060622 Troubleshooting Simulation

060622 Troubleshooting Simulation - Distillation...

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Unformatted text preview: Distillation Troubleshooting Distillation Simulation Stanislaw K. Wasylkiewicz Aspen Technology, Inc. A tool called azeotrope pressure sensitivity analysis (APSA) can shed light on the dependence of an azeotrope’s composition and temperature on changes in pressure. R igorous, robust and reliable thermodynamic models are crucial for the synthesis and design of separation systems for azeotropic mixtures. Incorrect prediction of azeotropes often leads to infeasible separation sequences. Although much progress in the modeling of physical and chemical equilibrium has been made, there is no universal model that can be used for any mixture at any conditions without adjusting various empirical parameters. Furthermore, because we often neglect some terms that we think are insignificant in rigorous thermodynamic models, the adjustable empirical parameters must account for not only what they were supposed to describe (e.g., interactions between molecules in liquid phase), but also all effects that have been neglected (1). This makes the models less predictable and their extrapolation to multicomponent mixtures questionable. Even if model predictions for all binary pairs are consistent with experimental vaporliquid equilibrium (VLE) data, we have to verify behavior of the whole mixture before using a thermodynamic package for rigorous simulations. Several excellent tools have recently been developed for selecting, verifying and troubleshooting thermodynamic models. Phase diagrams, residue curve maps (RCMs) and distillation region diagrams (DRDs) are invaluable for this purpose because of their visualization capabilities. However, they are restricted to ternary and quaternary mixtures. There are no such restrictions for the azeotrope pres22 www.cepmagazine.org June 2006 CEP sure sensitivity analysis (APSA), where temperature and composition bifurcation diagrams can be created for mixtures of any number of components. Since pressure changes from stage to stage in distillation columns, APSA is an excellent new tool for quick model verification and troubleshooting of real, non-isobaric distillation columns. It qualitatively reveals changes in the separation space that are difficult to find using an RCM or a DRD. This article describes, through several case studies, some frequently encountered modeling problems during simulation of non-isobaric azeotropic distillation columns, and applies the new troubleshooting tools to these simulations. An overview of the tools The shape of the separation space, including distillation boundaries, distillation regions and azeotropes (singular points of the maps), can be easily examined on RCMs (2). Visual analysis of an RCM’s structure provides valuable insight into the underlying thermodynamics, making RCMs useful for screening binary VLE parameters based on alternative databanks and regressions strategies (3). Because RCMs depict VLE behavior in a ternary composition space, they can be more relevant than binary phase diagrams in assessing the validity of various parameter sets for distillation modeling. Reference 3 shows examples of troubleshooting phase equilibria that include using data outside their intended range, employing VLE instead of vapor-liquid-liquid equilibrium (VLLE) calculations, using parameter sets opti- mized for different regression objectives, and choosing the appropriate model for the vapor phase. Reference 4 presents examples of utilizing RCMs and VLLE diagrams for selection of the appropriate thermodynamic model and verification of interaction parameters, and Refs. 5 and 6 explain how these methods can be applied in troubleshooting distillation columns. Conveniently, RCMs can now be readily generated using commercial process simulation or synthesis software. Moreover, the individual points of the maps can be calculated for any number of components and used to test phase equilibrium models. Azeotropes determine distillation regions and distillation boundaries. Therefore, knowledge of temperatures and compositions of all the azeotropes in a mixture at a specified pressure is critical for both the design and operation of distillation systems. Calculating them is complicated by the strong non-linearities encountered in VLLE and the presence of multiple solutions, both real and spurious. One can attempt to find all of the solutions by using a nonlinear solver with several starting points. However, even with extreme calculation effort, this approach does not guarantee that all of the azeotropes will be found. Several techniques have been proposed to solve this problem, e.g., the Levenberg-Marquardt algorithm (7), the interval Newton method (8), a global optimization method (9), etc. The most reliable and robust method for calculating all the azeotropes in a homogeneous mixture has been proposed by Fidkowski, et al. (10) and later generalized to include heterogeneous liquids (11). This method combined with an arc length continuation and rigorous stability analysis (12) is an efficient way to find all of the homogeneous and heterogeneous azeotropes predicted by a thermodynamic model at a specified pressure. In the real world, plant operation is not static. Changes in product quality and quantity often require operation at different pressures. Even when operating near steady state, many columns exhibit significant pressure gradients between the distillate and the bottoms. Thus, it is critical to understand the pressure sensitivity of the azeotropes in a mixture. When upper and lower pressure limits are specified, the analysis can start from one pressure limit and then the azeotrope composition can be calculated for gradually increasing or decreasing pressures. This simple parametercontinuation procedure can follow any known azeotrope. However, it cannot find new azeotropes that appear as the pressure changes. An alternative is to apply rigorous azeotrope calculation procedures at each pressure interval. Such an approach, though, would be extremely computationally intensive and time consuming. Table 1. Temperatures and compositions of binary azeotrope WA at selected pressures. Pressure, kPa 50 100 150 Temperature, ºC Mole Fraction of W Mole Fraction of A 80.64 98.79 110.44 0.960958 0.955925 0.952532 0.039042 0.044075 0.047468 To overcome these difficulties, we have developed a new method called azeotrope pressure sensitivity analysis (APSA) that reveals how the compositions and temperatures of azeotropes change with pressure. It applies bifurcation theory together with an arc length continuation to perform the calculations (13). This allows us to not only follow individual azeotropes but also to find any new azeotrope that appears in a specified pressure interval. Therefore, all bifurcation pressures, where azeotropes appear or disappear, can be found. The computation time required for the entire pressure sensitivity analysis is similar to the time necessary for the homotopy-continuation method to find all azeotropes at a single pressure. The pressure-sensitivity of azeotropes provides new opportunities in the design of azeotropic distillation sequences. Increasing or decreasing operating pressures in individual columns changes the composition of azeotropes and positions of distillation boundaries, and can even cause their appearance or disappearance. This can have enormous effects on the topology of the RCM and the feasibility of distillation sequences. APSA shows opportunities for pressure-swing distillation and heat integration between columns in the sequence. Pressure-swing distillation can often be an attractive alternative for breaking homogeneous azeotropes and sometimes can considerably simplify complex separation systems. Pressure-sensitivity information can also be important in the design and troubleshooting of real distillation columns, especially where there is a substantial pressure drop in the column. In some cases, this can lead to a switch in topology of distillation regions inside the column and cause serious problems in convergence of simulators in steady-state and dynamic modes. Troubleshooting non-isobaric extractive distillation Let us consider a typical separation problem. A mixture containing mostly components A and W is to be separated. There is a binary azeotrope between components A and W. Since the azeotrope is not sensitive to pressure change (Table 1), an entrainer, C, was selected to separate the binaCEP June 2006 www.cepmagazine.org 23 Distillation Azeotrope pressure sensitivity analysis Distillate The sensitivity of C+W azeotropes to changes in W pressure has been known C and studied for years. The Upper Reflux Reflux Feed magnitude of pressure effects depends on the mixture. Sometimes, composiLower Feed tions of azeotropes change Reboil Reboil very little (e.g., the ethanolA+W water azeotrope (13)). However, there are mixtures C where compositions of some Bottoms A Bottoms azeotropes change rapidly with pressure and even ■ Figure. Extractive distillation is used to break the binary azeotrope. azeotropes that appear or disappear as pressure varies. Knapp (14) introduced the concept of a bifurcation ry mixture in an extractive distillation sequence of two dispressure, where an azeotrope appears or disappears, and tillation columns (Figure 1). The first column was set up at showed the necessary conditions for a homogeneous binaa constant pressure of 150 kPa and converged quickly to the ry azeotrope to bifurcate. An azeotrope exists on one side desired products: high-purity A and a binary mixture of W of a bifurcation pressure and a tangent pinch on the other and C. Then a pressure drop in the column was taken into side. As the pressure increases or decreases away from the account. This time, the required high recovery of compobifurcation pressure, the severity of the tangent pinch nent A in the bottom of the column was never achieved, decreases. Therefore, a distillation column should not even with an extreme reflux and a large number of stages. operate near a bifurcation pressure. For the three key components (W, A and C), distillaIn real distillation columns, pressure changes from tion region diagrams were created for three selected stage to stage. This can lead to a switch in topology of dispressures to examine the three-component space for tillation regions and cause serious problems in both real azeotropes and distillation boundaries, as shown in operation and in convergence of calculations for simulaFigure 2. By examining the DRDs, one can easily conclude that it is impossible to achieve complete recovery tors in steady-state or dynamic modes. In such cases, of component A in the bottom product of the first colinformation about the bifurcation pressures could be umn at 50 kPa because of the presence of a distillation extremely useful in troubleshooting both for simulators boundary at this pressure. But in our simulation case, and real operations. pressure at the top of the column does not drop as low The APSA method (15) is based on bifurcation theory — it always stays above 100 kPa. To troubleshoot this together with an arc length continuation. The method finds case further, we will use APSA. all bifurcation pressures within specified pressure limits and allows one not only to follow individual azeotropes, but also to efficientA A A ly find any azeotrope that appears within the pressure range. (More details are 50 kPa 100 kPa 150 kPa available in Ref. 13.) This article applies the APSA tool to create various bifurcation diagrams, which are extremely useful in troubleshooting of azeotropic distillation columns. The pressure sensitivity analysis of C WC W W C azeotropes starts with a branch for each pure component and each azeotrope ■ Figure 2. Distillation region diagrams for ternary mixture W-A-C at 50, 100 and150 kPa, found at 50 kPa. Each branch is folbased on the NRTL-Ideal model. Top Vapor 24 www.cepmagazine.org June 2006 Distillate CEP Top Vapor 1.0 A Mole Fraction NRTL 50–150 kPa 0.8 0.7 Branch WA Branch WC 0.6 Branch WAC 0.5 90 95 100 105 110 115 Pressure, kPa 120 125 130 ■ Figure 5. Composition branches WC and WAC for pressure analysis of azeotropes for ternary mixture W-A-C between 85 and 130 kPa, based on the NRTL-Ideal model. 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 W ■ Figure 3. Homotopy continuation branches WA, WC and WAC for pressure analysis of azeotropes for ternary mixture W-A-C between 50 and 150 kPa, based on the NRTL-Ideal model. 106 104 Temperature, °C 0.4 0.0 85 0.2 102 100 Branch WA Branch WC Branch WAC 98 96 94 85 Branch WAC, Component C Branch WAC, Component A 0.3 C 0.6 0.2 0.4 0.0 0.0 Branch WAC, Component W 0.8 0.9 Branch WC 1.0 90 95 100 105 110 115 120 125 130 Pressure, kPa ■ Figure 4. Temperature branches WA, WC and WAC for pressure analysis of azeotropes for ternary mixture W-A-C between 85 and 130 kPa, based on the NRTL-Ideal model. lowed and continually checked for new bifurcations between 50 and 150 kPa or until the branch disappears. The corresponding homotopy continuation branches are shown in Figure 3, temperature branches in Figure 4, and composition branches in Figure 5. The binary azeotrope WA is not sensitive to pressure change (see also Table 1). On the other hand, the WC and WAC azeotropes are very pressure sensitive and exist only in a narrow pressure range (WAC between 89 and 127 kPa, WC only in the proximity of 127 kPa). There are two bifurcation points where the WAC branches collapses: one on branch WA (at 112 kPa), the other on branch WC (at 127 kPa). There is also a turning point on branch WAC at 89 kPa. Notice how much more information the APSA provides compared to DRD diagrams created for a few selected pressures (Figure 2). The DRDs confirm the existence of only one azeotrope, WA. The binary azeotrope WC exists only in a very narrow range of pressures (see Figure 4 and Figure 5) and is practically visible as a homotopy continuation branch WC only in Figure 3. The ternary azeotrope WAC was not found by the azeotrope searching algorithm (the 100-kPa DRD in Figure 2) because the homotopy method used in the algorithm cannot find isolas — i.e., continuation paths not connected to any homotopy branch that starts from a pure component (10). The model actually predicts two WAC azeotropes at 100 kPa (Figure 5) — one that is a saddle, and another that is an unstable node. Because two azeotropes have been missed and their contributions cancel each other, the consistency test is fulfilled and there is no warning during creation of DRD at 100 kPa. Troubleshooting the distillation of cyclohexanone-cyclohexanol-phenol Another problem in the simulation of distillation columns has been reported for the mixture of cyclohexanone (CC6one), cyclohexanol (CC6ol) and phenol. APSA has been applied to the mixture to verify the accuracy of predictions of two VLE models throughout a pressure range of industrial interest. The NRTL (nonrandom two-liquid) model predicts the existence of the ternary maximum-boiling azeotrope in a wide pressure range (only slightly pressure-sensitive), whereas the Wilson model predicts the existence of the ternary saddle azeotrope only in a very narrow range of pressures (extremely pressure sensitive). CEP June 2006 www.cepmagazine.org 25 Distillation tures of all azeotropes are so close that any small change in pressure can change their Wilson Wilson Wilson 5 kPa 10 kPa 15 kPa type and the structure of the DRD. At 5 kPa, the CC6olphenol azeotrope is a stable 118.16 102.44 128.22 118.15 node and the CC6one-phenol azeotrope is a saddle, where113.53 118.22 97.82 101.88 123.55 128.65 71.40 87.24 97.34 as at 15 kPa the CC6ol-pheCC6one Phenol CC6one Phenol CC6one Phenol nol azeotrope is a saddle and the CC6one-phenol azeotrope ■ Figure 6. Distillation region diagrams for the mixture of cyclohexanone (CC6one), cyclohexanol is a stable node. (CC6ol) and phenol at 5, 10 and 15 kPa, based on the Wilson model. The homotopy continuation method (11) was used to find all azeotropes at par0.8 ticular pressures. The topological consistency was 0.7 checked using a topological constraint (10, 18) and all Phenol diagrams presented are topologically consistent. If the 0.6 topological constraint is not fulfilled, one or more 0.5 azeotropes are missing or their properties have been estimated incorrectly. However, fulfillment of the topo0.4 logical constraint does not guarantee that all azeotropes CC6ol have been found or that the system properties have been 0.3 determined correctly. The topological constraint is a 0.2 necessary, but not a sufficient, condition for consistency 0.1 in azeotrope calculations (11). CC6one APSA was performed for the mixture between 5 kPa 0.0 and 15 kPa. Branches of solutions are shown in a compo5 6 7 8 10 11 12 13 14 15 sition bifurcation diagram (Figure 7). In this pressure 9 Pressure, kPa range, two bifurcation points have been found, as shown in Table 2: ■ Figure 7. Composition changes of azeotropes with pressure for the • B1 at 8.26 kPa, where the ternary CC6one-CC6olmixture of cyclohexanone (squares), cyclohexanol (diamonds) and phenol branch bifurcates from the CC6one-phenol branch, phenol (triangles) between 5 and 15 kPa, based on the Wilson model. and the CC6one-phenol azeotrope changes type from sadFor this ternary system, it is known from measuredle to stable node ments (16) that: • B2 at 10.94 kPa, where the ternary CC6one-CC6ol• there is a maximum-boiling azeotrope in the binary phenol branch collapses on the CC6ol-phenol branch, and system CC6one-phenol between 8.00 and 101.32 kPa the CC6ol-phenol azeotrope changes type from stable • there is a maximum-boiling azeotrope in the binary node to saddle. system CC6ol-phenol between 9.33 and 101.32 kPa Both binary azeotropes are only slightly sensitive to • the three-component system does not form a ternary pressure changes. On the other hand, the ternary azeotrope azeotrope at 12.00 kPa. (saddle) is extremely pressure-sensitive and exists only in Distillation region diagrams for the mixture are presentthe very narrow pressure range, between the two bifurcaed in Figure 6 for a few selected pressures. VLE calculations were based on Table 2. Results of bifurcation pressure search for the mixture of the Wilson model. Binary interaction cyclohexanol (CC6ol), cyclohexanone (CC6one) and phenol parameters were taken from Ref 17. between 5 and 15 kPa, based on the Wilson model. The Wilson model does not predict the existence of the ternary azeotrope at Bifurcation Pressure, Bifurcation Composition, Temperature, Point kPa mole fraction °C 5 kPa and 15 kPa. There is, however, a B1 8.26 0.0 0.262584 0.737416 113.54 very narrow range of pressures where the B2 10.94 0.323241 0.0 0.676759 120.34 ternary azeotrope exists. The temperaCC6ol CC6ol 99.25 Mole Fraction 85.19 26 www.cepmagazine.org June 2006 CEP CC6ol 108.19 in the wider pressure range of 1–100 kPa, all three azeotropes (two binary sadNRTL NRTL, NRTL 5 kPa 10 kPa 15 kPa dles and one ternary maximum-boiling) exist and do 105.57 119.57 128.53 not change their types. 145.12 129.55 155.05 APSA was performed for the mixture in the pressure 113.53 118.08 97.82 123.55 128.51 101.75 71.40 87.24 97.34 range 1–100 kPa. Branches CC6one Phenol CC6one Phenol CC6one Phenol of solutions predicted by the ■ Figure 8. Distillation region diagram for the mixture of cyclohexanone (CC6one), cyclohexanol NRTL model are shown in a (CC6ol) and phenol at 5, 10 and 15 kPa, based on the NRTL model. composition triangle in Figure 9. No bifurcation CC6ol pressures were found. In this case, the binary CC6ol-phe1.0 nol azeotrope is the most pressure-sensitive, whereas the ternary maximum-boiling CC6one-CC6ol-phenol 0.9 azeotrope is the least sensitive. This contradicts the predicNRTL 0.8 1–100 kPa tions of the Wilson model (Figure 7). Performing both equilibrium and azeotrope calcula0.7 tions for this ternary system is challenging. The two 0.6 models give qualitatively different predictions for the ternary CC6one-CC6ol-phenol azeotrope: an extremely 0.5 pressure-sensitive saddle azeotrope in a very narrow 0.4 range of pressures for the Wilson model, and a moderately pressure-sensitive maximum-boiling azeotrope in 0.3 a wide pressure range for the NRTL model. At the 0.2 same time, the binary azeotropes are predicted equally well by both models and are consistent with binary 0.1 experimental data. More experiments for the ternary system are neces0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 sary, especially in the pressure range between the CC6one Phenol bifurcation pressures (8.26 and 10.94 kPa), to allow us ■ Figure 9. Branches of pressure sensitivity analysis of to accept or reject the Wilson model predictions. Based azeotroopes for the mixture of cyclohexanone (CC6one), cycloon the only one available experimental data point for hexanol (CC6ol) and phenol between 1 and 100 kPa, based on the ternary mixture at 12.00 kPa (16), we can conclude the NRTL model. that the NRTL model should be corrected (better intertion pressures 8.26 and 10.94 kPa. Experiments have action parameters should be regressed). Generally, if a shown that the three-component system does not form the model is expected to reflect reality, interaction parameternary azeotrope at 12.00 kPa (16). This agrees well with ters should be regressed for the model using experithe Wilson model predictions. New experiments are needmental data covering the particular pressure range of ed in the pressure range between the two bifurcation presinterest. In this case, special attention is required for sures to check the model predictions. It must be emphathe saturated pressure correlation for pure components sized here that, unlike stable and unstable azeotropes, it is (e.g., the Antoine equation). Since CC6ol and CC6one much more difficult to confirm experimentally the exisare close-boiling components, small inaccuracies in tence of a saddle azeotrope. prediction of saturated pressure can cause significant Distillation region diagrams for the mixture calculatchanges in the DRD structure. ed based on the NRTL model are presented in Figure 8 Closing thoughts for the same pressures as for the Wilson model. Binary interaction parameters were taken from Ref. 17. The It is extremely important to select the proper therNRTL model predicts the existence of the ternary maximodynamic model and carefully verify the behavior of mum-boiling azeotrope for all of these pressures. Even the mixture for a particular set of components before CC6ol 85.19 CC6ol 99.25 CC6ol 108.19 CEP June 2006 www.cepmagazine.org 27 Distillation any attempt is made to simulate a distillation column. DRDs are extremely useful for this verification because of their visualization capabilities. They are, however, restricted to ternary and quaternary mixtures. There are no such restrictions for APSA, which involves calculating bifurcation pressures and creating temperature and composition bifurcation diagrams for any numbers of components. This provides an excellent tool for both design and troubleshooting of real distillation columns. The extreme sensitivity of azeotropes to pressure change in the examples discussed here has been detected in several distillation systems, especially when close-boiling components were present. If detected, this extreme sensitivity should trigger more careful examination of the thermodynamic model (applicability, parameters) and perhaps some additional VLE measurements. At a minimum, it should draw attention to the situation so the particular pressure range can be avoided both in the design and operation of the distillation column. Changes in product quality and quantity often require operation of distillation columns at different pressures. Even when operating at a near-steady-state condition, many columns exhibit significant pressure gradients between the distillate and bottoms. In some cases, this can lead to a switch in the topology of the distillation regions and cause serious problems in convergence of calculations for steady-state or dynamic simulators. APSA provides an understanding of the dependence of an azeotrope’s compositions and temperatures on changes in pressure. This information can be of critical importance in the design and troubleshooting of distilla- tion systems. APSA can also be used to verify the suitability and accuracy of the VLE models throughout a pressure range if the system is known to have particular C EP azeotropes at particular pressures. Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. STANISLAW K. WASYLKIEWICZ, PhD, P.Eng., is a senior advisor at Aspen Technology, Inc. (900, 125 – 9th Ave. SE, Calgary, Alberta T2G 0P6, Canada; Phone: (403) 303-1047; E-mail: [email protected]), where his primary emphasis is conceptual design and simulation of distillation processes. He is currently working on new tools for petroleum distillation in the computer program RefSYS, a new product that enables companies to optimize refinery-wide performance using an integrated model of their facilities. He is a graduate in chemical engineering from the Technical Univ. of Wroclaw (Poland), where he received his MSc and PhD and taught for several years. Prior to joining the Conceptual Design Team of Hyprotech (Calgary, Canada), he worked as a researcher at the Univ. of Massachusetts (Amherst), where he was developing Mayflower, software for the conceptual design of distillation systems. Throughout his engineering career, he has become involved in several areas of expertise, including thermodynamics, phase equilibrium, process synthesis, simulation and optimization, and the design of non-azeotropic, azeotropic, heterogeneous and reactive distillation columns. He has published over 100 scientific papers and contributed to technical books. He is a member of AIChE and a registered professional engineer in Alberta, Canada. 28 www.cepmagazine.org June 2006 CEP 13. 14. 15. 16. 17. 18. Agraval, R., et al., “Uncovering the Realities of Simulation (Parts 1 and 2),” Chem. Eng. Progress, 97 (5), pp. 42–52 and 97 (6), pp. 64–72 (May and June, 2001). Doherty, M. F., and M. F. Malone, “Conceptual Design of Distillation Systems,” McGraw-Hill, New York, NY (2001). Villiers, W. E., et al., “Navigate Phase Equilibria via Residue Curve Maps,” Chem. Eng. Progress, 98 (11), pp. 66–71 (Nov. 2002). Wasylkiewicz, S. K., and H. K. Shethna, “VLE Data Estimation for Synthesis of Separation Systems for Azeotropic Mixtures,” AIChE Spring National Meeting, Paper No. 4e, New Orleans, LA (Mar. 2002). Wasylkiewicz, S. K., “Diagrams Troubleshoot Acetic Acid Dehydration Simulation,” in “Distillation Troubleshooting,” by Kister, H. Z., Wiley, Hoboken, NJ (2006). Wasylkiewicz, S. K., “Modeling Ternary Mixture Using Binary Interaction Parameters,” in “Distillation Troubleshooting,”by Kister, H. Z., Wiley, Hoboken, NJ (2006). Chapman, R. G., and S. P. Goodwin, “A General Algorithm for the Calculation of Azeotropes in Fluid Mixtures,” Fluid Phase Equilibria, 85, pp. 55-69 (1993). Maier, R. W., et al., “Reliable Computation of Homogeneous Azeotropes,” AIChE J., 44, pp. 1745-1755 (1998). Harding, S. T., et al., “Locating All Homogeneous Azeotropes in Multicomponent Mixtures,” Ind. Eng. Chem. Res., 36, pp. 160-178 (1997). Fidkowski, Z. T., et al., “Computing Azeotropes in Multicomponent Mixtures,” Comput. Chem. Eng., 17, pp. 1141-1155 (1993). Wasylkiewicz, S. K., et al., “Computing All Homogeneous and Heterogeneous Azeotropes in Multicomponent Mixtures,” Ind. Eng. Chem. Res., 38, pp. 4901-4912 (1999). Wasylkiewicz, S. K., et al., “Global Stability Analysis and Calculation of Liquid-Liquid Equilibrium in Multicomponent Mixtures,” Ind. Eng. Chem. Res., 35, pp. 1395-1408 (1996). Wasylkiewicz, S. K., et al., “Pressure Sensitivity Analysis of Azeotropes,” Ind. Eng. Chem. Res., 42, pp. 207-213 (2003). Knapp, J. P., “Exploiting Pressure Effects in the Distillation of Homogeneous Azeotropic Mixtures,” PhD Thesis, Univ. of Massachusetts, Amherst (1991). Wasylkiewicz, S. K., et al., “Pressure Sensitivity Analysis of Azeotropes in Synthesis of Distillation Column Sequences,” Hungarian J. of Industrial Chemistry, 28, pp. 41-45 (2000). Gmehling, J., et al., “Azeotropic Data,” VCH Verlagsgesellschaft GmbH. Weinheim (1994). Gmehling, J., et al., “Vapor-Liquid Equilibrium Data Collection, DECHEMA Chemistry Data Series,” Vol. I, DECHEMA, Frankfurt (1981). Zharov, W. T., and L. A. Serafimov, “Physicochemical Fundamentals of Distillation and Rectification,” Khimiya, Leningrad (1975). ...
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This note was uploaded on 12/29/2011 for the course CHE 128 taught by Professor Scott,s during the Fall '08 term at UCSB.

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