.9 40.8 41.0 2.5 5.2 8.0 11.0 13.8 2.2 4.6 7.2 10.1 2.7 5.8 8.7 11.1 13.8 3.0 6.4 9.6 12.4 m2s 1.94 1.96 1.98 2.00 2.02 2.07 2.09 2.06 2.04 m 2 Pa s 6.6 6.6 6.6 6.6 6.6 8.9 8.9 8.9 8.9 4.1 8.5 12.8 17.0 21.1 3.9 8.0 12.4 16.8 182 2.5 2.5 2.5 2.5 2.5 2.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 41.1 60.9 61.0 61.2 61.2 61.3 24.1 24.3 24.7 25.2 24.7 40.0 40.4 41.0 41.6 41.7 61.5 60.6 60.3 60.7 60.7 12.9 2.3 4.7 7.4 10.2 12.8 0.7 1.6 2.3 3.1 3.9 0.6 1.4 2.0 2.8 3.5 111 182 138 160 11 15.1 2.5 5.6 8.3 10.5 13.1 1.9 3.1 5.6 6.8 8.4 2.2 4.3 6.8 8.8 10.9 2.69 4.22 3.12 3.73 0.20 2.06 2.28 2.24 2.21 2.23 2.25 7.91 7.95 7.99 8.04 8.07 2.60 2.60 2.60 2.82 2.98 2.89 3.04 2.93 2.99 2.66 8.9 12.2 12.2 12.2 12.2 12.2 2.5 2.5 2.5 2.5 2.5 11.5 11.5 11.5 11.5 11.4 14.4 14.3 14.3 14.3 14.3 20.8 3.5 7.5 11.6 15.3 19.0 0.9 2.0 3.0 4.0 5.0 11 11 11 76 126 63 111 83 96 7 The results were also reinterpreted in terms of the rigorous model to confirm the above results. The data presented in Table 5.3 were used in the parameter estimation using the rigorous model. 183 k (m /km ol.se c) 10 5 3 2 10 4 60 C 0.00 3 0 40 C 0 .003 1 0.0032 -1 1/T (K ) 0 25 C 0.0033 0 .0034 0 0 .002 9 Figure 5.2 Second-order rate constant for the reaction between CO2 and 65wt% DGA using the rigorous model, from data at zero loading. Figure 5.3 is the parity plot for the calculated and measured fluxes of CO2 for the DGA system. For most experiments the measured flux is within 5% of the calculated flux. m3 1 E 1 = k 2( 298K) exp a k DGA R T 298K (5.30) kmol.s m3 k 2(T =298K) = 2.2E+04 kmol.s kJ E a = 48.5 mol 184 Calculated CO Flux (moles/cm sec) 2 10 -6 2 25 C 40 C -7 o o o 10 60 C -7 10 10 2 Measured CO Flux (moles/cm sec) 2 -6 Figure 5.3 Comparison between the experimental and calculated interfacial fluxes of CO2 using the rigorous model for the 65 wt% DGA at zero loading. From equations 5.29 and 5.30, it can be seen that the pseudo first order model yielded results very close to those of the rigorous model. This result is due to the fact that the DGA concentration is not significantly different from that in the bulk solution. It demonstrates that that the pseudo first order approximation applies at these low loading conditions. There is a good agreement between the activation energy for the DGA reaction found in this work and those reported by other researchers. Pacheco et al (2000) obtained larger activation energy of 66.1 kJ/mol compared to other researchers. 185 However, the rate constant in this work is approximately four times larger than the rate constants reported by other researchers as can be seen in Table 5.4. There are two possible explanations for this obseravation. In the first case, the DGA reaction with CO2 follows the zwitterions mechanism and in this case DGA catalyzes itself and therefore leads to this high value of the rate constant. In the second case, with 65 wt% DGA the wetted-wall column is operated at high vapor flow rates compared to lower DGA concentrations. It was found that, as the flow rate increased from that used at lower DGA concentrations, the film surface towards the bottom part of the column, when the gas first contacts the falling liquid, becomes less stable. This might have the effect of inducing turbulence in the gas layer close to the interface and thereby enhancing the rate of mass transfer. In order to understand the DGA concentration effect on mass transfer, the absorption rate of CO2 into 25wt% DGA was investigated since lower vapor flow rates can be used. Figure 5.4 shows the temperature dependence of the rate constant. There is an excellent agreement between the rate constants for the 25wt% DGA reaction and those reported by other researchers. For this system the second order rate constant is given by: m3 Ea k2 kmol.s = k 2 ( 298K ) exp R m3 k 2(T =298K) = 6.66E + 03 kmol.s kJ E a = 40.1 mol 1 1 (5.31) T 298K 186 10 5 k (m /km ol.se c) 10 4 3 2 100 0 0.0029 60 C 0.00 3 0 40 C 0 25 C 0 0 .003 1 0 .003 2 0.0033 0 .0034 -1 1 /T (K ) Figure 5.4 Second-order rate constant for the reaction between CO2 and 25wt% DGA. The results of this work and other researchers are presented in Table 5.4. Table 5.4 Reference Kinetic data for DGA Temp. (range) K 278-313 298 278-298 298-318 298-333 298-313 298-333 DGA mol/L k298 K m3/(kmole.s) 5923 4480 4517 3990 5080 6663 22947 Eact kJ/mole 40.7 39.4 44.3 66.1 40.1 49.1 Experimental technique Stopped Flow Hikita et al (1977b) Barth et al., 1986 Alper (1990) Little et al. (1992) Pacheco et al. (2000) This work 0.0150.032 0-0.050 0.1,0.2 0.1-3 2.4-4.8 2.4 6.2 Stopped Flow Stirred Cell Wetted wall column Wetted wall column 187 Figure 5.5 shows also the comparison between the results of the 25wt% DGA and the 65wt% DGA in this work and other investigators. 10 6 k (m /k m ol.se c) 10 5 3 10 2 4 H ikita et al., 1977 II Ba rth et al., 19 86 Alper, 199 0 Littel et a l., 1 992 III Pa checo et a l., 20 00 Th is work - 65 wt% D G A Th is work - 25 wt% D G A 100 0 0.003 0.00308 0.0031 6 0.0032 4 0.0033 2 0.0034 -1 1 /T (K ) Figure 5.5 Second-order rate constant for the reaction between CO2 and DGA at zero loading. The above relation (6.30) for 25 wt% DGA is valid only up to 40 0C. For the 65wt% DGA the relation is valid from 25 0C to 60 0C. The data of Pacheco (1998) at low loading for 50 wt% DGA was also analyzed and the results are presented in Figure 5.6. The activation energy obtained in the 50 wt% is approximately 49.1 kJ/mol; however, the rate constant is approximately two times 188 greater than than previously published values. We can comment that increasing the DGA concentration increases the rate consant as seen in the 65wt% DGA and the 50 wt% DGA. An almost perfect line can be obtained if we exclude the data at 60 0 C for 25 wt% DGA. The activation energy is calculated to be roughly 40.1 kJ/mol. However, the activation energy will be much smaller for 25 wt% DGA if the data set at 60 0C were included. 65w t% D G A - This work 50wt% D G A - Pacheco (1998) 25w t% D G A - This work k (m /km ole.se c) 10 5 3 2 10 4 60 C 0.0030 6 0 40 C 0.0031 5 1 /T(K) 0.0032 4 0 25 C 0.00333 0 Figure 5.6 Second-order rate constant for the reaction between CO2 and DGA. In order to confirm the above results, we choose to plot it in trems of the raw rate data since the above analysis could change for different values of diffusivity and Hery s constants. The results with 65 wt% DGA and 25 wt% DGA at low CO2 loading are compared to results with 50 wt% DGA by Pacheco et al. 189 (2000) in figure 5.7. The three data sets were plotted in terms of the normalized flux, kG , defined as the ratio of CO 2 flux to the partial pressure difference of the CO2 at the interface and the CO2 in the bulk solution. At zero loading, the partial pressure of CO2 in the bulk solution is zero; therefore, the normalized flux is the ratio of CO2 flux to the partial pressure of the CO2 at the interface. As can be seen in figure 5.7 and 5.8, kG varies less than k 2 with DGA concentration since kG is proportional to the square root of k2. 10 -9 T his work - 65 wt% D G A Pa checo et al.- 50 wt% D G A T his work - 25 wt% D G A ' k 10 -10 G (m ole /Pa.c m .s) 20 2 30 40 T, C o 50 60 70 Figure 5.7 Comparison between the data obtained in this work for the 65 wt% and 25 wt% DGA solution and Pacheco et al., (2000) for the 50 wt% DGA solution at low loading. 190 It is clear that as the DGA concentration increases the rate increases. We are tempted by the fact that second order rate constant is a function of the DGA concentration. Although it was mentioned at the beginning of this section that instability of the film close to the bottom of the column could enhance mass transfer rates, the fact that the 50 wt% gave us a two order of magnitude higher than previusely published values makes us believe that DGA concentration affects the normalized flux and second order rate constant in the same way as the 65 wt% does. With 65wt% DGA, with an increase in temperature an increase in the rate constant is observed, following the classical Arrhenius behavior. However, for the 25wt% DGA and at temperatures below 400C an Arrhenius behavior is obtained. Above 40 0C the rate constant curve shows a clear break from the Arrhenius trend, essentially showing no activation energy for the reaction. These deviations from Arrhenius behavior may be explained in terms of reaction kinetics. Two limiting cases for the zwitterion mechanism can be seen for the 25wt% DGA solution; For the 25 wt% DGA and above 40 0C, the zwitterion formation reaction is rate-limiting and the reaction rate appears to be first-order in both the amine and carbon dioxide concentrations. Increasing the temperature increases reversibility of reaction 5.1 by increasing the rate constant of the reverse reaction. In addition, at high temperatures; k -1 >> {k DGA [DGA] + k H 2O [H 2 O] + k OH [OH - ]} for the 25 wt% DGA - solution and k -1 << {k DGA [DGA] + k H 2 O [H 2 O] + k OH [OH - ]} for the 65 - wt% DGA. However, below 40 0C the zwitterion deprotonation reactions are rate limiting, the overall reaction rate appears to be second order in the amine concentration. Therefore, we get the following; 191 k -1 << {k DGA [DGA] + k H 2 O [H 2 O] + k OH [OH - ]} for the 25 wt% DGA and - the 65 wt% DGA. The activation energy and pre-exponential factor were obtained with a fit to only the data points taken at 25 0C and 40 0C. 5.5.2 CO2 reactive absorption into partially loaded aqueous DGA solutions The rate data presented in this work is unique in that it is obtained with variation of loading instead of a zero loading like much of the other data presented in table 5.2. The quality of the rate data was analyzed for three important error parameters: gas film resistance, approach to equilibrium; and percent removal of CO2 (Dang, 2001). Gas film resistance determines the error of the interfacial partial pressure. If it is higher than 70%, the error calculated in the interfacial partial pressure may be more than 30%. The approach to equilibrium determines the error into kG . Rate data measured far away from equilibrium introduce s less possible error of the kG . The percent removal of CO 2 indicates the error of measured flux. The more percent CO2 removal is, the less error of the measured flux. The detailed data and error analysis are in Appendix X. The data included in the analysis in this section had less than 50% gas film resistance, 20% to 50% CO2 removal and 0 to 0.5 approach to equilibrium. The rigorous, PFO and IPFO models were used to extract the second order rate constant from the rate data in loaded solutions. The regressions were done for each temperature instead of for all temperatures simultaneously. Figures 5.8, 5.9 and 5.10 show the second order rate constant as a function of CO2 loading at 25 0 C, 40 0C, and 60 0C respectively. As can be seen the second rate constant increases with increase in CO2 loading for all three temperatures. 192 10 8 P FO m ode l R igorous m odel IPF O m odel k (m /k m ol.se c) 10 7 10 6 3 2 10 5 10 4 0 0.0 5 0 .1 0.15 0 .2 0.2 5 0.3 0.3 5 C O loadin g, m ol CO /m ol D G A 2 2 0 .4 Figure 5.8 Second-order rate constant for the reaction between CO2 and 65 wt% DGA.at 25 0C. 10 8 10 k (m /k m ol.se c) 7 10 6 3 10 5 2 10 4 P F O mod el R ig oro us m odel IP F O mo del 100 0 0 0.0 5 0 .1 0.1 5 0 .2 0.25 0.3 0.3 5 C O lo adin g, m ol C O /m ol D G A 2 2 0 .4 Figure 5.9 Second-order rate constant for the reaction between CO2 and 65 wt% DGA.at 40 0C. 193 10 7 k (m /km ol.se c) 10 6 3 10 2 5 P FO model R igorous model IP F O model 10 4 0 0.05 0.1 0.1 5 0 .2 0.2 5 0 .3 C O loadin g, m ol C O /m ol DG A 2 2 0.35 Figure 5.10 Second-order rate constant for the reaction between CO2 and 65 wt% DGA.at 60 0C. The interesting result of the comparison of the three models is that the IPFO model matches very well the rigorous model. The knowledge of good values for the DGA diffusivities would allow the use of the IPFO model, which has the advantage of converging faster than the rigorous integration. It can be seen also that the PFO model follows the rigorous model well at low loading, as expected, whereas it underestimates rate constant at loading greater than 0.25. At low CO2 loading the reaction rate with CO2 is not instantaneous but fast enough for most of the reaction to occur in the boundary layer. The PFO model is valid at these conditions when the DGA concentration at the gas liquid interface is not significantly different from that in the bulk solution. At high CO2 loading, the 194 DGA can be depleted at the gas liquid interface and therefore the PFO model no longer applies. Under these conditions, it is necessary to correct for the diffusion of the DGA and DGA products. The rigorous model and IPFO models account for this correction but the PFO corrects only for the diffusion of CO2 and not for the DGA and DGA products such as bicarbonate, free DGA, and DGA carbamate. The deviation between the rigorous model, IPFO model and the PFO model is even seen more pronounced at 60 0C. This is related to the slope of the equilibrium curve that is increasing as the temperature increases, and therefore the deviation between the total concentration of the DGA at the interface and in the bulk solution increases. Figures 5.11 and 5.12 show concentration profiles of species in the 65 wt% DGA at 313K and at loadings of 0.101 and 0.385, respectively generated using the rigorous model. These two points are in Figure 5.9. In Figure 5.10, it is easy to see that pseudo first order is a good approximation. There is not much depletion of DGA at the interface and there is still enough DGA around (about 15% depletion). This 15% depletion in the DGA concentration can be important if equilibrium matters. In the case of DGA, equilibrium is not important at such conditions. It is clear that both the DGA carbamate and protonated DGA are diffusing away from the interface since their concentration are decreasing in the direction of the bulk solution. This makes them appear as reaction products. On the other hand, Figure 6.12 shows that there is a significant amount of depletion of DGA at the interface at higher loadings (about 67% depletion). Under these conditions, the PFO does not apply. 195 6 5 C o ncentration (m ol/L) 4 3 2 1 0 0 0.2 0.4 0 .6 0 .8 D im ension Dista nce from Interface 1 DG A DG AH+ DGACOO- Figure 5.11 Concentration gradients for absorption of carbon dioxide into 65 wt% DGA. Loading=0.115, kol=2.79E-3 m/s, Pi/P*=392.0, T=313K. 3.5 3 C o ncentration (m ol/L) 2.5 2 1.5 1 0.5 0 0 0 .2 0.4 0 .6 0 .8 D im ension D ista nce from Interface 1 DGA DGAH+ DGACOO- Figure 5.12 Concentration gradients for absorption of carbon dioxide into 65 wt% DGA. Loading=0.385, kol=2.45E-3 m/s, Pi/P*=28.5, T=313K. 196 The reaction rate at high CO2 loading and high temperature becomes instantaneous. An analysis was done to estimate the relative importance of the kinetic term to the total reaction rate. The approximation is good if the fraction of the kinetic term is close to 1 and the instantaneous term is close to 0. As explained in the model development section, the IPFO approximation divides the boundary layer into two regions, one controlled by reaction rates and one controlled by diffusion of reactants and products. The liquid phase mass transfer resistance is determined by the resistances of the two regions in series. R liquid = R IPFO + R inst (5.31) RIPFO is the resistance of the reaction sub-layer, Rinst is the resistance of the diffusion region, where the reactions are instantaneous. Equation 5.31 can be written in the following form in terms of normalized flux kgI; 1 1 1 = I + I I k g k g ,IPFO k g ,inst The IPFO (kinetic controlled) term is given by equation 5.33. I k g,IPFO = (5.32) k 2[DGA]i D CO 2 H CO 2 (5.33) The instantaneous coefficient can be calculated using equation 5.34, derived in Dang (2001), and valid for small driving forces. I k g ,inst = 1 * PCO 2 [CO 2 ]* k 0, prod l (5.34) The instantaneous coefficient depends on the partial derivative of the equilibrium partial pressure with respect to the CO2 total concentration. It also depends on the physical mass transfer coefficient of the reaction products and 197 DGA, kl,0prod. The derivative was obtained using the Electrolyte-NRTL model described in chapter 5; kl,0prod was obtained using equation 5.27. The error introduced by extracting the second order rate constant from the rate data at high loading can be estimated by calculating the fractional resistance of the kinetic term. I kg I k g,kinetic fraction kinetic = (5.35) Table 5.5 shows the result of the analysis, done for 25 0C, 40 0C and 60 0C. At low loading for the three temperatures the instantaneous resistance is always negligible. At high loading it accounts for 5-15% of the total resistance. These results place some confidence on the value of the rate constant estimated. Table 5.5 Analysis of importance of the kinetics at low and high loadings for 25 0 C, 40 0C and 60 0C. T (0K) Loading 1/kgI,IPFO 1/kgI,inst Fraction 2 2 molCO2/mol cm s atm/mol cm s atm/mol Kinetic DGA 298.1 0.078 4.39E+04 1.27E+01 0.999 312.4 0.101 4.66E+04 1.26E+02 0.997 332.2 0.100 2.06E+04 9.23E+02 0.957 298.1 0.390 2.52E+05 1.13E+04 0.957 312.3 0.385 1.06E+05 1.61E+04 0.868 332.9 0.257 3.14E+04 3.57E+03 0.898 Figure 5.13 shows the sensitivity of the second order rate constant and the diffusion of products and reactants to the flux predicted by the rigorous model with 65 wt% DGA at 313K. 198 0.5 k 0.4 dln (CO Flux)/dln (i) 2 0.3 2 0.2 0.1 D DGA ,D ion 0 0 0.0 5 0 .1 0.15 0.2 0.2 5 0.3 0.3 5 CO loa ding, m ol C O /m ol DG A 2 2 0 .4 Figure 5.13 Sensitivity of calculated CO2 flux to values of the diffusion coefficients of reactants and products and second order rate constant. 313 K, kol=2.74E-3 m/s, Pi=10P*. The results can be divided into two regions. The first region is where the CO2 loading is less than 0.10 (low loading). The second region is where the CO2 loading is greater than 0.10 (high loading). At low loading (region 1), the rate constant of DGA and the diffusion of reactants and products is least sensitive. As the loading increases and the concentration of DGA drops, the rate constant of DGA and the diffusion coefficient of reactants and products becomes most sensitive (region 2). This shows that the removal of reaction products and the diffusion of DGA to the interface have become important phenomena at high 199 loading. The conclusion that can be drawn from this section is that the rate data at high CO2 loading contains a source of error, that tends to overpredict the second order rate constant, since part of the resistance is neglected. This problem becomes more important as the CO2 loading and temperature increases. Due to the importance of the diffusion of reactants and products at high CO2 loading, the parameters Dion and DDGA were regressed from the experimental data along with the second order rate constant. The second order rate constant was regressed as a function of loading and temperature as seen from Figures 5.8, 5.9 and 5.10: ln k 2 = A + B*ldg + C/T (5.36) where A, B and C are the fitting parameters, ldg is the CO2 loading in mol CO2 per mol DGA. The experimental data chosen to study the effect of loading on the second rate constant are shown in Appendix K. A limited set of data was regressed to minimize the computation time using the rigorous model. This work used 38 nodes with small spacing to achieve the desired accuracy. No attempt was made, however to reduce the number of nodes. A decrease in the number of nodes used will significantly reduce the number of equations to be solved and will decrease computation time. The values of the diffusion coefficients of the reactants and products used in the initial guess are those obtained by Pacheco (1998). We regressed theses values using the same temperature and viscosity dependence as obtained by Pacheco (1998). The following equation for the diffusion of reactants and products were used in the regression: D DGA = 2.845E 8* * 0.5752 (cP)T(K) D p,r = 2.845E 8* * 0.5752 (cP)T(K) (5.37) (5.38) 200 Table 5.6 presents the regressed values and confidence intervals obtained during the regression of DDGA, Dp,r, and k2. Figure 5.14 shows the effect of CO2 loading and temperature on the rate constant. Table 5.6 Results for the regression of DDGA, Dp,r and k2. Parameter Value A 0.30E+02 0.71E+01 B 0.42E+01 1.51E+00 C -0.61E+04 1.60E+03 0.75E+00 0.31E+00 10 7 0 0 0 25 C 40 C 60 C 10 6 k (m /km ol.se c) 3 10 5 2 10 4 0 0.0 5 0 .1 0.1 5 0 .2 0.25 0.3 0.3 5 CO lo ading, m ol CO /m ol D G A 2 2 0 .4 Figure 5.14 Effect of CO2 loading on the second rate constant at 25 0C, 40 0C and 60 0C for the system DGA- water-CO2. Lines are model predictions. 201 The small confidence interval of the regressed Dpr and DDGA places some confidence on the estimated values of the second order rate constant. The results in Figure 5.14 show that k2 is indeed increasing with CO2 loading since the effects of the diffusion of reactants and products are taking into account during the regression of k2. The data in Figures 5.8, 5.9 and 5.10 were included for comparison since most of the data were not included during regression. Figure 5.15 is the parity plot for the calculated and measured fluxes of CO2 for the DGA system at various CO2 loadings and three temperatures. For most experiments the measured flux is within 15% of the calculated flux. C alculated CO Flux (m oles/cm sec) 3.5 10 3 10 2.5 10 2 10 1.5 10 1 10 5 10 -6 -6 25C 40C 60C 2 -6 -6 -6 2 -6 -7 0 0 5 1 0 1 10 1.5 10 2 1 0 2.5 10 3 10 3.5 10 2 Measured C O Flux m oles/cm sec) 2 -7 -6 -6 -6 -6 -6 -6 Figure 5.15 Comparison between the measured and calculated interfacial fluxes of CO2 for the 65 wt% DGA at various CO2 loading. 202 We might also choose to express the rate of reaction in terms of activity. Usually, activity is defined as effective concentration of species. The true rate expression is a function of activity rather than concentration. The activity of a species, aA, is defined as the product of its molar concentration, [A], and a solution GHSHQGHQW DFWLYLW\ FRHIILFLHQW A (gamma) which is dimensionless; aA A [A] (5.39) The activity coefficients vary with ionic strength such that substitution of aA for [A] in any equilibrium constant expression frees the numerical value of the constant from dependence on the ionic strength. In low loading solutions, where the ionic strength is minimal, this effectiveness becomes constant, and the activity coefficient is unity. Under such circumstances, the activity and the molar concentration of the species are identical. For most purposes, the error introduced by the assumption of unity for the activity coefficient is not large enough to lead to false conclusions. However the disregard of activity coefficients may introduce numerical error in calculations; therefore the above results for the 65 wt% DGA, were reinterpreted using activity instead of concentrations. The equilibrium model in chapter 5 was used to calculate the activity coefficients of CO2 and DGA in the 65 wt% DGA.The results of the activity coefficients in the 50 wt% DGA and 25 wt% DGA are also included. Figures 5.16, 5.17 and 5.18 show the activity coefficients at 40 0C for the 25 wt% DGA, 50 wt% DGA and 65 wt% DGA solutions. 203 5 4 A ctivity coefficient DGACOO - 3 DGAH + 2 CO 1 DG A 0 0 0 .1 2 2 H CO 0 .2 3 0.3 2 0.4 0 .5 CO loading, m ol CO /m ol D G A Figure 5.16 Predicted activity coefficients for 65 wt% DGA at 313K 3 2 .5 A ctivity coeffic ient 2 1 .5 1 H CO 0 .5 0 0 0 .1 0 .2 0.3 0.4 CO loading, m ol CO /m ol D G A 2 2 3 DGACOO D GA H + - CO 2 DGA 0 .5 Figure 5.17 Predicted activity coefficients for 50 wt% DGA at 313K 204 1.4 1.2 A ctivity coeffic ient 1 D GA H 0.8 0.6 0.4 0.2 0 0 0 .1 0 .2 0.3 0.4 CO loa din g, m ol CO /m ol D G A 2 2 D G A C OO - CO + 2 H CO 3 DGA 0 .5 Figure 5.18 Predicted activity coefficients for 25 wt% DGA at 313K As can be seen in figures 5.16-5.18, the activity coefficients of the ions depart farther from unity as CO2 loading increases. From Equation 5.1and 5.2, we can write RCO2 as; R CO2 = k b [DGAH+ COO ] where K eq = a DGAH + COO a DGA a CO2 = DGAH + COO [DGAH+ COO ] DGA CO2 [DGA][CO2 ] Therefore, R CO2 = k b K eq [DGA][CO2 ] DGA CO2 DGAH + COO 205 The rate based activity constant can be written as a function of CO2 loading as follows; DGA CO2 DGAH + COO loaded DGA CO2 DGAH + COO unloaded k A = k ldg = 0 (5.40) It should be noted that the CO2 activity coefficient is calculated using the nitrous oxide analogy noted in section 5.3. Figure 5.19 shows the activity based rate constant at various loadings at 40 0C using the model fit in figure 5.14. The results in figure 5.14 are also included. 206 P red iction from activitie s, Eq 5.40 5 R egressed data, Eq 5.36 2 10 k (m /k m ol.se c) 1 04 9 10 4 8 10 4 7 10 6 10 5 10 4 10 4 4 4 5 3 2 0 0 .1 0 .2 0 .3 C O loading, m ol C O /m ol D G A 2 2 0 .4 Figure 5.19 Effect of CO2 loading on the second rate constant calculated based on concentration and on activity at 40 0C for the system DGA- water-CO2. Lines are model predictions. It can be seen that the concentration based rate constant calculated using Equation 5.40 shows a factor of 4 increase in k2 compared to the second order rate constant regressed from the kinetic data. Figures 5.20 through 5.23 show the model prediction of the normalized flux for the 65 wt% DGA solution at 40 0C. Low driving force (1.01P*CO2) is considered as well as high driving force (10P*CO2). Rate decreases as the loading increases; this is evident from the shape of the kG -loading plot. This is to be expected since the rate of the reaction depends on the concentration of the free DGA at the gas-liquid interface. Thus, increasing the CO2 loading, the 207 concentration of the reactive DGA at the interface decreases; and hence the reaction rate decreases. 3.5 1 0 3 10 (m ol/P a.cm .sec ) 2.5 1 0 2 10 1.5 1 0 1 10 5 10 -10 -10 P C O 2,i =1.01*P * CO 2,b -10 2 P -10 C O 2,i = 10*P * CO 2,b -10 ' k G -10 -11 0 0.0 5 0 .1 0.1 5 0 .2 0.25 0.3 0.3 5 C O lo ading, m ol CO /m ol D G A 2 2 0 .4 Figure. 5.20 Normalized flux of 65wt% DGA and CO2 at low and high driving force at 313K. 208 2 10 2 10 (m ol/P a.cm .sec ) 2 10 2 10 2 10 1 10 1 10 -10 -10 -10 2 -10 P C O 2,i = 10*P * CO 2,b -10 ' k G -10 P C O 2,i = 1.01*P * C O 2,b -10 0 50 10 0 150 P 20 0 * 25 0 300 35 0 40 0 CO2 (P a) Figure. 5.21 Normalized flux of 65wt% DGA and CO2 at low and high driving force at 298K. 4 10 3 10 (m ol/P a.c m .sec ) 2 10 2 10 2 10 1 10 5 10 -10 -10 -10 P C O 2,i =10*P * CO 2,b 2 -10 -10 P -10 C O 2,i =1.01*P k G * CO 2,b ' -11 0 20 0 40 0 P CO2 600 800 * (Pa) 1000 120 0 Figure. 5.22 Normalized flux of 65wt% DGA and CO2 at low and high driving force at 313K. 209 10 -9 (m ol/Pa.cm .sec ) P 10 -10 ' 2 CO 2,i = 10*P * CO 2 ,b k G P CO 2,i =1.01*P * CO 2,b 10 -11 0 100 0 200 0 P * CO 2 300 0 (P a) 4000 500 0 Figure. 5.23 Normalized flux of 65wt% DGA and CO2 at low and high driving force at 333K. 5.5.3 The influence of ionic strength on the rate constant for the reaction of diglycolamine and CO2 When CO2 is absorbed into aqueous solutions, including alkanolamines, it combines with water and dissociates into positive and negative ions. Depending on the components in the solutions, different species may end up carrying the positive and negative charges (typically protonated amines and negatively charged carbamates, bicarbonates in DGA solutions). Usually, in such solutions, ionic strength is an important parameter, because each ion is surrounded by an extended solvation shell, which can affect ionic activities and rate constants. Davies (1963) pointed out that ion association can modify the reaction in two ways: firstly, ion pair formation affects the total ionic strength of the medium; secondly, one (or 210 more) such ion pairs may be involved in the rate-determining step, thus altering the charge of the activated complex and reaction rate. In accordance with the zwitterion mechanism, R2NH+COO- is proposed as the intermediate complex in the rate-determining step. Although the role of ionic strength in reactions of neutral species has been known for some time, the magnitude of the effect has generally been thought to be far less than the effect of ionic strength on reactions of ions. Essentially, this effect arises from the second term in the expanded Debye-H ckel relationship for the activity coefficient, which leads to the following expression for the rate constant at any ionic strength: log k = log k o zazbA 1 + Ba + C (5.41) where ko is the rate constant at zero ionic strength, is the ionic strength, A and B are collections of physical constants, a is the distance of closest approach, and C is an unknown constant. The other two parameters, za and zb, are the charges on the reactants thus, when za or zb = 0: log k = log k o + C (5.42) and the logarithm of the rate constant is expected to show a linear dependence on the ionic strength. Although the parameters A and B can be calculated, and a estimated, there is no reliable method of calculating C, which must be determined by experiment. Kinetic studies on many different ion-ion reactions have demonstrated that for low to moderate ionic strengths, < 0.1 mol L-1, the rate constant is proportional to , indicating that A C. In the last section, it was shown that the second order rate constant is increasing with CO2 loading or ionic strength. The results in the previous section were reinterpreted in terms of equation 5.42. Figure 5.24 shows the second order 211 rate constant presented in Figure 5.14 as a function of ionic strength. Table 5.7 shows the values of k0 and C constant for the three temperatures. 10 6 60 C k (m /km o l.cm .sec) 0 40 C 10 5 0 2 25 C 0 3 2 10 4 0 0 .5 1 1 .5 Ionic strength (m ol/L) 2 2 .5 Figure 5.24 Effect of ionic strength on the second rate constant at 25 0C, 40 0C and 60 0C for the system DGA- water-CO2 Table 5.7 Results for the fit of k2 as a function of . Temperature, 0C ko C 3 2 6 (m /kmol.cm .sec) (m /kmol2.cm2.sec) 25 1.73E+04 0.674 40 5.00E+04 0.674 60 1.51E+05 0.674 R2 0.9991 0.9991 0.9991 212 To test the hypothesis that the rate constant is increasing with the ionic strength, glycolic acid was added to 65 wt% DGA solution in order to quantify the effect of ionic strength on the reaction rate constant. All of the studied solutions had a concentration of 65wt% DGA in water and zero CO2 loading. Note that the glycolic acid will react to from DGAH+ glycolate-. The first experiment was performed with no glycolic acid to establish the base case. For the rest of the experiments, glycolic acid was added to give 0.1, 0.2, 0.3, 0.4 moles glycolic acid/mole DGA. The data sets are given in Table 5.8. Figure 5.25 shows the normalized flux data at 40 0C. As can be seen in Figure 5.25, increasing glycolic acid concentration decreases the normalized flux. This is to be expected since the rate of the reaction depends on the concentration of the free DGA at the gas-liquid interface. Thus, increasing the acid concentration, the concentration of the reactive DGA decreases; and hence the reaction rate decreases. The data presented above have been obtained at conditions that greatly simplify the mathematical treatment of the problem. The most significant simplification arises from the pseudo-first-order assumption (PFO) for kinetics. Eq. (5.24) has been used to extract the second order rate constant of DGA/glycolic acid with carbon dioxide. Figure 5.26 shows the second order rate constant for the system DGA-Glycolic acid-CO2-water at 40 0C. 213 Table 5.8 65wt%DGA/water-glycolic acid experimental rate measurements at zero loading. Total pressures from 15-42 psig Glycolic T POUTCO2 *103 Flux *106 kgo*109 klo*105 PICO2*103 o acid/DGA C Pa m/s Pa kmol kmol mol mol 0 0 0 0 0 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 m2s m 2 Pa s 39.5 39.9 39.9 39.9 39.8 39.6 39.7 39.7 39.8 39.6 40.4 40.3 40.0 39.8 39.8 39.2 39.8 39.6 39.9 40.1 39.2 39.7 39.6 39.7 39.7 0.84 1.67 2.54 3.59 4.67 0.98 1.99 3.00 4.15 5.31 1.12 2.28 3.45 4.76 6.08 1.30 2.57 4.06 5.45 6.91 1.60 3.20 4.85 6.70 8.40 2.49 5.72 8.71 11.3 14.1 2.50 5.58 8.61 11.3 13.9 2.50 5.58 8.61 11.3 13.9 2.15 5.31 8.01 10.7 13.1 2.56 5.84 8.95 11.5 14.3 5.50 5.53 5.56 5.40 5.25 4.69 4.71 4.73 4.69 4.64 4.09 4.11 4.13 4.09 4.06 3.79 3.77 3.66 3.67 3.69 2.84 2.86 2.87 2.88 2.90 4.39 4.39 4.39 4.39 4.39 3.95 3.95 3.95 3.95 3.95 3.42 3.42 3.42 3.42 3.42 2.89 2.89 2.89 2.89 2.89 2.61 2.61 2.61 2.61 2.61 1.29 2.71 4.10 5.67 7.31 1.52 3.18 4.82 6.53 8.27 1.74 3.65 5.53 7.48 9.46 1.88 3.98 6.25 8.34 10.4 2.51 5.26 7.97 10.6 13.3 214 (m ole/atm .cm .s) 4 10 -5 2 3 10 -5 ' k G 2 10 -5 0 0 .1 0 .2 0 .3 0.4 0 .5 Moles glycolic acid/m ole D G A Figure 5.25 Normalized flux of 65wt% DGA and glycolic acid solvent at 40 0C. k (m /k m ol.se c) 3 10 9 10 8 10 7 10 5 4 4 4 2 0 0 .1 0 .2 0 .3 0.4 M oles glyco lic acid/m ol D G A 0 .5 Figure 5.26 Effect of glycolic acid on the second rate constant at 40 0C for the system DGA- water-CO2 215 The Henry s constants were determined using the N 2O solubility apparatus and the N2O analogy. The viscosity of the above mentioned solutions were also measured using the Cannon-Fenske viscometer. The measured values of the Henry s constant and viscosities used in the calculation of the second order rate constant are given in Table 5.9. Table 5.9 Measured values of Henry s con stants and viscosities in glycolic acidDGA solutions at 40 0C Solution HCO2, , cP 3 -1 atm.cm /mol 0.1 glycolic 45000 8.5 acid/mol DGA 0.2 glycolic 50000 11.7 acid/mol DGA 0.3 glycolic 54000 16.7 acid/mol DGA 0.4 glycolic 60000 20.5 acid/mol DGA It is interesting to see that increasing the glycolic acid concentration increases the second order rate constant. The rate constant increases by a factor of 2 from 0 to 0.4 moles glycolic acid per mol DGA. We also carried out systematic experiments at ionic strengths up to 3 M by adding potassium formate to 65wt% DGA solutions at zero loading. Table 5.10 summarizes the results. The results with no potassium formate added are included here for comparison. 216 Table 5.10 65 wt%DGA/water- potassium formate subset of the experimental rate measurements. Total pressures from 10-18 psig Potassium T POUTCO2 *103 Flux *106 kgo*109 klo*105 PICO2*103 o formate C Pa m/s Pa kmol kmol 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 kmol m3 m2s m 2 Pa s 25.2 25.2 25.1 25.2 24.4 39.3 39.4 39.5 39.6 39.7 24.9 25.4 26.0 25.7 25.9 40.0 39.8 39.7 39.6 39.9 40.0 40.3 40.1 40.2 40.2 1.1 2.4 3.7 4.9 6.2 1.0 1.9 3.0 4.0 5.1 0.9 2.1 3.2 4.4 5.5 1.1 2.2 3.4 4.6 5.8 1.1 2.2 3.4 4.6 5.8 1.7 4.1 6.1 8.3 9.9 2.1 5.1 7.7 10.3 12.4 1.6 4.4 6.5 8.6 10.7 2.0 4.8 6.8 9.2 11.3 2.0 5.1 7.6 10.1 12.1 5.4 4.9 4.9 5.0 5.0 5.5 5.5 5.5 5.6 5.6 6.5 5.4 5.4 5.5 5.5 5.0 5.0 5.0 5.1 5.1 4.8 4.9 4.9 4.9 4.9 2.72 2.72 2.72 2.72 2.72 3.02 3.02 3.02 3.02 3.02 2.61 2.61 2.61 2.61 2.61 3.03 3.03 3.03 3.03 3.03 3.46 3.46 3.46 3.46 3.46 1.4 3.2 4.9 6.5 8.1 1.4 2.9 4.3 5.8 7.2 1.2 2.9 4.4 5.9 7.4 1.5 3.2 4.8 6.4 8.0 1.6 3.3 5.0 6.6 8.2 The measured values of the Henry s constant and viscosities in the DGApotassium formate solutions are given in Table 5.11. Figure 5.27 and 5.28 show the normalized flux data and the second order rate constant as a function of ionic strength at 25 0C and 40 0C. 217 Table 5.11 Measured values of Henry s constants and viscosities in potassium formate (CHKO2) solutions -DGA solutions Solution T, 0C HCO2, kPa.L/mol-1 , cP 11.3 0M CHKO2 6.5 25 30654 M DGA 11.3 1M CHKO2 6.5 25 36557 M DGA 0M CHKO2 6.5 40 41598 6.7 M DGA 1M CHKO2 6.5 40 48515 6.7 M DGA 3M CHKO2 6.5 40 65597 6.7 M DGA 10 -4 25 C 40 C 0 0 ' k 10 -5 G (m ole/atm .cm .s) 0 2 0.5 1 1 .5 C HK O [M ] 2 2 2 .5 3 Figure 5.27 Normalized flux of fresh 65wt% DGA and potassium formate solutions. 218 1.2 1 0 1 10 k (m /km ol.sec) 8 10 6 10 4 10 2 10 0 10 5 25 C 5 0 0 40 C 4 4 3 4 2 4 0 0 0 .5 1 1.5 2 Ion ic strength (m ol/L) 2 .5 3 Figure 5.28 Effect of potassium formate on the second rate constant at 25 0C and 40 0C for the system DGA- water-CO2 The present results suggest that ionic strength has strong effect on the second order rate constant. The second order rate constant increases a factor of 3. The results in the 65 wt% DGA showed increases by a factor of 5 over the range of loading from 0 to 0.4 mol CO2/mol DGA. Figure 6.25 shows a comparison between the three results. Table 5.12 shows the slope of the line from equation 5.41. The results with potassium formate and 65 wt% DGA at 25 0C compares well to the results with 65 wt% DGA; however, at 40 0C the potassium formate and glycolic acid and 65 wt% DGA increases a factor of 2 to 3 with ionic strength compared with 65 wt% DGA which increase a factor of 5 over the range studied. 219 10 6 65 wt% DG A + glycolic acid, 40 C 65 wt% D GA , 40 C 0 0 k (m /km ol.se c) 10 5 65 w t% D G A , 25 C 0 3 2 65 wt% D G A + potassium form ate, 40 0 C 10 4 65 wt% D G A + potassium form ate, 25 0 C 0 0 .5 1 1.5 2 Ion ic stren gth (m ol/L) 2 .5 3 Figure 5.29 Effect of ionic strength on the second rate constant at 25 0C and 40 0 C for the system DGA-water-CO2, DGA-glycolic acid-water-CO2, and the system DGA-potassium formate-water-CO2 5.6 Conclusions Absorption experiments of CO2 into aqueous 65 wt% and 25 wt% DGA (diglycolamine) solutions were performed at 25-60 C in a wetted-wall column. The eddy diffusivity theory was used to simulate liquid-phase hydrodynamic characteristics. Two approximate models were used; the pseudo first order approximation (PFO), and the interface pseudo first order. The electrolyte-NRTL model was used to represent the activity coefficients of the species in solution. In the previous chapter, the NRTL model was verified using 13C NMR data, physical and chemical solubility data. 220 Table 5.12 Results for the fit of k2 as a function of for the results T, ko C 0 3 2 6 C (m /kmol.cm .sec) (m /kmol2.cm2.sec) 65 wt% DGA 25 1.73E+04 0.674 65 wt% DGA 40 5.00E+04 0.674 65 wt% 25 1.41E+04 DGA+potassium 0.730 formate 65 wt% 40 3.84E+04 0.230 DGA+potassium formate 65 wt% DGA+glycolic 40 8.90 E+04 0.510 acid R2 0.999 0.999 0.834 0.521 0.587 Kinetic rate constants have been regressed from the currently obtained experimental data. The following conclusions can be made; The 65 wt% DGA shows second order kinetics. The IPFO model matches very well the rigorous model. The PFO model underestimates the second order rate constant, especially at high loading . The reaction of DGA with CO2 is the dominant effect at low loading. At high loading, instantaneous reactions are approached and diffusion of reactants and products becomes an important phenomena. The natural log of the second order rate constant increases linearly with the ionic strength. The second order rate constant increases a factor of five at an ionic strength of 2.5 M. Experiments with 65 wt% DGA and glycolic acid and potassium formate show a comparable increase (a factor of 2 to 3) in rate constant with ionic strength as in 65 wt% DGA (a factor of 5 with ionic strength) at 25 0C and 40 0C. 221 Chapter 6: Absorption of CO2 in Aqueous MOR and MOR/DGA Blends 6.1 Introduction Although the reaction of CO2 with primary and secondary amines has been studied extensively only very limited information is available for the reaction between CO2 and morpholine (MOR). There are no kinetic data for CO2 absorption in DGA/MOR blends. Alper (1990) reported kinetic data at 298 K obtained by a stopped-flow technique for the reaction of CO2 and MOR. Littel (1991) obtained kinetic data at 303 K with the stirred cell reactor. All the reactions can be described by the zwitterion mechanism originally proposed by Caplow (1968). The results obtained by Littel with the stirred cell reactor are considerably lower than the results obtained by Alper with stopped-flow. Littel concluded that the overall reaction rate depends on both the zwitterion formation rate and the zwitterion deprotonation rate by amine. However, Alper found that the overall reaction rate depends entirely on the zwitterion deprotonation rate. Crook and Donnellan (1989) reported kinetic data at 298 K for MOR with the stopped flow technique. They questioned the validity of the zwitterion mechanism and proposed a single step, termolecular mechanism that postulates a loosely bound complex as the initial product. For this mechanism the forward reaction rate can be calculated according to: RCO2 = {kAM [R1R2NH]2 +kw{[R1R2NH]2[H2O]}[CO2] (6.1) Reaction rate 6.1 for the single step, termolecular mechanism according to Crooks and Donnellan can be regarded as a limiting case of the zwitterion 222 mechanism, if the zwitterion deprotonation is the rate-determining step. For reactions in which the zwitterion formation is the rate-determining step such as DGA, the agreement between both methods is satisfactory. Chapter 4 studied the equilibrium of DGA, MOR and DGA/MOR blends. Data was obtained at CO2 loading from 0.0 to 0.5 in solutions of 23.5 wt% MOR, 65 wt% DGA and 11 wt% MOR/53 wt% DGA at 298 to 333K. In this loading region, MOR species make a significant difference on the partial pressure. The electrolyte NRTL model has been used to model partial pressure data, C13 NMR data and N2O solubility data in the DGA, MOR and the blended amine system. Chapter 5 studied the rate of absorption in DGA. This chapter reports results with aqueous MOR and with DGA/MOR. The rigorous model, the PFO and IPFO models discussed in the previous chapter are also used here. The rate-based model is combined with the thermodynamics model of Chapter 4 to predict rate of CO2 absorption. Measurements for the blended amine are made at 0 to 0.4 mol CO2/mol amine, and 25 0C to 40 0C. 6.2 Physical Properties The Henry s law constant for CO 2 (HCO2) is obtained using the N2O analogy. Data for N2O solubility in MOR and DGA/MOR solutions has been determined using the the data in figure 4.5, equation 5.6 and equation 5.8. Diffusion coefficients for MOR are calculated using the diffusion coefficient of DGA corrected for molecular weight by multiplying by a factor of 1.2. Diffusion coefficients of all ions are arbitrarily set at the same value as MOR. The diffusion coefficient of CO2 in concentrated DGA is calculated as described in chapter 5. The solution viscosity is also calculated as described in chapter 5. The absorption rate of carbon dioxide was determined in a wetted wall column as discussed in Chapter 4 and 5. 223 6.3 CO2 Absorption in Aqueous MOR The kinetic data for MOR have been obtained at conditions that greatly simplify the mathematical treatment of the mass transfer problem. The most significant simplification arises from the pseudo first order assumption for kinetics discussed in Chapter 5. RCO2 = k2 [MOR]{[CO2]-[CO2]*}=k1{[CO2]-[CO2]*} k1=k2[MOR]BULK where [CO2]* is the equilibrium concentration of carbon dioxide. Table 6.1 presents the absorption data in 23.5 wt% MOR at zero solution loading. At low loading, the equilibrium partial pressure will approach zero. The enhancement factor will also be much greater than 1. Therefore, the CO2 flux as seen in chapter 6 under these conditions is given by; (6.2) N CO 2 = k 2 [MOR ]D CO 2 H CO 2 I PCO 2 (6.3) 224 Table 6.1 Rate of absorption data at zero loading into 23.5 wt% aqueous morpholine. Overall gas flowrates from 6.05 to 6.25 SLPM. Total pressures from 15-18 psig. [MOR]T T POUTCO2 Flux *107 klo*105 PICO2 kmol kgo*109 2 o C Pa m/s Pa kmol kmol m Pa s 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 m3 24.4 24.5 24.4 24.5 24.5 40.0 40.1 40.2 40.4 40.3 59.2 59.2 59.5 59.6 59.8 960 1911 2925 4117 5207 932 1874 2877 3853 4917 977 1999 3091 4121 5075 1.91 4.60 6.90 8.16 9.91 1.96 4.59 6.83 9.15 10.9 1.94 4.38 6.36 8.62 11.2 m2s 5.38 5.40 5.43 5.46 5.49 5.51 5.54 5.56 5.59 5.62 5.26 5.29 5.32 5.35 5.38 6.6 6.7 6.7 6.7 6.7 8.9 8.9 8.9 8.9 8.9 12.0 12.0 12.1 12.1 12.1 1318 2762 4185 5589 6970 1291 2705 4098 5471 6826 1349 2827 4280 5712 7122 From equation 6.3 we can see that a plot of the flux versus interfacial partial pressure will yield a straight line. Figure 6.1 shows the results at several temperatures and CO2 partial pressures. The data fit a straight line with a yintercept of approximately zero as predicted by equation 6.3. The second order rate constant was extracted by taking the best fit straight line of each series represented in Figure 6.1 and correcting the slope for the diffusion coefficient and Henry s law constant for carbon dioxide. 225 1.2 1 0 1 10 F lux (m ole s/c m .s) 8 10 6 10 4 10 2 10 2 -6 -6 -7 -7 -7 -7 25 C 40 C 60 C o o o 0 0 100 0 2000 3000 P interface (P a) 4000 500 0 Figure 6.1 Straight line fit for rate of CO2 absorption into aqueous 23.5 wt% MOR solutions at zero solution loading The value of the rate constant obtained in this work is shown in Table 6.2. Several other amines are compared to morpholine in Table 6.2. The rate constant obtained in this work is a factor of 4 higher than DGA as measured in this work in the same amine concentration range (see chapter 5). It is hypothesized in this work that the high reactivity of morpholine compared to other amines with similar pKa values is due to its cyclic nature. The temperature dependence is clearly weak consistent with the zwitterion mechanism. Temperature dependence of the rate constant is shown in Figure 6.2 as an Arrhenius plot. 226 Bronsted Correlation of Morpholine Kinetics at 25oC Rate Constant at pKa at 25oC Source 25oC (m3/kmol s) Morpholine 22259 8.70 This Work Piperazine 53700 9.83 Bishnoi (2000) Ethylenediamine 15000 9.90 Sharma (1966) Diglycolamine 6000 9.50 This work Morpholine 20000 8.70 Sharma (1966) Diethanolamine 1200 8.88 Sada et al. (1976) Piperidine 60000 11.12 Sharma (1964) Table 6.2 Amine 10 5 k (m /km ol.s) 3 2 10 4 60 C 0.00 3 0 40 C 0 25 C 0 0 .003 1 0.0032 0.0033 0 .0034 -1 1 /T (K ) Figure 6.2 Second order rate constant of MOR and carbon dioxide. 0 .002 9 227 Figure 6.3 shows the Bronsted correlation of CO2 reaction rates with secondary amines. In most cases, it has been observed that the second order rate constant of the cyclic amines lies above the Bronsted plot for amines with similar pKa. This is probably due to a reduction in steric hindrance around the amine group and a consequent increase in the zwitterion formation rate. Figure 6.3 shows also that the second order rate constant of the secondary amines varies as pKb1. 5 10 k (m /km ol.s) 10 4 3 10 3 10 2 M orp ho lin e Pipe rid in e Pyrrolidin e D ie than o lam in e Pipe razin e H yd roxye th ylp ip e ra zine Am in oe th ylp ipe razin e Th is w ork - M o rph olin e 2 2.5 3 3 .5 4 pK 4 .5 b 5 5.5 6 Figure 6.3 Bronsted correlation of CO2 reaction rates with secondary amines at 25 0 C. (Rochelle et al., 2000) Table 6.3 summarizes the available rate data for morpholine. Results for piperazine are also presented since they are related to the morpholine molecule. 228 The overall reaction of morpholine is a second order function of amine strength and seems to follow the zwitterion mechanism, however, piperazine demonstrates second order overall kinetics. Table 6.3 Reference Rate Data for the Morpholine (Rochelle et al., 2000) Amine Temp (K) [Amine] mol/l k1 = r s-1 [CO2] Experimental technique Sharma (1965) Morpholine 298 - 19952[MOR] Stirred cell Crooks and Morpholine Donnellan (1989) Alper (1990) Xu et al. (1992) Littel et al. (1992) Bishnoi (2000) Bishnoi and Rochelle (2000) Seo et al. (2000) Piperazine Piperazine Piperazine Morpholine Piperazine Morpholine 298 0.1-1.0 14200*[MOR] + 48*[MOR][H2O] 2 Stopped Flow 298 0.0250.50 3855*[MOR] + 16665*[MOR] 2 Stopped Flow 303333 303 <4 M Total 0.15-4 2.98*10 exp{-6424/T}[PZ] 11 Wetted Disk [ MOR ] 1 12400 + 1 12 . 1 [ MOR ] Stirred Cell 303 0.2 68000[PZ] Stirred Cell 298333 0.2,0.6 3.36 E 4 1 1 5.37 E 4 exp 8.314 T 298.15 Wetted Wall 303, 313 0.057 0.23 4096[PZ], 7075[PZ] Wetted Sphere 229 6.4 Rate Results with 11 wt% MOR/53 wt% DGA A subset of the experimental data obtained in this work for the blend is presented in Table 6.4. Figure 6.4 shows the normalized flux of CO2 in 11 wt% OR/53 wt% DGA. Appendix K presents the detailed experimental CO2 absorption data for the blend. Table 6.4 Rate of absorption into aqueous 11 wt% MOR/53 wt% DGA. Overall gas flowrates from 3.05 to 6.25 SLPM. Total pressures from 15-60 psig. [Amine]T kmol m3 T o C 24.6 40.0 59.4 24.7 39.9 58.5 25.3 40.5 60.4 25.7 39.8 60.5 POUTCO2 Pa 1046 810 650 1870 1824 1810 2089 1944 2492 4375 2530 26940 Flux *107 kmol kgo*109 kmol m 2 Pa s klo*105 m/s 2.94 4.14 6.09 2.25 3.32 5.13 1.95 2.87 4.68 1.77 2.54 4.24 PICO2 Pa 1507 1279 1195 3114 3079 3014 3113 3077 3143 6992 6185 32614 CO2 loading 0.13 0.13 0.13 0.27 0.27 0.27 0.36 0.36 0.36 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 2.29 2.75 3.42 2.99 3.05 2.99 2.46 2.76 1.55 2.81 4.43 7.43 m2s 5.25 5.99 6.38 2.54 2.59 2.65 2.55 2.59 2.54 1.25 1.42 1.45 230 10 -3 k , m oles/(cm .atm .sec) 10 -4 2 10 -5 10 -6 25C 40C 60C ' G 10 -7 0 0.1 0.2 0.3 0.4 Loading, m ol CO /m ol Am ine 2 0.5 Figure 6.4 Normalized flux of 11 wt% MOR/53 wt% DGA and CO2 6.5 Model Description The model developed by Bishnoi (2000), based on the eddy diffusivity theory, was used in this work. The following three equations are assumed to be kinetically controlled. CO2 + OHMOR:H2O + CO2 DGA:H2O + CO2 HCO3MORCOO- + H3O+ DGACOO- + H3O+ (6.4) (6.5) (6.6) 231 For each kinetically controlled reaction, we consider the overall reversible rate of reaction. Thus, for the DGA reaction with CO2 (reaction 6.6), we express the overall rate of reaction as: DGACOO H 3 O + R 6 = k DGA [DGA][CO 2 ] K6 + [ ][ ] (6.7) where the equilibrium constant K 6 = [DGACOO ][H O ] and is calculated by the [DGA][CO 2 ] 3 ratio of the species in the bulk solution. Note that water is left out of the kinetic and equilibrium expressions since it is considered to be constant across the boundary layer and, therefore, can be lumped with the apparent rate and equilibrium constants. In order to avoid having H3O+ as a species in the model, rates of reaction for carbamate formation are described as: Kw R 6 = k DGA [DGA][CO 2 ] DGACOO K 6 OH [ where : K w = H 3 O + OH [ ][ ] ] [ ] (6.8) Other rate expressions for equations 6.4 through 6.6 follow. The rate constant for reaction 6.4 is the expression presented by Pinsent et al. (1956). Reactions involving only a proton transfer are considered to always be in equilibrium. These reactions are: HCO3- + OHDGA:H2O MOR:H2O CO3= + H2O DGAH+ + OHMORH+ + OH(6.9) (6.10) (6.11) 232 There are ten species that need to be considered. At each node, therefore, there are 10 unknowns that need to be determined. The equations to be solved at each node are presented in table 6.3. Along with these 10 equations at each node, we define boundary conditions at the interface and in the bulk solution. We use the condition that all concentrations are equal to the equilibrium concentrations as liquid depth approaches infinity. We also assume phase equilibrium of CO2 at the interface leading to a known concentration of CO2 at the interface for a given interfacial partial pressure of CO2. The concentration of species which undergo proton exchange are defined by the combined buffer system flux being zero at the interface and chemical equilibrium between the two species involved in the proton exchange. Electroneutrality is also assumed at the interface. Table 6.5 also documents the boundary conditions used in this work. Table 6.5 Model Equations and Boundary Conditions Conservation Equations at Each Node Overall Species Material Balance 2[MOR] + 2[MORCOO-] + 2[MORH+] = 0 2[DGA] + 2[DGACOO-] + 2[DGAH+] = 0 2[CO2] + 2[HCO3-] + 2[CO3=] + 2[MORCOO-] + 2[DGACOO-] = 0 Equilibrium Relationships CO 3 K9 = HCO 3 OH K 10 [ ][ ] [DGAH ][OH ] = + [ ] K 11 = [MORH ][OH ] + [DGA] [MOR ] Material Balance for Molecular CO2 2[CO2]-(R10 + R11 + R12) = 0 Carbamate Material Balance 2[MORCOO-] + R11 = 0 2[DGACOO-] + R12 = 0 233 Electroneutrality [MORH+]+ [DGAH+]=[HCO3-]+ 2[CO3=]+[OH-]+[MORCOO-]+[DGACOO-] Boundary Conditions At x=0 [CO2]=[CO2]I DMOR [MOR] + DMORH+ [MORH+] = 0 DDGA [DGA] + DDGAH+ [DGAH+] = 0 K16[MOR] [MORH+][OH-] = 0 K17[DGA] [DGAH+][OH-] = 0 [MORCOO-] = 0 [DGACOO-] = 0 K15[HCO3-][OH-] [CO3=] = 0 DHCO3- [HCO3-] + DCO3= [CO3=] = 0 [MORH+]+ [DGAH+]=[HCO3-]+ 2[CO3=]+[OH-]+[MORCOO-]+[DGACOO-] At x = [i] = [i]o For all species i in solution The speciation was estimated using the solubility model presented in chapter 5. The rate constants used in model prediction for DGA and MOR are the rate constants estimated by the data in chapter 6 and in section 6.3 in this chapter for the single amine systems. Using these constants, the flux for each experimental point is estimated using the rigorous model described in the previous section and compared to the measured flux. Figure 6.5 compares the predicted flux to the measured flux for this series of data. 234 P redicted Flux/M eas ured F lux 25 C 40 C 60 C 0 0 0 1 0 .9 0 .8 0 .7 0 .6 0 0 .1 0 .2 0 .3 CO lo ading, m ol CO /m ol A m ine 2 2 0 .4 Figure 6.5 Comparison of predicted and experimental fluxes for absorption of carbon dioxide into 11 wt% MOR/53 wt% DGA. It can be seen that rigorous model consistently underestimates the flux of carbon dioxide and that the error seems to decrease with loading. This can be attributed to the fact that DGA catalyzes the reaction of CO2 and MOR as shown below; MOR + DGA+ CO2 MORCOO- + DGAH+ (6.12) This effect is consistent with the zwitterion mechanism observed for other secondary amines (Caplow, 1968; Danckwerts, 1979; Littel, 1991). The third order rate constant for the reaction of CO2, DGA and MOR was regressed to fit the 235 absorption data at low loading and found to follow the Arrhenius expression as shown in figure 6.6. These kinetics are ignored by the previous model. 10 6 k (m /km o l .cm .sec) 2 10 5 6 2 3 10 4 60 C 0.003 0 40 C 0 .003 1 0 .003 2 -1 0 25 C 0 .003 3 0.0034 0 0 .002 9 1 /T (K ) Figure 6.6 Third-order rate constant for the reaction between CO2 and 11 wt% MOR/53 wt% DGA using the rigorous model, from data at zero loading. As discussed in chapter 6, the third order rate constant was regressed against CO2 loading and temperature to fit the absorption rate data at 25 0C, 40 0C and 60 0C. Equation 6.13 shows the third order rate constant equation. It is in log form, and it is similar to equation 5.36. ln k 3 = A + B*ldg + C/T (6.13) 236 Figure 6.7 is the parity plot for the calculated and measured fluxes of CO2 for the 11 wt% MOR/53 wt% DGA system at various CO2 loadings and three temperatures. For most experiments the measured flux is within 15% of the calculated flux. The fitted parameters are shown in Table 6.5. C alc ula ted C O F lux (m ole s/c m sec ) 1.6 10 1.4 10 1.2 10 1 10 8 10 6 10 4 10 2 10 -6 25 C -6 -6 -6 -7 -7 -7 -7 0 0 0 40 C 60 C 2 2 0 0 3.4 10 6.8 1 0 1 .02 1 0 1.36 1 0 1.7 1 0 2 M easured C O F lux m oles/cm se c) 2 -7 -7 -6 -6 -6 Figure 6.7 Rigorous model fit of all MOR/DGA absorption data. Table 6.6 Results for the regression of Equation 6.13. Parameter Value A 0.378E02 B 0.20E01 C -0.84E04 237 10 (m /km o l .c m .sec) 6 0 60 C 2 2 10 5 40 C 0 6 M O R -D G A 25 C 0 k 10 4 0 0 .1 2 0 .2 2 0.3 0 .4 CO lo adin g, m ol CO /m ol A m ine Figure 6.8 kMOR-DGA for absorption of carbon dioxide into 11 wt% MOR/53 wt% DGA at 25 0C, 40 0C and 60 0C. 6.6 Rate Model Predictions Figures 6.9 to 6.11 show the model prediction of the normalized flux, kG , for CO2 absorption in 65 wt% DGA and 11 wt% MOR/53 wt% DGA at 25 0C, 40 0 C and 60 0C. If the MOR concentration is set to zero, the rate model can be applied to CO2/DGA/H2O. All the figures show that the addition of MOR to DGA can increase the CO2 absorption rate by a factor of 1.5 compared to the DGA 238 solution with the same total amine concentration. The increase in the rate is more obvious at low loading than at high loading. 11 w t% M O R /53 wt% DG A 65 w t% D G A k ' (m ol/Pa.c m.sec) 3 10 -10 2 2 10 -10 G 10 -10 0.0 1 0.1 P 1 CO2 * 10 (P a) 100 100 0 Figure 6.9 Normalized flux of CO2 in 11 wt% MOR/53 wt% DGA and 65 wt% DGA at 25 0C, kol=1.77E-3 m/s, Pi=10P*. 239 k ' (m ol/P a.cm.se c) 4 10 -10 2 3 10 -10 11 wt% M O R /53 w t% D G A 65 w t% D G A G 2 10 -10 10 -2 10 -1 10 P 0 * C O2 10 (P a ) 1 10 2 10 3 Figure 6.10 Normalized flux of CO2 in 11 wt% MOR/53 wt% DGA and 65 wt% DGA at 40 0C, kol=1.77E-3 m/s, Pi=10P*. 10 9 10 8 10 k ' (m ol/P a.c m.sec) 7 10 6 10 5 10 4 10 -9 -10 -10 -10 2 -10 -10 G -10 65 wt% D G A 11 w t% M O R/53 wt% D G A 3 10 -10 10 -3 10 -2 10 -1 P 10 0 * C O2 10 (P a) 1 10 2 10 3 Figure 6.11 Normalized flux of CO2 in 11 wt% MOR/53 wt% DGA and 65 wt% DGA at 60 0C, kol=1.77E-3 m/s, Pi=10P*. 240 6.7 Sensitivity to Model Parameters Figure 6.12 shows the sensitivity of different parameters to the flux predicted by the rigorous model with 11 wt% MOR/53 wt% DGA at 40 0C. 0 .5 0 .4 dln (CO flux)/dln (i) k 0 .3 k 0 .2 DG A-M O R DGA D ion 2 0 .1 k MOR 0 0 0.0 5 0 .1 0.1 5 0 .2 0.25 0.3 0.3 5 CO lo adin g, m ol CO /m ol A m ine 2 2 0 .4 Figure 6.12 Sensitivity of calculated CO2 flux to values of the diffusion coefficients of reactants and products and rate constants, 40 0C, kol=1.77E-3 m/s, Pi=10P*. The results can be divided into low and high loading regions. At low loading, the rate constant of DGA, MOR and the third-order rate constant of DGA and MOR are by far the most sensitive parameters showing that the dominant phenomenon in this region is the reaction of CO2 with DGA and MOR. Also, it can be seen that the DGA reaction is more sensitive than the MOR reaction and the 241 MOR-DGA reaction. This shows that the DGA reaction is the most dominant phenomena compared to DGA and MOR-DGA reactions. As the loading increases and the concentration of DGA and MOR drops, the rate constants of DGA, MOR and MOR-DGA become less important and this is replaced by the diffusion coefficient of ions at high loading showing that the removal of reaction products and the diffusion to the interface have become the dominant phenomena. 6.8 Deviation from Approximate Solutions Figure 6.13 and 6.14 shows the model prediction of the kG of CO 2 absorption into 11 wt% MOR/53 wt% DGA at 40 0C and a kol=1.77E-3 m/s using the pseudo first order approximation (PFO) and the rigorous model. 10 N o rm alize d flux (m o l/P a .cm .se c) -9 k IN ST G k 10 -10 PFO G 2 1 /(1/k 10 -11 PF O G + 1/k IN ST G ) k P = 10 *P * C O 2 ,b G C O 2 ,i 10 -12 0 0 .1 0 .2 0 .3 0 .4 C O lo adin g , m o l C O /m o l A m ine 2 2 0 .5 Figure 6.13 Comparison of rigorous model and PFO model for CO2 absorption at 40 0C, kol=1.77E-3 m/s, Pi=10P*. 242 10 N o rm alize d flux (m o l/P a.cm .sec ) -9 k IN ST G 2 k 10 -1 0 PF O G 1/(1 /k PF O G + 1/k IN ST G ) P 10 -1 1 C O 2 ,i = 1 .01 *P * C O 2 ,b k G 0 0 .1 0 .2 0 .3 0.4 C O lo adin g, m ol C O /m ol A m in e 2 2 0 .5 Figure 6.14 Comparison of rigorous model and PFO model for CO2 absorption rate at 40 0C, kol=2.74E-3 m/s, Pi=1.01P*. Both low driving force (1.01*P*CO2) and high driving force (10.0* P*CO2) are considered. At low loading, there appears to be no affect of an increase in driving force. At high loading, however, increasing the driving force from 1.01*P*CO2 to 10*P*CO2 can decrease the normalized flux by a factor of two. We first compare pseudo first order to the rigorous model at small driving force. The model predicted the kG essentially follows the pseudo first order approximation at low loading. Here, the major process occurring is the reaction of CO2 with DGA and MOR throughout the boundary layer. At 0.2 loading, we start to see significant deviations from pseudo first order behavior even at the low driving force conditions. This is because the carbamate forming reactions are 243 approaching instantaneous reactions. Pseudo first order is not a good assumption at high loading. A simple addition of the pseudo first order resistance and the instantaneous resistance (1/kGPFO+1/kGINST) leads to very accurate prediction of the normalized flux with low driving force, but over predicts the normalized flux at high loading with the high driving force. This is understandable since the concentration at the interface is not significantly different from that in the bulk solution with low driving force. At high loading, the amine is significantly depleted at the interface; therefore, the concentration at the interface is significantly different from that in the bulk solution. 6.9 Conclusions MOR Performance The kinetics of MOR shows zwitterion behavior. The rate constant is an order of magnitude higher than primary amines such as MEA or DGA. MOR/DGA Blend Performance A 11/53 wt % blend of MOR/DGA provides almost 50% rate enhancement from 65 wt% wt % DGA at low loading at 25 0C, 40 0C and 60 0C. Approximate Solutions Pseudo first order is a good approximation to absorption into MOR/DGA blends at low loading. At high loading, instantaneous reactions are approached. A simplified model that combines the resistance of pseudo first order reactions in series with instantaneous reactions matches the rigorous model well with low driving force. 244 Important Phenomena at Different Conditions The reaction of DGA with CO2 is the dominant effect at low loading. At high loading, instantaneous reactions are approached and diffusion of reactants and products becomes an important phenomena. 245 Chapter 7: Conclusions and Recommendations 7.1 Effects of Heavy Hydrocarbon Impurities on Hollow Fiber Membranes Performance in Natural Gas Separation The state-of-the-art membranes for removal of CO2 from high-pressure natural gas are asymmetric in form and comprised of high Tg polyimide. Some previous fundamental studies have considered the effects of high pressure CO2 on dense homogeneous membranes. Nevertheless, few fundamental studies have been published on the effects of high pressure CO2 and only one study (White et al., 1995) with heavier hydrocarbons (C6+) on performance of asymmetric flat sheet hollow fibers have been reported. Some actual field tests have shown extremely complex responses of hollow fiber asymmetric membranes. The goal of this work was to investigate the effect of heavy hydrocarbons in natural gas feeds on permeation and sorption in hollow fiber membranes. Matrimid 5218 is a polyimide that is available in the market. Its permeation properties, combined with its processability (i.e., solubility in common solvents) make it an attractive candidate for gas separation applications. Furthermore, its mechanical strength and high glass transition temperature, better suit it for more rigorous working environments than other noncelluslosics such as polysulfone (Clausi and Koros, 2000). In addition, due to economic purposes, more membrane-based processes in natural gas treatments are currently running, with polyimide as membrane materials instead of cellulose acetate. The improved separation factors and high productivity of polyimide hollow fiber membranes provide a step change in natural gas processing costs compared to cellulose acetate. Therefore, the choice for our study was the Matrimid 5218. Toluene and n-heptane were chosen as model compounds to represent aromatic and aliphatic in 246 natural gas streams. Permeation and sorption data were obtained using permeation and pressure decay sorption systems. The evaluation was based on a typical feed gas composition of 10% CO2/90 % CH4 at a given feed gas temperature of 35 oC. Parameters that were varied were the temperature, total feed pressure and toluene/n-heptane concentration. In addition to steady state tests in the presence and absence of n-heptane and toluene, hollow fiber modules were conditioned for five days with ternary mixture of CO2, CH4 and one or the other of these heavy hydrocarbons. Following this conditioning process, the modules were studied with the simple binary 10% CO2/90 % CH4 mixture. These conditioning studies provide insight into the fundamental effects induced in the membrane due to the long term exposure to the complex mixtures. By combining both gas solubility and permeation improved understanding of the complex gas/hydrocarbon/polymer interaction was achieved. From this investigation the following conclusions were reached: Marked hysteresis is observed in permeation levels of CO2 and CH4 with small losses in selectivity following conditioning with 10/90 CO2/CH4 + 300 ppm toluene for five days at 35 0C. Conditioning of the hollow fiber membranes with 10/90 CO2/CH4 + 300 ppm toluene at 35 0C and 200 psia resulted in 60% to 80% increase in the CO2 and CH4 permeability relative to the unconditioned fibers. At 600 psia, the permeability of CO2 and CH4 increased 115% and 155% respectively relative to unconditioned fibers. There was a corresponding 2-15% decrease in the selectivity of CO2/CH4 in the conditioned sample. Essentially no hystresis was observed for hollow fiber membranes after conditioning with 10/90 CO2/CH4 + 500 ppm n-heptane for five days at 35 0 C. The permeability of CO2 returned essentially to its original value following conditioning with 10/90 CO2/CH4 + 500 ppm n-heptane at 200 247 psia. The selectivity loss is 2-3%. The conditioning also with 10/90 CO2/CH4 + 500 ppm n-heptane at 600 psia did not enhance the CO2 permeance as opposed to toluene; however, the selectivity decreased 14% during conditioning. It appears that the high partial pressure of CH4 allow a large enough sorption in the langmuir sites to enable CH4 to compete with CO2 and the heavier hydrocarbons for newly introduced free volume. Solubility measurements of CO2 and CH4 after conditioning with 10/90 CO2/CH4 + 300 ppm toluene suggest that increases in permeability after conditioning with 10/90 CO2/CH4 + 300 ppm toluene are not primarily due to increase in packing defects in the glass. If such an effect was at play one would expect a large shift upward in the sorption isotherm after exposure. The fact that the Langmuir capacity constant is somewhat similar on both before and after exposure suggests that any increases in Langmuir capacity are small or are accompanied by increases in dissolution capacity as well. The conditioning induced increase in permeability was a result of an increase in diffusivity caused by a decrease in the intersegmental resistance to mobility of the polymer chain. Conditioning, which is believed to occur because of a reduction in intersegmental steric hindrance to chain motions resulting from penetrant induced swelling of the polymer, tends to increase the diffusivity. The loosening of the polymer matrix presumably tends to increase the size and frequency of transient gaps available for diffusive jumps. Transport conditioning will preferentially increase the diffusivity of the larger penetrant, CH4 in this case, relative to the small penetrant, CO2 in this case, and should result in a decrease in the diffusivity selectivity. The increase in CO2 and CH4 diffusivity following conditioning with 10/90 CO2/CH4 + 300 ppm toluene at 600 psia was 150% and 177% respectively relative to unconditioned sample. Conditioning at 200 psia resulted in 75% and 87% increases relative to unconditioned samples. 248 No hystresis was observed for hollow fiber membranes conditioning with 10/90 CO2/CH4 + 300 ppm toluene for five days at 55 0C. This interesting result is believed to be due the reduction in the sorption level of toluene in the glassy polymer due to the increase in temperature. A similar result was found for 10/90 CO2/CH4 + 100 ppm toluene. The presence of n-heptane and toluene during exposure inhibits the transport of CO2 and CH4. This result is consistent with the the dual mode sorption theory which suggests the competition effect should be most apparent for highly condensable feed components, like toluene and nheptane. For example, the CO2 permeability during conditioning with 10/90 CO2/CH4 + 500 ppm n-heptane at 600 psia and 35 0C decreased 10% relative to the CO2 permeability during conditioning with the 10/90 CO2/CH4. On the other hand, the CO2 permeability during conditioning with 10/90 CO2/CH4 + 300 ppm toluene at the same pressure and temperature decreased 40% relative to their respective during conditioning with the 10/90 CO2/CH4. These results are consistent with observations for permeability hystresis seen after conditioning with 10/90 CO2/CH4 + 300 ppm toluene. Toluene is strong swelling and a strong competitive agent compared to n-heptane. The term strong competitive is taken to mean components whose critical temperature, Tc, is greater than the measurement temperature. In this regard, the critical temperature of toluene is 591.7 K, and that of n-heptane is 540.2 K. It should be remembered also the nature of interaction of the aromatic chains of Matrimid 5218 with the aromatic ring of toluene. In comparison to toluene, n-heptane is a straight chain aliphatic. The high Tc of toluene and its aromaticity should be responsible for its high swelling activity compared to n-hepatne. Our results indicated that defect-free, non-nodular morphology offers advantages in performance compared to defective fibers. Earlier work 249 (Gunaidi, 2000) showed serious losses in selectivity of defective fibers of the same polymer compared to defect-free fibers. Recommendations for Future Work The acquisition of further data at higher feed pressure, higher CO2 composition, and higher concentration of toluene and n-heptane will increase the range of the data obtained in this work and increase our understanding of this important material. We suggest also doing additional sorption experiments using film materials and using quartz spring apparatus in order to characterize diffusion of toluene and n-heptane and their affinities to the membrane. Valuable future work will also include mixed gas sorption measurements. While theses measurements are very difficult to perform, the results would provide valuable information about the characteristics of mixture feed streams. A glassy polymer has a "non-equilibrium" state resulting from the highly rigid nature of the polymers. The standard method of asymmetric membrane formation in our labs is by nonsolvent-induced phase separations. We believe this technique produces selective layers containing nanoscale pores during the phase separation, which are trapped in the glassy matrix. If this view were correct, nanoporosity of the membrane would increase the membrane's susceptibility to capillary condensation of condensable hydrocarbons. A new asymmetric membrane formation technique markedly decreases the membranes sensitivity to condensable hydrocarbons. It is believed that this new formation process suppresses nucleation and growth of nanometer scale solvent/nonsolvent-rich phases leading to essentially dense polymer films. 250 Develop new polymeric materials more resistant to aromatic agents. Polyimide has been found as a good material for CO2 removal from the natural gas streams in the absence of aromatics. The modeling of toluene induced swelling in glassy polymers needs more attention. There are no available models in literature that predicts plasticization in the presence of toluene. Fundamental data on sorption, dilation and diffusion needs to be collected in order to develop thermodynamic models of the gas/hydrocarbon/polymer system. 7.2 Carbon Dioxide Absorption and Solution Equilibrium in Morpholine and Diglycolamine Our study of MOR and DGA solutions for CO2 removal from natural gas started by examining aqueous CO2/H2O/MOR system, CO2/H2O/DGA system. Equilibrium partial pressure and absorption data for CO2 in aqueous 23.5 wt% MOR, and 65 wt% DGA were obtained in a wetted wall column. 13 C NMR data were acquired for the MOR/D2O/CO2 system and DGA/D2O/CO2. The NMR data were combined with CO2 solubility data and the nitrous oxide data to determine the important ionic reaction products in the CO2/MOR/H2O system, CO2/DGA/H2O system. The absorption data in aqueous MOR, and DGA were used to obtain a second order rate constant for the MOR/CO2 and DGA/CO2 reactions. Equilibrium partial pressure, NMR and absorption data were also acquired for the MOR/DGA blend. The thermodynamics of this system were modeled using the electrolyte NRTL model and the SRK equation of state along with the equilibrium constants obtained from the aqueous work. The absorption data were analyzed using a rigorous boundary layer model based on eddy diffusivity theory (Bishnoi, 2000), pseudo first order approximation model (PFO) and interface pseudo first order approximation model (IPFO). The rigorous model was used to make 251 predictions for the performance of MOR/DGA blends compared to 65 wt% DGA at industrial conditions. Thermodynamic Interactions of MOR/CO2, DGA/CO2,MOR/DGA/CO2 13 C NMR data have shown that CO2 reacts with MOR and DGA to form MOR carbamate, DGA carbamate, protonated MOR and protonated DGA. The MOR and DGA carbamate stability constant was found comparable to other secondary amines such as DEA and primary amines such as MEA in both its absolute value and its temperature dependence. The MOR carbamate is a factor of 5 to 7 times less stable than the DGA carbamate. At low loading in the CO2/H2O/MOR system and CO2/H2O/DGA, the main reaction product is MOR carbamate and DGA carbamate. This is replaced by protonated MOR and protonated DGA at high loading. In the MOR/DGA blend, MOR and DGA carbamate are the dominant reaction product at low loading. The main reaction products at high loading are the protonated MOR and DGA. The main difference between the blend and MOR alone is that the MOR carbamate is stabilized in the blended system. This was attributed to the equilibrium between carbamate MOR and carbamate DGA in the blend. CO2 solubility in DGA was found to be greater than MOR alone or MOR/DGA blends. Morpholine at 11 wt% of the total amine (65 wt% total) increases the CO2 equilibrium partial pressure by a factor of 5 to 7 at high loading and converges below 0.2 loading. The solvent working capacity of 65 wt% DGA was found to be 10% greater than 11 wt% MOR/53 wt% DGA. The heat of reaction of 11 wt% MOR/53 wt% DGA was found to be comparable to the 65 wt% DGA. The MOR was found also to be more volatile than DGA by a factor of 100 at 60 0C 252 Kinetics of MOR/CO2, DGA/CO2, MOR/DGA/CO2 The rate constant of MOR with CO2 to form carbamate has been experimentally determined to be 4 times greater than DGA even though the pKa is comparable. It is hypothesized that this large increase in the rate constant is due to the reduced hindrance around the nitrogen caused by the cyclic nature of the MOR molecule. The second-order rate constant in 65 wt% DGA at 250C for the reaction with CO2 is 4 times larger than previously published values. On the other hand, the 25 wt% DGA yields a rate constant, which is in good agreement with literature values. The 50 wt% DGA yields a rate constant which is two times greater than the 25 wt% results. This finding suggests that the second order rate constant is probably a function of DGA concentration. The second order rate constant in 65 wt% DGA increases by a factor of 5 over the loading range from 0 to 0.4 at 25 0C, 40 0C and 60 0C. Experiments with 65 wt% DGA + glycolic acid and 65 wt% DGA + potassium formate at 25 0C and 40 0C showed similar trends. The rate constant increases a factor of 2 to 3 in these solutions. The glycolic acid and potassium formate were added to 65 wt% DGA in order to modify the ionic strength environment. Rate of absorption into blends of MOR/DGA show that DGA kinetics increase 50% at low loading in the presence of MOR. This behavior is consistent with the zwitterion mechanism. The data at low to moderate loading cannot be fit with the single amine rate constants without considering the reaction of CO2, DGA and MOR to MOR carbamate as a finite rate reaction. Recommendations The acquisition of further data for the MOR/DGA system in 50 wt% DGA and at 40 0C, 60 0C and 120 0C will increase our understanding of this system at 253 industrial conditions. NMR data at higher temperature will help quantify the temperature dependence of the carbonate stability constant. Proton NMR measurements should be performed in the blend system in order to differentiate between protonated MOR and protonated DGA. One of the concerns in the rate measurements in concentrated DGA solutions is the increase in turbulence at the gas liquid interface and possibly wave formation. Therefore, we recommend doing desorption experiments of CO2 from 95 wt% ethylene glycol into pure nitrogen. We also recommend rate measurements in a stirred cell reactor. The presence of MOR in DGA has two opposite effects: MOR enhances CO2 absorption rate by 50% at low loading and decrease the working capacity by 10%. It should be noted that the higher the rate, the lower the circulation rate and the lower the working capacity, the higher the circulation rate. We recommend, therefore, system modeling of the CO2 absorption process using DGA in the presence of MOR. The modeling will show which solvent will require less solvent circulation rate to achieve the separation. It should be noted also that DGA has the advantage of lower vapor pressure compared to DGA. 254 Appendix A: Modeling of Asymmetric Hollow Fiber Membrane Modules used for High-Pressure Natural Gas Purification The use of polymeric membranes is a potential for several traditional processes used for gas separation. Separation processes of commercial interest include hydrogen recovery from hydrocarbons in refineries and petrochemical processes, oxygen/nitrogen separation from air, dehydration, and acid gas treatment of natural gas (Spillman, 1989; Loeb and Sourirajan, 1963; Spillman and Cooley, 1989; Schell et al., 1989). The inherent advantages of membrane systems include their low capital cost associated with their installation, ease of operation, potentially low energy consumption, and weight and space efficiency. Membranes are available in a wide variety of configurations such as hollow fiber, spiralwound, plate and frame modules; however, the hollow fiber modules are often a favored configuration because of the very high membrane area which can be packed in a given package volume (Scott, 1995). Because of their widespread industrial use they have attracted considerable attention in modeling efforts. Several mathematical models have been developed for hollow fiber membranes in the literature. Comprehensive reviews of the existing models for the various flow patterns; cocurrent, countercurrent, and crossflow are given by Shindo et al. (1985), Kowali et al. (1992) and Lipscomb (1996). Since any mathematical model must include some assumptions posed by the physical problem, evaluation of these assumptions underlying the model development is important. Successful membrane modeling and simulation can provide valuable information for the design, optimization and economics of the overall separation process. This chapter investigates the validity of the common assumption regarding a negligible bulk term in current hollow fiber membranes models. 255 Hollow fiber models usually include mass; momentum; energy balance equations, the relationship governing transport across the membrane, and appropriate boundary conditions. Transport equations describing permeation fluxes across the membrane usually are known to include both molecular diffusion and bulk motion given by Eq. (A.1) in the case of binary mixtures of A and B. The diffusion transport through a pore-free polymeric medium can be well described by the so-called Fick s first law of diffusion. Eqs. (A.1a) and (A.1b) shown below are the diffusion and the bulk transport equations for component A respectively. The effective diffusivity of A in the membrane medium is D Am (cm2/s). The mass flux of permeant i with respect to a fixed frame of reference is ni (g/cm2.s), and i is the mass fraction composition of permeant i in the membrane (g/g). The density of the system comprised of both polymer and sorbed penetrants is . The mass flux of the polymer, n p , is zero at steady state since the membrane is stationary (Kamaruddin and Koros, 1997). bulk n A = n bulk + n B A diff n A = D Am (A.1) (A.1a) (A.1b) d A dx n bulk = (n A + n B + n P ) A A In simulations of hollow fiber separators the contribution of bulk flow conditions is generally neglected. This assumption in some cases is completely reasonable when the sorption amount of penetrants, A and B , are negligible such as the sorption of simple gases H2, He, O2, and N2. In a recent study, Kamaruddin and Koros (1997) have shown that for CO2/CH4 separation using 6FDA-TADPO polypyrrolones and phenol/water separation using a polyetherblock-polyamide membranes bulk contributions are significant. Paul and EbraLima (1975 I, II & III) have also shown the importance of the bulk flux term in 256 single component permeation in a highly swollen membrane. However, to the best of our knowledge, studies concerning the frame of reference effects on hollow fiber modules have not been reported in the literature. The purpose of the present chapter is to investigate the influence of bulk flux contribution on the performance of membrane separators. This chapter discusses the CO2/CH4 separation in 6FDA-TADPA polypyrrolone membranes where a theoretical study of the influence of the frame of reference model (FM) in hollow-fiber separation modules is performed for the CO2/CH4 separation in direct comparison with the diffusion model (DM). The consequences of not considering the bulk flow contributions are discussed. The model can also be extended to multicomponent mixtures as shown below, but for the present case, the binary separation illustrates the key points involved and is considered the first step for more realistic models. Methane recovery, membrane selectivity to CO2 and stage cut are compared with those calculated by the purely diffusion model (DM). The FM model is fundamentally more correct than the DM because the convection motion is directly incorporated into the model and effects, which are neglected in the DM caused by other components are taken into account. However, the FM is more difficult to solve numerically. The dual mode model has been used to simulate the permeation of multicomponent components in hollow fiber membranes as shown by Thundyil et al. (1999). Chern at al. (1985) presented a bicomponent model on hollow fiber membranes using the dual mode model. Taveria et al. (2001) also presented a multicomponent model on hollow fiber membranes accounting for the permeability pressure and composition dependence according to the dual mode model. 257 A.1 Model Development The proposed model considers a hollow fiber module as shown in Figure. A.1 for the countercurrent configuration. For CO2/CH4 separation, the CO2/CH4 feed gas enters the module where it is separated into a permeate stream and a retentate stream. The membrane acts as a CO2 permselective barrier, so CO2 is concentrated in the permeate and CH4 is concentrated in the retentate stream. A one-dimensional mathematical model is solved for the case of the so-called dual mode sorption and transport description of permeation in glassy polymers, thereby, allowing concentration dependence of the effective diffusion and sorption coefficients. . High pressure CO2-rich Natural gas High pressure CH4-rich Residue Low pressure permeate < 2% CO2 to pipeline Figure A.1 Simplified block diagram of carbon dioxide/methane separation in a countercurrent hollow-fiber module. 258 The following assumptions are made: Steady state operation. Isothermal operation (T=308 K). Pressure change in the shell side is negligible. Pressure change in the tube side is given by Hagen-Poiseulle equation. Resistance of the porous support is negligible. Resistance of the shell and the tube side boundary layers is negligible. Uniform flow distribution within the module. No defects in the separating layer. Uniform dimensions of all the fibers. Plug flow conditions for the permeate and the retentate sides. The permeability changes along the fibers are described by the dual-mode transport model (Thundyil et al., 1999; Chern et al., 1985; Taveira et al., 2001). Hollow fiber deformation is negligible. Negligible plasticization Constant membrane density. The last assumption, constant bulk density is not seriously in error based on related sorption and dilation data from Fleming and Koros (1988). While the other above conditions are important and can cause performance to depart dramatically from expectations, they are not addressed here. According to these assumptions, the steady-state mass balance equations for species i, on both the retentate and the permeate sides, are given by; 259 d Ri = Ni dz d Pi = Ni dz (A.2a) (A.2b) where Ri and Pi are the axial molar flow rates of species i on the retentate and the permeate sides, respectively, z is the axial direction. The pressure on the shell side p R is assumed constant and equal to the feed pressure. The pressure on the permeate side p P is calculated for each individual stage using the Hagen-Poiseulle equation as shown below (Pan and Habgood, 1978 II): 2 dp P 256 mix P RT = dz d i4 N F (A.3) where d i is the inner diameter of the fibers; R is the universal gas constant; T is the temperature; mix is the gas mixture viscosity calculated using Wilke s method which has an average error of less than 1% compared to the experimental values (Reid et al., 1977); P is the total permeate flow rate; N F is the total number of fibers in the hollow fiber module. The membrane is divided up into a predetermined number of stages, M small enough that the flow properties, and hence, the pressure and composition gradients are almost constant in each element. This stepwise procedure is generally referred to as succession of states method with fixed length interval (Thundyil and Koros, 1997). The first stage is at the feed end and the Mth stage is at the residue end. The driving force is assumed constant over each of the stages considered. At each stage, the radial permeation fluxes of species i, N i , must be determined by solving the multicomponent mixture permeation relations. Since the membrane thickness is very small with respect to the radius of the fiber, curvature effects can be neglected and the problem can be then solved in cartesian coordinates. With 260 this in mind the multicomponent mixture permeation system comprises NC components and the polymer as shown below; nc d 1 + 1 n j + n P 1 dx j= ... ... N nc = Dnc N P = D P nc d nc + nc n j + n P 1 dx j= nc d P + P n j + nP 1 dx j= (A.4) N 1 = D1 As noted by Paul in the context of diffusion thru elastomeric membranes, the mass flux of the polymer N P is zero at steady state since the membrane is stationary (Paul and Ebra-Lima, 1975 I, II & III). The mass flux of component j can be obtained by integrating Eq (A.4) with the following boundary conditions; x = 0; 1 = 10 x = ; 1 = 1 A.2 Numerical Solution Assuming constant density within the membrane and average effective diffusion coefficients evaluated between the upstream and downstream conditions; Kamaruddin and Koros (1997) analyzed the situation for a binary feed. Extending this analysis to multicomponent feeds with NC components results in Eq (A.6); ... ... nc = nc 0 ... ... nc = nc (A.5) 261 nc r j j 2 ri i =1 DDj ln nc r j1 ri j i =1 n j = nc ri r i =1 j (A.6) where r j and ri are given by; rj = nj n ref (A.7) n ri = i nref where nref is the reference component and can be taken to be equal to the mass flux of the slowest component in the mixture. The fraction of the bulk flux contribution of component j, bulk , is the ratio of the mass flux of component j j due to bulk flow relative to the total mass flux as shown in Eq. (A.8). Since the mass fraction of component j, j is decreasing in the direction of the mass flux, an average mass composition, avg , should be used in Eq.(A.8) when estimating j the fraction of the bulk flux contribution. bulk j = avg j n i =1 nc i nj = avg j i =1 nc ri rj (A.8) Average mass composition in the membrane of component j can be calculated as follows; avg j ( x)dx = dx 0 j 1 0 1 (A.9) 262 where j (x) is mass fraction profile of component j in the membrane and is a function of position and can be calculated by integrating Eq.(4.4) with the following boundary conditions; x = 0; 1 = 10 ... ... nc = nc 0 x = x; 1 = 1 (x ) ... ... nc = nc (x ) Integrating we have, nc ri nj r nc ri 1 i =1 j 1 1 j1 exp j ( x) = nc DDj r i =1 r j ri i =1 j x (A.11) (A.10) When the local mass composition j (x) is averaged over the membrane thickness we obtain; nc r DDj 1 1 1 j1 i = nc nc ri i =1 r j n j ri r i =1 j i =1 r j nc ri n j i =1 r j exp DDj avg j 1 (A.12) An expression for the bulk flux contribution of component j can be obtained by substituting Eq. (A.12) into Eq.(A.8); nc r DDj = 1 1 j1 i nc i =1 r j n j ri i =1 r j nc r n j i i =1 r j exp DDj bulk j 1 (A.13) 263 The permeance Q j ,k of component j on stage k is defined as the permeability Pj , k divided by the skin layer thickness . Permeability can be obtained by normalizing the mass flux, diffusional or total (bulk and diffusional) flux, with the thickness and driving force (partial pressure or fugacity difference), and can be written for component j on stage k as follows; Q j ,k = Pj ,k = MW j (p j ,1 p j , 2 ) 22400n j ,k (A.14) where p j ,1 and p j , 2 are the partial pressures on both sides of the membrane at stage k respectively; n j , k is the mass flux of component j at stage k, and MW j is the molecular weight of component j. It is more convenient to work with the mass flux units since the molar volume of gaseous penetrants are generally not known. Using Eq. (A.13), we can calculate the diffusion based permeability, Pjdiff , from the observed permeability, Pjobs as follows; Pjdiff = 1 bulk Pjobs j ( ) (A.15) The observed permeability can be obtained from Eq.(A.14) with the total observed (bulk and diffusion) mass flux. The mass fraction can be calculated using the dual mode model. The dual mode model idealizes glassy polymers as having two distinct environments, unrelaxed volume (defects) and dense matrix (Koros , 1976; Hopfenberg et al., 1973; Vieth et al., 1976; W.J. Koros, 1980). The unrelaxed volume (defects) exists because of the inability of the polymer chains to pack perfectly below their glass transition temperature (Tg). In effect, glassy polymers have not reached equilibrium packing conditions; however, the state of the polymer is metastable because the relaxation time of the polymer chains is extremely long. The population of the components sorbed in the free volume is referred to as the Langmuir s population while those occupying the dense matrix 264 are referred to as the Henry s population. A companion transport model assigns separate mobilities to the penetrants in the Langmuir and Henry s law populations. For the case of local equilibrium this model is mathematically equivalent to assuming that only a fraction, F , of the Langmuir s population is able to perform diffusive jumps equivalent to those or the Henry s population. The mobile concentration of component j is shown in Eq. (A.16) using the dual mode transport model. As explained earlier, the mobile mass fraction mobile should be used when j describing permeant transport in glassy polymers. k Dj p j M j Fj K j 1+ = nc 22400 1+ bj f j i =1 mobile j (A.16) where k Dj is the Henry s law constant of component j which characterizes the sorption in the dense region of the polymer matrix; b j is a constant that is a measure of the affinity of the penetrant to the Langmuir sites. The constant F j discussed above can be shown to be equal to the ratio of the diffusion coefficients of Langmuir s population to Henry s popu lations of component j; and f j is the fugacity of component j. The gas phase fugacity of pure and mixed CO2/CH4 can be calculated using the virial equation of state (Prausnitz et al., 1986). The fugacity should be used instead of partial pressure since CO2/CH4 is non-ideal mixture. The K j constant can be calculated by the following equation; Kj = ' C Hj b j k Dj (A.17) ' where C Hj is the Langmuir capacity constant. Different numeric techniques have been proposed in literature for solving the differential equations of hollow-fiber models: shooting methods with initial 265 value algorithms (C.Y. Pan et al., 1978), weighed residues methods (Tessendorf, 1998) and finite difference methods (Chern et al., 1985) are the most commonly used. In the present work, finite difference solution technique is used. A.3 Simulations Results and Discussion The study was conducted for the countercurrent flow configuration. The study used data for CO2/CH4 separation using 6FDA-TADPO polypyrrolones. This polymer is known to its unique properties in resisting CO2 plasticization better than most other polymers, so it was a good ideal example to illustrate the bulk flux effects at high CO2 pressure without such plasticization complication. Table A.1 gives the dual mode parameters of the 6FDA-TADPO polypyrrolone membrane at 35 0C. The default parameters for simulation are given Table A.2. Although only counter-current flow configuration is considered, similar conclusions can be obtained for cocurrent configuration. Table A.1 Fugacity based dual-mode and partial immobilization parameters of CO2 and CH4 at 35 0C in 6FDA-TADPO polypyrrolone (Kamaruddin and Koros, 1997). CO2 CH4 F (DH /DD) DD (cm2 s ) atm ) C H (cm3 (STP) cm ) b (atm ) 0.084 1.196e-7 (STP) cm 0.026 1.12e-8 0.327 22.838 0.160 kD (cm3 1.526 34.084 1.023 266 Table A.2 Default parameters for simulations. Parameter Default value Thickness of membrane 0.1 micron Feed flow rate Feed pressure Permeate pressure (at exit) Temperature Feed mole fraction Fiber OD Fiber ID Fiber active length Number of fibers 50 000 SCFH 1000 psia 20 psia 308 K 50/50 CO2/CH4 250 microns 125 microns 100 cm 300 000 A.4 Frame of Reference Model (FM) versus Diffusion Model (DM) In order to understand the influence of considering the bulk flux contribution, when modeling hollow-fiber permeation, one should first understand how it directly affects permeation and sorption. This has been analyzed in detail by Kamaruddin and Koros (1997) for the CO2/CH4 separation using 6FDA-TADPO polypyrrolone membranes. Similar conclusions can be taken for the present separation using hollow-fiber membranes, nevertheless there are some aspects worth to pinpoint. In pure component permeation, the reference term in Eq.(A.4) is a function of the sorption level of the penetrant; however, in the case of binary mixture (A and B) permeation, the reference term is a function of both the penetrant sorption level and the permeation flux of the two components as can be seen from Eq.(A.8). If the sorption level is small, neglecting the bulk flux term is a reasonable assumption; however, if the mass flux of component A is much higher 267 avg than B (r is high), then the reference term of B can be significant even though B value is small, therefore; the bulk flux term of B cannot be neglected. For component A, r has negligible effect on the bulk term as r approaches high values. avg In the asymptotic limit as r goes to infinity, the bulk flux contribution of A is A . Therefore, the diffusion model (DM), which neglects these coupling effects, results sometimes not only in quantitative errors but also in large qualitative deviations as discussed by Kamaruddin and Koros (1997). In hollow-fiber modules, the partial pressure can significantly change along the fiber on each side of the membrane, affecting the amount of sorption of avg avg penetrants, A and B , and the permeation flux of both mobile components along the membrane. Therefore, a hollow-fiber model considering diffusion model is expected to lead to quite different results from the ones obtained from a more accurate permeation model, such as the frame of reference model. The differences between these results are analyzed for three different concentration scenarios. Effect of CO2 mole fraction Let us consider the CO2/CH4 separation as shown in Figure. A.1. The CO2 mole fraction has a significant impact on the bulk flux contribution of CO2 and CH4. Increasing the faster component (CO2) feed-side mole fraction increases the value of r , the mass flux ratio of CO 2 to CH4, as can be seen in Figure A.2a. Increasing the CO2 mole fraction increases also the CO2 and decreases the CH4 sorption levels in the membrane from the dual mode and competitive sorption standpoint. Figure A.2b and c shows the CO2 and CH4 concentration profile along the membrane for the 10/90, 50/50 and 90/10 CO2/CH4 mixtures. As can be seen in Figure A.2b, the CO2 concentration decreases from the feed/permeate side to the residue side because the CO2 is selectively permeating to the low-pressure side of the membrane. 268 500 10/90 CO2/CH4 50/50 CO2/CH4 90/10 CO2/CH4 a 400 300 r 200 100 0 Residue 7 10 6 10 CO concentration (g/g) 5 10 4 10 3 10 2 10 1 10 -2 0 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate b 10/90 CO2/CH4 50/50 CO2/CH4 90/10 CO2/CH4 -2 -2 -2 -2 2 -2 -2 0 10 0 0 Residue 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate 269 8 10 7 10 CH concentration (g/g) 6 10 5 10 4 10 3 10 2 10 1 10 -3 c -3 -3 -3 -3 -3 4 -3 -3 0 10 0 10/90 CO2/CH4 50/50 CO2/CH4 90/10 CO2/CH4 0 0.2 Axia l p o s itio n , x/L R e s id u e 0.4 0.6 0.8 F e e d /P e rm e a te 1 Figure A.2 Effect of CO2 feed mole fraction on (a). r ; (b). CO 2 average concentration inside the membrane; (c). CH4 average concentration inside the membrane. The CO2 concentration decrease in the feed side causes the CH4 concentration to increase; hence, decreasing the average concentration of avg avg avg CO 2 while increasing CH 4 inside the membrane. Although r and CH 4 have opposite effects, the bulk flux contribution of CH4 can still be significant as shown in Figure. A.3b. The bulk flux contribution of CH4 is much more sensitive to the r value than the bulk flux contribution of CO 2. This is due in part to the fact that the bulk flux contribution of CO2 is proportional to 1/r while the bulk flux contribution of CH4 is proportional to r . This is quite logic when one component is much faster than the other component, the slower component is swept along avg by the faster component. Looking back at Eq.(A.8), when CH 4 value is small, the 270 bulk flux of CH4 might be small compared to the total mass flux of CO2 and CH4; however, the bulk flux of CH4 might still be significant relative to the diffusional flux of CH4. Therefore, the bulk flux of CH4 cannot be neglected. On the other hand, as discussed earlier, the impact of r on CO 2 is the opposite of CH4; the avg value of the bulk flux contribution of CO2 approaches CO 2 when r is large; therefore, increasing the CO2 feed-side mole fraction can increase the bulk flux contribution of CO2 but to a lesser degree than CH4. As a direct result, the diffusion model underestimates the permeation fluxes, therefore, predicting a lower permeability than obtainable in Figure.A.4 and Figure.A.5. It is clear that the bulk flux contribution for CH4 has been detrimental to the separation process. 271 0.07 0.06 Fraction of bulk flux contribution 0.05 0.04 0.03 0.02 0.01 0 10/90 CO2/CH4 50/50 CO2/CH4 90/10 CO2/CH4 a 0 Residue 0.4 0.35 Fraction of bulk flux contribution 0.3 0.25 0.2 0.15 0.1 0.05 0 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate b 10/90 CO2/CH4 50/50 CO2/CH4 90/10 CO2/CH4 0 Residue 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate Figure A.3 Effect of CO2 feed mole fraction on (a). CO2 bulk flux contribution; (b). CH4 bulk flux contribution. 272 40 10/90 CO2/CH4 - FM model 10/90 CO2/CH4 - DM model 39 CO Permeance (GPU) a 38 37 2 36 35 0 Residue 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate 40.5 b CO Permeance (GPU) 40 50/50 CO2/CH4 - FM model 50/50 CO2/CH4 - DM model 39.5 2 39 38.5 0 Residue 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate 273 41.5 41 CO Permeance (GPU) 40.5 40 39.5 39 38.5 38 c 90/10 CO2/CH4 - FM model 90/10 CO2/CH4 - DM model 2 0 Residue 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate Figure A.4 Simulation of CO2 permeance for (a) 10/90 CO2/CH4 feed (b) 50/50 CO2/CH4 feed (b) 90/10 CO2/CH4 feed as a function of axial position, considering the diffusion model (DM) and the frame of reference model (FM). 274 1.48 10/90 CO2/CH4 - FM model 10/90 CO2/CH4 - DM model 1.46 CH Permeance (GPU) a 1.44 1.42 4 1.4 1.38 0 Residue 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate 1.9 1.8 CH Permeance (GPU) 1.7 1.6 1.5 1.4 1.3 50/50 CO2/CH4 - FM model 50/50 CO2/CH4 - DM model b 4 0 Residue 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate 275 2.4 2.2 CH Permeance (GPU) 2 1.8 1.6 1.4 1.2 0 Residue 0.2 0.4 0.6 Axial position, x/L 90/10 CO2/CH4 - FM model 90/10 CO2/CH4 - DM model c 4 0.8 1 Feed/Permeate Figure A.5 Simulation of CH4 permeance for (a) 10/90 CO2/CH4 feed (b) 50/50 CO2/CH4 feed (b) 90/10 CO2/CH4 feed as a function of axial position, considering the diffusion model (DM) and the frame of reference model (FM). These observations are even more pronounced for high feed pressures, because, according to the dual-mode transport model, as discussed below, increasing the feed-side total pressure, increases the amount of sorption of avg avg penetrants, CO 2 and CH 4 in the membrane. Under these conditions, the diffusion model can overestimate selectivity up to 25%. The extent of the error depends on the fraction of the bulk flux contribution, the higher the bulk flux contribution the higher the inaccuracy. The bulk flux contribution effects become negligible at low CO2 mole fractions as can be seen in (Figure. A.3) for the 10/90 CO2/CH4 gas mixtures case. Following this line of reasoning, one would expect increasing membrane thickness, and decreasing membrane area, which causes the CO2 mole fraction in 276 the feed side to increase thereby also increasing the bulk flux contribution of CO2 and CH4. But let us analyze first in more detail the effect of feed pressure on the bulk flux contribution of CO2 and CH4. A.5 Effect of Feed Pressure As the feed pressure increases, so does the mobile sorption levels of CO 2 and CH4, as can be seen from the dual-mode expression described by Eq. (A.16). This effect results in an increase in the bulk flux contribution of both components, bulk2 and bulk4 . Figure A.6a and b shows the effect of increasing the total feed CO CH pressure for the 50/50 gas mixture on the total CO2 and CH4 concentration in the membrane, a classical dual mode response. The CH4 concentration increases along the axial membrane length at a fixed total pressure because its partial pressure in the feed as well as the permeate sides of the membrane increases from the feed entry to the retentate exits the module. This increase results in an increase in the CH4 total average concentration inside the membrane between the feed inlet and retentate exit. Nevertheless, the 100 psi feed pressure case shows little increase in avg CH 4 along the membrane length, which can be explained in terms of the dual avg mode model. At low feed pressures, CH 4 is comprised of both the Henry s and Langmuir modes, which both have opposite effects on CH4 sorption. At high feed avg pressures, CH 4 is dominated by the Henry s mode. This is why in Figure. A.6 for avg 500 psi and 1000 psi feed pressures, CH 4 increases as the feed and permeate sides avg CH4 partial pressure increases. On the other hand, CO 2 concentration decreases along the membrane length from the feed side to the retentate side. In the case of 100 and 500 psi feed pressures, there was little dependence on pressure because of the competitive nature of sorption. 277 Similar results are also found for the 10/90, and the 90/10 CO2/CH4. Plasticization is assumed negligible as noted earlier because to the 6FDA-TADPO polypyrrolone has been shown to have a unique ability to resist CO2 plasticization. Moreover, and also with CO2 mixtures, less plasticization is observed because the CH4 competes with the CO2 for sorption sites as opposed to the pure CO2 case. For cases where this assumption does not apply, even more complexity will need to be accommodated. 278 4 10 4 10 CO concentration (g/g) 3 10 3 10 2 10 2 10 1 10 5 10 -2 -2 100 psia total feed pressure 500 psia total feed pressure 1000 psia total feed pressure a -2 -2 -2 2 -2 -2 -3 0 Residue -3 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate 7 10 6 10 CH concentration (g/g) 5 10 4 10 3 10 2 10 1 10 b -3 -3 -3 100 psia total feed pressure 500 psia total feed pressure 1000 psia total feed pressure -3 4 -3 -3 0 10 0 0 Residue 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate Figure A.6 Effect of total feed pressure on (a) average CO2 concentration inside the membrane (b) average CH4 concentration inside the membrane as a function of axial position, for 50/50 CO2/CH4 feed considering the frame of reference model (FM). 279 The effect of feed pressure on the r-value is not so straightforward. For low feed pressures, the r-value increases with pressure, a typical dual-mode response, but the opposite happens for high feed pressures (Figure. A.7). For the 10/90 gas mixture and at low feed pressures, the sorption in Langmuir sites in the permeate is greater than the sorption in the corresponding Langmuir sites in the feed side (depending on the permeate pressure) (Thundyil et al., 1999). Consequently, under this unusual case, the overall flux of the faster component will, according to the model, be lower than that contributed by the dissolved sites alone, and the permeability will be lower than k D DD . Increasing the total feed pressure, this negative gradient in the Langmuir sites is moderated by the increase in the CO2 sorption levels in the dissolved mode on the feed side which explains why the rvalue increases as the pressure goes from 100 psia to 500 psia. On the other hand, at still higher feed pressure (1000 psia) the r-value decreases. 280 8 7 6 5 4 3 2 1 500 psia 1500 psia 1000 psia 100 psia a 10/90 CO /CH feed 2 4 r 0 Residue 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate 70 60 50 b 100 psia 300 psia r 40 30 20 10 500 psia 1000 psia 50/50 CO /CH feed 2 4 0 Residue 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate 281 600 500 c 200 psia 400 r 300 200 500 psia 1000 psia 100 0 90/10 CO /CH feed 2 4 0 Residue 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate Figure A.7 Simulation of average r , the mass flux ratio of CO 2 to CH4 in the membrane for (a) 10/90 CO2/CH4 feed (b) 50/50 CO2/CH4 feed (b) 90/10 CO2/CH4 feed as a function of axial position, considering the frame of reference model (FM). These complex effects mean that there will be a negligible gradient for transport through the Langmuir sites and transport will be nearly governed by the dissolved mode. Therefore, for high CO2 feed partial pressures, increasing pressure from 1000 psia to 1500 psia decreases the r-value. This case never happens for pure gases because there is no competitive sorption, and consequently the CO2 sorption levels on the feed side will always be greater than on the permeate side. This situation also does not happen for CH4 because the permeate is leaner in CH4 than the feed. In the case where there is vacuum in the permeate this case also does not happen even though the permeate is richer in CO2 since the membrane surface in the permeate is maintained at all positions at zero pressure, the CO2 and CH4 sorption levels on the permeate side 282 will always be zero. Increasing the CO2 concentration in the feed to 50% and 90% will increase the Langmuir sorption on the feed side relative to the sorption on the permeate side, thereby making the Langmuir gradient less negative than the 10/90 case. As a result the r-value for the 50/50 mixture decreases at lower feed pressure values as compared to the 10/90 case as can seen in Figure A.7b. For the 90/10 CO2/CH4, the feed is close to the pure component and the Langmuir concentration need not be greater on the permeate side than on the feed side, as is the case when the feed stream is only 50% CO2 or less. This is why in (Figure. A.7(c)), the rvalue decreases as the feed pressure increases, a typical dual-mode response. Clearly, the sorption level, the r-value and the bulk flux contribution are avg avg coupled. As noted before, CO 2 and CH 4 increases with the increase in the feed pressure as shown in (Figure. 4.8). However, the effect of feed pressure on the rvalue is complicated since competitive sorption determines the sorbed concentrations on the feed and permeates side of the membrane (depending on the permeate pressure). At low CO2 feed partial pressures, increasing the feed pressure increases the r-value, and therefore, the bulk flux contribution of both components as can be seen from Eq.8. On the other hand, high CO2 feed partial pressures causes decreases in the r-value and in this case the bulk4 can reach plateau as CH shown in (Figure. A.8) for the 90/10 case. One conclusion can be taken from this analysis; the bulk flux contribution is more significant for higher permeate pressures (and higher intrinsic selectivity polymers), since this implies higher negative gradients in the Langmuir mode, and therefore, higher r-values as feed pressure increases. 283 A.6 Effect of Membrane Thickness and Area The bulk flux contribution of the 50/50 gas mixture was analyzed by plotting the required membrane area against the bulk flux contribution of CO2 and CH4. Membrane area can be increased by either increasing the fiber length or diameter. Simulations were performed here by increasing the fiber lengths. Simulations were not performed with increasing fiber diameters, because no effect would be observed, given the assumptions of the model. The active length of the fibers is varied between 10-250 cm. Clearly increasing the membrane area decreases bulk2 and bulk4 as can be seen in Figure A.9. The increase in the CO CH membrane area decreases the CO2 mole fraction in the feed side, and therefore leads to lower bulk2 and bulk4 . CO CH 284 6 5 CO bulk flux contribution (%) 4 3 2 1 0 0 200 400 600 800 1000 10/90 CO2/CH4 50/50 CO2/CH4 90/10 CO2/CH4 a 2 1200 Fugacity (psia) 30 25 CH bulk flux contribution (%) 20 15 10 5 0 10/90 CO2/CH4 50/50 CO2/CH4 90/10 CO2/CH4 b 4 0 200 400 600 800 Fugacity (psia) 1000 1200 Figure A.8 Bulk flux contribution of (a) CO2 (b) CH4 in 10/90 CO2/CH4, 50/50 CO2/CH4 and 90/10 CO2/CH4 feed as a function of total feed pressure. 285 25 20 Bulk flux contribution (%) 15 Carbon dioxide Methane 10 5 0 0 1 2 3 4 2 -6 Membrane area (cm ) [x10 ] 5 6 Figure A.9 Effect of membrane area on bulk flux contribution of CO2 and CH4 in 50/50 CO2/CH4 feed. This means that nearly all of the faster gas permeates in the first stages of the membrane and, in these conditions, the faster gas mole fraction is relatively small for the rest of the membrane length. In a counter current arrangement, this means that the bulk flux contribution is only higher in a small fraction of its length, located at the very end. As a net result, the bulk flux contribution of CO2 and CH4 decreases with the increase of membrane area. On the other hand, low membrane area lead to high CO2 mole fraction in the feed side and therefore, high bulk2 and bulk4 (Figure. A.10). This suggests that in the limit of a single stage, the CO CH bulk flux contribution of CO2 and CH4 is expected to reach a maximum. 286 5 a CO bulk flux contribution (%) 4 3 10 cm 250 cm 2 2 1 0 Residue 30 25 CH bulk flux contribution (%) 20 15 10 5 0 0 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate b 10 cm 250 cm 4 0 Residue 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate Figure A.10 Effect of membrane area on bulk flux contribution of CO2 and CH4 in 50/50 CO2/CH4 feed as a function of axial position. 287 This theoretical limit is consistent with observations from Kamaruddin and Koros (1997) for lab film experiments. One should also notice that increasing the membrane thickness (Figure. A.11) has the same effect as increasing the membrane area, since a given recovery of CO2 into the product is specified. The justification is analogous for these two cases. Figure A.12a shows the effect of increasing the membrane thickness on the bulk flux contribution of CO2 and CH4. Figure A.12b shows the bulk flux contribution profile of CO2 and CH4 along the membrane length for 0.1 um and 1.0 um thickness. 25 20 Bulk flux contribution (%) Carbon dioxide Methane 15 10 5 0 0 0.2 0.4 0.6 0.8 Membrane thickness, um 1 1.2 Figure A.11 Effect of membrane thickness on bulk flux contribution of CO2 and CH4 in 50/50 CO2/CH4 feed. 288 4.5 4 CO bulk flux contribution (%) 3.5 3 2.5 2 0.1 um 1.0 um a 2 1.5 1 0 Residue 30 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate b CH bulk flux contribution (%) 25 20 0.1 um 1.0 um 15 4 10 0 Residue 5 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate Figure A.12 Effect of of membrane thickness on bulk flux contribution of CO2 and CH4 in 50/50 CO2/CH4 feed as a function of axial position. 289 A.7 Effect of Permeate Pressure Increasing the permeate pressure for the 50/50 CO2/ CH4 gas mixture causes the CO2 concentration inside the membrane to increase and the CH4 concentration to decrease (due to the higher average CO2 mole fraction on the feed side of the membrane). Figure A.13b and c show the average mass concentration in the membrane for vacuum pressure, 20 psia and 50 psia permeate pressure along the membrane length. In the case of zero permeate pressure the flow is perpendicular to the membrane surface, cross flow type configuration and the cross flow model was used to simulate the flow pattern. As can be seen in Figure A.13b and c, the CO2 concentration is decreasing and the CH4 is increasing since CO2 is permeating along the membrane length. Increased permeate pressure reduces CO2 permeation by decreasing its driving force across the membrane. This can be clearly seen at the permeate exit where the CO2 permeate partial pressure is at its maximum. The CH4 permeation flux is also affected, but not as much. Therefore, increasing permeate pressure increases the r-value. Figure A.13a shows how r , the mass flux ratio of CO 2 to CH4, decreases from the feed/permeate end to the residue end. The effect of the permeate pressure, is clearly seen in Figure. A.13a: r increases with the decrease of permeate pressure especially at the feed end. However, this tendency becomes small along the membrane length, due to the decrease in CO2 permeate pressure for the three cases considered. 290 100 vacuum 20 psia 50 psia a 80 60 r 40 20 0 Residue 5 10 -2 0 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate 4 10 CO concentration (g/g) -2 vacuum 20 psia 50 psia b 3 10 -2 2 10 -2 2 1 10 -2 0 10 0 0 Residue 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate 291 7 10 -3 c -3 6 10 CH concentration (g/g) 5 10 -3 4 10 -3 4 3 10 -3 2 10 -3 vacuum 20 psia 50 psia 0.2 0.4 0.6 Axial position, x/L 0.8 1 Feed/Permeate 0 Residue Figure A.13 Effect of permeate pressure on (a). r ; (b). CO 2 average concentration inside the membrane; (c). CH4 average concentration inside the membrane in 50/50 CO2/CH4 feed. As a result, the two curves for 20 psia and 50 psia overlap at the residue end as shown in Figure A.13a; however, the vacuum pressure curve crosses the other two curves because of its high CO2 removal. This example shows that the crossflow opertaion at vacuum pressure outperforms the countercurrent configuration at 20 psia and 50 psia. As a net result, bulk2 increases and bulk4 CO CH decreases with the increase of pressure in the permeate side as shown in Figure A.14. The crossflow model shows the smallest effect of bulk flux contribution of CO2 and CH4, which is 2% and 5% respectively. 292 18 16 Bulk flux contribution (%) 14 12 10 8 6 4 2 Carbon dioxide Methane 0 10 20 30 40 Permeate pressure, psia 50 60 Figure A.14 Effect of permeate pressure on bulk flux contribution of CO2 and CH4 in 50/50 CO2/CH4 feed in a hollow-fiber module, operating in countercurrent. A.8 Diffusion and Frame of Reference Models Comparisons Let us consider the 10/90, 50/50 and 90/10 CO2/CH4 gas mixtures (typically shell side feed systems) based on the same gas separation as described before (Table. A.2). For the 10/90 CO2/CH4, bulk flux contribution of CO2 and CH4 was found to be negligible. Methane recovery, and percent stage cut are represented in Fig. A.15 and A.16 for the two permeation models, where a permeate pressure of 20 psia is considered, for three different concentrations. Some conclusions can be taken from Figure. A.15 and A.16, apart from whatever permeation model is used. The effect of feed pressure, is clearly seen: increasing the feed pressure increases the CO2 and CH4 permeation flux due to higher CO2 and CH4 driving across the membrane. Therefore, increasing feed pressure at fixed permeate pressure decreases methane recovery and increases percent stage cut. 293 The effect of not considering the frame of reference transport model is also illustrated in Figure. A.12 and Figure. A.13. Recovery is overestimated by the diffusion model by up to 7% and percent stage cut is underestimated by up to 6%. As already referred, the diffusion permeability model underestimates permeation fluxes. This difference is more significant for high CO2 partial pressures, due to the higher bulk flux contribution of CO2 and CH4. Figure A.17a shows the separation factor plotted against the feed pressure for three different permeate pressures. In the case of the 10/90 CO2/CH4 mixtures neglecting the bulk flux contribution is a good approximation because CO2 is present in small concentration. 12 10 8 % Stage cut FM model DM model a 2.5 2 % Error 6 4 2 0 10/90 CO /C H feed 2 1.5 1 4 0 200 400 600 800 Feed presure (psia) 1000 0.5 1200 294 45 40 35 % Stage cut 30 25 20 15 10 50/50 CO2/CH4 feed FM model DM model b 4.5 4 3.5 3 2.5 2 1.5 % Error 0 200 400 600 800 Feed pressure (psia) 1000 1 1200 90 80 70 % Stage cut 60 FM model DM model 7 6 5 % Error 4 50 40 30 20 90/10 CO /CH feed 2 4 3 2 1 1000 c 0 200 400 600 Feed pressure (psia) 800 Figure A.15 Percent stage cut and percent error ([% stage cut FM - % stage cut DM]/ [% stage cut DM] x 100%) as a function of feed pressure for (a). 10/90 CO2/CH4 feed; (b). 50/50 CO2/CH4 feed; (c). 90/10 CO2/CH4 feed considering the frame of reference model (FM) and the diffusion model (DM). 295 100 95 % Methane recovery 50/50 CO /CH feed 2 4 90 90/10 CO /CH feed 2 4 85 10/90 CO /CH feed 2 4 FM model DM model 80 0 200 400 600 800 1000 1200 Feed pressure (psia) Figure A.16 Simulation of CH4 recovery as a function of feed pressure, in a hollow-fiber module, operating in countercurrent, considering the frame of reference model (FM) and the diffusion model (DM) for 10/90 CO2/CH4 feed; 50/50 CO2/CH4 feed; and. 90/10 CO2/CH4 feed. As the CO2 concentration increases, the contribution of bulk flux contribution of both components increases and this increases the difference between the two models prediction as can be seen for the 50/50 CO2/CH4 case in Figure A.17b. Ignoring the bulk flux contribution could lead to incorrect results about the membrane performance. The difference also increases as the pressure increases, because of the increase in the bulk contribution of CO2 and CH4 as noted earlier. Under these conditions, the diffusion permeability model can overestimate selectivity up to 25% -- a rather serious error. 296 60 a 10/90 CO /CH feed 2 4 FM model DM model CO CH membrane selectivity 50 vacuum pressure 40 P permeate = 10 psia 30 P 20 permeate 4 = 20 psia 2/ 10 0 200 400 600 800 1000 1200 1400 1600 Feed pressure (psia) 60 FM model DM model CO CH membrane selectivity 50 vacuum pressure 40 50/50 CO2/CH4 feed 30 2/ 4 20 P permeate = 10 psia = 20 psia 600 800 1000 P 10 0 200 permeate b 1200 400 Feed pressure (psia) Figure A.17 Simulation of CO2/CH4 selectivity as a function of feed pressure for different permeate pressures, in a hollow-fiber module, operating in countercurrent, considering the frame of reference model (FM) and the diffusion model (DM) for (a). 10/90 CO2/CH4 feed; and (b). 50/50 CO2/CH4 feed. 297 Under a vacuum permeate, the selectivity isotherms, for material exhibiting dual mode behavior would show a uniform decreasing trend with total feed pressure as seen in Figure. A.17a and Figure. A.17b. In the case of non-zero permeate pressure, there is predicted to be a trade -off between the effects of competition and the effect of permeate pressure on the Langmuir concentration on the permeate side. At low feed pressures, the depression in separation factor caused by the permeate pressure will dominate. It is clear that permeate pressure is predicted to have the effect of reducing the selectivity of the membrane significantly. This observation has been demonstrated both experimentally and theoretically by Thundyil et al (1999). In terms of system design the most important parameters to consider are the compression power requirements for the downstream gas, the membrane selectivity, and methane recovery in order to achieve optimal separation of the CO2 and CH4 gases in the natural gas mixture. Unsuccessful membrane modeling and simulation can lead to erroneous information for the design, optimization and economics of the overall separation process; thereby undermining project success. The frame of reference model is fundamentally more correct than the simple diffusion model and, therefore, should be used in all membrane design calculations. Adding effects of plasticization, while not important for this particular membrane material is expected to be necessary for cellulose acetate and some polyimides at high CO2 feed pressures. A.9 Conclusions When modeling hollow-fiber membrane modules, it is common to neglect the bulk term in the transport equations. This work shows that this simplification may imply incorrect estimation of the membrane modules performance. In comparison to the frame of reference model formulation, the diffusion model overestimates CH4 recovery, membrane selectivity and underestimates cut- 298 fraction. This is particularly critical for systems with high CO2 partial pressure in the feed-side. Differences of up to 35% have been found for the present case. The simple diffusion based model was shown to overpredict membrane selectivity as high as 25% for the 90/10 CO2/CH4 mixture at 1000 psia feed pressure. The CH4 recovery was also overpredicted up to 7% by the diffusion model and stage cut was also underpredicted up to 7% by the diffusion model. This is very important from the design point of view. These additional permeation fluxes resulting from the bulk motion must be taken into account when sizing the downstream compressor. The lack of proper sizing may result in pre- mature compressor failures The frame of reference model FM is fundamentally more correct than the diffusion model DM and therefore, it should be used in all the modeling efforts of hollow fiber membranes. Natural gas not only contains CO2 and CH4 but also contains significant quantities of other fast species such as H2S and H2O that could contribute significantly to the total bulk contribution. This study was conducted for the binary system CO2 and CH4 but it can be extended for multicomponent mixtures as shown earlier on the model development section. The bulk flux contribution was shown to increase as the membrane thickness increases and membrane area decreases, due to the higher CO2 mole fraction on the feed side of the membrane. Increasing the permeate pressure also serves to increase the CO2 concentration on the feed side of the membrane, and therefore the bulk flux contribution of CO2 and CH4. In the case of a single stage, the bulk flux contribution of CO2 and CH4 is expected to reach a maximum. This situation in fact applies in most laboratory characterization of membrane properties with mixed gases. 299 Appendix B: Program Documentation B.1 Countercurrent-flow Membrane Program % Code simulates COUNTERCURRENT, MULTI-COMPONENT gas separation % in a hollow-fiber membrane module global Q k NC FeedPr PermPr F P FeedFl PermFl rjacob fvalue delP N=200; NC=2; kD=[0.02*76/14.7 0.006*76/14.7]; b=[0.01*76/14.7 0.001*76/14.7]; CH=[30. 20.]; DD=[2.27*1e-8 2.75*1e-9]; FF=[0.1 0.03]; K(1)=CH(1)*b(1)/kD(1); K(2)=CH(2)*b(2)/kD(2); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%% % Pressures : psia for i=1:N+2, FeedPr(i) = 200.; PermPr(i) = 20; end %%%%Temperatures : Kelvin T = 308.0; % Flow rates : cc-STP/sec for i=1:N+2, TotFeed(i)=0.0; TotPerm(i)=0.0; end (SCFH*7.43) TotFeed(N+2) = 50000.0*7.43; 300 % Feed Composition : mole fraction and flow rate F(N+2,1) = 0.50; F(N+2,2) = 0.50; FeedFl(N+2,1) = F(N+2,1)*TotFeed(N+2); FeedFl(N+2,2) = F(N+2,2)*TotFeed(N+2); % input shell-side(1) or bore-side feed(2) nval = 1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%% % FIBER DATA DENS=1.405; Nfibers = 300000; t=0.5*1d-4; % Fiber dimensions : centimeters (microns*1e-4) DO = 250.0*1D-4; DI = 125.0*1D-4; %Active fiber length : centimeters ActiveL = 100.0; dz = ActiveL/N; % Mass transfer area per stage delAk = 2*pi*DO/2*ActiveL*Nfibers/N; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%% % COMPONENT DATA % Molecular weights lb/lbmole MW =[44.00 16.00]; % Critical Temperatures : Kelvin Tc =[304.2 190.6]; % Critical Pressures : bar Pc =[73.8 46.0]; % Critical Volumes : cm3/mol Vc =[94.0 99.0]; % Permeance : cc-STP/cm^2-sec-psia (GPU*1e-6*5.17) % (1 GPU = 1e-6 cm3-STP / cm2-sec-cm Hg) for i=1:N+2, Q(i,1) = DD(1)*kD(1)/t; Q(i,2) = DD(2)*kD(2)/t; end sum1 =0; for j = 1:NC, 301 sum1 = sum1 + Q(N+1,j)*F(N+2,j); end sum2 = 0; for j = 1:NC, P(N+1,j) = Q(N+1,j)*F(N+2,j)/sum1; parF = F(N+2,j)*FeedPr(N+2); parP = P(N+1,j)*PermPr(N+1); if parP > parF P(N+1,j) = F(N+2,j)*FeedPr(N+2)/PermPr(N+1); end sum2 = sum2 + P(N+1,j); end if sum2 > 1 for j = 1:NC, P(N+1,j) = P(N+1,j)/sum2; end end %%%%%%%%%%%%%%%%%%% stage calculations begin %%%%%%%%%%%%%%%%%%%%% for i=N+1:-1:2, k = i; newton; TotFeed(i)=0; TotPerm(i)=0; for j = 1:NC, PermFl(i,j) = Q(i,j)*delAk*(FeedPr(i+1)*F(i+1,j) -PermPr(i)*P(i,j)); TotPerm(i) = TotPerm(i)+PermFl(i,j); FeedFl(i,j) = FeedFl(i+1,j)-PermFl(i,j); TotFeed(i) = TotFeed(i)+FeedFl(i,j); P(i-1,j) = P(i,j); end F(i,1) = FeedFl(i,1)/TotFeed(i); F(i,2) = FeedFl(i,2)/TotFeed(i); end 302 P(1,1)=0; P(1,2)=0; PermFl(1,1)=0; PermFl(1,2)=0; P(N+2,1)=0; P(N+2,2)=0; PermFl(N+2,1)=0; PermFl(N+2,2)=0; for i=2:N+1, TotPerm(i) = TotPerm(i) + TotPerm(i-1); end for iter=1:1000, % Calculate new feed flow rates for i=N+2:-1:2, for j=1:NC, fF(i,j)= F(i,j)*FeedPr(i); fP(i,j)= P(i,j)*PermPr(i); end DENF(i)=1+b(1)*fF(i,1)+b(2)*fF(i,2); DENP(i)=1+b(1)*fP(i,1)+b(2)*fP(i,2); end for i=N+2:-1:2, for j=1:NC, wFeed(i,j)=kD(j)*fF(i,j)*MW(j)/(22400*DENS)*(1+FF(j)*K( j)/DENF(i)); wPerm(i,j)=kD(j)*fP(i,j)*MW(j)/(22400*DENS)*(1+FF(j)*K( j)/DENP(i)); end end for i=2:N+1, for j=1:NC, PermFl(i,j)=FeedFl(i+1,j)-FeedFl(i,j); PermFl(i,j)=PermFl(i,j)*MW(j)/22400; 303 end end tolr=1d-10; iter1=0; errr=10000.; while errr > tolr, iter1=iter1+1; errr=0; for ii=2:N+1, r1(ii)= PermFl(ii,1)/PermFl(ii,2); AG1=(1-wPerm(ii,1)*(1+1/r1(ii)))/(1wFeed(ii,1)*(1+1/r1(ii))); AG2=(1-wPerm(ii,2)*(1+r1(ii)))/(1wFeed(ii,2)* (1+r1(ii))); PermFl(ii,1)=DENS*DD(1)*log(AG1)/(1+1/r1(ii)); PermFl(ii,2)=DENS*DD(2)*log(AG2)/(1+r1(ii)); rvalue(ii)=PermFl(ii,1)/PermFl(ii,2)r1(ii); errr = errr + abs(rvalue(ii)); end end for ii=2:N+1, ta1=(1+1/r1(ii)); ta2=(1-wFeed(ii,1)*ta1)*DENS*DD(1); ta3=ta2/(PermFl(ii,1)*ta1); ta4=exp(PermFl(ii,1)*ta1/DENS/DD(1))-1; ta5=1/ta1*(1-ta3*ta4); wavg1(ii)=ta5; bulk(ii,1)=ta1*ta5; tb1=(1+r1(ii)); tb2=(1-wFeed(ii,2)*tb1)*DENS*DD(2); tb3=tb2/(PermFl(ii,2)*tb1); tb4=exp(PermFl(ii,2)*tb1/DENS/DD(2))-1; tb5=1/tb1*(1-tb3*tb4); wavg2(ii)=tb5; bulk(ii,2)=tb1*tb5; 304 end for i=N+1:-1:2, deltPr(i,1)=F(i,1)*FeedPr(i)-P(i,1)*PermPr(i); deltPr(i,2)=F(i,2)*FeedPr(i)-P(i,2)*PermPr(i); Q(i,1)= 22400*PermFl(i,1)/(MW(1)*deltPr(i,1))/t; Q(i,2)= 22400*PermFl(i,2)/(MW(2)*deltPr(i,2))/t; end for j=1:NC, [B,C,D] = coeffmatrix(TotPerm,TotFeed,PermPr,FeedPr,Q,delAk,j); r(N)=-D(N)*FeedFl(N+2,j); D(N) = 0.; B(1) = 0.; [r] = thomas (B,C,D,r); for i=2:N+1, FeedFl(i,j)=r(i-1); end clear r end for i=2:N+1, TotFeednew(i) = 0; for j=1:NC, TotFeednew(i) = TotFeednew(i) + FeedFl(i,j); end end TotFeednew(N+2) = TotFeed(N+2); % Calculate new permeate flow rates PermFl(1,1)=0; PermFl(1,2)=0; for i=2:N+1, TotPermnew(i) = 0; for j=1:NC, 305 PermFl(i,j)=PermFl(i-1,j)+FeedFl(i+1,j)FeedFl(i,j); end TotPermnew(i)= TotPermnew(i-1)+TotFeednew(i+1)TotFeednew(i); end TotPermnew(1) = 0; for i=2:N+1, for j=1:NC, F(i,j) = FeedFl(i,j)/TotFeednew(i); P(i,j) = PermFl(i,j)/TotPermnew(i); end end for k=N+1:-1:2, nv=-1; for j=1:NC, X(k,j) = P(k,j); end XPr(k) = PermPr(k); Xtotal(k) = TotPermnew(k); [Vmix]=viscosity(k,NC,T,MW,Tc,Pc,X); [XPr]=pressure(k,NC,T,DI,dz,Vmix,XPr,Xtotal,Nfibers,nv) ; PermPr(k) = XPr(k); end % check post-iteration error errfeed = abs(TotFeednew(2)-TotFeed(2)); errperm = abs(TotPermnew(N+1)-TotPerm(N+1)); ratiof = errfeed/TotFeednew(2); ratiop = errperm/TotPermnew(N+1); if ratiof > 1e-8 | ratiop > 1e-8 for i=N+1:-1:2, TotFeed(i) = TotFeednew(i); 306 TotPerm(i) = TotPermnew(i); end else dsumCO2p=0; dsumCH4p=0; rsumCO2p=0; rsumCH4p=0; for i=N+1:-1:2, PermFl(i,1)=FeedFl(i+1,1)-FeedFl(i,1); PermFl(i,2)=FeedFl(i+1,2)-FeedFl(i,2); dsumCO2p=dsumCO2p+PermFl(i,1)*MW(1)/22400*(1bulk(i,1)); dsumCH4p=dsumCH4p+PermFl(i,2)*MW(2)/22400*(1bulk(i,2)); rsumCO2p=rsumCO2p+PermFl(i,1)*MW(1)/22400; rsumCH4p=rsumCH4p+PermFl(i,2)*MW(2)/22400; end dsump=dsumCO2p*22400/MW(1)+dsumCH4p*22400/MW(2); rsump=rsumCO2p*22400/MW(1)+rsumCH4p*22400/MW(2); BulkCO2=(rsumCO2p-dsumCO2p)/rsumCO2p*100; BulkCH4=(rsumCH4p-dsumCH4p)/rsumCH4p*100; dyCO2=dsumCO2p*22400/MW(1)/dsump; dyCH4=dsumCH4p*22400/MW(2)/dsump; ryCO2=rsumCO2p*22400/MW(1)/rsump; ryCH4=rsumCH4p*22400/MW(2)/rsump; dse=(dyCO2/dyCH4)/(F(N+2,1)/F(N+2,2)); rse=(ryCO2/ryCH4)/(F(N+2,1)/F(N+2,2)); sel=[rse;dse] SCUTR=(rsump)/TotFeed(N+2)*100; SCUTD=(dsump)/TotFeed(N+2)*100; 307 CH4RR=(FeedFl(N+2,2)rsumCH4p*22400/MW(2))/FeedFl(N+2,2)*100; CH4RD=(FeedFl(N+2,2)dsumCH4p*22400/MW(2))/FeedFl(N+2,2)*100; break end end x1=N+2:-1:2; x2=N+1:-1:2; for i=2:N+2, x1(i-1)=(x1(i-1)-2)/(N+2); y1(i-1)=F(i,1); y2(i-1)=F(i,2); end %plot(x1,y1,x1,y2) %hold on for i=N+1:-1:2, x2(i-1)=(x2(i-1)-1)/(N+1); PA2(i-1)=P(i,1)*PermPr(i); PB2(i-1)=P(i,2)*PermPr(i); y5(i-1)=bulk(i,1); y6(i-1)=bulk(i,2); y7(i-1)=r1(i); PA1(i-1)=F(i,1)*FeedPr(i); PB1(i-1)=F(i,2)*FeedPr(i); term1a(i-1)=DD(1)/(PA1(i-1)-PA2(i-1)); term1b(i-1)=DD(2)/(PA1(i-1)-PA2(i-1)); term2a(i-1)=kD(1)*(PA1(i-1)-PA2(i-1)); term2b(i-1)=kD(2)*(PA1(i-1)-PA2(i-1)); term3(i-1)=PA1(i-1)/(1+b(1)*PA1(i-1)+b(2)*PB1(i1)); term4(i-1)=PA2(i-1)/(1+b(1)*PA2(i-1)+b(2)*PB2(i1)); term5a(i-1)=FF(1)*CH(1)*b(1)*(term3(i-1)-term4(i1)); term5b(i-1)=FF(2)*CH(2)*b(2)*(term3(i-1)-term4(i1)); 308 Pa(i-1)=term1a(i-1)*(term2a(i-1)+term5a(i1))*14.7/76*1e6/t; Pb(i-1)=term1b(i-1)*(term2b(i-1)+term5b(i1))*14.7/76*1e6/t; end %plot(x2,Pb) %plot(x2,term2) %plot(x2,PA2,x2,PB2) %plot(x2,PA1,x2,PB1) %grid on %axis ([0 1 0 1]) %figure %plot(x2,y5,x2,y6) %xlabel('Feed Axial position, x/L Residue') %ylabel('Fraction of Bulk Flux Contribution') %title('Bulk Flux Contribution of CO2 and CH4 in a 90/10 CO2/CH4 mixed-gas mixture') %gtext('CO2') %gtext('CH4') %grid on %axis tight %figure %plot(x2,y7) %grid on %axis tight function [XPr] = pressure(k,NC,T,DI,dz,Vmix,XPr,Xtotal,Nfibers,nv) N=200; RI = DI/2; convtot = Xtotal(k)*(14.7/XPr(k))*(T/273.15); const = 8.0*Vmix/pi/(RI^4)*dz*convtot*1.45e-4/Nfibers; XPr(k-1) = XPr(k)-const*nv; 309 function [r] = thomas (b, d, a, r) %% function [r] = thomas (a, d, b, r) %% thomas algorithm for tridag. systems %% note: a, b, d are all of length n %% with a(n) = 0 and b(1) = 0. %% n = length(d); for k=1:n-1 a(k) = a(k) / d(k); r(k) = r(k) / d(k); d(k+1) = d(k+1) - b(k+1)*a(k); r(k+1) = r(k+1) - b(k+1)*r(k); end r(n) = r(n) / d(n); for j=n-1:-1:1 r(j) = r(j) - a(j)*r(j+1); end function [B,C,D] = coeffmatrix(TotPerm,TotFeed,PermPr,FeedPr,Q,delAk,j) N=200; com2 = TotPerm(2)/(PermPr(2)*delAk*Q(2,j)); C(1)=1+com2*(1+Q(2,j)*delAk*FeedPr(2)/TotFeed(2)); D(1) = -1*(com2+1); for i=3:N+1, com1 = TotPerm(i-1)/(PermPr(i-1)*delAk*Q(i-1,j)); com2 = TotPerm(i)/(PermPr(i)*delAk*Q(i,j)); B(i-1) = -1*com1*(1+Q(i-1,j)*delAk*FeedPr(i1)/TotFeed(i-1)); C(i1)=1+com1+com2*(1+Q(i,j)*delAk*FeedPr(i)/TotFeed(i)); D(i-1) = -1*(com2+1); end function yy = jacobian global Q k NC FeedPr PermPr F P FeedFl PermFl rjacob fvalue delP N=200; sumd=0; 310 for j=1:NC, sumd=sumd+Q(k,j)*(FeedPr(k+1)*F(k+1,j)PermPr(k)*P(k,j)); end for j=1:NC, rum = Q(k,j)*(FeedPr(k+1)*F(k+1,j)PermPr(k)*P(k,j)); for jj=1:NC, if j==jj rjacob(j,jj)= 1 - ( (1*sumd*PermPr(k)*Q(k,j) + rum*PermPr(k)*Q(k,j)) / (sumd*sumd) ); else rjacob(j,jj)= 1*rum*Q(k,jj)*PermPr(k)/(sumd*sumd); end end fvalue(j)= P(k,j)-rum/sumd; end function yyyyy = gaussian global Q k NC FeedPr PermPr F P FeedFl PermFl rjacob fvalue delP % modify matrices rjacob and fvalue simultaneously for i=1:NC-1, for j=i+1:NC, quo=rjacob(j,i)/rjacob(i,i); for k=i:NC, rjacob(j,k)=rjacob(j,k)-quo*rjacob(i,k); end fvalue(j)=fvalue(j)-quo*fvalue(i); end end % solve for delP vector delP(NC) = fvalue(NC)/rjacob(NC,NC); for i=NC-1:-1:1, sum=0; 311 for j=i+1:NC, sum=sum+rjacob(i,j)*delP(j); end delP(i)=(fvalue(i)-sum)/rjacob(i,i); end function y = newton global Q k NC FeedPr PermPr F P FeedFl PermFl rjacob fvalue delP tolf = NC*1D-3; tolp = NC*1D-3; for ntrial=1:300, jacobian; errf = 0.0; for j=1:NC, errf = errf + abs(fvalue(j)); end if errf < tolf return end for j=1:NC, fvalue(j) = -fvalue(j); end fvalue=[fvalue(1);fvalue(2)]; delP=rjacob\fvalue; errp = 0.0; for j=1:NC, P(k,j) = P(k,j) + delP(j); errp = errp + abs(delP(j)); end if errp < tolp return end end disp('Crossflow did not converge') 312 function [Vmix] = viscosity(k,NC,T,MW,Tc,Pc,X) N=200; for i=1:NC, Tr(i) = T/Tc(i); a(i) = 5.682*((MW(i)^3)*(Pc(i)^4)/Tc(i))^(1.0/6.0); b(i) = 0.807*Tr(i)^0.618 - 0.357*exp(-0.449*Tr(i)); c(i) = 0.340*exp(-4.058*Tr(i)) + 0.018; V(i) = a(i)*(b(i)+c(i)); end for i=1:NC, for j=1:NC, if i==j phi(i,j) = 1.0; else phi(i,j) = ((1+(V(j)/V(i))^0.5*(MW(i)/MW(j))^0.25)^2)/((8*(1+MW(j) /MW(i)))^0.5); end end end Vmix=0.0; for i=1:NC, sump=0.0; for j=1:NC, sump = sump + X(k,j)*phi(i,j); end Vmix = Vmix + (X(k,i)*V(i))/sump; end % units : Pa-s (micropoise*1e-7) Vmix = Vmix*1e-7; B.2 Equilibrium Program The rigorous VLE follows the model of Austgen (1989) and is too long to be listed here.An electronic copy is archieved with Dr. Gary Rochelle. 313 B.3 Rigorous Rate Model for MOR / DGA An excerpt of the rigorous rate model is shown below. Since a list of the whole program would be too long, we only show the equations that must be solved for one grid size. C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C VARIABLES DICTIONARY: SCALARS: n: NUMBER OF NODES H1: STEPSIZE FOR GRID SIZE ONE R: DIMENSIONLESS DISTANCE FROM INTERFACE I: INTEGER COUNTER, IDENTIFIED NODE NUMBER C: COSINE OF pi/2r AT R S: SINE OF pi/2r AT R T: TAN OF pi/2r AT R T1: TERM ONE IN MATERIAL BALANCE EQUATIONS SEE APPENDIX E T2: TERM 2 T3: TERM 3 T4: TERM 4 VECTORS Dr(l)=DERIVATIVE OF SPECIES L D2r(l)=SECOND DERIVATIVE OF SPECIES L RR: VECTOR OF FINITE RATE REACTIONS 1: CO2+OH- HCO32: DGA+H2O+CO2 DGACOO-+H3O+ 6: MOR+H2O+CO2 MORCOO-+H3O+ 8: MOR+DGA+CO2 MORCOO-+DGAH+ DELTA(n)=RESIDUALS: THESE ARE ALL 0 AT SOLUTION. Y(n*11): VECTOR OF MOLEFRACTIONS. AT A GIVEN NODE, SPECIES COME IN THE FOLLOWING ORDER 1: CO2 2: HCO33: CO3= 4: OH5: DGA 6: DGAH+ 7: DGACOO- 314 C C C C C C C C C C C C C C C C 8: MOR 9: MORH+ 10: MORCOOKF: FORWARD REACTION RATE CONSTANTS, SEE RR FOR REACTION NUMBERS K; EQUILIBRIUM CONSTANTS: NUMBERS ARE SAME AS RR. IN ADDITION: 3: HCO3- + OH- CO3= + H2O 4: H2O H3O+ + OH5: DGA+H2O DGAH+ + OH7: MOR+H2O MORH+ + OHCALCULATE RESIDUALS FROM NODES 1 TO N1 USING GRIDSIZE H1 CALCULATE RESIDUALS FROM NODES 1 TO N1 USING GRIDSIZE H1 do 10 i = 1,n1-1 r=real(i)*h1 C CALCULATE FIRST AND SECOND DERIVATIVES FOR ALL SPECIES AT EACH NODE C do 20 l=1,10 Dr(l)=1.0/(2.0*h1)*(-y(10*(i-1)+l) + y(10*(i+1)+l)) Dr2(l)=1.0/(h1*h1)*(y(10*(i-1)+l) -2.0*y(10*i+l) + y(10*(i+1)+l)) 20 continue C write (12,*) 'First Derivatives' C write (12,*) Dr C write (12,*) 'Second Derivatives' C write (12,*) Dr2 C C CALCULATE THE REACTION RATES FOR FINITE RATE C REACTIONS C RR(1)=kf(1)*y(10*i+1)*y(10*i+4) kf(1)/K(1)*y(10*i+2) RR(2)=kf(2)*y(10*i+1)*y(10*i+5)* kf(2)/K(2)*y(10*i+7)*K(4)/y(10*i+4) RR(3)=kf(3)*y(10*i+1)*y(10*i+8)- 315 * kf(3)/K(6)*y(10*i+10)*K(4)/y(10*i+4) RR(4)=kf(4)*y(10*i+1)*y(10*i+8)*y(10*i+5)* kf(4)/K(8)*y(10*i+10)*y(10*i+6) C CALCULATE TRIG FUNCTIONS AT R C c=cos(pi/2.0*r) s=sin(pi/2.0*r) ta=tan(pi/2.0*r) C C CALCULATE LEADING TERMS C t1=4.0*e/(pi*pi)*s*s*c*c t2=4.0/(pi*pi)*c*c*c*c*e/D(1) t3=-4.0/pi*e*s*s*s*c + 4.0/pi*e*ta*c*c t4=-4.0/pi*e/D(1)*c*c*c*s c write (12,*) 'Term 1 and 2' c write (12,*) t1,t2 c write (12,*) 'Term 3 and 4' c write (12,*) t3,t4 C C RESIDUALS CORRESPONDING TO THE PIPERAZINE MATERIAL BALANCE C C RESIDUALS CORRESPONDING TO TOTAL CARBON BALANCE delta(10*i+1)=(t1+D(1)*t2)*Dr2(1) + (t3+D(1)*t4)*Dr(1) * + (t1+D(2)*t2)*Dr2(2) + (t3+D(2)*t4)*Dr(2) * + (t1+D(3)*t2)*Dr2(3) + (t3+D(3)*t4)*Dr(3) * + (t1+D(7)*t2)*Dr2(7) + (t3+D(7)*t4)*Dr(7) * + (t1+D(10)*t2)*Dr2(10) + (t3+D(10)*t4)*Dr(10) C RESIDUAL CORRESPONDING TO CARBON DIOXIDE MATERIAL BALANCE delta(10*i+2)=(t1+D(1)*t2)*Dr2(1) + (t3+D(1)*t4)*Dr(1) * - RR(1)- RR(2)- RR(3)- RR(4) C RESIDUAL CORRESPONDING TO CO3= / HCO3- EQUILIBRIUM delta(10*i+3)=K(3)*y(10*i+2)*y(10*i+4) - y(10*i+3) 316 C Residuals corresponding to dga balance delta(10*i+4)=(t1+D(5)*t2)*Dr2(5) + (t3+D(5)*t4)*Dr(5)+ * (t1+D(6)*t2)*Dr2(6) + (t3+D(6)*t4)*Dr(6)+ * (t1+D(7)*t2)*Dr2(7) + (t3+D(7)*t4)*Dr(7) C Residual corresponding to dgacoo- balance delta(10*i+5)=(t1+D(7)*t2)*Dr2(7) + (t3+D(7)*t4)*Dr(7) * +RR(2) C Residuals corresponding to dga proton equilibrium delta(10*i+6)=K(5)*y(10*i+5)-y(10*i+6)*y(10*i+4) C RESIDUAL CORRESPONDING TO ELECTRONEUTRALITY delta(10*i+7) = y(10*i+6)+ y(10*i+9) * (y(10*i+2)+2.0*y(10*i+3)+y(10*i+4)+y(10*i+7)+y(10* i+10)) C Residuals corresponding to mor balance delta(10*i+8)=(t1+D(8)*t2)*Dr2(8) + (t3+D(8)*t4)*Dr(8)+ * (t1+D(9)*t2)*Dr2(9) + (t3+D(9)*t4)*Dr(9)+ * (t1+D(10)*t2)*Dr2(10) + (t3+D(10)*t4)*Dr(10) C Residual corresponding to dgacoo- balance delta(10*i+9)=(t1+D(10)*t2)*Dr2(10) + (t3+D(10)*t4)*Dr(10) * +RR(3)+RR(4) C Residuals corresponding to dga proton equilibrium delta(10*i+10)=K(7)*y(10*i+8)-y(10*i+9)*y(10*i+4) C C WRITE RESIDUALS FOR NODE I C C write (*,*) 'Residuals at Node ',i C do 30 l=1,14 C write (*,*) delta(14*i+l) C30 continue C 317 C FINISH CALCULATIONS AT NODE I 10 CONTINUE 318 Appendix C: Permeation Data Table C.1 Experimental data of conditioning by 10/90 CO2/CH4 mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 35 0C. Sample # 1 Pressure (psia) Gas Mixture PERMEANCE (GPU) CO2 CH4 CO2/CH4 before before before second day third day fourth day fifth day after after after 108.7 160.7 215.7 215.7 215.7 214.7 214.7 214.7 164.7 107.7 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 27.1 28.2 28.2 28.5 29.0 29.0 29.1 28.8 28.9 27.5 18.9 18.2 17.2 17.4 17.1 17.2 17.4 17.4 18.4 19.4 0.696 0.644 0.612 0.609 0.589 0.594 0.598 0.606 0.639 0.702 Table C.2 Experimental data of conditioning by 10/90 CO2/CH4 mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 35 0C. Sample # 2 Pressure (psia) Gas Mixture PERMEANCE (GPU) CO2 CH4 CO2/CH4 before first day second day third day fourth day fifth day after 200 200 200 200 200 200 200 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 33..3 33.4 32.9 33.0 33.1 32.8 32.7 8.6 8.9 8.3 8.2 8.3 8.3 8.3 0.258 0.267 0.251 0.249 0.250 0.254 0.254 319 Table C.3 Experimental data of conditioning by 10/90 CO2/CH4 + 500 ppm nheptane mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 35 0C. Sample # 1 Pressure (psia) Gas Mixture PERMEANCE (GPU) CO2 CH4 CO2/CH4 before before before first day second day third day fourth day fifth day after after after 110.7 162.7 215.7 204.7 216.7 220.7 220.7 220.7 214.7 158.7 100.7 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 29.4 29.8 29.6 29.3 28.4 28.2 28.2 28.1 28.1 28.4 27.0 16.3 14.7 13.8 12.8 11.7 11.5 11.5 11.5 11.8 13.4 15.1 0.553 0.492 0.464 0.435 0.411 0.407 0.409 0.409 0.420 0.471 0.560 Table C.4 Experimental data of conditioning by 10/90 CO2/CH4 + 500 ppm nheptane mixture CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 35 0C. Sample # 2 Pressure (psia) Gas Mixture PERMEANCE (GPU) CO2 CH4 CO2/CH4 before before before second day third day fourth day fifth day after after after 114.7 166.7 216.7 217.7 218.7 218.7 207.0 212.7 166.7 116.7 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 28.4 28.6 29.0 27.8 27.8 27.7 27.5 27.7 28.0 27.9 14.0 13.3 12.6 11.0 10.9 10.9 10.9 11.4 13.0 14.7 0.494 0.465 0.437 0.394 0.392 0.395 0.396 0.412 0.466 0.525 320 Table C.5 Experimental data of conditioning by 10/90 CO2/CH4 + 300 ppm nheptane mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 400 psia and 35 0C. Sample # 1 Pressure (psia) Gas Mixture PERMEANCE (GPU) CO2 CH4 CO2/CH4 before first day second day sixth day after 400 400 400 400 400 10/90 CO2/CH4 10/90 CO2/CH4 +300 ppm Heptane 10/90 CO2/CH4 +300 ppm Heptane 10/90 CO2/CH4 +300 ppm Heptane 10/90 CO2/CH4 29.1 28.7 28.4 28.9 28.5 15.6 14.3 13.8 13.6 14.1 0.537 0.499 0.487 0.471 0.494 Table C.6 Experimental data of conditioning by 10/90 CO2/CH4 + 300 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 35 0C. Sample # 1 Pressure (psia) Gas Mixture PERMEANCE (GPU) CO2 CH4 CO2/CH4 before before before second day third day fourth day fifth day after after after 114.7 10/90 CO2/CH4 166.7 10/90 CO2/CH4 216.7 10/90 CO2/CH4 217.7 10/90 CO2/CH4 +300 ppm Toluene 218.7 10/90 CO2/CH4 +300 ppm Toluene 218.7 10/90 CO2/CH4 +300 ppm Toluene 207.0 10/90 CO2/CH4 +300 ppm Toluene 212.7 10/90 CO2/CH4 166.7 10/90 CO2/CH4 116.7 10/90 CO2/CH4 28.1 28.9 29.4 27.3 26.9 27.0 27.0 25.9 25.1 24.7 18.2 17.6 16.9 10.7 11.0 11.1 11.2 27.1 26.8 27.1 0.646 0.608 0.575 0.391 0.407 0.412 0.415 1.046 1.068 1.096 321 Table C.7 Experimental data of conditioning by 10/90 CO2/CH4 + 300 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 35 0C. Sample # 2 Pressure (psia) Gas Mixture PERMEANCE (GPU) CO2 CH4 CO2/CH4 before second day third day fourth day fifth day after 200 200 200 200 200 200 10/90 CO2/CH4 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 30.4 28.9 28.4 28.4 28.3 27.2 11.0 7.2 7.3 7.4 7.5 17.2 0.362 0.249 0.257 0.261 0.265 0.632 Table C.8 Experimental data of conditioning by 10/90 CO2/CH4 + 300 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 600 psia and 35 0C. Sample # 1 Pressure (psia) Gas Mixture PERMEANCE (GPU) CO2 CH4 CO2/CH4 before before before first day second day third day fourth day fifth day after after after 203 400 604 610 610 611 612 614 602 400 206 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 32.4 31.0 28.2 22.7 22.6 22.6 22.6 22.5 24.1 24.8 25.1 15.1 11.4 9.5 6.5 6.7 6.5 6.6 6.7 20.6 21.3 20.7 0.465 0.368 0.337 0.285 0.294 0.290 0.295 0.299 0.856 0.861 0.827 322 Table C.9 Experimental data of conditioning by 10/90 CO2/CH4 + 300 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 600 psia and 35 0C. Sample # 2 Pressure (psia) Gas Mixture CO2/CH4 before first day second day third day fourth day fifth day after 600 600 600 600 600 600 600 10/90 CO2/CH4 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 28.1 22.1 22.5 22.5 22.5 22.4 23.5 PERMEANCE (GPU) CO2 CH4 10.5 7.86 8.13 8.15 8.20 8.30 21.0 0.374 0.356 0.361 0.362 0.364 0.371 0.894 Table C.10 Experimental data of conditioning by 10/90 CO2/CH4 + 500 ppm nheptane mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 600 psia and 35 0C. Sample # 1 Pressure (psia) Gas Mixture CO2/CH4 before before before first day second day third day fourth day fifth day after after after 216 415 618 605 605 605 600 610 212 414 608 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 33.7 35.3 34.4 34.1 32.9 31.1 30.5 30.0 29.9 29.8 29.3 PERMEANCE (GPU) CO2 CH4 10.0 8.5 7.7 7.6 7.8 7.9 7.8 7.9 11.7 9.8 8.5 0.298 0.242 0.225 0.224 0.237 0.255 0.257 0.263 0.392 0.330 0.290 323 Table C.11 Experimental data of conditioning by 10/90 CO2/CH4 + 500 ppm nheptane mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 600 psia and 35 0C. Sample # 2 ! ! Pressure (psia) Gas Mixture PERMEANCE (GPU) CO2 CH4 CO2/CH4 before first day second day third day fourth day fifth day after 600 600 600 600 600 600 600 10/90 CO2/CH4 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 29.6 29.4 28.7 28.1 27.5 26.1 25.9 8.0 8.1 8.1 8.2 8.3 8.4 9.0 0.270 0.276 0.282 0.292 0.302 0.322 0.347 Table C.12 Experimental data of conditioning by 10/90 CO2/CH4 mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 600 psia and 35 0 C. Sample # 1 Pressure (psia) Gas Mixture PERMEANCE (GPU) CO2 CH4 CO2/CH4 before before before first day first day second day third day fourth day fifth day after after after 210 402 614 614 611 606 602 600 600 600 400 200 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 31.5 29.8 27.4 27.4 28.4 28.2 28.2 29.1 28.4 30.3 30.1 28.4 10.8 9.4 8.6 8.6 9.6 8.4 9.7 9.8 9.9 10.4 13.5 9.9 0.343 0.315 0.315 0.315 0.339 0.297 0.343 0.336 0.349 0.342 0.449 0.349 324 Table C.13 Experimental data of conditioning by 10/90 CO2/CH4 + 100 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 400 psia and 55 0C. Sample # 1 " " Pressure (psia) Gas Mixture PERMEANCE (GPU) CO2 CH4 CO2/CH4 before first day second day third day fourth day fifth day after 200 200 200 200 200 200 200 10/90 CO2/CH4 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 20.6 21.7 21.6 21.4 21.3 21.1 20.5 23.4 18.2 18.0 18.0 17.8 17.6 23.3 1.139 0.838 0.834 0.843 0.839 0.837 1.138 Table C.14 Experimental data of conditioning by 10/90 CO2/CH4 + 300 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 55 0C. Sample # 1 Pressure (psia) Gas Mixture PERMEANCE (GPU) CO2 CH4 CO2/CH4 before first day second day third day fourth day fifth day after 200 200 200 200 200 200 200 10/90 CO2/CH4 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 20.4 22.5 22.6 22.4 23.1 22.6 20.6 18.0 12.6 12.4 12.3 12.2 12.3 17.7 0.884 0.560 0.550 0.547 0.529 0.544 0.861 325 Table C.15 Experimental data of conditioning by 10/90 CO2/CH4 + 100 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 55 0C. Sample # 1 # # Pressure (psia) Gas Mixture PERMEANCE (GPU) CO2 CH4 CO2/CH4 before second day third day fourth day fifth day after 200 200 200 200 200 200 10/90 CO2/CH4 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 +300 ppm Toluene 10/90 CO2/CH4 23.4 24.5 24.4 24.4 24.3 22.6 16.4 13.3 13.3 13.5 13.7 16.9 0.700 0.543 0.547 0.553 0.562 0.747 Table C.16 Experimental data of conditioning by 10/90 CO2/CH4 + 500 ppm toluene mixture on CO2 permeance, CH4 permeance and the CO2/CH4 selectivity at 200 psia and 55 0C. Sample # 1 Pressure (psia) Gas Mixture PERMEANCE (GPU) CO2 CH4 CO2/CH4 before before before first day second day third day fourth day fifth day after after after 100 150 200 200 200 200 200 200 200 150 100 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 +500 ppm Heptane 10/90 CO2/CH4 10/90 CO2/CH4 10/90 CO2/CH4 18.5 19.5 19.6 18.9 19.1 19.1 19.1 19.0 19.2 19.3 17.5 20.0 19.1 18.3 14.3 14.4 14.4 14.3 14.3 17.6 18.3 19.3 1.084 0.976 0.932 0.754 0.754 0.754 0.746 0.748 0.947 1.012 1.017 326 Appendix D: Equation for Compressibility Factors for Penetrants at 35 C The following were derived from least square curve fits on pressure and temperature dependent compressibility factor data for each of the penetrants [reference 13 in Anshu s thesis]. D.1 Nitrogen Z = 1 - 8.59x10-6 p + 1.08x10-9 p2 + 1.07x10-13 p3 D.2 Carbon Dioxide Z = 1 - 3.38x10-4 p + 6.17x10-8 p2 - 1.69x10-10 p3 D.3 Methane Z = 1 - 1.05x10-4 p + 3.82x10-9 p2 + 5.20e-12 p3 327 Appendix E: Desorption Isotherm Sample Calculation The following is a sample calculation for the desorption isotherm after conditioning with 10/90 CO2/CH4 + 500 ppm n-heptane and then probing with CO2. Using equations D.2, F.1, F.2, F.3 and Table E.1, PR, PC, zC and zC can be calculated as shown in Table E.2 and E.3. Table E.1 Voltage Measurements Evacuum,PS (V) 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 Evacuum,R (mV) 0.393 0.393 0.393 0.393 0.393 0.393 0.393 0.393 0.393 0.393 0.393 0.393 0.393 0.393 0.393 0.393 0.393 0.393 0.393 0.393 Evacuum,C (mV) -0.438 -0.438 -0.438 -0.438 -0.438 -0.438 -0.438 -0.438 -0.438 -0.438 -0.438 -0.438 -0.438 -0.438 -0.438 -0.438 -0.438 -0.438 -0.438 -0.438 EPS (V) 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 10.337 ER (mV) 1.669 1.897 1.466 1.662 1.038 1.321 0.731 1.006 0.392 0.684 0.393 0.540 0.393 0.470 0.390 0.434 0.394 0.417 0.392 0.406 EC (mV) 1.457 1.165 1.166 0.916 0.918 0.560 0.563 0.226 0.226 -0.113 -0.112 -0.267 -0.271 -0.349 -0.349 -0.388 -0.389 -0.408 -0.411 -0.419 Table E.2 Pressure and moles desorbed calculations PR (psia) 36.168 42.631 30.414 35.970 18.282 26.304 9.581 PC (psia) 50.789 42.963 42.990 36.290 36.343 26.748 26.829 zR 0.989 0.988 0.991 0.990 0.995 0.992 0.997 zC 0.985 0.987 0.987 0.989 0.989 0.992 0.992 - n P -0.499 -0.453 -0.699 328 17.375 -0.028 8.248 0.000 4.167 0.000 2.183 -0.085 1.162 0.028 0.680 -0.028 0.368 17.796 17.796 8.711 8.737 4.583 4.476 2.385 2.385 1.340 1.313 0.804 0.724 0.509 0.995 1.000 0.998 1.000 0.999 1.000 0.999 1.000 1.000 1.000 1.000 1.000 1.000 n P = moles sorbed 0.995 0.995 0.998 0.997 0.999 0.999 0.999 0.999 1.000 1.000 1.000 1.000 1.000 -0.905 -1.345 -1.009 -0.596 -0.456 -0.267 -0.236 -6.47 Table E.3 Concentartion Calculation, polymer sample volume = 0.239 cc. PC Moles sorbed C, cc(STP/cc - n P (psia) polymer = n P - n P 50.8 43.0 36.3 26.7 17.8 8.7 4.6 2.4 1.3 0.8 0.5 0 -0.499 -0.453 -0.699 -0.905 -1.345 -1.009 -0.596 -0.456 -0.267 -0.236 n P = 6.47 6.47 5.97 5.51 4.81 3.91 2.56 1.55 0.96 0.50 0.24 0.00 27.05 24.96 23.07 20.14 16.36 10.73 6.51 4.01 2.10 0.99 0.00 0 329 Appendix F: Working Equations for Sorption Isotherm Calculations When converting voltages to pressures, we take into account two deviations from ideal transducer performance: 1. Non-zero signal at vacuum. The transducer will give a non-zero voltage reading when the system is essentially at vacuum. 2. Variable DC voltage from power supply. The transducers are powered by a DC voltage supply which is designed to output ~10V. However, this output voltage may fluctuate due to changes in ambient conditions (mainly temperature) The working equation for converting voltage to pressure (psia) : P= P = pressure, psia E 1 E vacuum C.F E PS E vacuu, PS (F.1) C.F. = calibration factor; unique for each transducer; obtain from vendor E = voltage reading from transducer, V EPS = voltage reading from power source, V Evacuum = voltage reading from transducer at vacuum, V Evacuum, PS = voltage reading from power source at conditions of vacuum reading,V 330 Table F.1 Channel 1 Calibration P, psia 0 65.5 114.9 219.6 427.6 623 823 Evacuum,PS 10.356 10.356 10.356 10.356 10.356 10.356 10.356 Evacuum 0.432 0.432 0.432 0.432 0.432 0.432 0.432 EPS 10.356 10.356 10.356 10.356 10.356 10.356 10.356 E 0.432 2.748 4.492 8.2 15.543 22.444 29.522 E/EPSVvacuum/Evacuum,PS 0.00000 0.22364 0.39204 0.75010 1.45915 2.12553 2.80900 100 0 y = -0 .030 062 + 293.04 x R = 1 80 0 P (psia) 60 0 40 0 20 0 0 0 0 .5 1 E /E -E PS 1.5 vacuum /E 2 vacuum,PS 2 .5 3 Figure F.1 Calibration curve for channel # 1 331 Table F.2 Channel 2 Calibration P, psia Evacuum,PS Evacuum 0 65.5 114.9 219.6 427.6 623 823 10.356 10.356 10.356 10.356 10.356 10.356 10.356 -0.427 -0.427 -0.427 -0.427 -0.427 -0.427 -0.427 EPS 10.356 10.356 10.356 10.356 10.356 10.356 10.356 E -0.427 2.02 3.862 7.776 15.543 22.861 30.345 E/EPSVvacuum/Evacuum,PS 0.00000 0.23629 0.41416 0.79210 1.54210 2.24874 2.97142 100 0 y = 0.1445 8 + 276.98x R= 1 80 0 P (psia) 60 0 40 0 20 0 0 0 0 .5 1 E /E PS 1 .5 -E vacuum 2 /E 2 .5 vacuum,P S 3 3 .5 Figure F.2 Calibration curve for channel # 2 Therefore, C.FR = 1/293 and C.FC = 1/277. (F.2) 332 The equation of state: PV = znRT P = pressure (from transducer) [psia] V = volume (must be calibrated) [ml] z = compressibility factor (a function of pressure, see appendix D) R = ideal gas constant [ml psia / mol K] T = temperature [K] n = number of moles [mol] We utilize the fact that the number of sorbate moles initially introduced into the system remains constant. Initial : nT,I = nR, I + nC,I + nP, I Final : nT,F = nR, F + nC,F + nP, F where: R = Reservoir (or volume A) C = Sample cell (or volume B) P = Polymer sample I = Initial F = Final T = Total Since nT = constant, then nT = 0 = (nR, I + nC,I + nP, I) - (nR, F + nC,F + nP,F) 333 = nR + nC + nR nP nP = n = nC - We can express nC and nR in terms of pressure using: V P RT z Therefore, n P = where, PC, I PC, F 1 (VC VP )* zP RT zP C,I C,F +V R PR , I PR , F * zP zP R ,I R,F (F.3) VR = volume of the reservoir VC - VP = volume of sample cell - volume of sample VC and VR were determined from calibration by using a ball of known volume. Finally, to get the sorbate concentration, simply divide moles sorbed by the sample volume. Table F.3 Expansion No ball EPS (V) 10.336 10.336 10.336 10.336 10.336 10.336 10.336 10.336 10.336 10.336 10.336 ER (mV) 4.909 2.950 9.942 6.923 13.519 10.677 17.122 14.350 21.088 18.173 24.652 EC PR (mV) (psia) -0.431 128.188 2.265 72.655 2.265 270.861 6.458 185.279 6.458 372.260 10.411 291.696 10.411 474.396 14.273 395.816 14.273 586.822 18.340 504.189 18.341 687.853 Average Standard deviation PC (psia) 0.027 72.291 72.291 184.682 184.682 290.640 290.640 394.158 394.158 503.172 503.198 zR 0.987 0.992 0.972 0.981 0.962 0.970 0.952 0.959 0.941 0.949 0.931 zC 1.000 0.992 0.992 0.981 0.981 0.970 0.970 0.960 0.960 0.949 0.949 VR/VC 1.28391 1.28641 1.29011 1.29322 1.29479 1.29368 1.29035 0.00438 334 Table F.4 Expansion with ball (VB = 0.719 cm3) EPS (V) 10.336 10.336 10.336 10.336 10.336 10.336 10.336 10.336 10.336 10.336 10.336 ER (mV) EC (mV) PR (psia) PC (psia) zR 0.988 0.993 0.972 0.981 0.961 0.969 0.951 0.958 0.941 0.948 0.931 zC 1.000 0.993 0.993 0.981 0.981 0.969 0.969 0.959 0.959 0.948 0.948 V R/ (VC-VB) 1.36620 1.36451 1.36576 1.37145 1.36874 1.37070 1.368 0.003 4.515 2.786 9.930 6.950 13.667 10.861 17.383 14.674 20.968 18.323 24.886 -0.433 117.019 2.096 68.006 2.095 270.520 6.487 186.045 6.486 376.455 10.619 296.912 10.620 481.795 14.623 405.001 14.621 583.420 18.517 508.441 18.518 694.486 Average Standard deviation 0.000 67.788 67.761 185.486 185.459 296.242 296.269 403.567 403.513 507.943 507.970 VR/VC = 1.29035 and VR/(VC-VB) = 1.368, therefore; VR = 16.355 cm3 and VC = 12.675 cm3 335 Appendix G: Polynomial Fitting Parameters for Permeation and Sorption Results G.1 Permeation Results Fitting Table G.1 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 mixture at 200 psia and 35 0C Parameter CO2 CH4 Uncond Cond Uncond Cond A 19.593 20.882 0.87297 0.89485 B -0.015769 -0.11291 -0.002281 -0.0024876 C -0.0044115 -0.0022955 4.825e-06 5.1375e-06 R 1 1 1 1 Table G.2 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 + 500 ppm n-heptane mixture at 200 psia and 35 0C Parameter CO2 CH4 Uncond Cond Uncond Cond A 15.443 18.509 0.55753 0.66394 B -0.11976 -0.3169 -0.00061258 -0.0013311 C -0.0005279 -0.00081523 -2.7934e-08 7.8276e-08 R 1 1 1 1 Table G.3 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 + 300 ppm toluene mixture at 200 psia and 35 0C Parameter CO2 CH4 Uncond Cond Uncond Cond A 19.062 30.338 0.74309 1.1779 B -0.047475 -0.42965 -0.0010289 -0.00089034 C -0.0024133 0.013044 8.5658e-07 1.0512e-06 R 1 1 1 1 336 Table G.4 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 mixture at 600 psia and 35 0C Parameter CO2 CH4 Uncond Cond Uncond Cond A 13.066 19.2 0.4041 0.67 B -0.12621 -0.35 -0.0004075 -0.0015444 C 0.00087081 0.00325 4.4565e-07 1.7593e-06 R 1 1 1 1 Table G.5 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 + 500 ppm n-heptane mixture at 600 psia and 35 0C Parameter CO2 CH4 Uncond Cond Uncond Cond A 12.293 14.416 0.39639 0.48313 B -0.13167 -0.14933 -0.00065157 -0.0005618 C 0.00092086 0.00084802 6.1861e-07 3.79e-07 R 1 1 1 1 Table G.6 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 + 300 ppm toluene mixture at 600 psia and 35 0C Parameter CO2 CH4 Uncond Cond Uncond Cond A 21.175 18.612 0.64493 0.7483 B -0.33086 0.1337 -0.0011254 0.00052793 C 0.0022969 -0.0016612 1.028e-06 -6.0509e-07 R 1 1 1 1 337 G.2 Sorption Results Fitting Table G.7 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 at 600 psia and 35 0C Parameter CO2 CH4 Uncond Cond Uncond Cond A -0.10954 -0.39815 -0.029384 -0.32924 B 1.4012 1.2557 0.14833 0.15835 C -0.054667 -0.032233 -0.00044169 -0.00050493 D 0.0012007 0.0004567 8.1322e-07 1.0129e-06 E -9.6909e-06 -2.5049e-06 -5.8692e-10 -8.1267e-10 R 0.99945 0.99963 0.9997 0.99984 Table G.8 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 + 300 ppm toluene mixture at 600 psia and 35 0C. Parameter CO2 CH4 Uncond Cond Uncond Cond A -0.35637 -0.38796 -0.092317 -0.2926 B 1.1234 1.3136 0.12099 0.159 C -0.033667 -0.04227 -0.00036429 -0.00060642 D 0.00064854 0.00075903 7.612e-07 1.3311e-06 E -4.8373e-06 -5.1031e-06 -6.2818e-10 -1.0739e-09 R 0.99977 0.99967 0.99981 0.99981 Table G.9 Summary of fitting parameters, A, B, C, D and E, for CO2 and CH4 in unconditioned and conditioned samples with 10/90 CO2/CH4 + 500 ppm n-heptane mixture at 600 psia and 35 0C Parameter CO2 CH4 Uncond Cond Uncond Cond A -0.2029 -0.16018 -0.3261 -0.20857 B 1.2471 1.4831 0.14692 0.15863 C -0.038751 -0.059473 -0.00047941 -0.00053159 D 0.00068818 0.0012957 1.0072e-06 1.1122e-06 E -4.5684e-06 -1.0294e-05 -8.1374e-10 -8.9353e-10 R 0.99967 0.99923 0.99983 0.99987 338 Appendix H: CO2 Solubility and Rate Data In this Appendix, the gas film resistance, % CO2 removal and % approach to equilibrium are calculated as; % Gas film resistance = (PbulkCO2 - PintCO2)/( PbulkCO2 - P*CO2) *100% % CO2 removal = (PINCO2 - POUTCO2)/ PINCO2*100% % Approach to equilibrium = PintCO2/ P*CO2*100% Table H.1 65 wt% DGA solubility and rate T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp , g/cm3 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium $ 27.05 1.64E-07 27.20 3.97E-07 27.25 5.79E-07 27.75 7.37E-07 27.73 8.88E-07 1.16E-02 2.38E-02 3.58E-02 4.82E-02 6.05E-02 8.53E-03 1.65E-02 2.53E-02 3.49E-02 4.46E-02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.32E-02 2.77E-02 4.12E-02 5.50E-02 6.86E-02 1.01E-02 2.03E-02 3.08E-02 4.19E-02 5.31E-02 26 31 29 28 26 23 27 25 24 23 0.00 0.00 0.00 0.00 0.00 5.37E-05 2.47E-05 0 11.5 1.06 5.40E-05 2.47E-05 0 11.4 1.06 5.52E-05 2.47E-05 0 11.4 1.06 5.55E-05 2.47E-05 0 11.1 1.06 5.58E-05 2.47E-05 0 11.1 1.06 40.85 1.61E-07 41.10 3.92E-07 41.10 5.56E-07 41.10 7.22E-07 41.08 8.71E-07 1.14E-02 2.34E-02 3.52E-02 4.74E-02 5.95E-02 8.46E-03 1.63E-02 2.54E-02 3.47E-02 4.42E-02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.29E-02 2.71E-02 4.04E-02 5.39E-02 6.73E-02 9.97E-03 2.00E-02 3.06E-02 4.14E-02 5.23E-02 26 30 28 27 26 23 26 24 23 22 0.00 0.00 0.00 0.00 0.00 339 kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 5.50E-05 3.20E-05 0 6.5 1.05 61.98 2.78E-07 5.53E-05 3.23E-05 0 6.5 1.05 61.83 6.06E-07 5.65E-05 3.23E-05 0 6.5 1.05 62.20 9.38E-07 5.68E-05 3.23E-05 0 6.5 1.05 62.33 1.26E-06 5.71E-05 3.23E-05 0 6.5 1.05 62.15 1.59E-06 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % GFR % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg 3 1) ' 420(& % 3 1) ' & 420(65 1.07E-02 2.22E-02 3.35E-02 4.55E-02 5.68E-02 5.36E-03 1.07E-02 1.57E-02 2.14E-02 2.64E-02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.36E-02 2.85E-02 4.31E-02 5.85E-02 7.31E-02 8.22E-03 1.69E-02 2.54E-02 3.46E-02 4.32E-02 50 52 53 53 54 40 41 41 41 41 0.00 0.00 0.00 0.00 0.00 5.22E-05 6.16E-05 0 3.3 1.03 24.05 1.91E-07 5.24E-05 6.13E-05 0 3.3 1.03 24.25 3.05E-07 5.27E-05 6.19E-05 0 3.3 1.03 24.70 5.61E-07 5.21E-05 6.21E-05 0 3.3 1.03 25.15 6.78E-07 5.23E-05 6.19E-05 0 3.3 1.03 24.65 8.36E-07 7.95E-03 1.74E-02 2.57E-02 3.49E-02 4.38E-02 5.37E-03 1.33E-02 1.82E-02 2.59E-02 3.27E-02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 9.28E-03 1.95E-02 2.95E-02 3.94E-02 4.93E-02 6.76E-03 1.55E-02 2.23E-02 3.08E-02 3.87E-02 33 24 29 26 25 27 20 25 22 21 0.00 0.00 0.00 0.00 0.00 7.40E-05 2.54E-05 0 7.44E-05 2.53E-05 0 7.48E-05 2.52E-05 0 7.52E-05 2.50E-05 0 7.54E-05 2.52E-05 0 340 , cp B A@ 9 8 420(67 B A@ 9 8 420(67 B A@ 9 8 420(67 3 13.1 1.1 40.00 2.18E-07 13.0 1.1 40.35 4.34E-07 12.7 1.1 41.00 6.84E-07 12.5 1.1 41.60 8.82E-07 12.8 1.1 41.65 1.09E-06 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 7.55E-03 1.60E-02 2.41E-02 3.25E-02 4.08E-02 4.69E-03 1.04E-02 1.53E-02 2.11E-02 2.68E-02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 9.04E-03 1.89E-02 2.87E-02 3.83E-02 4.78E-02 6.24E-03 1.34E-02 2.01E-02 2.74E-02 3.44E-02 38 35 37 35 34 31 29 30 29 28 0.00 0.00 0.00 0.00 0.00 7.62E-05 3.26E-05 0 6.7 1.05 60.55 2.55E-07 7.66E-05 3.30E-05 0 6.6 1.05 60.65 5.42E-07 7.71E-05 3.38E-05 0 6.5 1.05 60.50 7.63E-07 7.75E-05 3.45E-05 0 6.3 1.05 60.55 1.07E-06 7.78E-05 3.45E-05 0 6.3 1.05 61.40 1.35E-06 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 7.31E-03 1.53E-02 2.38E-02 3.14E-02 3.91E-02 3.93E-03 8.16E-03 1.37E-02 1.74E-02 2.16E-02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 9.08E-03 1.90E-02 2.89E-02 3.86E-02 4.80E-02 5.79E-03 1.21E-02 1.92E-02 2.52E-02 3.13E-02 46 47 42 45 45 36 36 33 35 35 0.00 0.00 0.00 0.00 0.00 7.55E-05 6.20E-05 0 3.4 1.03 7.58E-05 6.35E-05 0 3.4 1.03 7.61E-05 6.32E-05 0 3.4 1.03 7.64E-05 6.28E-05 0 3.4 1.03 7.70E-05 6.44E-05 0 3.3 1.03 341 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 25.10 1.59E-07 24.88 3.34E-07 24.68 5.23E-07 24.83 6.71E-07 24.95 8.40E-07 8.92E-03 1.87E-02 2.89E-02 3.89E-02 4.86E-02 6.65E-03 1.40E-02 2.14E-02 2.93E-02 3.66E-02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.01E-02 2.12E-02 3.29E-02 4.39E-02 5.47E-02 7.83E-03 1.65E-02 2.54E-02 3.44E-02 4.30E-02 25 25 26 25 25 23 22 23 22 21 0.00 0.00 0.00 0.00 0.00 7.00E-05 2.54E-05 0 12.5 1.06 39.28 1.96E-07 7.04E-05 2.53E-05 0 12.6 1.06 39.20 4.34E-07 6.92E-05 2.53E-05 0 12.8 1.06 39.60 6.67E-07 6.95E-05 2.53E-05 0 12.7 1.06 40.05 8.67E-07 6.99E-05 2.52E-05 0 12.6 1.06 40.05 1.07E-06 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm H GF E D 420(6C H GF E D 420(6C 8.42E-03 1.79E-02 2.71E-02 3.64E-02 4.56E-02 5.69E-03 1.17E-02 1.77E-02 2.43E-02 3.08E-02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 9.86E-03 2.11E-02 3.20E-02 4.27E-02 5.33E-02 7.12E-03 1.50E-02 2.27E-02 3.07E-02 3.87E-02 32 34 35 33 33 28 29 29 28 27 0.00 0.00 0.00 0.00 0.00 7.19E-05 3.22E-05 0 6.9 1.05 59.30 2.85E-07 7.43E-03 7.07E-05 3.28E-05 0 6.9 1.05 59.45 6.49E-07 1.52E-02 7.11E-05 3.32E-05 0 6.8 1.05 59.58 9.99E-07 2.30E-02 7.15E-05 3.37E-05 0 6.7 1.05 59.95 1.32E-06 3.08E-02 7.19E-05 3.37E-05 0 6.7 1.05 59.80 1.65E-06 3.86E-02 342 PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 3.59E-03 6.47E-03 9.62E-03 1.33E-02 1.67E-02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 9.52E-03 2.00E-02 3.02E-02 4.03E-02 5.03E-02 5.67E-03 1.13E-02 1.70E-02 2.30E-02 2.89E-02 52 57 58 57 57 40 44 44 43 43 0.00 0.00 0.00 0.00 0.00 7.40E-05 5.72E-05 0 3.6 1.03 25.00 1.53E-07 7.44E-05 5.81E-05 0 3.5 1.03 24.83 3.21E-07 7.48E-05 5.76E-05 0 3.5 1.03 24.95 5.04E-07 7.53E-05 5.82E-05 0 3.5 1.03 25.08 6.51E-07 7.55E-05 5.89E-05 0 3.5 1.03 25.23 7.69E-07 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm T SR Q P 420(6I T SR Q P 420(6I 9.17E-03 1.93E-02 2.91E-02 3.91E-02 4.91E-02 6.93E-03 1.46E-02 2.18E-02 2.97E-02 3.81E-02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.03E-02 2.17E-02 3.28E-02 4.38E-02 5.47E-02 8.09E-03 1.70E-02 2.56E-02 3.46E-02 4.40E-02 24 24 25 24 22 22 21 22 21 20 0.00 0.00 0.00 0.00 0.00 6.85E-05 2.53E-05 0 12.6 1.06 40.18 1.77E-07 6.88E-05 2.53E-05 0 12.7 1.06 39.78 4.52E-07 6.92E-05 2.53E-05 0 12.6 1.06 40.00 6.80E-07 6.96E-05 2.52E-05 0 12.5 1.06 40.33 9.31E-07 7.00E-05 2.52E-05 0 12.4 1.06 39.88 1.09E-06 8.74E-03 1.77E-02 2.70E-02 3.59E-02 4.55E-02 6.24E-03 1.13E-02 1.74E-02 2.29E-02 3.03E-02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.01E-02 2.11E-02 3.20E-02 4.27E-02 5.33E-02 7.54E-03 1.47E-02 2.25E-02 2.98E-02 3.85E-02 343 % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 29 25 0.00 7.05E-05 3.38E-05 0 6.7 1.05 36 30 0.00 7.08E-05 3.33E-05 0 6.8 1.05 35 30 0.00 7.12E-05 3.36E-05 0 6.7 1.05 36 30 0.00 7.16E-05 3.40E-05 0 6.6 1.05 60.25 1.08E-06 2.22E-02 7.81E-03 0.00E+00 3.01E-02 1.58E-02 65 47 0.00 7.50E-05 6.32E-05 0 3.5 1.03 24.90 9.04E-07 33 28 0.00 7.19E-05 3.34E-05 0 6.8 1.05 59.93 1.42E-06 3.00E-02 1.11E-02 0.00E+00 4.03E-02 2.17E-02 63 46 0.00 7.52E-05 6.26E-05 0 3.5 1.03 24.90 1.07E-06 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PintCO2, atm P*CO2, atm kl, m/s CO2 ldg , cp 3 ` YX W V 4a066U ` YX W V 420(6U ` YX W V 420(6U 59.78 3.13E-07 7.17E-03 2.95E-03 0.00E+00 9.50E-03 5.27E-03 59 45 0.00 7.42E-05 6.24E-05 0 3.5 1.03 24.70 2.24E-07 60.08 7.01E-07 1.47E-02 5.31E-03 0.00E+00 1.99E-02 1.05E-02 64 47 0.00 7.46E-05 6.29E-05 0 3.5 1.03 24.70 7.30E-07 24.60 4.72E-07 9.93E-03 1.99E-02 3.02E-02 4.25E-02 5.50E-02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 2.62E-05 2.61E-05 2.62E-05 2.64E-05 2.64E-05 0 0 0 0 0 14.9 15.0 15.0 14.7 14.7 1.07 1.07 1.07 1.07 1.07 37.90 38.20 39.00 38.80 T, 0C 344 NCO2 moles/(cm2.sec) PintCO2, atm P*CO2, atm kl, m/s CO2 ldg , cp 3 2.65E-07 8.22E-03 0.00E+00 3.76E-05 0 7.6 1.06 58.70 3.10E-07 5.84E-07 1.63E-02 0.00E+00 3.78E-05 0 7.6 1.06 59.00 1.02E-06 8.75E-07 2.67E-02 0.00E+00 3.84E-05 0 7.6 1.06 59.30 1.35E-06 1.16E-06 3.55E-02 0.00E+00 3.82E-05 0 7.6 1.06 59.10 1.67E-06 T, 0C NCO2 moles/(cm2.sec) PintCO2, atm P*CO2, atm kl, m/s CO2 ldg , cp m3 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) g fe d c 4a066b g fe d c 4a066b fe d c 20(6b 59.30 6.51E-07 7.74E-03 1.51E-02 2.18E-02 2.94E-02 3.73E-02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 5.76E-05 5.84E-05 5.80E-05 5.84E-05 5.82E-05 0 0 0 0 0 4.1 4.1 4.1 4.1 4.1 1.05 1.05 1.05 1.05 1.05 25.08 2.76E-07 2.39E-02 1.21E-02 4.49E-06 3.04E-02 1.85E-02 49 39 0.00 2.34E-05 2.73E-05 0.078496 15.1 1.09 39.40 2.70E-07 25.05 5.88E-07 5.08E-02 2.54E-02 5.10E-06 6.46E-02 3.91E-02 50 39 0.00 2.32E-05 2.77E-05 0.082639 15.5 1.10 39.85 5.71E-07 25.90 8.78E-07 7.75E-02 3.98E-02 1.22E-05 9.78E-02 6.03E-02 49 38 0.00 2.33E-05 2.81E-05 0.109048 15.7 1.12 40.20 8.78E-07 26.18 1.15E-06 1.04E-01 5.49E-02 1.36E-05 1.31E-01 8.18E-02 47 37 0.00 2.34E-05 2.68E-05 0.11185 14.4 1.10 40.60 1.14E-06 345 PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 2.42E-02 1.27E-02 6.57E-05 3.05E-02 1.88E-02 48 38 0.01 2.34E-05 2.79E-05 0.100509 8.5 1.09 59.15 3.32E-07 2.23E-02 8.31E-03 1.12E-03 3.02E-02 1.59E-02 66 47 0.14 2.37E-05 5.16E-05 0.099954 4.3 1.08 23.63 2.41E-07 3.87E-02 2.46E-02 1.29E-04 4.66E-02 5.08E-02 2.64E-02 6.75E-05 6.40E-02 3.95E-02 48 38 0.00 2.35E-05 2.80E-05 0.098915 8.5 1.10 58.75 7.52E-07 4.59E-02 1.40E-02 1.09E-03 6.39E-02 3.16E-02 71 50 0.08 2.36E-05 5.08E-05 0.101709 4.4 1.08 23.75 5.10E-07 8.05E-02 5.10E-02 1.44E-04 9.71E-02 7.69E-02 3.97E-02 1.01E-04 9.70E-02 5.97E-02 48 38 0.00 2.36E-05 2.74E-05 0.11512 8.8 1.11 59.18 1.10E-06 7.20E-02 2.51E-02 1.22E-03 9.81E-02 5.10E-02 66 48 0.05 2.34E-05 5.13E-05 0.104342 4.4 1.08 23.95 7.51E-07 1.23E-01 7.99E-02 1.41E-04 1.48E-01 1.04E-01 5.55E-02 1.11E-04 1.29E-01 8.15E-02 47 37 0.00 2.37E-05 2.84E-05 0.116795 8.3 1.10 58.83 1.42E-06 9.85E-02 3.77E-02 1.20E-03 1.32E-01 7.12E-02 62 46 0.03 2.33E-05 5.07E-05 0.105935 4.4 1.09 24.03 1.00E-06 1.67E-01 1.08E-01 1.27E-04 1.99E-01 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm s rq p i 4a066h s rq p i 4a066h 346 POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 3.17E-02 36 32 0.01 1.71E-05 3.77E-05 0.231037 27.5 1.11 38.75 7.11E-07 8.29E-02 3.74E-02 6.20E-04 1.10E-01 6.07E-02 55 45 0.02 1.57E-05 2.85E-05 0.229324 13.8 1.10 59.18 3.23E-07 3.82E-02 1.86E-02 8.61E-03 5.00E-02 2.85E-02 66 43 0.46 6.60E-02 37 32 0.00 1.72E-05 3.79E-05 0.236329 27.8 1.11 38.88 1.36E-06 1.75E-01 8.70E-02 6.70E-04 2.25E-01 1.32E-01 50 41 0.01 1.56E-05 2.87E-05 0.232747 13.9 1.10 59.50 7.40E-07 7.87E-02 3.34E-02 9.57E-03 1.06E-01 5.66E-02 66 47 0.29 1.02E-01 35 31 0.00 1.72E-05 3.76E-05 0.233932 27.2 1.11 39.28 1.99E-06 2.68E-01 1.39E-01 7.34E-04 3.41E-01 2.07E-01 48 39 0.01 1.55E-05 2.87E-05 0.236161 13.8 1.10 60.10 1.15E-06 1.18E-01 4.77E-02 1.13E-02 1.60E-01 8.42E-02 66 48 0.24 1.39E-01 35 30 0.00 1.71E-05 3.71E-05 0.228127 26.5 1.11 39.38 1.06E-06 1.30E-01 6.09E-02 8.14E-04 1.71E-01 9.65E-02 54 44 0.01 1.53E-05 2.89E-05 0.24247 14.1 1.10 59.88 1.54E-06 1.59E-01 6.52E-02 1.16E-02 2.14E-01 1.14E-01 64 47 0.18 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach y xw v u 4a066t y xw v u 4a066t 347 to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 1.65E-05 3.95E-05 0.240598 6.3 1.09 23.33 6.38E-07 6.34E-02 3.15E-04 1.76E-05 0.279 32.9 1.12 39.73 2.52E-07 3.48E-02 2.31E-03 2.51E-05 0.306 16.5 1.12 58.80 2.33E-07 4.13E-02 1.74E-02 4.20E-05 0.297 7.5 1.11 25.10 2.82E-07 1.63E-05 3.94E-05 0.246212 6.4 1.09 24.43 1.25E-06 1.34E-01 3.54E-04 1.83E-05 0.28 30.6 1.12 40.30 5.36E-07 7.26E-02 3.60E-03 2.48E-05 0.33 17.2 1.12 59.13 5.47E-07 7.12E-02 1.86E-02 4.22E-05 0.299 7.5 1.11 1.64E-05 3.97E-05 0.253177 6.3 1.09 24.08 1.81E-06 1.96E-01 3.30E-04 1.81E-05 0.278 31.1 1.12 40.40 7.46E-07 1.18E-01 2.55E-03 2.54E-05 0.308 16.2 1.12 59.18 9.03E-07 9.99E-02 1.98E-02 4.21E-05 0.303 7.5 1.11 25.60 1.18E-06 1.64E-05 3.90E-05 0.257245 6.5 1.10 24.40 2.32E-06 2.82E-01 3.53E-04 1.83E-05 0.28 30.7 1.12 40.53 9.50E-07 1.64E-01 1.99E-03 2.60E-05 0.291 15.4 1.12 59.28 1.16E-06 1.41E-01 2.03E-02 4.22E-05 0.304 7.5 1.11 25.90 1.45E-06 T, 0C NCO2 moles/(cm2.sec) PintCO2, atm P*CO2, atm kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PintCO2, atm P*CO2, atm kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PintCO2, atm P*CO2, atm kl, m/s CO2 ldg , cp 3 T, 0C NCO2 4a066 4a066 4a066 4a066 25.40 5.87E-07 25.40 9.12E-07 348 moles/(cm2.sec) PintCO2, atm P*CO2, atm kl, m/s CO2 ldg , cp 3 4.96E-03 4.29E-05 2.21E-05 0.167 21.2 1.1 38.80 4.23E-07 1.70E-02 4.08E-03 3.12E-05 0.173 12.0 1.09 59.20 2.96E-07 1.46E-02 3.53E-04 5.06E-05 0.182 5.4 1.08 24.4 1.36E-06 3.34E-01 1.91E-01 1.48E-03 4.27E-01 2.55E-01 43 40 0.01 1.06E-02 4.84E-05 2.24E-05 0.164 20.7 1.1 38.70 8.68E-07 3.45E-02 4.66E-03 3.10E-05 0.176 12.1 1.09 59.50 7.14E-07 2.33E-02 2.31E-03 5.09E-05 0.184 5.4 1.08 1.88E-02 5.81E-05 2.23E-05 0.171 20.9 1.1 39.30 1.30E-06 5.17E-02 5.19E-03 3.14E-05 0.179 11.9 1.09 59.60 1.09E-06 3.49E-02 3.60E-03 5.09E-05 0.188 5.4 1.08 2.63E-02 2.64E-04 2.24E-05 0.177 20.8 1.1 39.80 1.72E-06 7.19E-02 3.54E-04 3.18E-05 0.181 11.7 1.09 59.90 1.36E-06 5.69E-02 2.55E-03 5.11E-05 0.194 5.4 1.08 24.8 1.82E-06 5.52E-01 3.51E-01 3.22E-03 6.77E-01 4.43E-01 37 34 0.01 3.80E-02 3.29E-04 2.26E-05 0.177 20.4 1.1 40.00 2.10E-06 9.13E-02 3.30E-04 3.18E-05 0.183 11.6 1.09 59.70 1.68E-06 7.37E-02 1.99E-03 5.09E-05 0.195 5.4 1.08 25.0 2.72E-06 8.16E-01 5.55E-01 3.18E-03 9.64E-01 6.84E-01 32 29 0.01 T, 0C NCO2 moles/(cm2.sec) PintCO2, atm P*CO2, atm kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PintCO2, atm P*CO2, atm kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium 4a0( 4a0( 4a0( 24.8 2.38E-06 6.67E-01 4.29E-01 1.38E-03 8.09E-01 5.43E-01 36 33 0.00 25.1 3.43E-06 9.53E-01 6.28E-01 3.22E-03 1.13E+00 7.94E-01 34 30 0.01 349 kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 9.54E-06 1.68E-05 0.36 37.9 1.14 1.00E-05 1.73E-05 0.35 36.2 1.14 39.3 1.02E-06 3.50E-01 2.47E-01 8.66E-03 4.16E-01 2.91E-01 30 30 0.04 9.89E-06 2.45E-05 0.38 20.3 1.14 1.06E-05 1.67E-05 0.39 38.9 1.15 39.4 1.21E-06 5.36E-01 4.18E-01 8.40E-03 6.08E-01 4.71E-01 22 23 0.02 1.02E-05 2.46E-05 0.38 20.1 1.14 9.03E-06 1.65E-05 0.39 40.0 1.15 40.0 1.41E-06 7.24E-01 5.86E-01 9.07E-03 8.03E-01 6.50E-01 19 19 0.02 1.02E-05 2.50E-05 0.38 19.7 1.14 41.1 3.54E-10 8.45E-05 7.87E-05 7.97E-05 8.74E-05 8.17E-05 121 7 1.01 6.12E-05 3.00E-05 0.107 1.04E-05 1.66E-05 0.39 39.4 1.15 40.0 1.68E-06 9.15E-01 7.49E-01 9.59E-03 1.01E+00 8.30E-01 18 18 0.01 1.01E-05 2.48E-05 0.39 19.9 1.14 41.2 2.02E-09 1.57E-04 1.25E-04 7.97E-05 1.74E-04 1.42E-04 42 19 0.64 6.16E-05 3.01E-05 0.107 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg 4a066 a0(6 41.3 -2.33E-09 3.75E-07 3.86E-05 7.97E-05 4.21E-48 3.71E-05 48 -100 2.06 6.08E-05 3.02E-05 0.107 350 , cp i hg f e 4a066d i hg f e 4a066d 3 3 8.2 1.07 58.5 -2.87E-08 4.81E-06 5.00E-04 1.45E-03 4.42E-48 4.88E-04 34 -100 2.89 5.79E-05 5.15E-06 0.104 4.6 1.06 23.8 -1.92E-09 3.55E-07 3.60E-05 1.39E-04 4.74E-48 3.50E-05 26 -100 3.85 5.38E-05 1.96E-05 0.230 27.0 1.11 24.1 -3.44E-10 1.01E-04 1.08E-04 1.39E-04 9.83E-05 1.05E-04 17 -6 1.29 5.42E-05 1.98E-05 0.230 26.5 1.11 8.2 1.07 58.7 -8.19E-09 1.08E-03 1.21E-03 1.45E-03 1.02E-03 1.14E-03 35 -12 1.20 6.25E-05 5.18E-06 0.106 4.5 1.06 24.5 3.02E-09 3.59E-04 3.04E-04 1.39E-04 3.86E-04 3.33E-04 25 14 0.46 5.53E-05 2.01E-05 0.230 25.9 1.11 8.2 1.07 58.3 -1.32E-09 1.35E-03 1.37E-03 1.45E-03 1.34E-03 1.36E-03 21 -2 1.06 6.29E-05 5.12E-06 0.107 4.6 1.06 24.6 1.72E-09 2.76E-04 2.45E-04 1.39E-04 2.92E-04 2.61E-04 23 11 0.57 5.49E-05 2.02E-05 0.230 25.6 1.11 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp i hg f e 4a066d 351 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % GFR % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 39.5 -6.39E-09 2.37E-04 3.48E-04 7.60E-04 1.86E-04 2.96E-04 21 -59 2.19 5.75E-05 2.91E-05 0.232 13.5 1.10 60.3 2.34E-08 8.80E-03 8.44E-03 7.85E-03 8.98E-03 8.62E-03 38 4 0.93 6.53E-05 4.29E-05 0.242 6.1 1.09 41.6 1.17E-08 3.08E-03 39.7 -4.75E-09 4.12E-04 4.95E-04 7.60E-04 3.73E-04 4.54E-04 24 -22 1.54 5.74E-05 2.90E-05 0.232 13.4 1.10 60.2 -2.41E-08 6.63E-03 7.00E-03 7.85E-03 6.45E-03 6.82E-03 30 -6 1.12 6.52E-05 4.29E-05 0.242 6.1 1.09 41.9 -5.32E09 1.25E-03 39.6 4.03E-09 1.04E-03 9.69E-04 7.60E-04 1.07E-03 1.00E-03 24 6 0.78 5.94E-05 2.90E-05 0.232 13.5 1.10 60.1 7.06E-08 1.10E-02 9.89E-03 7.85E-03 1.15E-02 1.04E-02 35 9 0.79 6.53E-05 4.27E-05 0.242 6.1 1.09 41.8 6.56E-09 2.57E-03 39.4 -9.63E-10 7.32E-04 7.49E-04 7.60E-04 7.24E-04 7.40E-04 59 -2 1.02 5.88E-05 2.91E-05 0.232 13.6 1.10 60.1 -8.16E-08 4.51E-03 5.76E-03 7.85E-03 3.91E-03 5.17E-03 37 -32 1.36 6.51E-05 4.27E-05 0.242 6.1 1.09 41.8 -7.86E09 8.44E-04 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm o nm l k 4a066j o nm l k 4a066j 41.4 -3.43E10 1.95E-03 352 PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 2.24E-03 1.83E-03 3.58E-03 2.62E-03 67 27 0.82 1.39E-05 2.73E-05 0.243 12.1 1.11 1.98E-03 1.83E-03 1.94E-03 1.97E-03 -22 -2 0.92 1.30E-05 2.73E-05 0.248 12.1 1.11 1.67E-03 1.83E-03 1.02E-03 1.51E-03 73 -49 1.09 1.25E-05 2.74E-05 0.250 12.1 1.11 2.07E-03 1.83E-03 2.86E-03 2.29E-03 68 20 0.89 1.31E-05 2.74E-05 0.261 12.1 1.11 1.49E-03 1.83E-03 5.22E-04 1.28E-03 66 -145 1.23 1.21E-05 2.74E-05 0.255 12.1 1.11 Table H.2 23.5 wt% MOR solubility and rate T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm 24.93 1.91E-07 u ts r q 4a0( p 25.03 4.60E-07 25.43 6.90E-07 25.28 8.16E-07 25.58 9.91E-07 1.11E-02 2.28E-02 3.47E-02 4.75E-02 5.97E-02 7.64E-03 1.44E-02 2.22E-02 3.28E-02 4.19E-02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.30E-02 2.73E-02 4.13E-02 5.52E-02 6.88E-02 9.47E-03 1.89E-02 2.89E-02 4.06E-02 5.14E-02 32 37 36 31 30 27 31 30 26 25 0.00 0.00 0.00 0.00 0.00 5.45E-05 6.65E-05 0.03 2.0 40.03 1.96E-07 5.47E-05 6.65E-05 0.03 2.0 40.05 4.59E-07 5.50E-05 6.67E-05 0.03 2.0 40.15 6.83E-07 5.53E-05 6.66E-05 0.03 2.0 40.35 9.15E-07 5.56E-05 6.67E-05 0.03 2.0 40.28 1.09E-06 1.09E-02 2.23E-02 3.41E-02 4.55E-02 5.74E-02 7.36E-03 1.42E-02 2.20E-02 2.94E-02 3.82E-02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.27E-02 2.67E-02 4.04E-02 5.40E-02 6.74E-02 353 POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 9.20E-03 32 28 0.00 5.58E-05 8.87E-05 0.03 1.3 59.20 1.94E-07 1.14E-02 7.74E-03 9.87E-04 1.33E-02 9.64E-03 35 28 0.13 5.33E-05 1.20E-04 0.03 0.90 24.23 -1.59E09 3.01E-07 2.96E-05 7.93E-05 4.85E-48 2.97E-05 37 2.68 5.42E-05 1.85E-02 37 31 0.00 5.61E-05 8.87E-05 0.03 1.3 59.18 4.38E-07 2.36E-02 1.54E-02 9.87E-04 2.79E-02 1.97E-02 36 29 0.06 5.36E-05 1.20E-04 0.03 0.90 24.80 3.78E-10 9.70E-05 9.01E-05 7.93E-05 1.01E-04 9.35E-05 39 7 0.88 5.46E-05 2.84E-02 36 30 0.00 5.64E-05 8.88E-05 0.03 1.3 59.48 6.36E-07 3.61E-02 2.43E-02 9.87E-04 4.22E-02 3.05E-02 34 28 0.04 5.39E-05 1.21E-04 0.03 0.90 24.23 1.99E-09 1.81E-04 1.45E-04 7.93E-05 2.00E-04 1.64E-04 36 18 0.55 5.50E-05 3.80E-02 35 30 0.00 5.67E-05 8.89E-05 0.03 1.3 59.63 8.62E-07 4.81E-02 3.22E-02 9.87E-04 5.64E-02 4.07E-02 34 28 0.03 5.42E-05 1.21E-04 0.03 0.90 24.48 3.75E-09 2.62E-04 1.94E-04 7.93E-05 2.98E-04 2.29E-04 37 23 0.41 5.54E-05 4.85E-02 33 28 0.00 5.70E-05 8.88E-05 0.03 1.3 59.78 1.12E-06 5.96E-02 3.90E-02 9.87E-04 7.03E-02 5.01E-02 35 29 0.03 5.45E-05 1.21E-04 0.03 0.90 24.43 5.44E-09 3.42E-04 2.47E-04 7.93E-05 3.93E-04 2.95E-04 36 25 0.32 5.70E-05 354 moles/(cm2.atm.sec) kl, m/s CO2 ldg 6.62E-05 0.08 6.64E-05 0.08 6.62E-05 0.08 6.63E-05 0.08 6.63E-05 0.08 T, 0C NCO2 moles/(cm .sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm .atm.sec) kl, m/s CO2 ldg T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm 2 2 40.03 6.46E12 3.85E04 3.85E04 3.62E04 3.85E04 3.85E04 0 0 0.94 5.73E05 8.87E05 0.08 39.83 3.77E09 5.34E04 4.69E04 3.62E04 5.68E04 5.02E04 38 11 0.77 5.81E05 8.86E05 0.08 39.83 4.00E09 2.30E04 3.01E04 3.62E04 1.96E04 2.68E04 54 -37 1.20 5.64E05 8.86E05 0.08 39.70 9.02E09 6.64E04 5.11E04 3.62E04 7.44E04 5.90E04 51 21 0.71 5.89E05 8.85E05 0.08 39.68 6.10E09 1.47E04 2.55E04 3.62E04 9.85E05 2.09E04 50 -112 1.42 5.62E05 8.85E05 0.08 39.65 1.15E08 8.14E04 6.12E04 3.62E04 9.14E04 7.22E04 45 21 0.59 5.7E05 8.85E05 0.08 60.00 -6.03E09 1.67E03 2.25E03 39.7 8.00E09 1.46E06 1.53E04 3.62E04 4.75E48 1.46E04 42 2.37 5.3E05 8.85E05 0.08 60.125 -1.34E08 1.66E-05 1.34E-03 59.80 -1.82E11 2.46E03 2.46E03 59.78 -6.03E09 1.67E03 2.25E03 59.95 -2.76E09 2.13E03 2.40E03 60.05 6.68E09 3.37E03 2.75E03 355 P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg 2.49E03 4.97E48 2.41E03 5 1.01 1.11E05 1.21E04 0.08 2.49E03 1.42E02 1.15E02 71 19 1.10 1.03E05 1.21E04 0.08 39.30 2.39E-07 4.28E-02 2.78E-02 1.16E-02 5.15E-02 3.51E-02 48 32 0.42 1.59E-05 8.83E-05 0.21 59.30 1.77E-06 2.04E-01 9.68E-02 6.07E-02 2.66E-01 1.53E-01 75 2.49E03 2.96E02 2.22E02 75 25 1.04 1.04E05 1.21E04 0.08 2.49E03 4.48E02 3.34E02 70 25 0.91 1.07E05 1.21E04 0.08 2.49E03 5.97E02 4.44E02 71 26 1.10 1.03E05 1.21E04 0.08 2.49E-03 7.44E-02 5.45E-02 53 27 1.86 1.02E-05 0.000121 0.08 40.05 1.32E-06 1.70E-01 8.82E-02 1.16E-02 2.18E-01 1.30E-01 52 40 0.13 1.61E-05 8.87E-05 0.21 59.90 8.28E-07 1.32E-01 8.10E-02 6.07E-02 1.61E-01 1.06E-01 71 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase 59.25 -7.40E07 4.77E-04 4.57E-02 6.07E-02 1.77E-47 4.99E-02 75 39.95 6.37E-07 8.38E-02 4.41E-02 1.16E-02 1.07E-01 6.41E-02 55 40 0.26 1.61E-05 8.87E-05 0.21 59.18 4.19E-07 9.08E-02 6.53E-02 6.07E-02 1.05E-01 7.76E-02 85 40.03 9.82E-07 1.27E-01 6.59E-02 1.16E-02 1.63E-01 9.71E-02 53 40 0.18 1.61E-05 8.87E-05 0.21 60.00 1.27E-06 1.69E-01 9.24E-02 6.07E-02 2.14E-01 1.32E-01 71 356 resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm 1.33 1.64E-05 1.20E-04 0.21 23.88 3.64E07 2.26E01 2.13E01 9.42E02 2.33E01 2.20E01 10 5 0.44 2.80E05 6.61E05 0.32 43 0.63 1.65E-05 1.20E-04 0.21 23.95 2.44E07 1.72E01 1.63E01 9.42E02 1.76E01 1.68E01 11 5 0.58 2.77E05 6.61E05 0.32 39.78 8.05E-07 1.21E+00 1.12E+00 5.30E-01 1.25E+00 1.17E+00 13 7 26 0.93 1.64E-05 1.20E-04 0.21 24.25 7.09E08 1.17E01 1.15E01 9.42E02 1.18E01 1.16E01 11 2 0.82 2.74E05 6.62E05 0.32 38 0.66 1.64E-05 1.21E-04 0.21 24.10 3.27E07 2.82E01 2.70E01 9.42E02 2.87E01 2.77E01 6 4 0.35 2.83E05 6.62E05 0.32 34 0.75 1.63E-05 1.21E-04 0.21 23.65 -2.90E07 1.06E-04 1.09E-02 9.42E-02 9.85E-48 1.10E-02 12 8.61 2.68E-05 6.6E-05 0.32 40.13 -6.52E-07 8.57E-04 7.23E-02 5.30E-01 3.63E-47 8.96E-02 14 % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal 24.28 -1.19E07 2.92E02 3.35E02 9.42E02 2.71E02 3.14E02 7 -16 2.81 2.78E05 6.62E05 0.32 40.55 -1.43E-07 3.31E-01 3.46E-01 5.30E-01 3.22E-01 3.40E-01 8 -6 39.93 1.01E-06 1.51E+00 1.40E+00 5.30E-01 1.56E+00 1.46E+00 11 6 357 % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg 0.47 9.38E-06 8.86E-05 0.32 1.53 9.30E-06 8.90E-05 0.32 0.38 9.34E-06 8.86E-05 0.32 7.32 9.12E-06 8.87E-05 0.32 Table H.3 11 wt% MOR/53 wt% DGA solubility and rate T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 24.6 2.29E-07 24.6 5.09E-07 24.8 7.54E-07 4.06E-02 2.59E-02 0.00E+00 4.86E-02 3.36E-02 36 31 0.00 5.12E-05 2.95E-05 0.001 11.4 1.06 40.3 8.57E-07 3.23E-02 1.81E-02 0.00E+00 3.99E-02 2.58E-02 44 35 0.00 6.05E-05 24.9 9.69E-07 5.47E-02 3.59E-02 0.00E+00 6.48E-02 4.57E-02 34 29 0.00 5.15E-05 2.99E-05 0.001 11.1 1.06 40.5 1.12E-06 4.34E-02 2.51E-02 0.00E+00 5.32E-02 3.50E-02 42 34 0.00 6.08E-05 1.25E-02 8.10E-03 0.00E+00 1.49E-02 1.03E-02 35 31 0.00 5.25E-05 2.94E-05 0.001 11.5 1.06 40.0 2.75E-07 1.01E-02 5.54E-03 0.00E+00 1.26E-02 7.99E-03 45 37 0.00 5.99E-05 2.67E-02 1.67E-02 0.00E+00 3.22E-02 2.19E-02 37 32 0.00 5.09E-05 2.95E-05 0.001 11.4 1.06 40.1 5.83E-07 2.11E-02 1.14E-02 0.00E+00 2.64E-02 1.66E-02 46 37 0.00 6.02E-05 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) { zy x w 4a066v 358 kl, m/s CO2 ldg , cp ~ } 4a066| ~ } 4a066| ~ } 4a066| 3 4.14E-05 0.001 6.6 1.05 59.4 3.42E-07 8.83E-03 3.48E-03 0.00E+00 1.18E-02 6.41E-03 61 46 0.00 6.38E-05 6.09E-05 0.001 3.7 1.03 24.7 2.99E-07 2.41E-02 1.23E-02 3.96E-05 3.07E-02 1.85E-02 49 40 0.00 2.54E-05 2.25E-05 0.130 20.2 1.07 4.15E-05 0.001 6.6 1.05 59.6 7.10E-07 1.85E-02 7.48E-03 0.00E+00 2.46E-02 1.36E-02 60 45 0.00 6.41E-05 6.11E-05 0.001 3.7 1.03 24.8 6.26E-07 5.04E-02 2.59E-02 3.96E-05 6.41E-02 3.87E-02 49 40 0.00 2.56E-05 2.26E-05 0.130 20.1 1.07 4.16E-05 0.001 6.6 1.05 59.8 1.04E-06 2.85E-02 1.24E-02 0.00E+00 3.72E-02 2.12E-02 57 43 0.00 6.45E-05 6.14E-05 0.001 3.6 1.03 24.8 9.30E-07 7.68E-02 4.07E-02 3.96E-05 9.68E-02 5.98E-02 47 38 0.00 2.57E-05 2.26E-05 0.130 20.0 1.07 4.17E-05 0.001 6.6 1.05 59.9 1.36E-06 3.84E-02 1.73E-02 0.00E+00 4.97E-02 2.89E-02 55 42 0.00 6.48E-05 6.16E-05 0.001 3.6 1.03 25.0 1.25E-06 1.02E-01 5.41E-02 3.96E-05 1.29E-01 7.98E-02 47 38 0.00 2.59E-05 2.27E-05 0.130 19.9 1.07 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 359 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 39.9 3.05E-07 2.37E-02 1.19E-02 2.43E-04 3.04E-02 1.80E-02 50 41 0.02 2.59E-05 3.32E-05 0.130 10.5 1.06 58.5 -1.19E07 4.59E-05 4.50E-03 4.83E-03 1.03E-47 4.72E-03 93 1.07 2.66E-05 5.14E-05 0.130 5.2 1.05 39.7 7.04E-07 4.84E-02 2.11E-02 2.43E-04 6.40E-02 3.55E-02 57 44 0.01 2.58E-05 3.30E-05 0.130 10.7 1.06 58.4 7.15E-07 4.71E-02 1.99E-02 4.83E-03 6.26E-02 3.43E-02 64 45 0.24 2.64E-05 5.12E-05 0.130 5.2 1.05 39.5 1.03E-06 7.49E-02 3.47E-02 2.43E-04 9.76E-02 5.61E-02 54 43 0.01 2.57E-05 3.29E-05 0.130 10.7 1.06 58.5 1.09E-06 7.26E-02 3.06E-02 4.83E-03 9.64E-02 5.30E-02 62 45 0.16 2.60E-05 5.13E-05 0.130 5.2 1.05 25.7 7.62E-07 39.6 1.37E-06 9.94E-02 4.67E-02 2.43E-04 1.29E-01 7.49E-02 53 42 0.01 2.61E-05 3.29E-05 0.130 10.7 1.06 58.7 1.43E-06 9.94E-02 4.37E-02 4.83E-03 1.31E-01 7.35E-02 59 44 0.11 2.57E-05 5.14E-05 0.130 5.2 1.05 25.5 9.78E-07 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 4a066 4a0( 58.5 2.99E-07 2.33E-02 1.20E-02 4.83E-03 2.98E-02 1.79E-02 61 40 0.40 2.65E-05 5.13E-05 0.130 5.2 1.05 T, 0C NCO2 25.3 2.46E-07 25.1 5.31E-07 360 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 2.53E-02 1.57E-02 2.29E-04 3.07E-02 2.06E-02 39 33 0.01 2.55E-05 1.95E-05 0.270 27.9 1.12 40.5 2.76E-07 2.44E-02 1.37E-02 1.31E-03 3.04E-02 1.92E-02 46 37 0.10 2.59E-05 2.87E-05 0.270 14.6 1.11 60.2 -1.72E07 6.78E-05 6.68E-03 1.46E-02 5.26E-02 3.19E-02 2.29E-04 6.41E-02 4.26E-02 40 33 0.01 2.56E-05 1.93E-05 0.270 28.3 1.12 40.6 5.85E-07 5.12E-02 2.85E-02 1.31E-03 6.39E-02 4.03E-02 45 37 0.05 2.58E-05 2.88E-05 0.270 14.5 1.11 60.8 4.80E-07 5.53E-02 3.62E-02 1.46E-02 8.07E-02 5.12E-02 2.29E-04 9.68E-02 6.65E-02 37 31 0.00 2.58E-05 1.98E-05 0.270 27.2 1.12 40.8 8.70E-07 7.87E-02 4.49E-02 1.31E-03 9.74E-02 6.26E-02 44 36 0.03 2.57E-05 2.90E-05 0.270 14.4 1.11 60.6 8.16E-07 8.24E-02 4.99E-02 1.46E-02 1.09E-01 7.10E-02 2.29E-04 1.29E-01 9.07E-02 35 30 0.00 2.59E-05 1.96E-05 0.270 27.6 1.12 41.5 1.14E-06 1.08E-01 6.30E-02 1.31E-03 1.32E-01 8.64E-02 42 35 0.02 2.54E-05 2.94E-05 0.270 14.0 1.11 60.6 1.13E-06 1.09E-01 6.44E-02 1.46E-02 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm 4a066 4a066 60.4 1.55E-07 2.77E-02 2.16E-02 1.46E-02 361 PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 1.06E-47 7.00E-03 45 2.19 2.60E-05 4.65E-05 0.270 6.6 1.10 3.10E-02 2.46E-02 47 21 0.68 2.54E-05 4.68E-05 0.270 6.5 1.10 6.58E-02 4.59E-02 47 30 0.40 2.51E-05 4.72E-05 0.270 6.4 1.10 1.00E-01 6.67E-02 48 34 0.29 2.50E-05 4.70E-05 0.270 6.5 1.10 25.4 8.08E-07 1.77E-01 1.14E-01 1.49E-03 2.15E-01 1.44E-01 36 33 0.01 1.28E-05 1.74E-05 0.360 35.6 1.14 40.5 1.43E-06 1.28E-01 2.74E-02 2.65E-03 1.93E-01 7.95E-02 80 59 1.34E-01 8.78E-02 47 34 0.23 2.52E-05 4.70E-05 0.270 6.5 1.10 24.9 9.37E-07 2.43E-01 1.70E-01 1.49E-03 2.85E-01 2.05E-01 30 28 0.01 1.29E-05 1.71E-05 0.360 36.8 1.14 40.3 1.88E-06 1.74E-01 4.15E-02 2.65E-03 2.59E-01 1.11E-01 77 57 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal 4a066 4a0( 25.7 2.81E-07 5.51E-02 3.26E-02 1.49E-03 6.90E-02 4.32E-02 42 37 0.05 1.25E-05 1.77E-05 0.360 34.7 1.14 39.7 -5.72E08 4.64E-05 4.10E-03 2.65E-03 2.15E-47 4.74E-03 156 25.5 5.88E-07 1.15E-01 6.82E-02 1.49E-03 1.43E-01 9.04E-02 41 37 0.02 1.26E-05 1.75E-05 0.360 35.2 1.14 40.2 9.28E-07 8.55E-02 1.97E-02 2.65E-03 1.28E-01 5.33E-02 79 58 39.8 4.43E-07 4.04E-02 9.17E-03 2.65E-03 6.10E-02 2.50E-02 83 59 362 % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 0.65 1.41E-05 2.54E-05 0.360 18.9 1.13 60.3 -3.53E07 2.77E-04 2.48E-02 9.98E-02 2.13E-47 2.87E-02 25 4.02 1.44E-05 4.22E-05 0.360 8.2 1.12 25.8 -1.86E-09 3.15E-07 3.10E-05 3.96E-05 4.35E-48 3.11E-05 78 1.28 6.05E-05 0.29 1.42E-05 2.54E-05 0.360 18.9 1.13 60.5 7.43E-07 2.93E-01 2.42E-01 9.98E-02 3.22E-01 2.66E-01 27 17 0.41 1.45E-05 4.24E-05 0.360 8.1 1.12 25.6 3.82E-09 1.46E-04 8.34E-05 3.96E-05 1.79E-04 1.16E-04 59 35 0.47 6.14E-05 0.13 1.41E-05 2.56E-05 0.360 18.6 1.13 60.4 2.80E-07 1.85E-01 1.65E-01 9.98E-02 1.96E-01 1.74E-01 23 11 0.60 1.42E-05 4.23E-05 0.360 8.1 1.12 25.8 1.71E-09 7.51E-05 4.71E-05 3.96E-05 9.01E-05 6.18E-05 79 31 0.84 6.09E-05 0.10 1.42E-05 2.58E-05 0.360 18.4 1.13 60.4 8.36E-08 1.25E-01 1.19E-01 9.98E-02 1.29E-01 1.22E-01 23 5 0.84 1.42E-05 4.23E-05 0.360 8.1 1.12 25.7 5.14E-09 2.22E-04 1.39E-04 3.96E-05 2.67E-04 1.83E-04 45 31 0.28 6.18E-05 0.06 1.42E-05 2.57E-05 0.360 18.5 1.13 60.9 -1.20E07 6.68E-02 7.53E-02 9.98E-02 6.20E-02 7.18E-02 26 -16 1.33 1.41E-05 4.30E-05 0.360 7.9 1.12 25.8 7.44E-09 2.88E-04 1.69E-04 3.96E-05 3.53E-04 2.33E-04 48 34 0.23 6.23E-05 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg , cp 3 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) 4a0( 4a0( 363 kl, m/s CO2 ldg T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg 2.35E-05 0.130 40.6 -5.71E09 9.35E07 9.28E05 2.16E04 4.25E48 9.33E05 43 2.33 6.21E05 3.38E05 0.130 2.33E-05 0.130 2.35E-05 0.130 40.7 7.38E09 4.48E04 3.34E04 2.16E04 5.07E04 3.93E04 49 22 0.65 6.49E05 3.39E05 0.130 2.34E-05 0.130 40.7 1.04E08 5.82E04 4.24E04 2.16E04 6.64E04 5.06E04 43 24 0.51 6.59E05 3.39E05 0.130 2.35E-05 0.130 40.8 -3.65E09 1.15E04 1.73E04 2.16E04 8.80E05 1.47E04 58 -67 1.25 6.27E05 3.4E-05 0.130 58.1 7.51E-07 3.26E-02 2.04E-02 5.09E-03 3.90E-02 2.69E-02 44 31 0.25 6.16E-05 5.10E-05 0.130 40.7 -1.06E09 1.83E04 2.00E04 2.16E04 1.75E04 1.92E04 52 -10 1.08 6.31E05 3.39E05 0.130 59.3 -1.41E-07 2.27E-05 2.33E-03 5.09E-03 4.31E-48 2.34E-03 46 2.18 6.11E-05 5.22E-05 0.130 40.8 2.93E09 3.20E04 2.75E04 2.16E04 3.44E04 2.98E04 44 13 0.79 6.40E05 3.39E05 0.130 59.1 1.55E-07 1.10E-02 8.45E-03 5.09E-03 1.23E-02 9.75E-03 43 21 0.60 6.13E-05 5.20E-05 0.130 58.3 4.76E-07 2.17E-02 1.39E-02 5.09E-03 2.58E-02 1.80E-02 47 30 0.37 6.14E-05 5.11E-05 0.130 364 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg 24.2 -6.10E09 9.85E-07 9.82E-05 2.29E-04 4.19E-48 9.84E-05 43 2.33 6.27E-05 1.87E-05 0.270 40.8 -6.90E08 1.19E-05 1.21E-03 2.82E-03 4.59E-48 1.22E-03 43 2.33 5.76E-05 2.89E-05 0.270 24.7 -2.71E09 1.07E-04 1.50E-04 2.29E-04 8.68E-05 1.30E-04 35 -50 1.53 6.32E-05 1.90E-05 0.270 40.9 1.52E-07 1.17E-02 9.08E-03 2.82E-03 1.31E-02 1.04E-02 30 20 0.31 5.79E-05 2.90E-05 0.270 24.8 6.14E-09 4.52E-04 3.58E-04 2.29E-04 5.00E-04 4.07E-04 42 19 0.64 6.56E-05 1.91E-05 0.270 40.7 3.73E-07 2.39E-02 1.75E-02 2.82E-03 2.73E-02 2.09E-02 30 24 0.16 5.81E-05 2.89E-05 0.270 25.1 6.59E-10 2.52E-04 2.41E-04 2.29E-04 2.57E-04 2.46E-04 45 4 0.95 6.42E-05 1.92E-05 0.270 40.5 5.60E-07 3.64E-02 2.68E-02 2.82E-03 4.13E-02 3.18E-02 29 23 0.11 5.85E-05 2.87E-05 0.270 24.9 8.43E-09 5.90E-04 4.63E-04 2.29E-04 6.55E-04 5.29E-04 35 19 0.49 6.66E-05 1.91E-05 0.270 41.0 7.24E-07 4.88E-02 3.65E-02 2.82E-03 5.51E-02 4.30E-02 27 22 0.08 5.89E-05 2.90E-05 0.270 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm 61.6 -2.36E07 3.88E-05 61.6 2.49E-08 1.24E-02 61.9 2.60E-07 2.41E-02 61.8 4.44E-07 3.60E-02 61.5 6.14E-07 4.80E-02 365 PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg 4.01E-03 1.16E-02 4.42E-48 4.02E-03 34 2.90 5.95E-05 4.83E-05 0.270 1.20E-02 1.16E-02 1.26E-02 1.22E-02 55 3 0.97 5.98E-05 4.83E-05 0.270 1.98E-02 1.16E-02 2.63E-02 2.20E-02 35 16 0.59 6.01E-05 4.87E-05 0.270 2.87E-02 1.16E-02 3.98E-02 3.25E-02 30 18 0.41 6.04E-05 4.86E-05 0.270 3.77E-02 1.16E-02 5.32E-02 4.32E-02 28 19 0.31 5.95E-05 4.82E-05 0.270 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg 24.8 6.33E-09 2.27E-03 2.04E-03 1.49E-03 2.39E-03 2.16E-03 29 10 0.73 2.82E-05 1.70E-05 0.360 25.0 -1.75E09 1.30E-03 1.37E-03 1.49E-03 1.27E-03 1.34E-03 35 -5 1.09 2.68E-05 1.72E-05 0.360 25.0 1.11E-09 1.64E-03 1.59E-03 1.49E-03 1.66E-03 1.61E-03 28 3 0.93 2.73E-05 1.72E-05 0.360 24.6 4.07E-09 1.95E-03 1.81E-03 1.49E-03 2.03E-03 1.88E-03 32 7 0.82 2.77E-05 1.70E-05 0.360 24.4 -4.32E09 9.47E-04 1.11E-03 1.49E-03 8.64E-04 1.03E-03 30 -20 1.34 2.63E-05 1.67E-05 0.360 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm 40.6 -1.08E07 2.85E-05 2.69E-03 7.15E-03 7.08E-48 2.93E-03 40.7 1.17E-07 1.85E-02 1.56E-02 7.15E-03 2.01E-02 1.70E-02 40.6 2.96E-07 3.79E-02 3.06E-02 7.15E-03 4.19E-02 3.41E-02 39.6 4.52E-07 5.72E-02 4.62E-02 7.15E-03 6.33E-02 5.16E-02 39.5 5.26E-07 7.73E-02 6.46E-02 7.15E-03 8.41E-02 7.08E-02 366 % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg 37 2.65 4.04E-05 2.59E-05 0.360 57.6 -4.55E07 1.21E-04 1.16E-02 6.61E-02 7.21E-48 1.26E-02 17 5.70 3.97E-05 3.92E-05 0.360 25 16 0.46 4.06E-05 2.60E-05 0.360 57.9 -2.46E07 2.36E-02 2.98E-02 6.61E-02 2.05E-02 2.71E-02 14 -33 2.22 4.00E-05 3.95E-05 0.360 24 19 0.23 4.08E-05 2.59E-05 0.360 57.6 -1.24E07 4.43E-02 4.73E-02 6.61E-02 4.26E-02 4.59E-02 14 -8 1.40 4.03E-05 3.92E-05 0.360 22 18 0.15 4.10E-05 2.53E-05 0.360 58.7 4.81E-09 6.39E-02 6.38E-02 6.61E-02 6.40E-02 6.39E-02 -5 0 1.04 4.08E-05 4.03E-05 0.360 25.4 1.74E-07 1.33E-01 1.20E-01 3.73E-02 1.41E-01 1.26E-01 14 11 0.31 1.28E-05 1.60E-05 0.450 18 16 0.11 4.14E-05 2.53E-05 0.360 58.9 2.11E-07 1.03E-01 9.78E-02 6.61E-02 1.06E-01 1.00E-01 14 5 0.68 4.08E-05 4.05E-05 0.360 25.5 2.57E-07 2.59E-01 2.40E-01 3.73E-02 2.69E-01 2.49E-01 8 8 0.16 1.37E-05 1.60E-05 0.450 24.7 -1.01E-07 8.58E-05 7.67E-03 3.73E-02 2.27E-47 8.81E-03 20 4.86 1.33E-05 1.55E-05 0.450 25.2 7.16E-08 6.30E-02 5.75E-02 3.73E-02 6.62E-02 5.99E-02 21 9 0.65 1.31E-05 1.58E-05 0.450 367 T, 0C NCO2 moles/(cm2.sec) PbulkCO2 atm PintCO2, atm P*CO2, atm PINCO2, atm POUTCO2, atm % Gas phase resistance % CO2 Removal % Approach to Equilibrium kg,CO2 moles/(cm2.atm.sec) kl, m/s CO2 ldg 40.9 -2.73E07 1.94E-04 1.75E-02 1.60E-01 1.92E-47 2.01E-02 11 9.15 1.58E-05 2.39E-05 0.450 41.2 -5.38E08 5.73E-02 6.07E-02 1.60E-01 5.54E-02 5.93E-02 3 -7 2.63 1.57E-05 2.41E-05 0.450 41.5 1.00E-07 1.75E-01 1.68E-01 1.60E-01 1.78E-01 1.71E-01 44 4 0.95 1.56E-05 2.43E-05 0.450 41.7 2.02E-07 2.95E-01 2.81E-01 1.60E-01 3.02E-01 2.88E-01 10 5 0.57 1.54E-05 2.43E-05 0.450 41.7 2.11E-07 4.67E-01 4.53E-01 1.60E-01 4.74E-01 4.60E-01 4 3 0.35 1.57E-05 2.43E-05 0.450 368 Appendix I: Additional C13 NMR Data I.1 65 wt% DGA Table I.1 T=27 0C C13 NMR of 65 wt% DGA, Loading = 0.377 mol CO2/mol DGA, Species (ppm) Methylene C s adjacent to nitrogen in DGA/ Protonated DGA Methylene C s adjacent to nitrogen in DGA carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side Methylene C s adjacent to oxygen in DGA carbamate on carbamate side Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side Carbonate / Bicarbonate DGA carbamate Area 28.53 16.53 49.55 27.17 16.35 45.69 16.80 1000.00 39.327 40.874 60.233 68.435 70.176 71.700 160.697 163.831 Table I.2 T=27 0C C13 NMR of 65 wt% DGA, Loading = 0.525 mol CO2/mol DGA, Species Methylene C s adjacent to nitrogen in DGA/ Protonated DGA Methylene C s adjacent to nitrogen in DGA carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side Methylene C s adjacent to oxygen in DGA carbamate on carbamate side Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side Area 38.463 40.365 59.795 66.100 69.649 71.28 Area 18.47 15.33 38.74 17.98 15.28 35.79 369 Carbonate / Bicarbonate DGA carbamate 159.791 163.349 151.08 1000.00 Table I.3 T=40 0C C13 NMR of 65 wt% DGA, Loading = 0.523 mol CO2/mol DGA, Species Methylene C s adjacent to nitrogen in DGA/ Protonated DGA Methylene C s adjacent to nitrogen in DGA carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side Methylene C s adjacent to oxygen in DGA carbamate on carbamate side Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side Carbonate / Bicarbonate DGA carbamate Area 38.790 40.674 60.090 66.480 69.927 71.526 159.842 163.515 Area 23.16 18.57 43.0 21.02 17.55 39.46 162.98 1000.00 Table I.4 T=60 0C C13 NMR of 65 wt% DGA, Loading = 0.332 mol CO2/mol DGA, Species Methylene C s adjacent to nitrogen in DGA/ Protonated DGA Methylene C s adjacent to nitrogen in DGA carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side Methylene C s adjacent to oxygen in DGA carbamate on carbamate side Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side Carbonate / Bicarbonate DGA carbamate Area 39.56 40.94 60.28 69.24 70.21 71.69 160.19 163.82 Area 46.22 22.19 71.50 45.42 21.62 69.66 44 2313 370 Table I.5 T=40 0C C13 NMR of 65 wt% DGA, Loading = 0.390 mol CO2/mol DGA, Species Methylene C s adjacent to nitrogen in DGA/ Protonated DGA Methylene C s adjacent to nitrogen in DGA carbamate Methylene C s adjacent to alcohol in D GA/ Protonated DGA & DGA carbamate Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side Methylene C s adjacent to oxygen in DGA carbamate on carbamate side Methylene C s adjacent to oxygen i n DGA/ Protonated DGA & DGA carbamate on noncarbamate side Carbonate / Bicarbonate DGA carbamate Area 39.513 41.077 60.418 68.627 70.352 71.870 160.510 163.983 Area 30.51 19.04 51.90 30.13 18.54 48.12 18.91 1000.00 Table I.6 T=60 0C C13 NMR of 65 wt% DGA, Loading = 0.385 mol CO2/mol DGA, Species Methylene C s a djacent to nitrogen in DGA/ Protonated DGA + Methylene C s adjacent to nitrogen in DGA carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side Methylene C s adjacent to oxygen in DGA carbamate on carbamate side Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side Carbonate / Bicarbonate DGA carbamate Area 41.280/39.751 Area 48.99 60.626 68.877 70.520 72.042 160.295 164.123 49.59 30.24 18.07 46.61 30.65 1000.00 371 Table I.7 T=27 0C C13 NMR of 65 wt% DGA, Loading = 0.168 mol CO2/mol DGA, Species Methylene C s adjacent to nitrogen in DGA/ Protonated DGA Methylene C s adjacent to nitrogen in DGA carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side + Methylene C s adjacent to oxygen in DGA carbamate on carbamate side + Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side Carbonate / Bicarbonate DGA carbamate Area 40.043 41.002/40.899 60.222 Area 120.4 24.3 150.9 70.307/71.031 /71.743 295.7 161.43 163.83 10 2316 Table I.8 T=60 0C C13 NMR of 65 wt% DGA, Loading = 0.180 mol CO2/mol DGA, Species Methylene C s adjacent to nitrogen in DGA/ Protonated DGA Methylene C s adjacent to nitrogen in DGA carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side + Methylene C s adjacent to oxygen in DGA carbamate on carbamate side + Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side Carbonate / Bicarbonate DGA carbamate Area 40.491 41.404 60.679 Area 52.0 11.3 65.1 72.146/71.476 /70.731 127.0 160.63 164.52/164.21 10.0 988.6 372 I.2 23.5 wt% MOR Table I.9 T=27 0C C13 NMR of 23.5 wt% MOR, Loading = 0.370 mol CO2/mol MOR, (ppm) 44.182 66.440 43.633 65.083 160.62 162.87 Area 2.172 2.049 5.177 4.961 26.7 100.0 Species Carbamate ring C s adjacent to carbamate side Carbamate ring C s adjacent to non carbamate side MOR / Protonated MOR on carbamate side MOR / Protonated MOR on noncarbamate side Carbonate / Bicarbonate MOR carbamate Table I.10 C13 NMR of 23.5 wt% MOR, Loading = 0.569 mol CO2/mol MOR, T=27 0C Species Carbamate ring C s adjacent to carbamate side Carbamate ring C s adjacent to non carbamate side MOR / Protonated MOR on carbamate side MOR / Protonated MOR on noncarbamate side Carbonate / Bicarbonate MOR carbamate (ppm) 44.5 66.5 43.0 64.0 160.4 163.0 Area 62.74 58.37 122.87 114.78 1000.00 1455.82 Table I.11 C13 NMR of 23.5 wt% MOR, Loading = 0.478 mol CO2/mol MOR, T=27 0C Species Carbamate ring C s adjacent to carbamate side Carbamate ring C s adjacent to non carbamate side MOR / Protonated MOR on carbamate side MOR / Protonated MOR on noncarbamate side Carbonate / Bicarbonate MOR carbamate (ppm) 44.492 66.753 43.553 64.526 160.678 163.146 Area 18.85 18.29 34.68 34.00 362.09 1000.00 373 Table I.12 C13 NMR of 23.5 wt% MOR, Loading = 0.258 mol CO2/mol MOR, T=27 0C Species Carbamate ring C s adjacent to carbamate side + MOR / Protonated MOR on carbamate side Carbamate ring C s a djacent to non carbamate side MOR / Protonated MOR on noncarbamate side Carbonate / Bicarbonate MOR carbamate (ppm) 44.4 67.0 63.0 161.0 163.0 Area 166.13 39.00 121.19 59.92 1000.00 Table I.13 C13 NMR of 23.5 wt% MOR, Loading = 0.427 mol CO2/mol MOR, T=27 0C Species Carbamate ring C s adjacent to non carbamate side MOR / Protonated MOR on noncarbamate side Carbonate / Bicarbonate MOR carbamate (ppm) 67.0 63.0 161 163 Area 43.35 80.06 217.38 1000.0 Table I.14 C13 NMR of 23.5 wt% MOR, Loading = 0.325 mol CO2/mol MOR, T=27 0C Species Carbamate ring C s adjacent to non carbamate side MOR / Protonated MOR on noncarbamate side Carbonate / Bicarbonate MOR carbamate (ppm) 67.0 63.0 161 163 Area 39.16 92.42 91.41 1000.0 Table I.15 C13 NMR of 23.5 wt% MOR, Loading = 0.392 mol CO2/mol MOR, T=40 0C Species Carbamate ring C s adjacent to carbamate side Carbamate ring C s adjacent to non carbamate side MOR / Protonated MOR on carbamate side MOR / Protonated MOR on noncarbamate side Carbonate / Bicarbonate MOR carbamate (ppm) 44.360 66.571 43.640 64.867 160.34 163.01 Area 4.037 3.835 9.446 9.094 32.1 100.0 374 Table I.16 C13 NMR of 23.5 wt% MOR, Loading = 0.370 mol CO2/mol MOR, T=40 0C Species Carbamate ring C s adjacent to carbamate side Carbamate ring C s adjacent to non carbamate side MOR / Protonated MOR on carbamate side MOR / Protonated MOR on noncarbamate side Carbonate / Bicarbonate MOR carbamate (ppm) 44.385 66.595 43.856 65.314 160.45 163.06 Area 2.304 2.045 5.807 5.675 36.2 100.0 Table I.17 C13 NMR of 23.5 wt% MOR, Loading = 0.569 mol CO2/mol MOR, T=40 0C Species Carbamate ring C s adjacent to carbamate side + MOR / Protonated MOR on carbamate side Carbamate ring C s adjacent to non carbamate side + MOR / Protonated MOR on noncarbamate side Carbonate / Bicarbonate MOR carbamate (ppm) 44.965 Area 216.79 65.997 161.036 163.590 183.32 1000.0 1175.15 Table I.18 C13 NMR of 23.5 wt% MOR, Loading = 0.478 mol CO2/mol MOR, T=40 0C Species Carbamate ring C s adjacent to carba mate side + MOR / Protonated MOR on carbamate side Carbamate ring C s adjacent to non carbamate side + MOR / Protonated MOR on noncarbamate side Carbonate / Bicarbonate MOR carbamate (ppm) 44.133 Area 164.99 67.027 160.568 163.373 149.64 534.97 1000.00 375 Table I.19 C13 NMR of 23.5 wt% MOR, Loading = 0.258 mol CO2/mol MOR, T=40 0C Species Carbamate ring C s adjacent to carbamate side + MOR / Protonated MOR on carbamate side Carbamate ring C s adjacent to non carbamate side + MOR / Protonated MOR on noncarbamate side Carbonate / Bicarbonate MOR carbamate (ppm) 45 Area 220.64 67 160.9 163.4 211.75 86.35 1000.00 I.3 11 wt% MOR/53 wt% DGA Table I.20 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.364 mol CO2/mol MOR, T=27 0C Species DGA carbamate MOR carbamate Carbonate / Bicarbonate Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side Methylene C s adjacent to oxygen in DGA carbamate on carbamate side Carbamate ring C s adjacent to non carbamate side + Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side Ring C s adjacent to non carbamate side in MOR/ Protonated MOR & MOR carbamate Methylene C s adj acent to alcohol in DGA/ Protonated DGA & DGA carbamate Ring C s adjacent to carbamate side in MOR/ Protonated MOR & MOR carbamate Methylene C s adjacent to nitrogen in DGA/ Protonated DGA (ppm) 164 162.1 162.5 72.0 70.0 68.0 Area 100 23.17 2.25 4.76 1.81 3.08 66.0 60.0 44.0 41.0 2.63 5.25 2.55 1.77 376 Methylene C s adjacent to ni trogen in DGA carbamate 39.0 3.07 Table I.21 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.271 mol CO2/mol MOR, T=27 0C Species DGA carbamate MOR carbamate Carbonate / Bicarbonate Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side Methylene C s adjacent to oxygen in DGA carbamate on carbamate side Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side Ring C s adjacent to non carbamate side in MOR/ Protonated MOR & MOR carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate Ring C s adjacent to carbamate side in MOR/ Protonated MOR & MOR carbamate Methylene C s adjacent to nitrogen in DGA/ Protonated DGA Methylene C s adjacent to nitrogen in DGA carbamate (ppm) 165 162.6 161 72.0 70.5 70.0 67.0 60.5 45.0 41.0 39.0 Area 1000 179.65 9.28 63.35 18.73 45.68 33.71 68.95 34.71 18.50 46.03 Table I.22 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.521 mol CO2/mol MOR, T=40 0C Species DGA carbamate + MOR carbamate Carbonate / Bicarbonate Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side (ppm) 163.4 159.8 72.0 Area 1000.0 139.32 33.42 377 Methylene C s adjacent to oxygen in DGA carbamate on carbamate side Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side + Ring C s adjacent to non carbamate side in MOR/ Protonated MOR & MOR carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate Ring C s adjacent to carbamate side in MOR/ Protonated MOR & MOR carbamate Methylene C s adjacent to nitrogen in DGA/ Protonated DGA Methylene C s adjacent to nitrogen in DGA carbamate 70.5 15.78 65.0 37.96 60.5 44.0 41.0 38.0 36.48 17.76 15.49 19.68 Table I.23 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.374 mol CO2/mol MOR, T=40 0C Species DGA carbamate MOR carbamate Carbonate / Bicarbonate Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side Methylene C s adjacent to oxygen in DGA carbamate on carbamate side Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side Ring C s adjacent to non carbamate side in MOR/ Protonated MOR & MOR carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate Ring C s adjacent to carbamate side in MOR/ Protonated MOR & MOR carbamate (ppm) 164 162.6 161 72.0 70.5 68.0 66.0 60.5 44.0 Area 1000 242.09 32.97 48.48 18.38 31.30 26.74 52.28 25.78 378 Methylene C s adjacent to nitrogen in DGA/ Protonated DGA Methylene C s adjacent to nitrogen in DGA carbamate 41.0 39.0 18.54 31.46 Table I.24 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.285 mol CO2/mol MOR, T=40 0C Species DGA carbamate MOR carbamate Carbonate / Bicarbonate Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side Methylene C s adjacent to oxygen in DGA carbamate on carbamate side Methylene C s adjace nt to oxygen in DGA/ Protonated DGA on carbamate side Ring C s adjacent to non carbamate side in MOR/ Protonated MOR & MOR carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate Ring C s adj acent to carbamate side in MOR/ Protonated MOR & MOR carbamate Methylene C s adjacent to nitrogen in DGA/ Protonated DGA Methylene C s adjacent to nitrogen in DGA carbamate (ppm) 164.2 162.8 160.8 72.5 70.5 70.0 67.0 60.5 45.0 41.0 40.0 Area 1000 187.69 16.27 63.44 19.28 44.98 33.48 66.64 33.52 18.98 45.15 Table I.25 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.522 mol CO2/mol MOR, T=60 0C Species DGA carbamate MOR carbamate Carbonate / Bicarbonate Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side (ppm) 163.0 159.8 158.2 72.0 Area 1000 153.96 30.66 34.34 379 Methylene C s adjacent to oxygen in DGA carbamate on carbamate side + Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side + Ring C s adjacent to non carbamate side in MOR/ Protonated MOR & MOR carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate Ring C s adjacent to carbamate side in MOR/ Protonated MOR & MOR carbamate Methylene C s adjacent to nitrogen in DGA/ Protonated DGA + Methylene C s adjacent to nitrogen in DGA carbamate 67.0 54.74 60.5 44.0 40.0 36.27 17.82 37.07 Table I.26 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.285 mol CO2/mol MOR, T=60 0C Species DGA carbamate + MOR carbamate Carbonate / Bicarbonate Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side Methylene C s adjacent to oxygen in DGA carbamate on carbamate side + Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side Ring C s adjacen t to non carbamate side in MOR/ Protonated MOR & MOR carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate (ppm) 164.4 160.6 72.5 70.5 Area 1000.0 19.19 52.21 53.99 67.0 60.5 27.65 54.60 380 Ring C s adjacent to carbamate side in MOR/ Protonated MOR & MOR carbamate Methylene C s adjacent to nitrogen in DGA/ Protonated DGA Methylene C s adjacent to nitrogen in DGA carbamate 45.0 41.0 40.0 27.77 15.54 38.42 Table I.27 C13 NMR of 11 wt% MOR/53 wt% DGA, Loading = 0.374 mol CO2/mol MOR, T=60 0C Species DGA carbamate MOR carbamate Carbonate / Bicarbonate Methylene C s adjacent to oxygen in DGA/ Protonated DGA & DGA carbamate on noncarbamate side Methylene C s adjacent to oxygen in DGA carbamate on carbamate side + Methylene C s adjacent to oxygen in DGA/ Protonated DGA on carbamate side + Ring C s adjacent to non carbamate side in MOR/ Protonated MOR & MOR carbamate Methylene C s adjacent to alcohol in DGA/ Protonated DGA & DGA carbamate Ring C s adjacent to carbamate side in MOR/ Protonated MOR & MOR carbamate Methylene C s adjacent to nitrogen in DGA/ Protonated DGA + Methylene C s adjacent to nitrogen in DGA carbamate (ppm) 163.0 159.8 158.2 72.0 Area 1000 153.96 41.66 37.34 67.0 54.74 60.5 44.0 40.0 40.05 20.76 39.91 381 Appendix J: C NMR Sample Calculation J.1 65 wt% DGA In Figure 4.9, the following quantities can be calculated; 13 From peaks 10 and 12; ADGACOO- = (67+68)/2=67.5 From peaks 4+8 and 2+6; ADGA/DGAH+ = (132+133)/2=132.5 From peaks 13, HCO3-, and (J.1); AHCO3- = 53/6451*67.5=0.55 (To correct for intensity of 13CO2 and normal 13 (J.1) C) Therefore, Loading = (0.55+67.5)/(67.5+132.5) = 0.340 mol CO2/mol DGA Assuming that CO3 = and CO2 are negligible fraction of total CO2 ADGAH+ = ADGACOO- + AHCO3- = 68.1 ADGA = ADGA/DGAH+ - ADGAH+ = 64.4 Fraction of Total DGA = 64.4/ (67.5+132.5) = 0.322 Kcarb = [DGACOO-]/([HCO3-][DGA]) This gives ; Kcarb = 67.5/(0.55*64.4) * 1/(6.18 M) = 61.2 M -1 J.2 23.5 wt% MOR In Figure 4.10, the following quantities can be calculated; From peaks 6 and 5; 382 AMORCOO- = (4.0+3.8)/4=1.95 From peaks 2+4 and 1+3; AMOR/MORH+ = (9.1+9.4)/4=4.6 From peaks 7, HCO3-, and (J.2); AHCO3- = 32.1/100.0*1.95=0.63 Therefore, (J.2) Loading = (0.63+1.95)/(1.95+4.6) = 0.392 mol CO2/mol MOR AMORH+ = AMORCOO- + AHCO3- = 2.58 AMOR = AMOR/MORH+ - AMORH+ = 2.05 Fraction of Total MOR = 2.05/ (4.6+1.95) = 0.312 Kcarb = [MORCOO-]/([HCO3-][MOR]) This gives ; Kcarb = 1.95/(0.63*2.05) * 1/(2.70 M) = 4.05 M -1 J.3 11 wt% MOR/53 wt% DGA In Figures 4.11-4.13, the following quantities can be calculated; From peaks 10 and 12; ADGACOO- = (17.69+17.38)/2=17.53 (J.3) (I.4) Peak 2+6 = Peaks 2+6+19 - Peaks 15+17 = 34.88 - 9.21= 22.34 From Peak 4+8 and (I.4), we get; ADGA/DGAH+ = (23.62+22.34)/2=22.98 Peak 19 = Peak 18 = Peak 14+16+18 - Peak 15+17 = 21.75 - 9.21 = 12.54 AMORCOO- = 12.54/2 = 6.7 (J.5) AMOR/MORH+ = 9.21/2 = 4.6 383 From peaks 13, 20, HCO3-, (J.3) and (J.5); AHCO3- =170.38/(1000.0+329.22)*(6.7+17.53)=3.05 Therefore, Loading = (17.53+6.7+3.05)/( 17.53+6.7+22.98+4.6) = 0.522 mol CO2/mol Amine 384 Bibliography Al-Ghawas, H.A., Hagewiesche, D.P., Ruiz-Ibanez and G. 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