lopeztoledod54214
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lopeztoledod54214

Course Number: LOPEZTOLED 54214, Fall 2009

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Copyright by Jacinto Lopez-Toledo 2006 The Dissertation Committee for Jacinto Lopez-Toledo certifies that this is the approved version of the following dissertation: Heat and Mass Transfer Characteristics of a Wiped Film Evaporator Committee: A. Frank Seibert, Supervisor Gary T. Rochelle, Supervisor James R. Fair Roger T. Bonnecaze Benny D. Freeman Richard L. Corsi Heat and Mass Transfer Characteristics of a...

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by Copyright Jacinto Lopez-Toledo 2006 The Dissertation Committee for Jacinto Lopez-Toledo certifies that this is the approved version of the following dissertation: Heat and Mass Transfer Characteristics of a Wiped Film Evaporator Committee: A. Frank Seibert, Supervisor Gary T. Rochelle, Supervisor James R. Fair Roger T. Bonnecaze Benny D. Freeman Richard L. Corsi Heat and Mass Transfer Characteristics of a Wiped Film Evaporator by Jacinto Lopez-Toledo, B. S., 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 August 2006 To the most important people in my life: Nancy, Guienisa, Yamil, and Anisa. Siempre recuerden que los amo. Acknowledgments I owe a debt of gratitude to my advisor, Dr. Frank Seibert for his great support and encouragement since I arrived at the Separations Research Program in the Summer of 1998, for letting me work under his supervision, and for all his advice until the completion of this work. Without all his help I would have not been able to finish my dissertation. I feel honored for being allowed to work with him; he was and always will be my mentor. I would also like to recognize the support from Dr. James Fair for all his input since the beginning of the project and for all the time he dedicated for the revision of my drafts and final dissertation. It was a pleasure to work with one of the finest experts in separation processes. I want to express my gratitude to Dr. Gary Rochelle for agreeing to be my co-Advisor and for his comments regarding this work, Dr. Roger Bonnecaze, Dr. Benny Freeman, and Dr. Richard Corsi for being part of my committee and for their valuable input. To the faculty of the Department of Chemical Engineering at the University of Texas. I want to recognize the support that I received from the Separations Research Program: Dr. Bruce Eldridge, Chris Lewis, Susan Dunn, Sande Storey, and Steve Briggs. My visit to SRP in the Summer of 1998 and admission to Graduate School in Fall of 2000 was encouraged by Dr. Jose Antonio Rocha-Uribe. Thank you for everything. I will always cherish your friendship. v To Consejo Nacional de Ciencia y Tecnolog (CONACyT), for the ia financial support provided during part of my studies. To Cargill-PGLA for their help in the gathering of experimental data, especially Mark Gusse, Troy Rhonemus, Jess Vassina, and Scott McElmury. To my family: my mother Juanita Toledo-Cristobal, my father Juan Lopez-Chevez, my brothers and sisters; Roberto, Isaias, Elizabeth, Jesus, Rosa, Ramon, and Agueda Lopez-Toledo; for their love and support. To my extended family: Felipe Ruiz Matus, Aurora Castillo de la Cruz, Marlene, Noel, Tomas, Juan Felix, Tomasa, and Felipe. To my friends: the Serrano-Sepulveda, Camacho-Gonzalez, MartinezCarrion, Monzalvo-Mosqueda, Pati~o, Valle-Miranda, Garcia-Piretti, Medinan Corzo, Huerta-Escamilla, Carriles-Sandoval, Contreras, Alonso-Rueda, Tzoc, Lopez, and Lopez-Garcia family. To Eric Chen, Roque Hernandez, Luis Rangel, Carlos Alcala, Jose Luis Gonzalez, Vladimir Amador, Marco Gallo, Ruy Tellez, Pedro Sanchez, Ignacio Perez, Juan Carlos Valencia, and Guadalupe Cruz. Thank you everybody for your friendship. vi Heat and Mass Transfer Characteristics of a Wiped Film Evaporator Publication No. Jacinto Lopez-Toledo, Ph.D. The University of Texas at Austin, 2006 Supervisors: A. Frank Seibert Gary T. Rochelle Wiped film evaporators (WFEs) are often used in the petrochemical, chemical and food industries to remove a volatile component from a very nonvolatile mixture. Wiped film evaporators provide a short residence time and are often operated under vacuum for temperature sensitive mixtures. The wiped film evaporator utilizes a set of wiper blades or rollers to spread and thin the liquid along the surface of the heated wall. The wipers or rollers also induced convection within the liquid film which promotes evaporation of the volatile compound and enhances mass transfer within the film. Unfortunately, very little has been published on wiped film evaporators and users must rely on equipment vendors even for preliminary evaluations. In this work, a rigorous heat and mass transfer model was developed for a vertical wiped film evaporator. The model includes the capability to perform a single stage flash calculation and for predicting physical properties vii from available DIPPR constants and from group contribution methods. The actual physical properties may also be added. The study includes evaluating the model with published and data obtained in this work. The effects of wiper type, number of wipers, rotational speed, Reynold's number and system properties were studied and compared with the rigorous model. Three test systems were evaluated: sucrose/water, glycerol/water and ethylene glycol/water. A new mass transfer model in vertical WFEs is proposed. The wellstudied falling film evaporator (FFE) is taken as the base case for the vertical wiped film evaporator. A heat transfer enhancement factor, defined as the ratio of the heat transfer coefficient for a wiped film evaporator to the heat transfer coefficient of a falling film evaporator, was applied to a falling film mass transfer model. The results of the rigorous model compared very favorably with experimental data obtained in this work and the published results. The rigorous model also allows the capability of a flash calculation. In general, the flash calculation agreed favorably with the experimental data and was shown to represent the wipe film evaporator in a process simulation. However, it should be noted the flash calculation does not provide mechanical and engineering details such as the required diameter and length, heat transfer area, number of blades or rollers and rotational speed. The goal of the study is to provide a computational tool which could be used to evaluate process changes to an existing wiped film evaporator or to assist in a preliminary design. The final design and evaluation of a process change should include the wiped film evaporation vendor. viii Table of Contents Acknowledgments Abstract List of Tables List of Figures Chapter 1. Introduction 1.1 Evaporation . . . . . . . . . . . . . . . . . . . 1.1.1 Function of an Evaporator . . . . . . . 1.2 Criteria for the Selection of the Evaporator . . 1.3 Types of Evaporator . . . . . . . . . . . . . . 1.3.1 Natural Circulation Evaporators . . . . 1.3.1.1 Horizontal Tube Evaporator . . 1.3.1.2 Short-Tube Vertical Evaporator 1.3.1.3 Long-Tube Vertical Evaporator 1.3.2 Forced Circulation Evaporators . . . . . 1.3.3 Film-Type Evaporators . . . . . . . . . 1.3.3.1 Wiped Film Evaporator . . . . 1.4 Research Objectives . . . . . . . . . . . . . . . Chapter 2. Literature Review 2.1 Boiling Mechanisms in Evaporation 2.1.1 Pool Boiling . . . . . . . . . 2.1.2 Nucleate Boiling . . . . . . . 2.1.3 Film Boiling . . . . . . . . . 2.2 Literature Review . . . . . . . . . . v vii xiii xv 1 1 4 5 6 8 8 8 10 12 13 15 19 22 22 22 23 24 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Chapter 3. 3.1 Heat 3.1.1 3.1.2 Modeling: Previous Work Transfer . . . . . . . . . . . . . . . . Falling Film Evaporators . . . . . . Wiped Film Evaporators . . . . . . 3.1.2.1 Heat Transfer Models Based 3.2 Mass Transfer . . . . . . . . . . . . . . . . 3.2.1 Falling Film Evaporators . . . . . . 3.2.2 Wiped Film Evaporators . . . . . . 3.3 Flash Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . on Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 35 35 39 42 47 47 49 50 52 52 53 59 63 76 76 76 78 81 82 83 86 86 87 90 96 97 97 98 98 Chapter 4. Model Development 4.1 Heat and Mass Transfer Model for Vertical Wiped Film Evaporators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Proposed Design Model . . . . . . . . . . . . . . . . . . . . . . 4.3 Comparison of Proposed Model With Published Data . . . . . 4.4 Simultaneous Heat and Mass Transfer . . . . . . . . . . . . . . Chapter 5. Experimental System and Procedures 5.1 Test Systems . . . . . . . . . . . . . . . . . . . . . 5.1.1 Water/Glycerol . . . . . . . . . . . . . . . . 5.1.2 Water/Sucrose . . . . . . . . . . . . . . . . 5.1.3 Water/Ethylene Glycol . . . . . . . . . . . 5.2 Experimental Setup . . . . . . . . . . . . . . . . . 5.3 Error Analysis . . . . . . . . . . . . . . . . . . . . 5.4 Experimental Conditions . . . . . . . . . . . . . . 5.5 Equipment . . . . . . . . . . . . . . . . . . . . . . 5.6 Calibration Curves . . . . . . . . . . . . . . . . . 5.7 Run Procedure . . . . . . . . . . . . . . . . . . . 5.8 Experimental Data . . . . . . . . . . . . . . . . . 5.8.1 Operating Conditions . . . . . . . . . . . . 5.8.2 Collected Data . . . . . . . . . . . . . . . . 5.8.3 Heat Balance . . . . . . . . . . . . . . . . . 5.8.4 Vapor Velocity and Entrainment . . . . . . x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 6. Analysis of Experimental Results and dation 6.1 Isothermal Flash . . . . . . . . . . . . . . . . . . . 6.1.1 Water-Sucrose . . . . . . . . . . . . . . . . 6.1.2 Water-Glycerol . . . . . . . . . . . . . . . . 6.1.3 Water-Ethylene Glycol . . . . . . . . . . . . 6.1.4 WFE as an Isothermal Flash . . . . . . . . 6.2 Heat and Mass Transfer Coefficient . . . . . . . . 6.2.1 Experimental Heat Transfer Coefficient . . 6.2.2 Predicted Mass Transfer Coefficient . . . . 6.3 WFE-SRP Model Applied to Experimental Data . 6.3.1 Water-Sucrose . . . . . . . . . . . . . . . . 6.3.2 Water-Glycerol . . . . . . . . . . . . . . . . 6.3.3 Water-Ethylene Glycol . . . . . . . . . . . . Model Vali103 . . . . . . . 103 . . . . . . . 103 . . . . . . . 105 . . . . . . . 106 . . . . . . . 106 . . . . . . . 107 . . . . . . . 108 . . . . . . . 120 . . . . . . . 132 . . . . . . . 132 . . . . . . . 134 . . . . . . . 139 Chapter 7. Conclusions and Future Work 149 7.1 Wiped Film Evaporator as an Isothermal Flash . . . . . . . . 149 7.2 Proposed Model: Simultaneous Heat and Mass Transfer . . . . 150 7.2.1 Heat Enhancement Factor and Mass Transfer Coefficient 151 7.2.1.1 Enhancement Relative to Falling Film Evaporator 151 7.3 WFE-SRP Computer Program . . . . . . . . . . . . . . . . . . 152 7.4 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Appendices Appendix A. WFE-SRP Computer Program A.1 Types of Calculation . . . . . . . . . . . . . A.1.1 Flash Calculation . . . . . . . . . . . A.1.2 WFE Calculation . . . . . . . . . . . A.2 Adding Components . . . . . . . . . . . . . A.2.1 Liquid Density . . . . . . . . . . . . . A.2.2 Liquid Viscosity . . . . . . . . . . . . A.2.3 Liquid Thermal Conductivity . . . . . 154 155 156 157 158 159 161 163 164 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi A.2.4 Vapor Pressure . . . . A.2.5 Liquid Heat Capacity A.2.6 Critical Constants . . A.3 Example: Adding Glycerol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 165 167 168 Appendix B. Marlotherm SH Heat Transfer Fluid 181 B.1 Product Information . . . . . . . . . . . . . . . . . . . . . . . 181 B.2 Typical Physical and Chemical Properties . . . . . . . . . . . . 183 References Vita 189 204 xii List of Tables 1.1 1.2 2.1 2.2 2.3 2.4 3.1 4.1 5.1 General Application Areas of Wiped Film Evaporators [6]. . . Summary of available literature for wiped film evaporators. . . Vendors of Wiped Film Evaporators [78]. . . . . . . . . . . . . Technical papers on Wiped Film Evaporator Technology [78]. Advantages and Disadvantages of Vacuum Evaporator Systems [23]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Where Wiped Film Evaporators are Used [24]. . . . . . . . . . Correlation constants for Equation 3.3 [4]. . . . . . . . . . . . Set of experimental data from Frank and Lutcha [25]. . . . . . Physical properties for several mixtures of glycerol and water at 5.3 kPa and 36 C), calculated using AspenPlus version 11.1 with the UNIQUAC thermodynamics option. . . . . . . . . . . Physical properties for several mixtures of sucrose and water at 40 C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Constants for Equation 5.7 [60]. . . . . . . . . . . . . . . . . . Physical properties for 75 wt% ethylene glycol and water at 4.3 kPa and 42 C, calculated using AspenPlus version 11.1 with the UNIQUAC thermodynamic option. . . . . . . . . . . . . . Effect of measurement errors in operational parameters over the experimental process side heat transfer coefficient. . . . . . . . Operational Parameters for Experimental Measurements . . . Main dimensions of the Cargill evaporator . . . . . . . . . . . Refractive index for different solutions of sucrose in water at 20 C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Refractive index for glycerol in water at 20 C . . . . . . . . . Refractive index for ethylene glycol in water at 20 C . . . . . Range of experimental conditions . . . . . . . . . . . . . . . . xiii 18 18 25 26 31 32 37 64 77 78 80 5.2 5.3 5.4 81 86 86 87 92 92 95 97 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 Experimental data for water-sucrose at different operating conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.13 Experimental data for water-glycerol at different operating conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.14 Experimental data for water-ethylene glycol at different operating conditions. . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 6.2 6.3 6.4 6.5 6.6 6.7 99 101 102 Equations for the calculation of physical properties for Marlotherm SH [83]. Temperature in C . . . . . . . . . . . . . . . . . . . 111 Experimental data for water-sucrose at different operating conditions with the experimental heat transfer coefficients. . . . . 115 Experimental data for water-glycerol at different operating conditions with the experimental heat transfer coefficients. . . . . 117 Experimental data for water-ethylene glycol at different operating conditions with the experimental heat transfer coefficients. 118 Predicted average mass transfer coefficient for the water-sucrose system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Predicted average mass transfer coefficient for the water-glycerol system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Correlated average mass transfer coefficient for the water-ethylene glycol system. . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 183 184 B.1 Physical and chemical properties of Marlotherm SH [83]. . . B.2 Physical properties for Marlotherm SH [83]. . . . . . . . . . xiv List of Figures 1.1 Batch evaporator . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 In a horizontal tube evaporator, the heating medium flows inside the tubes [28]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 In a short-tube vertical evaporator, the process liquid is inside the tubes and the heating medium outside the tubes [28]. . . . 1.4 In a long-tube rising-film vertical evaporator, feed flows upwards through the tubes and heating medium flows downward on the shellside [28]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Submerged-tube forced circulation evaporator shown as a circulating magma crystallizer [94]. . . . . . . . . . . . . . . . . . 1.6 The falling-film evaporator is a variation of the long-tube risingfilm design [28]. . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Diagram of a vertical thin-film vaporizer. . . . . . . . . . . . . 2.1 2.2 3.1 3.2 4.1 4.2 4.3 4.4 4.5 4.6 Interpretation of the boiling curve for water at atmospheric pressure [19]. . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross section of a wiped film evaporator showing the blade and bow wave formed in front of it. . . . . . . . . . . . . . . . . . Heat transfer coefficient resistances in a wiped film evaporator Two phase flash model for a wiped film evaporator. . . . . . . Sketch of a Vertical Wiped Film Evaporator. . . . . . . . . . . Heat transfer resistances in a wiped film evaporator. . . . . . . Heat Transfer Enhancement Factor (h ) as a function of the film Reynolds number. . . . . . . . . . . . . . . . . . . . . . . Heat Transfer Enhancement Factor (h ) as a function of the rotational Reynolds number. . . . . . . . . . . . . . . . . . . . Heat Transfer Enhancement Factor (h ) as a function of the Prandtl number. . . . . . . . . . . . . . . . . . . . . . . . . . Predicted vs. Experimental weight fraction for water in concentrate using data from Frank and Lutcha [25]. . . . . . . . . . . xv 7 9 10 11 13 14 16 23 27 41 51 53 54 60 61 62 65 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 6.1 Liquid mass fraction variation along the WFE. . . . . . . . . . Liquid and vapor flowrate variation along the WFE. . . . . . . Predicted vs. Experimental process side heat transfer coefficient using data from Frank and Lutcha [25]. . . . . . . . . . . . . . Predicted vs. Experimental overall heat transfer coefficient using data from Frank and Lutcha [25]. . . . . . . . . . . . . . . Differential section of a Wiped Film Evaporator. . . . . . . . . Predicted vs. Experimental weight fraction for concentrate using data from Frank and Lutcha [25]. . . . . . . . . . . . . . . Predicted vs. Experimental process side heat transfer coefficient using data from Frank and Lutcha [25]. . . . . . . . . . . . . . Predicted vs. Experimental overall heat transfer coefficient using data from Frank and Lutcha [25]. . . . . . . . . . . . . . . Simplified flow diagram of experimental installation for a wiped fim evaporator [95] . . . . . . . . . . . . . . . . . . . . . . . . Diagram of the original Wiped Film Evaporator from Cargill. Diagram of the roller wiper system. . . . . . . . . . . . . . . . Photo of the UIC Inc. Wiped Film Evaporator and condenser from Cargill. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dimensions of the ChemTech Services Wiped Film Evaporator from Cargill. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Refractive index variation with weight percent for the watersucrose system at 20 . . . . . . . . . . . . . . . . . . . . . . . Refractive index variation with weight percent for the waterglycerol system at 20 . . . . . . . . . . . . . . . . . . . . . . . Refractive index variation with weight percent for the waterethylene glycol system at 20 . . . . . . . . . . . . . . . . . . . Predicted concentration of water when simulating the wiped film evaporator as an isothermal flash for the water-sucrose system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relative error when simulating the wiped film evaporator as an isothermal flash for the water-sucrose system. . . . . . . . . . Predicted concentration of water when simulating the wiped film evaporator as an isothermal flash for the water-glycerol system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 67 68 69 70 73 74 75 83 88 89 90 91 93 94 96 104 105 6.2 6.3 107 xvi 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14 6.15 6.16 6.17 6.18 6.19 6.20 Relative error when simulating the wiped film evaporator as an isothermal flash for the water-glycerol system. . . . . . . . . . Predicted concentration of water when simulating the wiped film evaporator as an isothermal flash for the water-ethylene glycol system. . . . . . . . . . . . . . . . . . . . . . . . . . . . Relative error when simulating the wiped film evaporator as an isothermal flash for the water-ethylene glycol system. . . . . . Experimental heat transfer coefficient for the process side as a function of the liquid feed flow rate for water/glycerol at 360 rpm and 35 C and water/sucrose at 360 rpm and 40 C. . . . Experimental heat transfer coefficient for the process side as a function of the film Reynolds number for water/glycerol at 360 rpm and 35 C and water/sucrose at 360 rpm and 40 C. . . . Experimental heat transfer coefficient for the process side as a function of the rotational Reynolds number. . . . . . . . . . . Experimental heat transfer coefficient for the process side as a function of the Prandtl number. . . . . . . . . . . . . . . . . . Predicted average mass transfer coefficient for the water-sucrose system as a function of the dimensionless Sherwood number at different water concentrations. . . . . . . . . . . . . . . . . . . Predicted average mass transfer coefficient for the water-glycerol system as a function of the dimensionless Sherwood number and different concentrations of water. . . . . . . . . . . . . . . . . Predicted average mass transfer coefficient for the water-glycerol system as a function of the dimensionless Sherwood number . Predicted versus experimental exiting concentration of water using WFE-SRP for the water-sucrose system. . . . . . . . . . Relative error of the experimental exiting concentration of water using WFE-SRP for the water-sucrose system. . . . . . . . . . Predicted versus experimental exiting concentration of water using WFE-SRP for the water-sucrose system. . . . . . . . . . Relative error of the experimental exiting concentration of water using WFE-SRP for the water-sucrose system. . . . . . . . . . Predicted versus experimental exiting concentration of water using WFE-SRP for the water-glycerol system. . . . . . . . . . Relative error of the experimental exiting concentration of water using WFE-SRP for the water-glycerol. . . . . . . . . . . . . . Predicted versus experimental exiting concentration of water using WFE-SRP for the water-glycerol system. . . . . . . . . . xvii 108 109 110 120 121 122 123 128 129 130 134 135 136 137 139 140 141 6.21 Relative error of the experimental exiting concentration of water using WFE-SRP for the water-glycerol system. . . . . . . . . . 6.22 Predicted versus experimental exiting concentration of water using WFE-SRP for the water-ethylene glycol system. . . . . . 6.23 Relative error of the experimental exiting concentration of water using WFE-SRP for the water-ethylene glycol system. . . . . . 6.24 Predicted versus experimental exiting concentration of water using WFE-SRP for the water-ethylene glycerol system. . . . . 6.25 Relative error of the experimental exiting concentration of water using WFE-SRP for the water-ethylene glycol system. . . . . . A.1 Flowchart for the WFE-SRP Excel program. . . . . . . . . . . A.2 WFE-SRP. Main input screen. All the necessary information is provided in this worksheet. . . . . . . . . . . . . . . . . . . . . A.3 WFE-SRP output result for a flash calculation. . . . . . . . . A.4 WFE-SRP output result for a wiped film evaporator calculation. Results are shown for all segments. . . . . . . . . . . . . . . . A.5 Defining a new component based on UNIFAC groups. . . . . . A.6 Adding a new component with known DIPPR constants. . . . A.7 Groups for the prediction of liquid density. . . . . . . . . . . . A.8 Groups for the prediction of liquid viscosity. . . . . . . . . . . A.9 Groups for the prediction of liquid thermal conductivity. . . . A.10 Groups for the prediction of vapor pressure. . . . . . . . . . . A.11 Groups for the prediction of heat capacity for liquid. . . . . . A.12 Groups for the prediction of critical properties. . . . . . . . . . A.13 Structure of the glycerol molecule. . . . . . . . . . . . . . . . . A.14 First screen that shows when adding a new component in WFESRP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.15 Screen that appears after selecting `Add/Edit Components' in Figure A.14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.16 Defining groups for the UNIFAC model [33] and naming the new component. . . . . . . . . . . . . . . . . . . . . . . . . . . A.17 Defining groups for the prediction of the critical properties using the Joback and Reid [39] method. . . . . . . . . . . . . . . . . A.18 Defining groups for the estimation of the vapor pressure using the Li et al. [56] method. . . . . . . . . . . . . . . . . . . . . . xviii 142 145 146 147 148 156 157 158 159 160 161 162 163 165 166 167 169 169 170 171 172 173 174 A.19 Defining groups for the prediction of the liquid thermal conductivity using the Sastri and Rao [84] method. . . . . . . . . . . A.20 Defining groups for the estimation of the liquid density using the Ihmels and Gmehling [38] method. . . . . . . . . . . . . . A.21 Defining groups for the prediction of the liquid viscosity using the Hsu et al. [37] method. . . . . . . . . . . . . . . . . . . . . A.22 Defining groups for the estimation of the liquid heat capacity for the new component using the Rika and Domalski [79, 80] uz c method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.23 Defining groups for the prediction of the enthalpy of vaporization for the new component using the Li et al. [55] method. . . A.24 Selecting the new component Glycerol GCM from the available components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.1 Variation of density with temperature for Marlotherm SH. . 175 176 177 178 179 180 185 B.2 Variation of heat capacity with temperature for Marlotherm SH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 B.3 Variation of thermal conductivity with temperature for Marlotherm SH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 B.4 Variation of kinematic viscosity with temperature for Marlotherm SH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 xix Nomenclature Roman Letters aij A C0 Cp D DL g h ho hp K F kL F E W kL F E Constant in Equation 5.16 Heat Transfer Area [m2 ] Ackermann Factor [-] Heat Capacity [J/kg-K] Diameter [m] Liquid Diffusion Coefficient [m2 /s] Gravity Constant [m2 /s] Heat Transfer Coefficient [W/m2 K] Heat Transfer Coefficient for Hot Fluid [W/m2 K] Heat Transfer Coefficient for the Process Side [W/m2 K] Equilibrium Constant [-] Mass Transfer Coefficient for FFE [m/s] Mass Transfer Coefficient for WFE [m/s] Wall Thermal Resistance [W/m-K] Length [m] Rotational Speed [s-1 ] Number of Blades [-] Mass Transfer Rate for Liquid Phase [kg/s] xx kwall L N Nb NL Nu P Ps Pr q Q r Ref ReN ScL Tp Tv Uov wh wt x xF x y Z Nusselt Number [-] Total Pressure [Pa] Vapor Pressure [Pa] Prandtl Number [-] UNIQUAC Surface Area Parameter [-] Total Transferred Heat [W] UNIQUAC Volume Parameter [-] Film Reynolds Number [-] Rotational Reynolds Number [-] Schmit Number [-] Hot Fluid Temperature [ C] Evaporation Temperature [ C] Overall Heat Transfer Coefficient [W/m2 K] Hot Oil Flow Rate [kg/s] Weight fraction [-] Liquid Mole Fraction [-] Feed Mole Fraction [-] Liquid Equilibrium Mole Fraction [-] Vapor Mole Fraction [-] Dimensionless Length in Equation 3.3[-] xxi Greek Letters and Symbols h L wall w Enhancement Factor [-] Heat Transfer Enhancement Factor [-] Film Thickness [m] Characteristic Length in Falling Film [m] Wall Thickness [m] Increment [-] Thermal Conductivity [W/m-K] Heat of Vaporization of Water [J/kg] UNIQUAC Volume Fraction [-] Viscosity [Pa s] Density [kg/m3 ] Surface Tension [N/m] Superscripts FFE WFE Falling Film Evaporator Wiped Film Evaporator Subscripts L V Liquid Vapor xxii Abbreviations and Acronyms BR-AK BR-N BS-AK BS-N FFE FFEn FFEs HTC GCM SRP WFE WFEn WFEs WFE-SRP Bott and Romero-Ahmed and Kaparthi Bott and Romero-Numrich Bott and Sheikh-Ahmed and Kaparthi Bott and Sheikh-Numrich Falling Film Evaporator Falling Film Evaporation Falling Film Evaporators Heat Transfer Coefficient Group Contribution Methods Separations Research Program Wiped Film Evaporator Wiped Film Evaporation Wiped Film Evaporators Wiped Film Evaporator - Separations Research Program xxiii Chapter 1 Introduction 1.1 Evaporation Evaporation is an operation used to remove a liquid from a solution, suspension, or emulsion by boiling off a portion of the liquid. It is thus a thermal separation, or thermal concentration, process. We define the evaporation process as one that starts with a liquid product and ends up with a more concentrated, but still liquid and still pumpable concentrate as the main product from the process. There are actually a few instances where the evaporated, volatile component is the main product. Standiford [94] defines the unit operation of evaporation as the removal of volatile solvent from a solution or a relatively dilute slurry by vaporizing the solvent. In nearly all industrial applications the solvent is water, and in most cases the nonvolatile residue is the valuable constituent. Evaporation differs from distillation in that when the volatile stream consists of more than one component no attempt is made to separate these components. Although the product of an evaporator system may be a solid, the heat required for vaporization of the solvent must be transferred to a solution or a slurry of the solid in its saturated solution in order that the device be classified as 1 an evaporator rather than a dryer. It is not unusual for an evaporator to be used to produce a solid as its only product. For instance, table salt is produced by feeding a saturated brine to an evaporator, precipitating the salt as water is removed. A side stream of salt crystals in brine is withdrawn to a filter or centrifuge where the salt is recovered in essentially dry form; the filtrate is returned to the evaporator as a supplementary feed. Thus the heat required for evaporation of the water is transferred to a slurry in the evaporator even though the only material leaving the system is a solid, except for the evaporated water; usually a small bleed of brine is necessary to purge from the system the impurities entering with the feed brine. An evaporator consists of a heat exchenger or heated bath, valves, manifolds, controls, pumps, and condenser [28]. The most common designs are jacketed tanks, tubular heat exchangers, plate-and-frame heat exchangers, and wiped film evaporators. Evaporators are used in a wide variety of applications such as [94]: 1. Reducing the volume to economize on packaging, shipping, and storage costs, for instance of salt, sugar, caustic soda, orange juice, and milk 2. Obtaining a product in its most useful form, for instance salt from brine or sugar from cane juice 3. Eliminating minor impurities, for instance, from salt, sugar 4. Removing major contaminants from a product, for instance diaphragm cell caustic soda solutions contain more salt than caustic when produced 2 but practically all the salt can be precipitated by concentrating to a 50% NaOH solution 5. Concentrating a process stream for recovery of resources, for instance pulp mill spent cooking liquor, if concentrated sufficiently in an evaporator, can be burned in a boiler to produce steam, yielding also an ash that can be used to reconstitute fresh cooking liquor 6. Concentrating wastes for easier disposal, such as nuclear reactor wastes, dyestuff plant effluents, and cooling tower blowdown streams 7. Transforming a waste into a valuable product, such as spent distillery slop after alcohol recovery, which can be concentrated to produce an animal feed 8. Recovering distilled water from impure streams such as sea water and brackish waters. In most cases it is essential that the product is subjected to minimal thermal degradation during the evaporation process, requiring that temperature and time exposure must be minimized. This and other requirements brought on by the physical characteristics of the processed product have resulted in the development of a large range of different evaporator types. Additional demands for energy efficiency and minimized environmental impact have driven development toward very innovative plant configurations and equipment design [74]. 3 1.1.1 Function of an Evaporator The main function of an evaporator is to concentrate a solution or to recover a solvent. Minton [65] mentions that the evaporator design consists of three principal elements: heat transfer, vapor-liquid separation, and efficient utilization of energy. For evaporators to be efficient, the equipment selected and used must be able to accomplish several things [65]: 1. Transfer large amounts of heat to the solution with a minimum amount of metallic surface area. This requirement, more than all other factors, determines the type, size, and cost of the evaporator system. 2. Achieve the specified separation of liquid and vapor and do it with the simplest devices available. Separation may be important for several reasons: value of the product otherwise lost; pollution; fouling and corrosion of the equipment downstream with which the vapor is contacted. 3. Make efficient use of the available energy. This may take several forms. Evaporator performance often is rated on the basis of steam economy, pounds of solvent evaporated per pound of steam used. Heat is required to raise the feed temperature from its initial value to that of the boiling liquid, to provide the energy required to separate liquid solvent from the feed, and to vaporize the solvent. The greatest increase in energy economy is achieved by re-using the vaporized solvent as a 4 heating medium. Energy efficiency may be increased by exchanging heat between the entering feed and the leaving residue or condensate. When this method is used, each evaporator is known as an effect. 4. Meet the conditions imposed by the liquid being evaporated or by the solution being concentrated. Factors that must be considered include product quality, salting and scaling, corrosion, foaming, product degradation, holdup, and the need for special types of construction. Steam-heated evaporators are the most widely used in industry. The three principal requirements of these evaporators are [94]: Transfer to the liquid of large amounts of heat needed to vaporize the solvent. Efficient separation of the evolved vapor from the residual liquid. Accomplishing these aims with the least expenditure of energy justifiable by the capital cost involved. 1.2 Criteria for the Selection of the Evaporator During the design of evaporation plants, numerous and sometimes con- tradictory requirements have to be considered. They determine which type of construction and arrangement is chosen as well as the resulting process and economic data. The most important requirements are [74]: 5 Capacity and operational data, including quantities, concentrations, tem- peratures, annual operating hours, change of product and controls automation. Product characteristics, including heat sensitivity, viscosity and flow properties, foaming tendency, fouling and precipitation and boiling behavior. Required operating media, such as steam, cooling water, electric power, cleaning agents and spare parts. Capital and operating costs. Standards and conditions for manufacture, delivery, acceptance. Choice of materials of construction and surface finishes. Site conditions, such as available space, climate (for outdoor sites), con- nections for energy and product, service platforms. Legal regulations covering safety, accident prevention, sound emissions, environmental requirements, and others. 1.3 Types of Evaporator Standiford [94] presents a classification of evaporators based on the heating medium (steam) used to transfer heat. He classifies the steam-heated evaporators as natural circulation, forced circulation, and film-type. The simplest evaporator is the batch evaporator [28], shown in Figure 1.1. It has a jacketed vessel heated with steam or hot fluid. The product 6 is metered into a tank to a specified level through a feed nozzle. Heat is applied and the batch is allowed to heat to its boiling point. Vapors are removed until the desired concentration of the product is reached and the heat is then removed. This evaporator is not well-suited for temperature-sensitive materials because the residence time is usually long and the static head of the liquid increases the boiling point of the product at the bottom of the tank. Figure 1.1: Batch evaporator 7 1.3.1 Natural Circulation Evaporators These evaporators were the first developed commercially and still rep- resent probably the largest number of units in operation [94]. Glover [28] mentions that they are normally used for simple applications where the product is clean and temperature-stable, whereas forced-circulation evaporators are used for viscous, salting and scale-forming products. The most common natural-circulation evaporators are horizontal tube, short vertical tube, and long vertical tube. 1.3.1.1 Horizontal Tube Evaporator This is the oldest type of chemical evaporator [28], shown in Figure 1.2. It is the only evaporator where the heating medium is inside the tubes. Its principal advantage lies in the relatively small headroom required. 1.3.1.2 Short-Tube Vertical Evaporator This is also called a calandria vertical evaporator. It is still in widespread commercial use [28]. Its principal use at present is in the evaporation of canesugar juice [89]. Circulation past the heating surface is induced by boiling in the tubes, which are usually 50.8 to 76.2 mm in diameter by 1.2 to 1.8 m long. The body is a vertical cylinder, usually of cast iron, and the tubes are expanded into horizontal tube sheets that span the body diameter. The circulation rate through the tubes is many times the feed rate, so there must be a return passage from above the top tube sheet to below the bottom tube sheet. 8 Figure 1.2: In a horizontal tube evaporator, the heating medium flows inside the tubes [28]. Most commonly used is a central well or downtake as shown in Figure 1.3. Advantages of the short-tube vertical evaporator include [28]: low head-space required suitable for liquids that have moderate tendency to scale fairly high heat-transfer coefficients can be obtained with thin (up to 5-10 cP) liquids relatively inexpensive to manufacture 9 Figure 1.3: In a short-tube vertical evaporator, the process liquid is inside the tubes and the heating medium outside the tubes [28]. 1.3.1.3 Long-Tube Vertical Evaporator This is also known as a rising-film evaporator, shown in Figure 1.4. It is one of the most widely used tubular evaporators [28]. A shell-and-tube heat exchanger mounted to a vapor-liquid separator, it requires little floor space, but high head room. The dilute feed enters at the bottom of the tubesheet and flows upward 10 Figure 1.4: In a long-tube rising-film vertical evaporator, feed flows upwards through the tubes and heating medium flows downward on the shellside [28]. through the tubes, with the heating medium on the shellside. The feed is heated to its boiling point in the lower portion of the tubes. Bubbles form on the tubes at some distance further up and boiling begins, increasing the linear velocity and the rate of convective heat transfer. Near the top of the tubes, bubbles grow rapidly. In this bubble zone, slugs of liquid and bubbles rise quickly through the tubes and are discharged at high velocity from the top, where they impinge on a liquid/vapor separator that tends to break any foam that has formed. This allows the use of this type of evaporator for products 11 that tend to foam [28]. 1.3.2 Forced Circulation Evaporators This evaporator is suitable for the largest variety of applications and is usually the most expensive type [94]. It usually consists of a shell-and-tube heat exchanger, a vapor-liquid separator, and a pump to circulate the liquor from the body through the heater and back to the body. The system is usually arranged so that there is no boiling in the heater. The heat input is therefore absorbed as sensible heat, and vapor liberation does not occur until the liquor enters the flash chamber. Absorption of the heat input as sensible heat results in a temperature rise that reduces the net temperature difference available for heat transfer. To keep this temperature rise to reasonable limits, usually on the order of 26 K, requires circulating large volumes of liquor relative to the amount evaporated. There is also an upper limit to temperature rise, usually about 10 K, beyond which flashing at the entry to the flash chamber becomes so violent that large masses of liquor are ejected with the vapor. This makes entrainment separation more difficult and may impose structural shock loads on the separator. The head requirements of the circulating pump are generally quite low, consisting primarily of conventional friction and acceleration and deceleration losses at heater and body inlet and outlet, plus vortex losses in the body. Several configurations of forced circulation evaporators exist. The most common arrangement is shown in Figure 1.5 having an external vertical single- 12 pass heater and a tangential inlet to the body. Figure 1.5: Submerged-tube forced circulation evaporator shown as a circulating magma crystallizer [94]. 1.3.3 Film-Type Evaporators The long-tube falling film evaporator shown in Figure 1.6 is a variation of the long-tube rising-film evaporator, in which the equipment is turned upside 13 down so the tubular heat exchanger is on top of the vapor/liquid separator section. Feed enters at the top of the evaporator, where specially designed distributors evenly distribute the feed into each of the tubes. Distribution of the feed is very critical and there are many designs for the distributors, but generally most are built around some type of perforated plate placed over the top tubesheet [28]. Figure 1.6: The falling-film evaporator is a variation of the long-tube risingfilm design [28]. The principal advantages of the falling-film evaporator are good heattransfer performance, even at low temperature and low temperature differences, low initial cost, and excellent vapor-liquid separation characteristics. 14 Principal applications have been for citrus juices, where performance at low temperature and low holdup is important, and applications requiring low temperature differences, such as vapor compression or multiple-effect evaporators needing a large number of effects to be economical, e.q. for producing fresh water from saline waters. 1.3.3.1 Wiped Film Evaporator The wiped film evaporator (WFE), also known as an agitated thin-film evaporator (ATFE) is a device often used to purify liquids with viscosities up to 105 poise [64], to separate temperature-sensitive mixtures, or in general to provide short residence times in heated zones. Unfortunately, the heat and mass transfer mechanisms involved in wiped film evaporators are poorly understood. Users of the technology must rely on equipment vendors and experience for guidance. Wiped filmed evaporators are designed to spread a thin layer or film of liquid on one side of a metallic wall, with heat supplied to the other side. The unique feature of this equipment is not the thin film itself, but rather the mechanical wiping device for producing and agitating the film. This mechanical concept permits the processing of high-viscosity liquids, liquids with suspended solids, or situations requiring liquid rates too small to keep the thermal surface of a falling-film evaporator uniformly wet [70]. Most WFEs are vertical cylinders (see Figure 1.7) where the feed material is distributed to the inner surface. As the liquid flows downward, axially 15 Figure 1.7: Diagram of a vertical thin-film vaporizer. arranged blades or roller wipers distribute the liquid as a thin film, which is constantly mixed. This type of equipment can operate at very low pressure and provides minimum pressure drop. The length and diameter are often determined from the hydraulic and heat considerations. The WFE diameter should be large enough to minimize 16 any liquid entrainment. In this work, the vapor velocity was kept below 0.4 m/s. The application of falling film flooding models should provide guidance for the calculation of the diameter. The length would be determined from the necessary heat duty, overall heat transfer coefficient and the WFE diameter. The double-walled evaporator jacket is heated continuously by a suitable medium. A vacuum system (often a combination of several individual pumps) reduces the pressure in the distillation chamber. Depending on the temperature and the pressure in the chamber, vapors leave through the vapor discharge nozzle and travel to an external condenser. Nonvolatile substances are discharged at the lower end of the evaporator. Table 1.1 shows the typical applications of WFEs and operating conditions. The WFE can function as a stand-alone unit (i.e., for purification) or as a part of another unit (e.g., as a reboiler in a distillation column). Two WFE orientations are possible, horizontal or vertical. This study will concentrate on the commonly used vertically-aligned WFE. An extensive literature review on wiped film evaporators (see Table 1.2) indicates that heat transfer has been widely studied for different types of evaporators, and several papers present experimental data along with correlations for the prediction of the heat transfer coefficient. Among them the models of Abichandani and Sarma [1], Azzory and Bott [7], Bott and Romero [11], Bott and Sheikh [14], Miyashita and Hoffman [66], Miyashita et al. [67], Skelland [91], Skoczylas [92] can be cited. However, little information regarding mass transfer was found. Only one paper by Frank and Lutcha [25] presents mass 17 Table 1.1: General Application Areas of Wiped Film Evaporators [6]. Areas of application Operating 1 mm Hg & above Organics, General X Pesticides & Herbicides X Pharmaceuticals, Gen- X eral Vitamins X Food, General X Tomato Paste X X X X X X X Pressure Concentration Stripping Deodorization Below 1 Dehydration mmHg X X X X X X X X X50% total solids X X X X X Fats & Oil Fatty Acids Plastics & Resins Radioactive Waste Conc. Rerefining Used Oils Solvent Recovery X X X X X X X X X X X X X transfer data, and no papers present studies of mass transfer coefficient, or the analysis of simultaneous heat and mass transfer in wiped film evaporators. The objective of this study is to fill these gaps of knowledge by considering simultaneous heat and mass transfer. Table 1.2: Summary of available literature for wiped film evaporators. Area of Publication # of Publications Heat transfer data 20 Heat transfer models 20 Mass transfer data 1 Mass transfer models 0 Application to process simulators 2 Combined heat and mass transfer studies 0 18 The fundamental heat and mass transfer characteristics of wiped film evaporators (WFEs) are poorly understood, and at present the technology is considered to be a "black art." In general, an equipment vendor, based on pilot plant data and general process experience, determines the design of a WFE. While the vendor may have a good understanding of the technology, the knowledge is well-guarded. In many cases, the end user prefers to limit any information shared with the vendor and does not have the capability to analyze the performance of the unit, in order to know if there is room for improvement (i.e., increase throughput). 1.4 Research Objectives The main objectives of this study are to: Validate if the WFE can be treated as a single stage flash from experi- mental data. Propose a WFE mass transfer coefficient modeling approach and validate with overall experimental data. Evaluate available heat and mass transfer coefficient models. Develop rigorous WFE design and analysis model which incorporates heat and mass transfer and physical property estimation methods. Compare rigorous model with experimental data obtained in this work and by others. 19 The research study is focused on vertical wiped film evaporators. The general tasks performed in this study include: 1. Perform comprehensive literature review of wiped film evaporation and falling film evaporation technologies 2. Define research topic 3. Develop preliminary heat and mass transfer model 4. Test preliminary model with published data 5. Identify test systems for study 6. Obtain experimental WFE unit or access to a WFE unit 7. Develop experimental plan based on WFE equipment, test systems and preliminary model 8. Obtain experimental data 9. Compare experimental data with preliminary model 10. Modify preliminary model or develop new model based on additional experimental data 11. Develop Excel-based program for the design/rating of a WFE unit 12. Prepare dissertation. The experimental systems that were tested cover a wide range of physical properties. Some papers with experimental data used water/glycerol as the system [1, 11, 14]. Water/ethylene glycol is another experimental system which has been used to measure heat transfer coefficients [1]. Water/sugar solutions 20 have been used for heat transfer measurements [95] as well as for characteristic dimensions [25]. These three systems, water/glycerol, water/ethylene glycol, and water/sugar, were used to gather experimental data for this study. These three well-characterized test systems were studied. Two of the systems present a wide variation in viscosity (water/sugar and water/glycerol) for different temperatures and concentrations, while the other (water/glycol) presents a slight variation on almost all physical properties. The Excel-based program is referred to as WFE-SRP. It was necessary to include group contribution methods for the estimation of the vapor liquid equilibrium and other physical properties since many of the components involved in WFE are poorly characterized. Appendix A shows how to use the computer program, along with the available group contribution methods. 21 Chapter 2 Literature Review 2.1 Boiling Mechanisms in Evaporation There are three mechanisms of heat transfer: conduction, convection, and radiation. In wiped film evaporators the important mechanisms are convection and conduction. The vaporization of liquids may result from various mechanisms of heat transfer. Figure 2.1 shows a physical interpretation of the boiling curve. 2.1.1 Pool Boiling This refers to the type of boiling experienced when the heating surface is surrounded by a relatively large body of fluid which is not flowing at any appreciable velocity and is agitated only by the motion of the bubbles and by natural-convection currents. Two types of pool boiling are possible: subcooled pool boiling, in which the bulk fluid temperature is below the saturation temperature, resulting in collapse of the bubbles before they reach the surface, and saturated pool boiling, with bulk temperature equal to saturation temperature, resulting in net vapor generation [44]. 22 Figure 2.1: pressure [19]. Interpretation of the boiling curve for water at atmospheric 2.1.2 Nucleate Boiling Heat transfer by nucleate boiling is an important mechanism in the va- porization of liquids. It occurs in the vaporization of liquids in kettle-type and natural-circulation reboilers commonly used in the process industries. High rates of heat transfer per unit of area (heat flux) are obtained as a result of 23 bubble formation at the liquid-wall interface rather than from mechanical devices external to the heat exchanger. There are available several expressions from which reasonable values of the film coefficients may be obtained [44]. 2.1.3 Film Boiling In fully developed film boiling the vapor blankets the heating surface in a smooth continuous film except where the generated vapor escapes from the film in very large bubbles. If the heating surface is vertical and extends through the liquid level, the vapor can escape from the ends of the annular spaces and bubbles may not be generated. 2.2 Literature Review An extensive literature review on wiped film evaporators indicates that heat transfer has been widely studied and several correlations for the prediction of the heat transfer coefficient exist. However, a correlation of the mass transfer coefficient for wiped film evaporators has not been published, and simultaneous heat and mass transfer have not been studied, thus providing a niche that the present study is trying to fulfill. The fundamental heat and mass transfer characteristics of wiped film evaporators (WFEs) are poorly understood, and at present the technology is considered to be a "black art." In general, an equipment vendor, based on pilot plant data and general process experience, determines the design of a WFE. While the vendor may have a good understanding of the technology, 24 the knowledge is well-guarded. In many cases, the end user prefers to limit any information shared with the vendor and does not have the capability to analyze the performance of the unit, in order to know if there is room for improvement (i.e., increase throughput). In an earlier Separations Research Program (SRP) publication, Rocha-Uribe and Lopez-Toledo [78] provided a state-of-the-art review that includes a list of WFE vendors. Table 2.1 shows the updated information for several vendors of wiped film evaporators. Table 2.1: Vendors of Wiped Film Evaporators [78]. Company ChemTech Services (formerly UIC Inc) Artisan Industries Address P.O. Box 2097 Joliet, IL 60434 Phone 815-744-4696 800-343-5841 781-893-6800 262-268-9300 630-350-2200 704-394-8341 203-438-8915 585-235-1000 Fax and e-mail 815-744-3938 shortpathdistillation @uicinc.com 781-647-0143 info@artisanind.com 262-268-9400 sales@popeinc.com 630-350-9047 sales@aaronequipment.com 704-392-8507 info@lcicorp.com 203-431-4842 summitec@aol.com 73 Pond Street Waltham, MA 02451 Pope Scientific, P.O Box 80018 Inc Saukville, WI 53080 Aaron Equipment 735 E. Green St. Bensenville, IL 60106 LCI Coprporation P.O. Box 16348 (formerly Luwa) Charlotte, NC 28297 Summit Process 8 Hamilton Road Tech Ridgefield, CT 06877 Pfaudler, Inc. 1000 West Avenue P.O. Box 23600 Rochester, NY 14692 Gooch Thermal 1221 Route 22 East Systems Inc. Lebanon, NJ 08833 908-236-9350 908-236-9333 info@goochthermal.com Rocha-Uribe and Lopez-Toledo provided a table with a classification of the papers by type of information presented. Table 2.2 includes an updated list with additional references that were found during this study. 25 Table 2.2: Technical papers on Wiped Film Evaporator Technology [78]. Modeling 1. Kern and 1. Karakas [40] 2. 2. McKelvey and Sharps [63] 3. Billet [8] 4. Gruber and Rak [31] 5. McKenna [64] Theory Godau [29] Nakamura and Watanabe [72*] Correlations 1. Bott and Romero [11, 12] 2. Bott and Sheikh [14] Vendor 1. Nadjer [71] 2. Freese and Glover [26] 3. Tyzack [99, 100] 4. Lavis [53] 5. Schurter [85] 6. Arlidge [6] 7. Mutzenburg [70] 8. Parker [76] 9. Eckles [23] 10. Bishop and Arlidge [10] Related 1. King [41, 42] 2. Mutzenberg and Giger [69] 3. Cvengros [20] 4. Larson et al. [51] 5. Bott and Sheikh [13] 6. Chawankul et al. [16] 7. Chuaprasert et al. [17] 8. MartinezChitoy [59] 3. Komori et al. 3. Stankiewicz and Rao [95] [45, 46, 47*] 4. Burrows and 4. Cvengros et al. [21] Beveridge [15] 5. Sangrame et al. [82] 6. Frank and Lutcha [25] *Horizontal WFEs The earliest paper dealing with modeling of WFE is by Kern and Karakas [40] in 1959. In their paper the authors attempted to combine principles of heat and mass transfer, hydrodynamics, and rheology (viscosity correlations) in order to find equations for the prediction of the WFE performance. An expression for calculating the required power for mechanical agitation was provided. While the authors stated that their model is a first step towards a more complex model (i.e., to take into account variations in physical properties), the follow-up rigorous model has not been published and is assumed to be proprietary. 26 McKelvey and Sharps [63] examined the velocity profile and flow structure of the bow waves (see Figure 2.2) and their dependence on certain parameters (e.g. blade clearance and film thickness) and on throughput. Expressions for the velocity profile and power consumption were developed. However, mass transfer was not considered. The thickness of the film will depend on the system physical properties such as surface tension and viscosity, the clearance between the wall and roller wiper or blade, and the rotational speed. Figure 2.2: Cross section of a wiped film evaporator showing the blade and bow wave formed in front of it [28]. Gouw and Jentoft [30] modeled a glass wiped-film still using the equaA bow wave is formed in front of the wiping blades when the liquid flowrate is high enough to fill the clearance between the blades and the wall and it often presents turbulent flow. 27 tions for batch distillation, and they mentioned the possibility of extrapolating the results to commercial-size film evaporators. They assumed that the concentration of the film is uniform (i.e., there is no gradient from the surface of the evaporating film to the wall). Dodecane-octadecene was the test system. Their results, on a small scale, agree with the results obtained by Kirschbaum and Dieter [43] on an industrial-scale wiped-film evaporator using ethanolwater as the test system. Unterberg and Edwards [101] studied the evaporation of a saline solution wiped on the outside of a heated vertical copper tube at different salt concentrations. They noticed that free surface evaporation occurred with nonboiling feed. Film continuity was poor for pure water but better for the saline solutions. Gruber and Rak [31] modeled the WFE as a series of co-current flashes, where the liquid from the first flash flows to the second and then to the third, and so on, until it leaves the WFE. The vapors from all the flashes form the exiting vapor from the unit. This rather simple model required experimental data to develop correlations for liquid entrainment as a function of vapor velocity, for the heat transfer coefficient for the jacket as a function of hot oil flowrate and temperature, and for heat loss as a function of ambient temperature. Data were inputted into a Fortran code and the WFE operation was simulated with AspenPlus1 . AspenPlus is a simulation/design program for chemical processes sold by Aspen Technologies http://www.aspentech.com 1 28 Godau [29] developed approximate and exact solutions for the evaporator film thickness as a function of fluid density and viscosity, and evaporator throughput. He did not consider the influence of the wiper blades nor did he study mass transfer. Komori et al. [45, 46] examined the flow structure and mixing mechanisms in the bow wave, both theoretically and experimentally in model wiped film devices with a limited number of blades. They looked at the degree of mixing between the film and the bow wave, and attempted to determine optimum device configuration for adequate mixing. They did not consider mass transfer. A more rigorous WFE model was proposed by McKenna [64] and is the basis for the previous work of Rocha-Uribe and Lopez-Toledo [78]. The model focuses on analyzing the mass transfer phenomena and does not include a heat transfer analysis. It is also limited to a binary system (it was developed for a monomer-polymer solution). The model provides a tool to obtain order of magnitude estimates of device size, power requirements and throughput; uncertainties in parameter values can affect the design. Bott and Romero [11] and Bott and Sheikh [14] presented experimental data and correlations for predicting the heat transfer rate coefficient. They studied different WFE column configurations (6, 12 and 24-in long by 1.0 in i.d.) using water and water/glycerol mixtures. They correlated their results 29 using an expression of the following form: N u = f Rea1 Rea2 P ra3 Nba4 (D/L)a5 N f but they did not consider mass transfer in their calculations. Other authors who used expressions similar to Equation 2.1 and who have also presented experimental heat transfer data are Stankiewicz and Rao [95], Abichandani et al. [2], and Skoczylas [92]. Expressions for the characteristic dimensions of WFEs are also available. Among them, the models of Bott and Romero [12] and Frank and Lutcha [25] are worth mentioning since the later paper provides experimental data from where mass transfer data can be extracted. Bott and Romero used a water/glycol system while Frank and Lutcha studied water and water/sugar mixtures. Vendors (see Table 2.1) report characteristics and advantages of WFEs over other evaporators (i.e., falling film, rising film, etc.). Freese and Glover [26] mention the different types of rotors available for WFEs and the different configurations (horizontal and vertical) of the unit. Mutzenburg [70] explains how the WFE performs (flow patterns inside the unit, residence time, etc), as well as the characteristic overall heat transfer coefficient for particular applications. Parker [76] describes WFE design and associated costs based on fixed clearances and geometry, vertical or horizontal. Eckles [23] recommends operating at vacuum when the purification cannot be achieved at atmospheric conditions and/or when the product is 30 (2.1) thermally unstable. The author also recommends WFE for the separation of medium-viscosity materials (up to 500 centipoises). Table 2.3 shows the advantages/disadvantages of vacuum evaporator systems (another advantage for the falling film evaporator not mentioned in Table 2.3 is that it does not have moving parts), while Fischer [24] provides a list of various WFE applications (see Table 2.4). Table 2.3: Advantages and Disadvantages of Vacuum Evaporator Systems [23]. Type Advantages Disadvantages Poor separation efficiency Falling-film Relatively simple design evaporators High throughput per unit size Not suitable for viscous feed mate(since it is a continuous process) rials Laminar films can have large Ts through the film, which can lead to "hot areas" near the heating surface Wiped-film High throughput per unit size Limited separation efficiency (since it is a continuous process) Many designs do not allow operaevaporators Can handle high viscosity materition at lower pressures als Can incorporate baffles to eliminate contamination of the product by the feed material Short-path Run at the lowest possible operat- Limited separation efficiency ing pressure of any system systems (in Potential for direct contamination general) Capable of a high throughput per of the product by the entrained parunit size (due to continuous operticles in the feed mixture ation) Have the shortest thermal history A large body of operating and deof any process sign correlations exists as a result of a considerable number of these systems currently in operation) 31 Table 2.4: Where Wiped Film Evaporators are Used [24]. Steam Heated Acetic derivatives Solvent recovery Cresylic acid Glycols Amines Cyclohexyl phthalate Ketones Isopropenyl acetone Fatty alcohols (to C16 ) Insecticides Phenothiazine Herbicides Caprolactum Ethylene glycol recov. Lactic acid Isocyanates Caprolactam Solvent recovery Cresylic acids Glycols Cumene hydroperoxide Ethanolamines Hydrazine Nonyl phenol Isomers Rosin acid Fatty alcohols Amine solutions Anthracene oil recovery Isocyanates Acetic derivatives Petroleum sulfonates Caprolactamum Acrylonitriles Chlorinated paraffins Cumene hydroperoxide Cyclohexyl phthalate Dibutyl maleate Laural mercaptan Resorcinol Trixylene phosphate Acetic acid Naptha oil solutions Insecticides Didecyl phthalate Distillation High Temperature Fractionation Stripping Deodorization Chlorinated paraffins Vaseline Petroleum jelly Naphtha oil solutions Concentration, Dehydration Fuels Formaldehyde Caprolactam recovery Urea Insecticides Ammonium nitrate Nitrochalk Pyrethrum extract Sodium isopropyl xanthate Dyes (water soluble) Phosphoric acid Aniline dye General chemicals Food Isocyanates Solvent recovery Acrylonitriles Amines (above C16 ) Chlorinated hydrocarbons Dibutyl maleate Didecyl phthalate Sucrose ester Laural mercaptan Resorcinol Trixylne phosphate Hydroxquinoline Dibasic acids Rasin acids Naphthenic acids Fatty alcohols (from C16 ) Triethanolamine Dimethyl tertiary amines Benzoates Recovery of volatile oils Oleomargarine resins Flavor extract Spice extracts Flavor extract Peel oils Peel oils 32 Undisclosed organic compounds Essential oils Vitamin C Amino esters Flavors Essential oils Tallow nitrile Glycerin Fatty acids Tall oil Dioctyl phthalate Diisooctyl phthalate Phenolic resins Glycerin Fatty acids Tall oil Styrene Adiponitrile Tricresyl phosphate Latex Urea-formaldehyde resin Liquid rubbers Water-soluble polymers Tobacco extract Atomic wastes Tomato paste Coffe, tea Candies Beer malt Milk, whey Meat extracts Tannin extract Ketoglutamic acid Pharmaceuticals Vitamin A Sugal sol. Enzymes Ascorbic acid Amino acids Choline chloride Hormone and antibacterial sol. Dextran compounds Fats and Oils Glue Gelatine Saccharin extract Tocopherol Liver extract Amino acids Plastics, resins Silicone oils Olive oils Saccharin oil Edible oils Phenolic resin Tricresyl phosphate Olive oil Tallow Edible oils Vegetable oil plasticizers Cumene resin Dioctyl phthalate Misc Melamine resin Polystyrene Rubber polymers Varnish Diisooctyl phthalate Latex (rubber) Polystyrene Viscose rayon (degassing) A review of the literature indicates that WFE heat and mass transfer characteristics have not been studied simultaneously. A few papers present experimental heat transfer data for different systems (water/sugar and water/glycerol) along with heat transfer coefficient correlations. However a WFE mass transfer coefficient correlation has not been published. Frank and Lutcha provide limited experimental data that can be used to calculate mass transfer coefficients. Their data were used primarily for the prediction of the thickness of the film inside a WFE with variable clearance. Much work has been performed regarding heat transfer for vertical and horizontal WFEs, but limited research for mass transfer is reported in the literature. There are equations to predict the velocity profiles for the gap between the wipers and the wall, and for the calculation of the heat transfer coefficient, but there are no equations for the calculation of the mass transfer coefficient. Mass transfer has not been studied simultaneously with heat transfer. Thus a significant gap of WFE knowledge is missing and we hope to fill this gap with the present dissertation. Falling film evaporators (FFEs) can represent a base case of vertical WFEs (i.e., FFE = WFE without agitation). Much information has been published regarding FFE. A recent "state-of-the-art" study of falling film evaporation was conducted by Thome [96]. His studies will be useful because the existing models for FFEs can be used to predict a "base value" (i.e., heat transfer coefficient), and with the available models for WFEn, an "enhancement factor" can be calculated as a ratio of FFEn to WFEn. Because mass 33 transfer models for FFEs are also available, the mass transfer coefficient for WFEn will be predicted using the enhancement factor times the mass transfer coefficient for FFEn. Al-Najeem et al. [4] present a semi-mechanistic model for the prediction of FFE heat transfer coefficients in vertical tube evaporators. They solved the governing energy equation and fitted the solution to an equation which is valid over wide ranges of Reynolds and Prandtl numbers. Ahmed and Kaparthi [3] present a correlation for the calculation of the heat transfer coefficient as a function of the Reynolds and Prandtl numbers. It was developed from experiments that were carried out using water and aqueous solutions of glycerol. Numrich [75] developed a FFE model, using a modification of the Prandtl analogy, to predict the heat transfer coefficient. This model shows good agreement with existing experimental data for Prandtl numbers up to 50. 34 Chapter 3 Modeling: Previous Work As mentioned in Chapter 2, the modeling of heat transfer in wipedfilm evaporators has been reported. In the following paragraphs the available models for heat and mass transfer for falling film and wiped film evaporators will be discussed. 3.1 Heat Transfer Heat transfer has been studied by several authors such as Ahmed and Kaparthi [3], Al-Najeem et al. [4], Alhusseini et al. [5], Krupiczka et al. [49], Numrich [75], Tsay and Lin [98], for falling film evaporators, and Abichandani and Sarma [1], Abichandani et al. [2], Bott and Romero [11, 12], Bott and Sheikh [13, 14], Kern and Karakas [40] for wiped film evaporators. 3.1.1 Falling Film Evaporators Al-Najeem et al. [4] present a semi-mechanistic model for the prediction of heat transfer coefficients in vertical falling film evaporators. The case solved assumed steady turbulent flow of incompressible fluids having constant properties along a vertical plane surface or inside a vertical circular tube. The 35 following assumptions were made: Uniform film thickness. Fully developed hydrodynamic condition. The resulting two-dimensional momentum equation and boundary conditions in dimensionless form are given by: d dW (R) (s - R)n Em (R) + ( + ) (s - R)n = 0 dR dR W (R) = 0 at R = 0 dW (R) = i at R = 0 dR where n = 0 for a plane wall, and n = 1 for a circular tube. The solution for the local dimensionless heat transfer coefficient is: h (Z) = 1 (s 0 (3.1a) (3.1b) (3.1c) Q2 Z - R)n W (R)dR 1 + 0 [1 - H(R)]2 dR - 2 (s - R)n Eh (R) i=1 e-i Z N 2 i (3.2a) 2 where h 2/3 g 1/3 2/3 um Q2 = Q0 Ls2n g 1/3 h = Q0 = q0 S/KT (3.2b) (3.2c) (3.2d) A more useful equation for the prediction of the local dimensionless heat transfer coefficient h in terms of Reynolds and Prandtl numbers was 36 developed: C h (Z) = C1 ReC2 P rL 3 + C4 Z C5 ReC6 L L (3.3) where h is defined by Equation 3.2b, ReL is the liquid Reynolds number and P rL is the liquid Prandtl number. Constants C1 to C6 are given in Table 3.1. Equation 3.3 is valid for the turbulent region defined by Al-Najeem et al. as 1.8 P rL 5.5 and 4, 000 ReL 20, 000. Unfortunately, Equation 3.3 sometimes predicts negative Nusselt numbers (i.e., when the P r numbers is greater than 5.5), and it will not be used. Table 3.1: Correlation constants for Equation 3.3 [4]. Z 0.2 7.69400 10-02 2.00100 10-01 3.47240 10-01 -8.31145 10-01 2.43700 10-01 1.39580 10-02 0.2 < Z 1.0 1.0000 10-06 1.0000 1.6477 1.0100 10-04 -1.8195 4.9515 10-01 C1 C2 C3 C4 C5 C6 Ahmed and Kaparthi [3] used a copper tube of 3.015 cm internal diameter in their study. Their experiments were carried out using water and aqueous solutions of glycerol over a wide range of Reynolds and Prandtl numbers (3 Re 10250; 3.6 P r 950). The correlation is: 0.345 0.4 N uL = 6.92 10-3 ReL P rL (3.4) Numrich [75] developed a simpler model for the heat transfer coefficient in a turbulent falling film. He used a modification of the Prandtl analogy to 37 formulate a new expression for the prediction of the heat transfer coefficient. His model shows good agreement with existing experimental data for Prandtl numbers up of 50. The equation for the prediction of the heat transfer coefficient is: 0.4 N uL = 0.003Re0.44 P rL L (3.5) where the Nusselt number is defined as: N uL = h 2/3 g 1/3 (3.6) This equation is the same as Equation 3.2b, the equation that AlNajeem et al. [4] define as the dimensionless heat transfer coefficient (h ). Equation 3.5 is valid for the turbulent region, which Numrich defines as P rL 3 and 1, 200 ReL 40, 000. Other authors present similar correlations to Equation 3.5. Krupiczka et al. [49] provide the following correlation: N uL = 1 + C(B0 Ka1/11 )1.6 N uLz where for B0 Ka1/11 > 10-6 , and for B0 Ka1/11 10-6 , C = 7.05 107 C=0 (3.7a) (3.7b) (3.7c) where N uLz is given by the correlation of Chun and Seban [18]: 0.65 N uLz = 0.0038Re0.4 P rL L (3.8) 38 and Ka is the Kapitza number, B0 is the boiling number, given by: Ka = 4 g 3 q B0 = mH (3.9) (3.10) If the flow regime is in the laminar region, Chun and Seban propose the following correlation: N uL = 0.821Re-0.22 if Re < Rec where Rec = 5900P r-1.06 3.1.2 Wiped Film Evaporators Heat transfer has been widely studied in wiped film evaporators for a wide range of applications and for different types of evaporators. Skelland [91] developed one of the earliest correlations for a scrapedfilm Votator (horizontal evaporator). He used different systems for the experiments: glycerol, water, and two similar glyceride oils in four different Votators. His correlated equation is: k hp = 4.9 Dt Dt u 0.57 (3.11) Cp 0.47 Dt N u 0.17 Dt L 0.37 (3.12) The thermal performance of a heat exchanger is characterized by a heat transfer coefficient, particularly the inside film heat transfer coefficient, since in the majority of applications of WFE, the latter represents the limiting thermal resistance [58]. 39 Maingonnat and Corrieu [58] present a discussion of the methods for calculating the heat transfer coefficient that have been used by several authors for scraped film heat exchangers. There are two theoretical methods (two-step and three-step mechanisms) as well as an empirical approach. The film heat transfer coefficient can be determined experimentally. The measurement of flow rates of the two fluids and their temperatures at the inlet and outlet of the WFE will make it possible to calculate the overall heat transfer coefficient (Uov ). Once Uov is determined using the expression Uov = Q Aln T (3.13) where Aln is the logarithmic mean of the inside and outside surface areas of the wall: Aln = A e - Ai Ae ln Ai (3.14) If the two fluids are considered to be in plug flow, the temperature difference is the logarithmic mean of the differences between the fluids at the entry and exit of the WFE. Figure 3.1 shows all the resistances present in a WFE. The three heat transfer coefficients (HTCs) involved in the calculation are: External HTC between heating fluid and the exchange surface (ho ). HTC of the heat exchange surface (wall ). Internal HTC between the process fluid and heat transfer surface (hp ). 40 Figure 3.1: Heat transfer coefficient resistances in a wiped film evaporator The expression for the calculation of hp is: 1 1 1 1 = - - hp Uov Rwall ho where Rwall is the wall resistance and defined as the ratio ductivity divided by the thickness of the wall). The value of ho can be determined either experimentally or using a suitable correlation. When steam is used as the heating medium, ho can be calculated with the equation for film condensation on vertical tubes or vertical (3.15) wall (thermal conwall 41 walls [9, 61]: 4 ho = 3 3 2 g s s 3s 1/3 (3.16) where is the rate of steam (mass flow) per unit length (kg/m). When a different hot fluid is used, the correlation presented by Sieder and Tate [90] can be used if the flow is laminar (i.e., Re 2, 100): ho D -1/3 = 1.86n1 L n1 = 4wCp w 0.14 (3.17) (3.18) For the transition region (2, 000 < Re < 10, 000), Knudsen et al. [44], recommend the equation from Hausen: ho D = 0.116 Re2/3 - 125 P r1/3 1 + D L 2/3 w 0.14 (3.19) For turbulent flow (Re > 10, 000), Knudsen et al. [44] suggest the use of the Dittus-Boelter equation: ho D = 0.0243Re0.8 P r0.4 w 0.14 (3.20) where the physical properties are evaluated at the bulk temperature. 3.1.2.1 Heat Transfer Models Based on Mechanism There are two models for the mechanisms of heat transfer: two-step and three-step. 42 Two-step mechanism. This mechanism was discussed by Kool [48] and is described here: First: Heat penetrates by molecular conduction into a thin layer of the product which is assumed to be immobile along the wall during the interval between two consecutive scrappings of the wall. The quantity of heat exchanged is calculated from Fourier's law for transient conduction. Second: Heat is transmitted by convection. The layer of product is removed from the wall by the blade and is mixed radially with the rest of the product; simultaneously, "fresh" product is brought into contact with the wall. The expression found by Kool is: hp = 1.24 (L CpL L N Nb )0.515 h0.03 wo (3.21) with the following condition: 2 < hwo 1 < 30 (L CpL L N Nb )0.5 (3.22) where hwo is the HTC between the heating fluid and the internal surface of the heat exchange wall. Latinen [52] and Harriot [34] presented a different expression for the internal HTC. They calculated the quantity of heat transferred between the internal surface of the exchange wall and the product. The simple expression is: hp = 2 L CpL N Nb 43 (3.23) Equation 3.23 can be written as a function of dimensionless numbers as [52]: hp = 2 ReN P rNb (3.24) Three-step mechanism. Trommelen, Beek, and van de Westelaken [97] added an extra step between one and two. They noted that the perfect radial mixing assumed cannot truly occur. Between the stage of molecular conduction and radial heat convection, they describe an intermediate step where the film of product which has been separated from the wall and is on the blade, and only partly gives up its heat to the stream of product flowing between the blade and the rotor. The product which is brought back into contact with the wall after leaving the blade is at a higher temperature than would have occurred if the radial mixing had been perfect. Trommelen et al. [97] found that this partial equalization reduced the heat transfer by a factor less than unity. Their expression for the internal HTC is: N u = 1.13 where = 2.0P r-0.25 for ReN > Recr and Recr is around 280. Heat transfer in vertical wiped film evaporators was studied by other authors. Bott and Romero [11] and Bott and Sheikh [14] present correlations for the prediction of the inside HTC. 44 (3.26) ReN P rNb (3.25) Bott and Romero used three experimental scraped surface falling film vertical heat exchanger tubes: 15.24 cm, 30.48 cm, and 60.96 cm by 2.54 cm diameter. Water and water-glycerol mixtures were used as test systems. Flowrates of 455 kg/hr-m (based on wetted perimeter) to 1,592 kg/hr-m were used, while the rate of rotation was varied from 370 to 1,600 rpm. The number of blades mounted on the shaft were also varied: from 1 to 4. They made 108 runs using pure water (83 runs) and water-glycerol (13 runs for 28.5%, 4 runs for 33.85%, 4 runs for 43.53%, and 4 runs for 61.85% in water content). They correlated their experimental data as a function of dimensionless parameters: N u = 0.018Re0.46 Re0.6 P r0.87 f N D L 0.48 Nb0.24 (3.27) This correlation was accurate within 20% in the range of the variables studied. The dependence on the ratio of diameter to length is not clear but is though to relate to the effect of liquid entry and corresponding liquid spreading and film thickness. The length of these systems is relatively short compared to traditional mass transfer internals (e.g., packed columns). Bott and Sheikh [14] later ran a similar series of experiments at atmospheric pressure using an evaporator with 3.81 cm ID by 45.72 cm long tubes, with the same experimental systems but with more data points for waterglycerol mixtures (45%, 62%, and 85% in glycerol content). For the 45% glycerol system, different numbers of blades were used: 2, 6, and 8. The range of flowrate was from 258 kg/hr-m to 1,482 kg/hr-m. The speed of rotation was varied from 600 to 1400 rpm. 45 Their results for boiling water show that hp is weakly dependent on the film Reynolds number (Ref ), even at low speed rotations (6000 rpm). An increase in the rotational speed N increases the HTC. The effect of N was varied as hp N 0.37 . Kirschbaum and Dieter [43] found the dependence to be hp N 0.33 , in close agreement to the value found by Bott and Sheikh [14]. Their correlation is: N u = 0.65Re0.25 Re0.43 P r0.30 Nb0.33 f N (3.28) Azzory and Bott [7] studied the heat transfer coefficient in a vertical scraped surface evaporator. They found an expression similar to the one found by Trommelen et al. [97], Equation 3.25. Azzory and Bott also found that the HTC is independent of the flow rate above a certain rotational speed (180 rpm). Their correlation is: hp = 8.74 f Cp kN Nb (3.29) where f is defined as f= Pr + 3.5 500 (3.30) As shown in Equation 3.15, the rate of heat transfer will level off with an increasing process heat transfer coefficient (i.e., increase in rotational speed) as the hot fluid and the wall resistance begin to control. 46 3.2 Mass Transfer Whereas heat transfer in falling and wiped film evaporators has been thoroughly studied, the same cannot be said for mass transfer. There are several papers for falling film evaporators Hoke and Chen [36], Krupiczka et al. [50], Nielsen et al. [73], Salvagnini and Taqueda [81], Spedding and Jones [93], Yksel and Schlnder [103, 104]. Just a few authors present studies for u u wiped film evaporators: McKenna [64], Miyashita and Hoffman [66], Miyashita et al. [67]. 3.2.1 Falling Film Evaporators Hoke and Chen [36] present the formulation of the governing equations and boundary conditions that describe the evaporation of two-component liquid films falling down a vertical surface. They solve the equations numerically. Spedding and Jones [93] present mass and heat transfer data for humidification of air in a glass wetted-wall column with a 4.04 cm inside diameter and the length varied between 0.72 m and 3.54 m. Their only correlation is for the thickness of the theoretical film, given by: di 0.830.015 = 0.016 0.002Ref (3.31) Gilliland and Sherwood [27] studied gas-side mass transfer in a wettedwall column, evaporating water and eight different organic liquids into air flowing over a wetted surface with an inside diameter of 2.54 cm and 117 cm long. Air was flowing cocurrent and countercurrent at different pressures (0.1 47 to 3 atm). Their correlation is: kc d pBM = 0.023 DAB P du 0.83 D 0.44 (3.32) This correlation is valid for gas-phase Reynolds numbers from 2,000 to 27,000. Nielsen et al. [73] measured the rate of gas and liquid phase mass transport in a pilot scale wetted-wall column with an internal diameter of 3.26 cm and a length of 5 m, developing empirical correlations for the physical liquid and gas phase mass transfer coefficient. The correlations are: 0.426 ShL = 0.01613Re0.664 ReL Sc0.5 G L 0.207 ShG = 0.00031Re1.05 ReL Sc0.5 G G (3.33) (3.34) Which are valid for gas-phase Reynolds numbers from 7,500 to 18,300 and liquid-phase Reynolds numbers from 4,000 to 12,000. Yih and Chen [102] used a a long wetted-wall column for absorption of CO2 and O2 into falling water films on the outside of a stainless steel pipe 2.72 cm OD and 183 cm absorption length. The studied range of Reynolds number was from 129 to 10500. Their correlations is: F kL F E = a Reb ScL f 2/3 1/3 1/2 DL L g 2/3 L (3.35) where: a = 1.099 10-2 , b = 0.3955 for 49 < Ref < 300 a = 2.995 10-2 , b = 0.2134 for 300 < Ref < 1600 a = 9.777 10-4 , b = 0.6804 for 1600 < Ref < 10500 48 These values of a, b, and Ref were correlated by Yih and Chen using their experimental values as well as the data from 10 other authors. 3.2.2 Wiped Film Evaporators Only a few papers analyze mass transfer in wiped film evaporators. McKenna [64] developed a model for the devolatilization (removal of monomer) of polymer solutions in a WFE. He considered fluid transport (velocity profile) and mass transfer in the evaporator, but not heat transfer. Another conclusion was that the capacity of the WFE increases as the rotational speed increases, up to a limit where the gain in mass transfer is overshadowed by the increase in power consumption. Miyashita and Hoffman [66] used an electrochemical technique, described by Mizushina [68], in a scraped-film heat exchanger with a 78.7 mm ID by 457.2 mm in length and two blades. They measured mass transfer coefficients, later converted to heat transfer coefficients using the heat and mass transfer analogy. The expression is: N u = 0.15 (ReN P r)0.5 Rea f where a= 1 - 3.74 10-2 N 9 (3.37) (3.36) Later, Miyashita et al. [67] extended the range of the Schmidt number, using the same technique as in the earlier paper [66]. Their correlation for 49 mass transfer is: Sh = 1.53Re0.51 Sc0.33 f di di - ds 0.44 (3.38) with the following restrictions 1320 < Sc < 5810 2.94 < di < 7.2 di - ds (3.39) (3.40) The previous equation for mass transfer coefficient was converted to heat transfer coefficient by using the mass and heat transfer analogy: N u = 1.53Re0.51 P r0.33 f di di - ds 0.44 (3.41) which has the same restrictions for the Schmidt number in Equation 3.38. 3.3 Flash Calculation As mentioned in Chapter 2, a wiped film evaporator may be modeled as a series of isothermal flashes [31]. Here only a single-stage isothermal flash will be considered. Figure 3.2 shows the variables involved in the calculation of a single-stage two-phase flash at a specified pressure (P ) and temperature (T ). The equations to solve are [86]: f () = zi (1 - Ki ) 1 + (Ki - 1) i zi xi = 1 + (Ki - 1) Ki zi yi = 1 + (Ki - 1) Q = V HV + LhL - F HF 50 n (3.42) (3.43) (3.44) (3.45) V is the fraction of generated vapor with respect to the feed, Ki is F i P vap , and HV , hL , HF are the the equilibrium constant calculated as Ki = P enthalpies of the vapor, liquid, and feed respectively. where = Figure 3.2: Two phase flash model for a wiped film evaporator. When solving the previous equations, information about the heat duty, vapor and liquid flowrates, and the distribution of components in the liquid and vapor are obtained. From these equations, it can be seen that several parameters for the wiped film evaporator (i.e., number of blades, rotational speed) are not included. In order to take into account their impact, a more rigorous model is needed. This model is presented in Chapter 4. 51 Chapter 4 Model Development 4.1 Heat and Mass Transfer Model for Vertical Wiped Film Evaporators A vertical wiped film evaporator (WFE) is a countercurrent vapor- liquid contactor (see Figure 4.1) and is closely related to the well-studied falling film evaporator (FFE). Relative to the FFE, the WFE has the ability to renew the vapor-liquid surface through mechanical wiping. The wiping action may also induce waves (i.e., turbulence) that enhance the mass transfer area. Thus the efficiency of a WFE should be greater than that of a FFE. Unfortunately, as noted in Chapter 3, little information has been published on the subject of wiped film evaporation. In particular, very little fundamental experimental WFE mass transfer data, and no WFE mass transfer correlations, have been reported. In contrast, the literature contains a significant amount of data and fundamental models on heat transfer within wiped film evaporators. Likewise, numerous studies on falling film evaporators have been reported. In this Chapter, a method to predict the mass transfer coefficient in a vertical WFE is proposed, based on existing correlations for the prediction of heat transfer coefficient in WFE and FFE, and mass transfer coefficient for FFE. 52 4.2 Proposed Design Model The relationship between the overall heat transfer coefficient Uov and the individual heat transfer resistances (Figure 4.2) is derived from heat bal- Figure 4.1: Sketch of a Vertical Wiped Film Evaporator. The heat added to the system generates evaporation at the surface of the falling liquid and the rotating blades generate turbulence at the surface. 53 ances around the heating medium, the wall, and liquid. qo = ho (To - TW o ) qw = wall (TW o - TW L ) wall qp = hp (TW L - TL ) where q is the heat flux per unit area at each interface. Figure 4.2: Heat transfer resistances in a wiped film evaporator. The previous equations state that the amount of heat transferred from the medium to the wall must be equal to the amount passing through the wall 54 and the amount transferred to the liquid. Equating all the heat terms and solving for q, the following expression for the overall heat transfer coefficient results: 1 wall 1 1 = + + Uov ho wall hp (4.1) where Uov is the overall heat transfer coefficient (W/m2 -K), ho is the heat transfer coefficient for the heating medium (W/m2 -K), wall is the thermal resistance of the wall (W/m-K), wall is the thickness of the wall (m), and hp is the heat transfer coefficient for the liquid film (W/m2 -K). As mentioned in Chapter 3, the process side HTC, hp , can be calculated from experimental data. Equation 3.13 is used to calculate Uov , then Equation 3.16 (steam) or 3.17 (other fluid) is used to calculate the hot fluid side HTC, ho . The wall resistance is readily calculated using the thermal conductivity of the wall as well as it thickness. Finally, Equation 3.15 is used to calculate the process side HTC, hp . The present research was focused on modeling hp (the heat transfer W coefficient inside the WFE) and kL F E (mass transfer coefficient inside the WFE). Preliminary studies had indicated that hp in WFEs is a function of the number of blades, the speed of rotation, and the physical properties of the system (i.e., viscosity, thermal conductivity, etc.) Considering the WFE as a stage-wise unit (i.e., dividing the length into small "stages", see Figure 4.1) and assuming plug flow (i.e., no backmixing), the performance of a WFE can be predicted using the equations below. 55 Applying mass balance, energy balance, and equilibrium considerations to the stage, the amount of generated vapor (V , kg/s) can be calculated. Mass balance: Ln + Vn = F + Vn-1 Ln xn + Vn yn = F xF + Vn-1 yn-1 Equilibrium: Kn = yn xn (4.4) (4.2) (4.3) Energy balance: Ln hL,n + Vn hV,n = F hL,F + Vn-1 hV,n-1 + q Vn-1 = where q = Uov ATlm Ln hL,n + Vn hV,n - F hL,F - q hV,n-1 (4.5) The proposed model will perform an overall heat and material balance and a transferring component material balance. The model also takes into account a subcooled feed. The possibility of correcting correlations for falling film evaporator and applying them to wiped film evaporators was analyzed, and was found that it can be used. Additional experimental data were needed in order to verify this approach. 56 The initial approach was to use an enhancement factor , defined as the ratio of the WFE heat or mass transfer coefficient to the FFE heat or mass transfer coefficient. Since little information has been reported on WFE mass transfer, the enhancement factor was initially evaluated based on reported WFE and FFE heat transfer information. The heat transfer enhancement factor, h , is defined as follows: h = hW F E p hF F E p (4.6) where hW F E is the heat transfer coefficient for the WFE, and hF F E is for the p p FFE. Two published models for the prediction of the heat transfer coefficient for WFE were selected: Bott and Sheikh [14] and Bott and Romero [11]. These correlations are of the form: N u = f Rea1 Rea2 P ra3 Nba4 (D/L)a5 Nba6 N f (4.7) where the parameters a1 to a6 were correlated using heat transfer coefficient data. Nb is the number of blades, D is the diameter, L is the length, N is the rotational speed, and the dimensionless numbers are: hp D is the Nusselt number Nu = 4F Ref = is the film Reynolds number D D2 N ReN = is the rotational Reynolds number Cp Pr = is the Prandtl number. 57 The expression for each particular WFE heat transfer coefficient model is as follows. Bott and Romero [11]: 0.87 N u = 0.018Re0.46 Re0.6 P rL (D/L)0.48 Nb0.24 f N (4.8) Bott and Sheikh [14]: 0.3 N u = 0.65Re0.25 Re0.43 P rL Nb0.33 f N (4.9) Two FFE heat transfer coefficient models for different N u values were evaluated: Ahmed and Kaparthi [3], and Numrich [75]. The expression for each model is as follows. Ahmed and Kaparthi [3] 0.345 0.4 N u = 6.92 10-3 Ref P rL (4.10) Numrich [75] 0.4 N u = 0.003Re0.44 P rL f (4.11) In these models, the Nusselt number is defined as: Nu = where L = hL 2 2 g 1/3 (4.12) = the characteristic length. Figures 4.3, 4.4, and 4.5 show the variation of the heat transfer enhancement factor (h ) with the film Reynolds number, rotational Reynolds 58 number, and Prandtl number using the four possible combinations of models for the heat transfer coefficient (two for WFEs and two for FFEs). Figure 4.3 shows that as the film Reynolds number (Re) increases, the heat transfer enhancement factor decreases, having a high value at low Re. This means that the performance of the equipment will be expected not to change significantly after a critical Re is achieved. For this particular case, the value is around 2000. Figure 4.4 shows that as the rotational Reynolds number (ReN ) increases, the heat transfer enhancement factor increases. This is due to the increase in the speed of rotation, which also increases the HTC for the wiped film evaporator. This is consistent with what other authors have found [14, 43, 66]. There is a region of the rotational speed where the evaporator is operated typically, highlighted by the square box. Figure 4.5 presents a sharp increase in the enhancement factor as a function of the Prandtl number (P r). This is because as the Prandtl number increases, usually the viscosity increases, and the HTC in a falling film evaporator will decrease, while in a wiped film evaporator, the HTC will increase. 4.3 Comparison of Proposed Model With Published Data The set of Equations 4.1-4.3 and 4.5 can be applied to a given set of experimental data. Considering the starting point as the top of the unit (see 59 Figure 4.3: Heat Transfer Enhancement Factor (h ) as a function of the film Reynolds number. D=0.21 m; L=1.521 m; L =4.73 cP; kL =0.468 W/m-K; L =1222 kg/m3 ; CpL =4179.6 J/kg-K; N =13.66 1/s; Nb =2; ReN =constant; P r=constant. Figure 4.1, Page 53), from the mass and energy balance: F xF + Vn-1 yn-1 = Ln xn + Vn yn F + Vn-1 = Ln + Vn F hL,F + Vn-1 hV,n-1 + q = Ln hL,n + Vn hV,n 60 Figure 4.4: Heat Transfer Enhancement Factor (h ) as a function of the rotational Reynolds number. D=0.21 m; L=1.521 m; L =4.73 cP; kL =0.468 W/mK; L =1222 kg/m3 ; CpL =4179.6 J/kg-K; Nb =2; Ref =constant; P r=constant. From the experimental data, the feed flowrate (F ) and its composition (xF ), the amount of vapor (Vn ) and its composition (yn ), and the amount of heat transferred are known, and the temperature of the stage can be calculated (using the bubble point equation). Knowing the temperature, the amount of 61 Figure 4.5: Heat Transfer Enhancement Factor (h ) as a function of the Prandtl number. D=0.21 m; L=1.521 m; kL =0.468 W/m-K; L =1222 kg/m3 ; CpL =4179.6 J/kg-K; Nb =2; Ref =constant; ReN =constant. vapor (Vn-1 ) and its composition (yn-1 ) can be calculated. From this, the amount of liquid entering the next stage (Ln ) and its composition (xn ) can be calculated. The same procedure can be applied until the last segment (i.e., bottom of the unit) is solved. 62 A set of experimental data from Frank and Lutcha [25] for sugar solutions is available and shown in Table 4.1. These data were originally used to find an expression for the film thickness but we can use them in order to verify the proposed model. Figure 4.6 shows the results for the exit concentration of water, when the proposed approach is applied. Figure 4.7 shows the variation of the liquid mass fraction of the more volatile component (water) from the top (i.e., the feed point) to the bottom of the WFE, while Figure 4.8 shows the variation of liquid and vapor flow rates. As shown in Figures 4.9 and 4.10, the prediction of the process side heat transfer coefficient and the overall heat transfer coefficient using the model of Bott and Sheikh [14] is better than the prediction using Bott and Romero [11]. 4.4 Simultaneous Heat and Mass Transfer In this section, the simultaneous heat and mass transfer in wiped film evaporators will be analyzed [88]. Figure 4.11 shows a differential section of the WFE. The mass, components, and energy balances are as follows: Lin + Vin = Lout + Vout Lin xin + Vin yin = Lout xout + Vout yout Lin hL,in + Vin hV,in + qin = Lout hV,out + Vout hV,out (4.13) (4.14) (4.15) Overall, component, and energy balances on each stream for an element of contact area A gives the differential conservation equations. The mass 63 Table 4.1: Set of experimental data from Frank and Lutcha [25]. D=0.21 m; L=1.521 m N (1/s) F (kg/s) VN (kg/s) xF (%)a 13.66 0.1614 0.0354 96.49 6.08 0.1624 0.0270 96.49 6.08 0.1125 0.0239 96.49 13.66 0.1135 0.0301 96.49 13.66 0.0654 0.0274 96.49 6.00 0.0655 0.0191 96.49 13.66 0.1739 0.0294 93.84 6.03 0.1655 0.0242 93.60 6.03 0.1149 0.0212 93.60 13.66 0.1203 0.0265 93.60 13.66 0.1147 0.0262 93.60 13.66 0.1645 0.0373 98.36 6.00 0.1588 0.0297 98.36 6.00 0.1204 0.0274 98.49 13.66 0.1202 0.0330 98.49 13.66 0.0610 0.0294 98.59 6.00 0.0705 0.0251 98.59 6.00 0.1142 0.0283 98.59 13.66 0.1192 0.0353 98.59 6.66 0.1426 0.0152 90.81 6.66 0.1110 0.0150 90.81 13.33 0.1515 0.0172 90.81 13.33 0.1008 0.0150 90.81 6.66 0.1881 0.0161 90.73 6.66 0.0970 0.0122 88.73 6.66 0.1446 0.0107 88.73 13.33 0.1945 0.0158 88.54 13.33 0.1526 0.0139 88.54 a x1 (%) Tv (o C) Tp (o C) q (W/m2 ) 94.77 60 105.0 82617.2 95.09 60 105.0 62658.2 95.21 60 105.0 56396.4 94.52 60 105.0 71068.4 88.39 60 105.0 64995.4 93.48 60 105.0 45325.7 90.23 60 105.0 68459.0 91.02 59 105.0 55248.4 89.69 59 105.0 48412.5 87.65 60 105.0 61597.5 86.24 60 105.0 60852.4 97.78 60 105.0 86264.1 97.88 60 105.0 68500.1 97.84 60 105.0 64298.3 97.60 60 105.0 77864.4 96.60 60 105.0 69035.3 97.21 60 105.0 58481.1 97.82 60 105.0 65594.6 97.67 60 105.0 82058.2 87.26 60 95.0 31963.4 85.71 60 95.5 32317.4 86.73 60 95.0 38117.6 84.95 60 95.0 33445.6 88.08 60 95.0 32816.8 81.77 60 95.0 27691.2 85.55 60 95.0 23250.0 84.80 60 96.0 34660.8 84.12 60 95.0 30754.7 mol concentration of water balance on an element of the gas stream shown in Figure 4.11 gives: V |A + N1 A = V |A+A (4.16) 64 Figure 4.6: Predicted vs. Experimental weight fraction for water in concentrate using data from Frank and Lutcha [25]. D = 0.21 m, L = 1.521 m, wall = 0.004 m. No mass transfer considered. Dividing by A and letting A 0, dV = N1 dA And similarly for the liquid dL = N1 dA (4.18) (4.17) 65 Figure 4.7: Liquid mass fraction variation along the WFE. 0=Top of the unit. 1.6=Bottom of the unit The energy balance on the gas stream is: qA = V hV |A+A - V hV |A - N1 h1 A (4.19) where the last term on the right-hand side accounts for the enthalpy added to the control volume by the evaporated component. Dividing by A and letting A 0: d(V hV ) = q + N1 h1 dA 66 (4.20) Figure 4.8: Liquid and vapor flowrate variation along the WFE. 0=Top of the unit. 1.6=Bottom of the unit. And similarly for the liquid d(LhL ) = q + N1 h1 dA (4.21) From Figure 4.11 the total flux of enthalpy into a differential element of thickness dy is made up of two parts: The conduction heat flux: -k dt dy The flux of enthalpy due to diffusion: NA CpA (t - t0 ) + NB CpB (t - t0 ) 67 Figure 4.9: Predicted vs. Experimental process side heat transfer coefficient using data from Frank and Lutcha [25]. D = 0.21 m; L = 1.521 m, wall = 0.004 m. No mass transfer considered. where t0 is a standard state temperature. Evaluating these quantities for the flux entering and leaving the differential element and setting their difference equal to zero, the temperature distribution in the film must satisfy k d2 t dt - (NA CpA + NB CpB ) =0 dy 2 dy (4.22) The solution that satisfies the conditions that t = t1 at the interface (wall) 68 Figure 4.10: Predicted vs. Experimental overall heat transfer coefficient using data from Frank and Lutcha [25]. D = 0.21 m; L = 1.521 m, wall = 0.004 m. No mass transfer considered. where y = 0 and t = t2 at the bulk-gas boundary of the film is y -1 t(y) = t1 + (t2 - t1 ) exp (C0 ) - 1 exp C0 where C0 is the Ackermann correction factor defined by C0 = (NA CpA + NB CpB ) /hp (4.24) (4.23) and hp = /. The conduction flux of heat at the interface is found from this 69 Figure 4.11: Differential section of a Wiped Film Evaporator. result as qc = -k dt dy = hp (t1 - t2 ) 0 C0 exp (C0 ) - 1 (4.25) And the total heat flux is equal to the heat flux by conduction and the flux of enthalpy due to diffusion: q = hp (t - ti ) C0 1 - exp (-C0 ) 70 (4.26) The Ackermann factor or correction in Equation 4.23 takes into account the contribution from mass transfer to heat transfer. The presence of mass transfer can either or raise lower the rate of heat conduction depending on the direction of mass transfer. The factor is positive when material is transferred from the vapor to the liquid stream, decreasing the amount of heat transfer (i.e., condensing). When material is transferred from the liquid to the vapor stream, an increase in the amount of heat is generated. The interface temperature lies between Tp , the temperature of the heating medium and the bulk temperature of the liquid, and it can be found from an energy balance at the interface. U (Tp - ti ) = q + A NA = hp (t - ti ) C0 + A NA 1 - exp (-C0 ) (4.27) The equation to calculate the rate of mass transfer is: W NA = kL F E L (xA - x ) A (4.28) where xA is the mole fraction of the component in the liquid and x is the A equilibrium concentration. W In order to predict kL F E , the value of h is needed (see Equation 4.6), and the heat and mass transfer analogy is assumed. The FFE mass transfer model of Yih and Chen [102] (based on its fit with previous data) is used to predict the mass transfer coefficient for FFE: F kL F E = a Reb f 1/2 ScL DL L g 1/3 L 2/3 2/3 (3.35) 71 The equation to predict the mass transfer coefficient, assuming heat and mass transfer analogy is: F W kL F E = h kL F E (4.29) The correlation presented by Yih and Chen [102] was developed absorbing O2 and CO2 into falling water films. Because the solubility of these components in water is small, they do not include a correction for the effect of high concentration in water. When the transferring component is present in high concentrations, a correction factor is needed [35, 87]. In the evaporation process, the transferring component is oftentimes present in high concentration, thus a correction factor will be included: W kL F E = h F kL F E (1 - xA )m (4.30) The effect of the correction factor will be to enhance the apparent mass transfer coefficient in the WFE. When the heat and mass transfer effects are considered (i.e., using the previous equations) the results are shown in Figures 4.12 to 4.14. It can be seen that the prediction of the exiting concentration of water and heat transfer coefficient improves over the calculated values when no mass transfer is considered. The differential equations are solved using the Euler's forward method. 72 Figure 4.12: Predicted vs. Experimental weight fraction for concentrate using data from Frank and Lutcha [25]. D = 0.21 m, L = 1.521 m, wall = 0.004 m. Mass transfer is considered. 73 Figure 4.13: Predicted vs. Experimental process side heat transfer coefficient (hp ) using data from Frank and Lutcha [25]. D = 0.21 m; L = 1.521 m, wall = 0.004 m. Mass transfer is considered. 74 Figure 4.14: Predicted vs. Experimental overall heat transfer coefficient (Uov ) using data from Frank and Lutcha [25]. D = 0.21 m; L = 1.521 m, wall = 0.004 m. Mass transfer is considered. 75 Chapter 5 Experimental System and Procedures The experimental work for the present research was conducted at the Blair, Nebraska, plant of Cargill Inc. A glass laboatory wiped film evaporator (WFE) was made available to the Separations Research Program (SRP). The experiments were performed at a Cargill's facility in the midwest. 5.1 Test Systems The following test systems were selected: water-glycerol, water-sucrose, and water-ethylene glycol. These systems cover a wide range of physical properties. 5.1.1 Water/Glycerol Earlier papers on WFE heat transfer used the system water/glycerol. The system is well-characterized and its physical properties do not change dramatically over a small change in concentration and/or pressure (P ) and/or temperature (T ) (except for viscosity which shows a moderate variation). Table 5.1 gives physical properties for different water-glycerol mixtures. The system has been used for heat transfer studies by other authors in wiped film 76 evaporators [1, 11, 14]. Their results will be utilized for comparison with data obtained in this work. Table 5.1: Physical properties for several mixtures of glycerol and water at 5.3 kPa and 36 C), calculated using AspenPlus version 11.1 with the UNIQUAC thermodynamics option. Composition is based on wt% glycerol. The balance is water. Property 38 wt% 58 wt% MW, kg/kmol 25.95 33.77 3 L , kg/m 1,092.2 1,158.8 L , cP 1.42 2.56 L , W/m-K 0.407 0.358 Cp,L , J/kg-K 3,258.3 2,920.2 DL 1012 , m2 /s 9.55 11.60 , N/m 0.0697 0.0684 hL , kJ/kg -12,530.6 -10,800.0 75 wt% 45.41 1,214.8 5.49 0.328 2,644.2 17.24 0.0663 -9,327.5 Expressions for the calculation of physical properties (i.e., viscosity, density, thermal conductivity) exist in the literature. The DIPPR equations [22] will be used to predict physical properties as follows: L = 0.92382 i 0.22114 T 1+(1- 850 ) 0.24386 h (5.1) (5.2) (5.3) 6 Cp,L = 78468 + 480.71T L = 0.258 + 1.1340 10-4 T L = exp 120.62 - P vap 15959 2.693 10 - 17.118 ln T + T T2 13808 = exp 99.986 - - 10.088 ln T + 3.5712 10-19 T 6 T (5.4) (5.5) where T is the temperature in K, L is the liquid density in kmol/m3 , Cp,L is the liquid heat capacity in J/kmol-K, L is the liquid thermal conductivity in 77 W/m-K, and L is the viscosity of the liquid in Pa-s. 5.1.2 Water/Sucrose Another good experimental system for heat and mass transfer analysis is water/sucrose solutions. Table 5.2 shows physical properties for this system at different weight fractions of sucrose. Although it has a wide variation in viscosity and other properties (e.g., density) several authors have used the system (e.g., Frank and Lutcha [25] for characteristic dimension and Stankiewicz and Rao [95] for heat transfer analysis) and analytical expressions for the calculation of physical properties of the mixture are available in the literature. Table 5.2: Physical properties for several mixtures of sucrose and water at 40 C. Composition is based on wt% sucrose. The balance is water. Property 36 wt% 48 wt% 55 wt% 65 wt% MW, kg/kmol 27.34 33.04 37.61 46.89 3 , kg/m 1,147.6 1,209.1 1,247.6 1,305.9 , cP 2.56 5.91 11.51 43.84 , W/m-K 0.507 0.466 0.442 0.408 Cp , J/kg-K 3,391.2 3,126.0 2,971.3 2,750.3 D 1012 , m2 /s 3.1810-10 2.0810-10 1.5210-10 0.8510-10 , N/m 0.0720 0.0733 0.0742 0.0757 h, kJ/kg 133.5 122.2 115.6 106.1 P vap , kPa 30.54 30.52 30.50 30.46 For instance, the viscosity of the solution can be calculated with the 78 following equation [60]: 1.25 L = 10(22.46-0.114+(1.1+43.1 )) = 30 - t 91 + t wt = 19 - 18wt (5.6) where wt is the mass fraction of sucrose in the solution, t is the temperature in C, and L is the viscosity of the solution in mPas. One advantage of this system is that the vapor phase will consist of water only which leads to more reliable methods for the prediction of physical properties. The expressions for other properties of water in sucrose, are as follows [60]. For density of the sucrose solution, L in kg/m3 : 6 Ai ti-1 L = i=1 6 1 + 1.6887 10-2 t 5 + i=1 Bi wti 4 + i=1 3 Ci wt i t - 20 100 t - 20 100 + 3 i=1 2 Di wt i t - 20 100 t - 20 100 2 (5.7) 4 + i=1 Ei wti + i=1 Fi wti For the heat capacity, Cp,L in J/kg-K: Cp,L = 4186.8 - 2510wt + 7.5wt t For the thermal conductivity, L in W/m-K: L = (5.466 10-6 t2 - 1.176 10-3 t - 0.3024)wt+ 0.563 + 1.976 10-3 t - 7.847 10-6 t2 79 (5.9) (5.8) i 1 2 3 4 5 6 Table 5.3: Constants for Equation 5.7 [60]. A B C D E 999.8395 385.1761 -46.2720 59.7712 -47.2207 16.9526 135.3705 -7.1720 7.2491 -21.6977 -3 7.9905 10 40.9299 1.1597 12.3630 27.6301 4.6242 10-5 -3.9646 5.1126 -35.4791 1.0585 10-7 13.4853 17.5254 2.8103 10-10 -17.2890 For the diffusion coefficient, DL in m2 /s: DL = exp -21.2176 - 14.9109 1 + 18.9998 exp 17144.76 + 1046.46e2.89439wt 8.31432 1 - wt wt -0.75 F 18.3184 12.3081 (5.10) 1 1 - 298.15 273.15 + t The thermodynamic equilibrium is predicted using the equations from Peres and Macedo [77]. The equations are: ln(i ) = ln iC + ln iR where: ln iC = ln i xi +1- i xi ji ij j - i + j ji i ij + j (5.12) (5.13) (5.14) (5.11) ln iR = 5qi 1 - ln (i + j ji ) - i = j x i ri 2/3 2/3 x j rj qi x i qi x i i i = (5.15) 80 aij = aij,0 + aij,1 (T - T0 ) + aij,2 T ln ij = exp - aij T T0 + T - T0 T (5.16) (5.17) 5.1.3 Water/Ethylene Glycol The system water/ethylene glycol has also been used for heat transfer studies in falling film evaporators by Leuthner et al. [54] and Hameed and Muhammed [32]. Table 5.4 shows the physical properties for a mixture of 75% weight fraction of ethylene glycol in water. While the test system does not have a large variation in physical properties, some properties are in the low end of the range, thermal conductivity and heat capacity are lower for this system compared to the other two. Thus the three systems provide a wide range of variation in physical properties. Table 5.4: Physical properties for 75 wt% ethylene glycol and water at 4.3 kPa and 42 C, calculated using AspenPlus version 11.1 with the UNIQUAC thermodynamic option. Property 75 wt% MW, kg/kmol 38.52 3 , kg/m 1,074.2 , cP 2.20 , W/m-K 0.288 Cp , J/kg-K 2,805.2 D 1010 , m2 /s 3.518 , N/m 0.0587 h, kJ/kg -9,467.8 P vap , kPa 8.25 As for the water/glycerol system, the DIPPR equations [22] will be 81 used to predict physical properties as follows: L = Cp,L 1.315 i 0.21868 T 1+(1- 720 ) 0.25125 = 35540 + 436.78T - 0.18486T 2 h (5.18) (5.19) (5.20) (5.21) (5.22) L = 0.088067 + 9.4712 10-4 T - 1.3114 10-6 T 2 L = exp -20.515 + P vap 2468.5 2.4998 1012 + 1.2435 ln T + T T5 10411 = exp 84.09 - - 8.1976 ln T + 1.6536 10-18 T 6 T where T is the temperature in K, L is the liquid density in kmol/m3 , Cp,L is the liquid heat capacity in J/kmol-K, L is the liquid thermal conductivity in W/m-K, and L is the viscosity of the liquid in Pa-s. 5.2 Experimental Setup Figure 5.1 shows a schematic of a representative experimental installa- tion, similar to the one used by Stankiewicz and Rao [95]. Liquid is pumped from the feed tank to the heat exchanger where it is preheated to the boiling temperature. The feed temperature is controlled to maintain a value within a specified variation (e.g., 1 C) using a temperature controller. The feed solution entering the WFE is spread with a distributor mounted on the shaft, providing complete circumferential coverage of the surface by the liquid. Evaporation takes place under vacuum in the vertical WFE. Vapors are separated from the concentrate in the glass separation chamber and condensed in tubular water coolers. Condensate is pumped out and collected for measurements. 82 Concentrated liquid is pumped out to a collecting tank. After volumetric measurements, condensate and concentrate are remixed and the solution is returned to the feed tank. Figure 5.1: Simplified flow diagram of experimental installation for a wiped fim evaporator [95] 5.3 Error Analysis Laboratory experiments involve taking measurements of physical quan- tities. A discrepancy between the measured value and the true value of the quantity may arise from different sources. To obtain an experimental result with an estimate of the degree of 83 uncertainty in the measurements, the types of errors, the ways to reduce the errors, and how to treat the data properly need to be known. For the calculation of the heat transfer coefficient for the liquid film (hp ), Equation 4.1 (page 55) will be used. In order to calculate hp , the overall heat transfer coefficient Uov , needs to be known. The following equations provide a way to calculate it when using hot oil for heating purposes: Q = wh Cp,h (Th,i - Th,o ) Q = U ATlm Uov = Tlm wh Cp,h (Th,i - Th,o ) ATlm (Th,i - TL ) - (Th,o - TL ) = Th,i - TL ln Th,o - TL (5.23) (5.24) (5.25) (5.26) where Tlm is the logarithmic mean temperature difference between the inlet and outlet conditions. Thus the experimental hp is calculated using the equation: ATlm 1 w hp = - - wh Cp,h (Th,i - Th,o ) ho wall -1 (5.27) From Equation 5.27, the measured variables that can influence the value of hp are: Temperature of the evaporating liquid (TL ) Flowrate of the hot oil (wh ) Temperature of the hot oil at inlet (Th,i ) and outlet (Th,o ) 84 In order to know the experimental error associated with these parameters, the following equations will be used. Error associated with TL : hp = A(Th,i - Th,o ) TL h2 wh Cp,h (ln TR )2 (Th,i - TL )(Th,o - TL ) p (5.28) Error associated with wh : hp = A 2 h2 wh Cp,h p ln TR wh (5.29) Error associated with Th,i : hp = A Th,i (ln TR )2 (Th,i - TL ) (5.30) h2 wh Cp,h p Error associated with Th,o : hp = - A Th,o (ln TR )2 (Th,o - TL ) (5.31) h2 wh Cp,h p In all the previous equations, TR is defined as follows: TR = Th,i - TL Th,o - TL Equations 5.28 to 5.31 were derived using the equation: (variable) = [variable] (measurement) [measurement] (5.32) Table 5.5 shows the effect of the error in measured variables to be taken in the experiments and its effect on the experimental process side heat transfer coefficient, based on the proposed model. 85 Table 5.5: Effect of measurement errors in operational parameters over the experimental process side heat transfer coefficient. Variable TL , C Th,i , C Th,o , C Mh , kg/s 3% error 5.9 29.9 12.6 5.9 5% error 10.2 50.9 10.4 9.9 10% error 22.7 n.c. n.c. 19.9 5.4 Experimental Conditions A full range of operating conditions was run, and is shown on Table 5.6 Table 5.6: Operational Parameters for Experimental Measurements Parameter Range Liquid rate 8-58 kg/hr-m2 Inlet Concentration (weight fraction %) 35-75 Speed of Rotation (rpm) 180-540 Number of Roller Wipers 3 Film Reynolds Number 0.1-4.0 5.5 Equipment The experimental equipment for this research was made available by Cargill Inc. at their Blair, Nebraska, plant. The experimental data were taken in summer 2003. The WFE was manufactured by UIC Inc. (now ChemTech Services Inc), model KDL-6. The unit was modified to allow the measurement of process conditions (i.e., temperature of vapor and liquid). The heat was provided by a hot oil. Marlotherm SH [83] was used for this purpose. Appendix B describes the characteristics of this heating medium. 86 Table 5.7: Main dimensions of the Cargill evaporator Diameter (m) 0.08 Length (m) 0.2141 Wall thickness (mm) 2.5 Number of rollers 3 Roller clearance Variable Jacket clearance (m) 0.012 Figure 5.2 represents a diagram of the modified experimental equipment. In Figure 5.4 a picture of the evaporator and condenser is shown. In Table 5.7 the main dimensions of the WFE are displayed, and Figure 5.5 depicts these dimensions. Figure 5.3 shows a diagram of the roller wipers, thin film, and heating media. The measurement of the roller wipers is 9 mm ID and 12 mm OD, while the guiding wire-rod is 3 mm. The clearance between the rollers and the wall is variable, and will be a function of the system physical properties and the rotational speed. The rollers will contact the WFE glass wall when no liquid is feed to the evaporator. 5.6 Calibration Curves Before running the experiments it was necessary to have a method for reading the concentration of each component in water. The refractive index method was used. For this purpose, the Mettler/Toledo RA-510M Refractometer was available. Solutions of known weight percent were prepared for each system and 87 were read using the refractometer. For the water-sucrose system, the solutions were prepared up to 65% only because the maximum solubility of sucrose at 20 C is 66.7%. Table 5.8 shows the refractive index for this system, and Figure 5.6 shows a plot of the refractive index versus the weight concentration. At the beginning of each reading, the refractive index of pure water was read in order to check for consistency of the measurements. For the system water-glycerol, the solutions were prepared up to 90%, and the refractive index for pure glycerol was also recorded. Table 5.9 presents Figure 5.2: Diagram of the original Wiped Film Evaporator from Cargill. 88 Figure 5.3: Diagram of the roller wiper system. Roller clearance is variable. the refractive index for the solutions at 20 C, and Figure 5.7 presents a plot of the refractive index versus the composition in weight percent. For the system water-ethylene glycol, the solutions were also prepared up to 90%, and the refractive index for pure ethylene glycol was also recorded. Table 5.10 presents the refractive index for the solutions at 20 C, and Fig- 89 Figure 5.4: Photo of the UIC Inc. Wiped Film Evaporator and condenser from Cargill. ure 5.8 presents a plot of the refractive index versus the composition in weight percent. 5.7 Run Procedure Before collecting experimental data, several tests were run using pure water as the feeding material. This was done for three reasons: 1. Cleaning the equipment: the WFE was used sporadically by Cargill 90 during the period when the data were collected. 2. Training for running the equipment: using water only as feed allowed learning the operation of the unit. 3. Heat balance and troubleshooting: during the first week, several problems with the evaporator were corrected (i.e., original pressure gauge was Figure 5.5: Dimensions of the ChemTech Services Wiped Film Evaporator from Cargill. 91 Table 5.8: 20 C Refractive index for different solutions of sucrose in water at Weight % 4.99 9.99 20.05 30.00 39.96 49.76 54.81 59.95 65.05 RI 1.3403 1.3478 1.3639 1.3811 1.3997 1.4196 1.4303 1.4418 1.4536 Table 5.9: Refractive index for glycerol in water at 20 C Weight % 0.00 10.01 20.00 30.00 39.90 49.87 59.99 69.92 80.00 90.03 100.00 RI 1.3331 1.3426 1.3525 1.3627 1.3728 1.3831 1.3935 1.4034 1.4133 1.4228 1.4319 replaced to allow the correct reading of the high vacuum conditions). The steps to follow for the experiments were: 1. Start cooling system (this was used to condensate the vapor generated in the WFE). 92 Figure 5.6: Refractive index variation with weight percent for the watersucrose system at 20 . 1.1. Turn on cooling refrigerator. 1.2. Turn on cooling pump. 2. Start vacuum system (in order to set the desired operating pressure). 2.1. Pre-heat oil in vacuum pump using the heat gun. 93 2.2. Put dry ice in alcohol mixture, inside cold finger, to prevent any vapor to affect the pressure reading. 2.3. Turn on vacuum pump. 2.4. Pull off vacuum to desired operating conditions. 3. Set the temperature of the hot oil bath and turn on bath. Figure 5.7: Refractive index variation with weight percent for the waterglycerol system at 20 . 94 Table 5.10: Refractive index for ethylene glycol in water at 20 C Weight % 0.00 10.01 19.99 30.02 39.99 50.06 60.09 70.02 80.00 90.03 100.00 RI 1.3331 1.3452 1.3577 1.3708 1.3846 1.3987 1.4134 1.4282 1.4434 1.4584 1.4730 4. Set feeding pump to desired volumetric flow rate and turn on. 5. Start the agitator (rotor) and set speed of the wipers. 6. Take samples after "steady state" is reached (it was determined that steady state was reached after 1 hour of making a change to an operating condition). 6.1. Start stopwatch and close bottom valves (to collect the liquid residue). 6.2. Record initial weight, temperatures (vapor and liquid), and rotational speed. 6.3. Close valves when about 500 grams are fed to the evaporator, and record time. 6.4. Weight vapor and liquid streams. 6.5. Take samples and read refractive index. 95 Figure 5.8: Refractive index variation with weight percent for the waterethylene glycol system at 20 . 5.8 Experimental Data In this section, the collected experimental data are presented. During the experiments with water-sucrose, crystals of sugar were formed due to the low feed rate and high rate of evaporation. Pure water was needed to clean up the evaporator. 96 When using water-glycerol, the silicone-based sealant for the glass junctions was being dissolved. 5.8.1 Operating Conditions Table 5.11 presents the ranges of experimental conditions studied during these experiments. As can be seen, wide variations of liquid viscosity, density, and flowrates were studied. The three systems include these parameters. Table 5.11: Range of experimental conditions Liquid rate 8 - 58 kg/hr-m2 Vapor velocity 0.2 - 0.4 m/s Rotational speed 180 - 540 rpm Inlet concentration (weight%) 35 - 75 Liquid density 895 - 1280 kg/m3 Liquid viscosity 3 - 50 cp Liquid Reynold number 0.1 - 6.0 5.8.2 Collected Data Data were collected for the three systems at different conditions. Ta- bles 5.12 (for water-sucrose), 5.13 (for water-glycerol), and 5.14 (for waterethylene glycol) show the experimental data collected using the steps mentioned before. 97 5.8.3 Heat Balance In general, the calculated heat transferred form the hot oil (Equa- tion 5.33) and the heat transferred in the evaporator (Equation 5.34) matched nicely indicating heat loss was not significant. Qhot oil = moil (Cpoil Toil,in - Cpoil Toil,out ) (5.33) (5.34) Qprocess = mwater Hvap,water + mf eed Cpf eed (Tout - Tf eed ) For example, in run 1. For the hot oil side: Qhot Qhot oil oil = (992.4)(1.548 10-3 ) = 215.9Watts 1 ((1825.8)(94.3) - (1811.3)90.4) 60 For the process side: Qprocess = (7.6437 10-5 )(2.4049 106 ) + (4.5770 10-4 )(3041.73)(42.8 - 29) Qprocess = 203.0Watts Then the heat loss was 12.9 Watts or 6.0% for this run. 5.8.4 Vapor Velocity and Entrainment Vapor velocities up to 0.40 m/s were studied, and no entrainment was observed when running the experiments. 98 Table 5.12: Experimental data for water-sucrose at different operating conditions. 99 Feed kg/hr 1.648 1.640 1.638 3.321 2.472 2.470 2.468 2.464 1.645 1.640 1.636 2.494 2.488 2.483 3.330 3.327 3.325 3.382 3.365 1.659 1.664 Tf eed C 29.0 30.0 30.0 31.8 29.7 31.6 31.8 32.5 30.0 30.2 31.0 28.7 29.0 29.0 28.0 29.0 29.5 29.5 30.5 27.0 27.5 Sucrose xin xout % % 46.94 56.61 46.92 56.47 46.97 57.04 47.29 51.56 47.68 53.59 47.87 53.90 47.84 53.99 47.87 53.77 47.89 57.18 47.96 58.08 47.96 58.24 48.22 54.94 48.30 55.33 48.41 55.74 48.59 53.37 48.61 53.62 48.55 53.60 50.48 54.74 49.62 53.87 49.25 60.09 49.85 62.03 Vapor kg/hr 0.275 0.277 0.281 0.264 0.262 0.273 0.272 0.268 0.267 0.278 0.281 0.306 0.312 0.316 0.294 0.306 0.307 0.246 0.253 0.309 0.325 Liquid kg/hr 1.374 1.363 1.354 3.052 2.196 2.200 2.189 2.197 1.377 1.360 1.354 2.183 2.174 2.156 3.030 3.018 3.013 3.115 3.097 1.350 1.337 P torr 55.0 55.0 54.9 54.1 54.3 54.5 54.5 54.5 54.9 54.9 54.9 41.2 41.3 41.2 41.2 41.2 40.8 54.8 54.8 40.2 40.0 Evaporator Hot Oil Ttop Tbot Speed Tin Tout Flow C C rpm C C L/min 39.8 42.8 300 94.3 90.4 1.548 39.8 40.0 420 94.3 90.4 1.529 39.9 40.0 540 94.3 90.3 1.542 39.8 40.0 540 94.3 90.3 1.534 39.5 40.0 180 94.3 90.3 1.521 40.0 40.0 360 94.3 90.4 1.596 39.9 40.0 540 94.3 90.4 1.565 39.8 40.0 180 94.3 90.5 1.577 39.9 40.0 180 94.3 90.4 1.514 39.9 40.0 360 94.3 90.3 1.521 39.9 40.0 539 94.3 90.3 1.526 34.9 35.0 182 94.4 90.1 1.524 34.9 35.0 360 94.3 90.1 1.524 35.0 35.0 540 94.3 90.1 1.584 35.0 35.0 180 94.3 90.2 1.548 35.1 35.0 360 94.3 90.2 1.575 35.0 35.0 540 94.3 90.1 1.529 39.8 40.0 181 94.3 90.3 1.518 40.0 40.0 360 94.3 90.2 1.513 35.1 35.0 180 94.3 90.3 1.573 34.2 35.0 360 94.3 90.1 1.601 Continued on next page Table 5.12 continued from previous page 100 Feed kg/hr 1.662 2.557 1.703 1.692 2.578 2.571 1.705 3.430 2.486 2.483 1.568 0.780 2.350 1.564 Tf eed C 27.8 29.6 28.7 30.0 27.5 28.0 28.8 29.2 30.4 30.5 25.5 27.2 29.4 30.0 Sucrose xin xout % % 49.76 62.19 55.21 61.59 55.39 65.82 53.66 64.21 53.98 61.26 54.02 61.58 53.98 66.32 54.16 59.57 47.56 53.22 47.52 53.33 36.31 43.91 36.31 57.01 36.27 40.85 36.27 45.86 Vapor kg/hr 0.332 0.263 0.266 0.272 0.306 0.312 0.313 0.309 0.271 0.273 0.269 0.284 0.257 0.327 Liquid kg/hr 1.330 2.288 1.431 1.412 2.271 2.256 1.389 3.117 2.216 2.213 1.299 0.496 2.087 1.237 P torr 40.0 55.2 56.1 55.9 41.9 41.9 42.0 41.8 55.7 55.7 59.1 59.1 59.1 42.1 Tin C 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 Evaporator Ttop Tbot Speed C C rpm 33.8 35.0 540 38.1 40.0 360 38.5 40.0 360 38.7 40.0 540 33.8 35.0 360 34.0 35.0 539 34.9 35.0 360 33.1 35.0 540 37.8 40.0 540 38.7 40.0 540 39.0 40.0 361 38.0 40.0 360 39.9 40.0 360 33.8 35.0 360 Hot Oil Tout Flow C L/min 90.1 1.539 90.4 1.527 90.4 1.505 90.5 1.563 90.0 1.514 90.0 1.519 90.1 1.507 90.1 1.549 90.4 1.576 90.4 1.542 90.3 1.528 90.4 1.527 90.3 1.527 90.0 1.520 Table 5.13: Experimental data for water-glycerol at different operating conditions. 101 Feed kg/hr 1.556 1.555 0.775 1.552 0.774 1.162 1.549 0.770 1.158 1.545 1.156 0.733 0.732 1.100 1.467 1.467 0.731 1.598 1.203 2.010 1.605 Glycerol xin xout Vapor % % kg/hr 57.85 70.90 0.277 58.01 71.04 0.278 58.00 85.16 0.245 58.47 69.36 0.238 58.40 75.57 0.175 58.62 76.80 0.269 58.66 71.49 0.270 58.41 89.78 0.266 58.53 79.50 0.300 58.53 73.38 0.306 58.42 79.28 0.299 38.28 65.65 0.300 38.05 66.09 0.303 38.14 53.38 0.306 38.11 48.60 0.307 38.18 50.16 0.343 38.23 70.71 0.329 74.22 85.83 0.216 75.02 90.06 0.203 74.98 84.13 0.218 74.96 86.59 0.217 Tin C 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 94.3 Evaporator Liquid Pressure Tevap Speed kg/hr torr C rpm 1.279 40.4 40.6 360 1.277 39.8 40.3 540 0.530 39.8 40.3 360 1.313 39.8 40.5 180 0.599 39.8 40.4 180 0.893 39.7 40.5 360 1.279 39.7 40.5 540 0.504 29.1 34.7 360 0.858 29.1 34.7 360 1.239 29.1 34.7 360 0.857 29.1 34.7 360 0.433 38.9 36.2 360 0.429 38.7 36.0 540 0.793 38.8 36.1 360 1.160 38.8 36.1 360 1.124 29.1 31.0 360 0.402 29.0 30.9 360 1.383 38.3 46.3 360 1.000 38.3 46.8 360 1.793 38.3 46.8 360 1.389 38.3 46.8 360 Hot Oil Tout Flow C L/min 89.4 1.464 89.5 1.488 89.9 1.469 89.7 1.438 90.8 1.451 89.4 1.438 89.3 1.441 88.9 1.425 89.0 1.421 89.5 1.386 89.3 1.384 88.9 1.436 89.2 1.436 89.0 1.447 89.0 1.450 88.7 1.443 88.9 1.432 90.0 1.438 90.2 1.444 89.8 1.437 90.0 1.440 Table 5.14: Experimental data for water-ethylene glycol at different operating conditions. Feed kg/hr 1.125 1.495 1.871 1.121 1.118 1.498 Ethylene Glycol xin Vapor y xout % kg/hr % % 72.78 0.209 1.99 88.70 73.62 0.211 1.57 85.37 73.89 0.217 1.87 83.34 73.98 0.202 2.30 89.66 74.16 0.207 2.12 90.47 73.73 0.359 4.15 95.71 Evaporator Liquid Pressure Tevap Speed kg/hr torr C rpm 0.916 32.0 45.1 360 1.284 35.1 43.5 361 1.654 35.0 44.3 359 0.920 32.0 44.4 360 0.911 32.0 43.9 540 1.139 31.8 48.8 538 Hot Oil Tin Tout Flow C C L/min 94.3 90.1 1.448 94.3 89.9 1.444 94.3 89.9 1.497 94.3 90.2 1.464 94.3 90.2 1.467 119.2 113.5 1.666 102 Chapter 6 Analysis of Experimental Results and Model Validation 6.1 Isothermal Flash A wiped film evaporator is thought to be simulated using a commercial process simulator as an isothermal flash to calculate the required heat duty and composition distribution of the vapor and liquid streams. Experimental results are presented which are compared with theoretical calculations assuming an isothermal flash. 6.1.1 Water-Sucrose When applying the flash Equations 3.42-3.45 to the water-sucrose system, as shown in Figure 6.1, results are consistent with the experimental residue concentration for the wiped film evaporator. The calculations are based on Equations 5.11-5.17 to predict the activity coefficient and 5.8 for the prediction of enthalpy. When using group contribution methods (GCM) for this system, the predicted concentration of water presents a small deviation from the experimental results, but it is still within 5%. The deviation can be attributed to the prediction of activity coefficients by the UNIFAC method. Figure 6.2 presents the relative error for the compositions when using the two 103 methods for activiy coefficient and enthalpy. Figure 6.1: Predicted concentration of water when simulating the wiped film evaporator as an isothermal flash for the water-sucrose system. The good agreement between the experimental and predicted concentrations is a result of the nearly isothermal conditions of the experimental data. 104 Figure 6.2: Relative error when simulating the wiped film evaporator as an isothermal flash for the water-sucrose system. 6.1.2 Water-Glycerol When applying the flash equations to the water-glycerol system, the results, as shown in Figure 6.3, are somewhat consistent with the experimental compositions for the wiped film evaporator for both DIPPR and GCM predictions when the experimental composition of water is high (i.e., > 60%). 105 When the concentration of the exiting water is low, the deviations from the flash calculations is a little higher but whitin engineering design. The slight deviation is a result of the greater evaporation rate which results in a deviation in isothermal conditions. The average error shown in Figure 6.4 for this system is still well within engineering design. 6.1.3 Water-Ethylene Glycol The experimental data for this system is limited to six data points. The experimental results, shown in Figure 6.5 when applying the flash equations show more deviation than that predicted but are within 20%. The deviation is a result of a slight temperature difference (4-8 C) observed during the experimental runs. We suspect one of the data points to be bad. Figure 6.6 shows the relative error between the predicted and experimental concentration of water in the ethylene glycol liquid stream. 6.1.4 WFE as an Isothermal Flash As can be seen from the previous plots (Figures 6.1, 6.3, and 6.5), an isothermal flash can sometimes represent the product distribution of a wiped film evaporator. This is true when the temperature gradient in the evaporator is small (i.e., in the order of 1 - 2 C). When the gradient is significant (i.e., > 4 C), an isothermal flash is less likely to represent the results of a wiped film evaporator. 106 Figure 6.3: Predicted concentration of water when simulating the wiped film evaporator as an isothermal flash for the water-glycerol system. 6.2 Heat and Mass Transfer Coefficient In this section, the back-calculation of the process-side heat transfer W coefficient (hp ) and the prediction of the mass transfer coefficient (kL F E ) from the experimental data for the three systems is presented. 107 Figure 6.4: Relative error when simulating the wiped film evaporator as an isothermal flash for the water-glycerol system. 6.2.1 Experimental Heat Transfer Coefficient The process-side heat transfer coefficient was regressed using the data described in Chapter 5 using the Cargill wiped film evaporator and the three experimental systems (water-sucrose, water-glycerol, and water-ethylene glycol). The process side heat transfer coefficient (hp ) can be deduced by assuming 108 Figure 6.5: Predicted concentration of water when simulating the wiped film evaporator as an isothermal flash for the water-ethylene glycol system. a hot oil heat transfer coefficient model and using Equation 4.1. 1 1 wall 1 = + + Uov ho wall hp (4.1) 109 Figure 6.6: Relative error when simulating the wiped film evaporator as an isothermal flash for the water-ethylene glycol system. Solving for 1 , Equation 3.15 is obtained: hp (3.15) 1 1 1 1 = - - hp Uov Rwall ho where the wall resistance can be calculated as Rwall = wall , the heat transfer wall coefficient for the hot fluid side (ho ) is calculated using a model [90], and the 110 overall heat transfer coefficient (Uov ) measured from the experiments as: Uov = where: Qused = V Hvap,water + wCp (Tf eed - Tbot ) Tlm = (Th,i - Tbot ) - (Th,o - Ttop ) Th,i - Tbot ln Th,o - Ttop A = DL (6.2) (6.3) Qused A Tlm (6.1) (6.4) A sample calculation using the first point from Table 5.12 is presented 1.2 W/m-K = below. The wall resistance will be constant and equal to Rwall = 0.0025 m 480 W/m2 -K. The external resistance ho is calculated using Equations 3.17-3.18 [62]. The physical properties for the hot fluid are calculated at the average temperTh,i + Th,o ature using equations provided in the Appendix B, and shown in 2 Table 6.1 Table 6.1: Equations for the calculation of physical properties for Marlotherm SH [83]. Temperature in C Property Thermal conductivity Heat capacity Density Kinematic viscosity Equation = 0.1333 - 0.00013T Cp = 1.4745 + 0.003726T = 1058.4 - 0.7184T = 12294T -1.792 Units W/m-K J/kg-K kg/m3 mm2 /s 111 Tavg = Th,i + Th,o 94.3 + 90.4 = 2 2 Tavg = 92.35 = 0.1333 - 0.00013T = 0.1333 - 0.00013(92.35) = 0.1213 W/m-K Cp = 1.4745 + 0.003726T = 1.4745 + 0.003726(92.35) Cp = 1, 818.6 J/kg-K = 1058.4 - 0.7184T = 058.4 - 0.7184(92.35) = 992.06 kg/m3 = 12294T -1.792 = 992.06 12294(92.35)-1.792 = 0.00367 kg/m-s w = (1.5293 liter/min) 992.06 kg/m3 w = 0.0253 kg/s The equations from Sieder and Tate [90] are used to calculate the hot fluid side heat transfer coefficient ho : ho D -1/3 = 1.86n1 L n1 = 4wCp wall 0.14 1 1000 1 60 (3.17) (3.18) 112 Substituting values in these equations: n1 = (0.1213)(0.2141) L = 4wCp 4(0.0253)(1, 818.6) wall 3.67-3 15.4-3 0.14 0.14 n1 = 4.43 10-4 ho D -1/3 = 1.86n1 ho D = 1.86(4.43 10-4 )-1/3 0.1213 ho = 20.09 0.024 ho = 100.8 W/m2 -K It can be assumed that all the vapor stream is water, allowing one to calculate the theoretical amount of heat to vaporize the stream. The heat of vaporization of water is calculated using the DIPPR [22] equation: Hvap,water 52053 T = 1- 18.01528 Tc T T 0.3199-0.212 T +0.25795( T c c ) 2 kJ/kg (6.5) Then the necessary amount of heat to vaporize an amount of water is: Qreq = V Hvap,water + wCp (Tf eed - Tbot ) The required heat for this case is: (6.6) Hvap,water = 52053 313.05 1- 18.01528 647.096 313.05 313.05 0.3199-0.212 647.096 +0.25795( 647.096 ) 2 Hvap,water = 2404.68 kJ/kg Qreq = 0.2765 2404.57 103 + 4.55 10-4 3043.5 (40 - 30) 3600 Qreq = 198.53 W 113 The next to last step to calculate hp is to calculate the overall heat transfer coefficient Uov : Tlm = Tlm (94.3 - 40) - (90.4 - 39.8) 94.3 - 40 ln 90.4 - 39.8 = 52.43 198.53 (0.08)(0.2141) 52.43 (6.7) (6.8) (6.9) (6.10) Uov = Uov = 70.37 W/m2 -K Finally, hp is calculated: 1 1 1 1 = - - hp Uov Rwall ho 1 1 1 1 = - - = 0.014211 - 0.002083 - 0.009921 hp 70.37 480 100.8 1 = 0.0021171 hp hp = 472.3 W/m2 -K The above procedure is applied to all the experimental data from Tables 5.12, 5.13, and 5.14. The results are presented in Tables 6.2, 6.3, and 6.4. Again, it should be noted that the calculation of the process side heat transfer coefficient required the assumption of a hot oil heat transfer coefficient model. As shown in this example, only 15% of the heat transfer resistance is present on the process side, while 70% of the resistance is on the hot oil side. In general, these results indicate the hot oil side heat trasnfer resistance was the controlling side. 114 Table 6.2: Experimental data for water-sucrose at different operating conditions with the experimental heat transfer coefficients. 115 Feed kg/hr 1.648 1.640 1.638 3.321 2.472 2.470 2.468 2.464 1.645 1.640 1.636 2.494 2.488 2.483 3.330 3.327 3.325 3.382 3.365 1.659 Tf eed C 29.0 30.0 30.0 31.8 29.7 31.6 31.8 32.5 30.0 30.2 31.0 28.7 29.0 29.0 28.0 29.0 29.5 29.5 30.5 27.0 Sucrose xin xout % % 46.94 56.61 46.92 56.47 46.97 57.04 47.29 51.56 47.68 53.59 47.87 53.90 47.84 53.99 47.87 53.77 47.89 57.18 47.96 58.08 47.96 58.24 48.22 54.94 48.30 55.33 48.41 55.74 48.59 53.37 48.61 53.62 48.55 53.60 50.48 54.74 49.62 53.87 49.25 60.09 Vapor kg/hr 0.275 0.277 0.281 0.264 0.262 0.273 0.272 0.268 0.267 0.278 0.281 0.306 0.312 0.316 0.294 0.306 0.307 0.246 0.253 0.309 Liquid kg/hr 1.374 1.363 1.354 3.052 2.196 2.200 2.189 2.197 1.377 1.360 1.354 2.183 2.174 2.156 3.030 3.018 3.013 3.115 3.097 1.350 P torr 55.0 55.0 54.9 54.1 54.3 54.5 54.5 54.5 54.9 54.9 54.9 41.2 41.3 41.2 41.2 41.2 40.8 54.8 54.8 40.2 Evaporator Ttop Tbot Speed C C rpm 39.8 42.8 300 39.8 40.0 420 39.9 40.0 540 39.8 40.0 540 39.5 40.0 180 40.0 40.0 360 39.9 40.0 540 39.8 40.0 180 39.9 40.0 180 39.9 40.0 360 39.9 40.0 539 34.9 35.0 182 34.9 35.0 360 35.0 35.0 540 35.0 35.0 180 35.1 35.0 360 35.0 35.0 540 39.8 40.0 181 40.0 40.0 360 35.1 35.0 180 HTC Uov ho hp W/m2 -K W/m2 -K W/m2 -K 71.8 101.6 502.5 71.3 100.8 497.1 72.5 101.0 550.0 72.4 100.6 556.4 72.2 101.7 519.3 72.5 102.1 523.5 71.8 101.4 504.6 72.3 103.4 483.7 70.1 101.5 430.1 72.0 101.0 525.7 72.1 100.7 536.4 75.1 100.1 801.0 74.7 98.7 850.9 74.9 99.3 835.9 76.9 101.1 972.5 76.6 100.3 993.5 75.3 98.6 952.3 73.7 102.1 590.1 73.2 101.2 592.5 74.1 101.9 625.7 Continued on next page Table 6.2 continued from previous page 116 Feed kg/hr 1.664 1.662 2.557 1.703 1.692 2.578 2.571 1.705 3.430 2.486 2.483 1.568 0.780 2.350 1.567 Tf eed C 27.5 27.8 29.6 28.7 30.0 27.5 28.0 28.8 29.2 30.4 30.5 25.5 27.2 29.4 30.0 Sucrose xin xout % % 49.85 62.03 49.76 62.19 55.21 61.59 55.39 65.82 53.66 64.21 53.98 61.26 54.02 61.58 53.98 66.32 54.16 59.57 47.56 53.22 47.52 53.33 36.31 43.91 36.31 57.01 36.27 40.85 36.27 45.86 Vapor kg/hr 0.325 0.332 0.263 0.266 0.272 0.306 0.312 0.313 0.309 0.271 0.273 0.269 0.284 0.257 0.327 Liquid kg/hr 1.337 1.330 2.288 1.431 1.412 2.271 2.256 1.389 3.117 2.216 2.213 1.299 0.496 2.087 1.237 P torr 40.0 40.0 55.2 56.1 55.9 41.9 41.9 42.0 41.8 55.7 55.7 59.1 59.1 59.1 42.1 Uov W/m2 -K 75.1 75.7 68.3 66.8 68.7 72.6 73.9 72.8 73.4 70.4 72.1 70.6 68.8 71.5 74.3 hp W/m2 -K 773.0 977.5 389.6 356.6 378.7 674.1 785.4 652.0 703.3 434.4 519.7 476.6 388.0 491.9 789.8 Evaporator Ttop Tbot Speed C C rpm 34.2 35.0 360 33.8 35.0 540 38.1 40.0 360 38.5 40.0 360 38.7 40.0 540 33.8 35.0 360 34.0 35.0 539 34.9 35.0 360 33.1 35.0 540 37.8 40.0 540 38.7 40.0 540 39.0 40.0 361 38.0 40.0 360 39.9 40.0 360 33.8 35.0 360 HTC ho W/m2 -K 100.7 98.9 100.0 99.2 101.6 98.0 98.3 98.7 98.9 101.8 101.3 100.2 101.2 101.2 98.8 Table 6.3: Experimental data for water-glycerol at different operating conditions with the experimental heat transfer coefficients. 117 Feed kg/hr 1.556 1.555 0.775 1.552 0.774 1.162 1.549 0.770 1.158 1.545 1.156 0.733 0.732 1.100 1.467 1.467 0.731 1.598 1.203 2.010 1.605 Glycerol xin xout Vapor % % kg/hr 57.85 70.90 0.277 58.01 71.04 0.278 58.00 85.16 0.245 58.47 69.36 0.238 58.40 75.57 0.175 58.62 76.80 0.269 58.66 71.49 0.270 58.41 89.78 0.266 58.53 79.50 0.300 58.53 73.38 0.306 58.42 79.28 0.299 38.28 65.65 0.300 38.05 66.09 0.303 38.14 53.38 0.306 38.11 48.60 0.307 38.18 50.16 0.343 38.23 70.71 0.329 74.22 85.83 0.216 75.02 90.06 0.203 74.98 84.13 0.218 74.96 86.59 0.217 Liquid kg/hr 1.279 1.277 0.530 1.313 0.599 0.893 1.279 0.504 0.858 1.239 0.857 0.433 0.429 0.793 1.160 1.124 0.402 1.383 1.000 1.798 1.389 Evaporator Pressure Tevap Speed torr C rpm 40.4 40.6 360 39.8 40.3 540 39.8 40.3 360 39.8 40.5 180 39.8 40.4 180 39.7 40.5 360 39.7 40.5 540 29.1 34.7 360 29.1 34.7 360 29.1 34.7 360 29.1 34.7 360 38.9 36.2 360 38.7 36.0 540 38.8 36.1 360 38.8 36.1 360 29.1 31.0 360 29.0 30.9 360 38.3 46.3 360 38.3 46.8 360 38.3 46.8 360 38.3 46.8 360 HTC Uov ho 2 W/m -K W/m2 -K 72.5 98.4 72.3 98.7 60.0 98.2 63.0 97.6 43.8 97.8 67.6 97.7 69.2 97.8 65.1 93.7 74.2 93.7 76.5 92.8 73.7 92.8 74.2 95.0 74.7 94.8 76.7 95.1 77.4 95.2 84.2 91.5 79.8 91.2 57.1 101.0 52.3 101.4 58.6 101.3 56.3 101.3 hp W/m2 -K 478.3 462.4 456.0 217.0 97.5 489.6 412.2 965.2 783.4 655.8 763.4 637.6 686.3 567.9 532.3 1010.2 1183.4 287.8 341.1 274.4 319.5 Table 6.4: Experimental data for water-ethylene glycol at different operating conditions with the experimental heat transfer coefficients. Ethylene Glycol xin Vapor y xout % kg/hr % % 72.78 0.209 1.99 88.70 73.62 0.211 1.57 85.37 73.89 0.217 1.87 83.34 73.98 0.202 2.30 89.66 74.16 0.207 2.12 90.47 73.73 0.359 4.15 95.71 Liquid kg/hr 0.916 1.284 1.654 0.920 0.911 1.139 Evaporator Pressure Tevap Speed torr C rpm 32.0 45.1 360 35.1 43.5 361 35.0 44.3 359 32.0 44.4 360 32.0 43.9 540 31.8 48.8 538 Hot Oil Uov ho W/m2 -K W/m2 -K 66.8 98.2 71.5 99.4 70.9 100.7 64.7 98.9 67.8 99.0 78.9 97.8 hp W/m2 -K 368.4 542.1 477.9 306.5 378.5 2680.0 Feed kg/hr 1.125 1.495 1.871 1.121 1.118 1.498 118 Figure 6.7 shows the experimental heat transfer coefficient for the process side (hp ) for water/glycerol at 35 C and 360 rpm and for water/sucrose at 40 C and 360 rpm, as a function of the liquid feed rate, for two different feed concentration of glycerol and three feed concentrations of sucrose. As the flowrate is increased, the HTC increases as expected. This trend is present in other studies of heat transfer coefficients in WFE. When plotting the process side HTC as a function of the film Reynolds number for the same system and conditions (water/glycerol at 360 rpm and 35 C, and water/sucrose at 360 rpm and 40 C), as depicted in Figure 6.8, a similar behavior is observed as for the flowrate. The heat transfer coefficient increases with the film Reynolds number increases, and decreases when the feed concentration is increased. Figure 6.9 shows the experimental heat transfer coefficient for the process side (hp ) for the water/glycerol system as a function of the rotational Reynolds number evaluated at 360 rpm and 35 C for two different concentration of glycerol in the feed, and for water/sucrose at 360 rpm and 40 C and three different feed concentrations of sucrose. The same functionality shown in Figure 6.8 (film Reynolds number) was observed. Figure 6.10 shows the ratio of the Nusselt number divided by the product of the film Reynolds number, rotational Reynolds number, and rotational speed as a function of the Prandtl number for the same water/glycerol and water/sucrose data points. 119 Figure 6.7: Experimental heat transfer coefficient for the process side as a function of the liquid feed flow rate for water/glycerol at 360 rpm and 35 C and water/sucrose at 360 rpm and 40 C. 6.2.2 Predicted Mass Transfer Coefficient A WFE mass transfer coefficient model is proposed which relates the ratio of the WFE heat transfer coefficient and the FFE heat transfer coefficient. The ratio is assumed to apply to mass transfer because of the analogy of heat 120 Figure 6.8: Experimental heat transfer coefficient for the process side as a function of the film Reynolds number for water/glycerol at 360 rpm and 35 C and water/sucrose at 360 rpm and 40 C. and mass transfer. The heat enhancement factor is predicted with the following equation: h = hW F E p hF F E p (4.6) F And the mass transfer coefficient for a falling film (kL F E ) with the 121 Figure 6.9: Experimental heat transfer coefficient for the process side as a function of the rotational Reynolds number. correlation from Yih and Chen [102]: F kL F E = a Reb ScL f 1/2 DL L g 1/3 L 2/3 2/3 (3.35) W The mass transfer coefficient for wiped film evaporator (kL F E ) is pre- 122 Figure 6.10: Experimental heat transfer coefficient for the process side as a function of the Prandtl number. dicted with the equation: W F kL F E = h kL F E (4.29) Two WFE and two FFE heat transfer coefficient models were evaluated. As a result, four possible combinations of the heat enhancement factor were 123 W evaluated. Tables 6.5, 6.6, and 6.7 show the correlated values for kL F E for water-sucrose, water-glycerol, and water-ethylene glycol, respectively. Figures 6.11, 6.12, and 6.13 show the predicted mass transfer coefficient as a function of the dimensionless Sherwood number for the liquid at different feed concentration. This number is obtained using the models of Bott and Romero [11] for the HTC for the WFE, Ahmed and Kaparthi [3] for the HTC for the FFE, and Yih and Chen [102] for the mass transfer coefficient for the FFE, as follows: ShW F E = h ShF F E L L h = ShF F E = L 0.48 0.018Re0.46 Re0.6 P r0.87 D N f L 0.345 0.4 6.92 10-3 ReL P rL 1/2 1.099 10-2 Re0.3955 ScL f (6.11) Nb0.24 (6.12) (6.13) substituting the correlations for the Sherwood number for WFE: 0.5105 0.47 ShW F E = 0.02859Ref Re0.6 P rL (D/L)0.48 Nb0.24 Sc0.5 L N L (6.14) Figure 6.11 shows that the average mass transfer coefficient increases when the concentration of water in the feed is higher (i.e., lower viscosity). As the viscosity of the system increases (i.e., more sucrose), the resistance to mass transfer increases. 124 W Table 6.5: Predicted average mass transfer coefficient for the water-sucrose system, kL F E 104 , m/s. Physical properties were calculated using fitted correlations from experimental data [60] and Group Contribution Methods (GCM) Ref ReN 125 Feed kg/hr 1.564 0.780 1.568 2.350 1.659 2.494 3.330 2.472 2.464 3.382 1.645 1.648 1.664 3.327 2.488 2.470 3.365 1.640 1.640 1.662 0.73 4710.5 0.73 6643.0 0.70 8332.8 2.00 10413.7 1.28 3098.3 1.28 6168.1 1.26 9196.2 1.27 3080.2 0.68 2643.8 0.64 5052.5 0.63 7506.1 0.98 2429.7 0.95 4700.9 0.93 6901.4 1.45 2551.9 1.43 5060.2 1.43 7589.3 1.52 2630.2 1.66 5711.0 0.44 1774.7 W P r kL F E , Equations 5.6-5.10, 5.11-5.17 BS-AK BS-N BR-AK BR-N 56.1 1.86 4.31 3.03 7.02 55.7 2.25 5.25 3.47 8.06 57.1 2.59 6.04 3.81 8.88 45.2 4.39 9.43 5.71 12.25 50.9 1.81 4.02 2.97 6.59 51.2 2.67 5.95 3.87 8.64 51.5 3.39 7.58 4.60 10.27 51.3 1.77 3.94 2.89 6.44 60.2 1.29 3.00 2.25 5.24 63.1 1.90 4.46 2.95 6.91 63.7 2.40 5.64 3.46 8.14 66.4 1.56 3.55 2.43 5.52 67.9 2.33 5.31 3.21 7.33 69.5 2.91 6.67 3.74 8.56 62.3 1.88 4.14 2.76 6.09 62.9 2.82 6.23 3.68 8.12 62.9 3.59 7.94 4.37 9.67 60.9 1.85 4.05 2.72 5.97 55.5 2.95 6.45 3.94 8.59 91.1 1.01 2.45 1.64 3.96 W kL F E , GCM BS-AK BS-N BR-AK BR-N 10.11 18.69 25.81 47.69 12.03 22.29 29.10 53.94 13.92 25.81 32.27 59.86 21.36 37.01 42.34 73.38 9.46 16.81 24.03 42.68 13.58 24.21 30.82 54.96 17.25 30.78 36.57 65.26 8.81 15.69 22.53 40.16 7.00 12.94 19.55 36.11 10.45 19.38 25.99 48.21 13.00 24.15 30.27 56.22 8.29 14.93 20.83 37.52 12.38 22.33 27.70 49.98 15.61 28.20 32.64 58.95 10.04 17.57 23.60 41.32 14.78 25.92 31.00 54.36 18.61 32.68 36.46 64.03 10.41 17.95 24.71 42.62 15.91 27.50 33.66 58.18 6.02 11.28 16.59 31.07 Continued on next page Table 6.5 continued from previous page Ref ReN 126 Feed kg/hr 3.325 2.483 3.321 2.468 1.636 1.638 2.486 2.483 2.578 1.705 2.557 1.703 3.430 2.571 1.692 0.36 2971.0 0.35 4361.5 0.55 2632.4 0.26 2025.2 0.32 3796.8 0.49 2393.0 0.48 3537.0 0.23 1818.0 0.72 3810.4 1.24 8947.1 1.28 9207.3 1.69 13252.1 0.39 8168.3 3.08 14859.3 1.29 10663.4 BR-N 40.19 56.05 43.21 37.34 46.18 41.63 48.90 35.58 52.55 68.66 68.66 89.55 60.08 95.93 68.84 W P r kL F E , Equations 5.6-5.10, 5.11-5.17 BS-AK BS-N BR-AK BR-N 109.6 1.43 3.52 2.02 4.96 112.1 2.13 5.08 2.96 7.05 124.6 1.55 3.71 1.92 4.59 163.6 1.09 2.75 1.42 3.59 129.8 1.57 3.91 2.00 4.96 137.2 1.53 3.70 1.86 4.49 139.1 1.93 4.67 2.19 5.28 182.5 1.07 2.72 1.37 3.50 128.9 2.38 5.56 2.57 5.99 53.0 3.53 7.83 4.82 10.70 51.4 3.54 7.86 4.84 10.75 22.8 4.48 9.60 8.59 18.42 38.0 2.25 5.25 4.84 11.26 20.1 6.09 12.46 10.84 22.20 28.6 3.89 8.52 7.16 15.67 W kL F E , GCM BS-AK BS-N BR-AK 8.72 16.38 21.39 13.13 24.28 30.30 10.73 19.08 24.30 8.12 15.02 20.20 10.72 19.86 24.93 10.36 18.64 23.15 13.00 23.41 27.15 7.72 14.48 18.98 15.28 26.79 29.99 18.29 32.53 38.61 18.29 32.52 38.60 19.76 36.24 48.84 10.39 20.44 30.52 23.82 42.16 54.19 14.79 27.81 36.61 W Table 6.6: Predicted average mass transfer coefficient for the water-glycerol system, kL F E 104 , m/s. Physical properties were calculated using DIPPR equations and Group Contribution Methods (GCM) Ref ReN Pr 127 Feed kg/hr 1.555 0.774 1.203 2.010 1.605 1.598 1.161 1.158 1.545 1.156 0.770 0.775 1.556 0.733 0.731 1.467 1.100 1.467 1.549 1.554 0.731 2.40 0.89 0.73 1.26 0.95 1.35 1.50 1.03 1.72 1.08 0.60 0.84 2.32 1.58 1.15 3.03 2.75 4.11 2.34 2.48 1.49 W kL F E , DIPPR BS-AK BS-N BR-AK 7183.7 24.0 1.31 2.75 2.51 5752.9 32.0 0.78 1.77 1.68 5930.5 62.8 0.86 2.03 1.27 6114.1 60.6 1.14 2.57 1.53 5833.2 64.1 0.98 2.26 1.36 7796.0 46.6 1.28 2.85 1.87 12629.6 28.1 1.61 3.54 2.87 9118.7 41.2 1.35 3.06 2.27 10844.5 32.6 1.72 3.75 2.80 9509.4 38.8 1.34 3.04 2.27 8084.1 50.5 0.92 2.17 1.65 11092.3 33.9 1.14 2.61 2.16 14188.4 24.5 1.93 4.08 3.29 22212.8 15.0 2.14 4.64 4.94 17233.3 20.2 1.93 4.38 4.27 20651.7 15.8 3.31 6.83 6.47 24336.9 13.2 3.28 6.81 7.02 25863.1 12.2 3.97 7.97 8.04 14120.1 24.5 1.94 4.11 3.31 22189.1 23.3 2.60 5.49 4.18 32291.8 15.7 2.84 6.26 6.11 W kL F E , GCM BR-N BS-AK BS-N BR-AK 5.29 1.29 2.78 2.12 3.81 0.77 1.83 1.38 3.00 0.80 1.99 0.91 3.44 1.17 2.72 1.24 3.15 0.98 2.36 1.07 4.18 1.13 2.66 1.29 6.31 1.60 3.62 2.42 5.17 1.40 3.25 2.01 6.10 1.73 3.87 2.43 5.15 1.37 3.18 1.99 3.92 0.90 2.21 1.37 4.98 1.11 2.63 1.76 6.97 1.93 4.19 2.84 10.72 2.14 4.72 4.50 9.73 1.89 4.29 3.79 13.35 3.44 7.17 6.19 14.59 3.30 6.94 6.48 16.16 3.97 8.06 7.42 7.01 1.91 4.15 2.78 8.80 2.52 5.46 3.47 13.49 2.85 6.31 5.56 BR-N 4.58 3.31 2.27 2.90 2.58 3.04 5.47 4.69 5.42 4.61 3.35 4.19 6.15 9.89 8.58 12.91 13.62 15.08 6.04 7.50 12.31 Figure 6.11: Predicted average mass transfer coefficient for the watersucrose system as a function of the dimensionless Sherwood number (ShW F E = L 0.47 0.5 0.02859Re0.5105 Re0.6 P rL (D/L)0.48 Nb0.24 ScL ) at different water concentraN f tions in the feed. 128 Figure 6.12: Predicted average mass transfer coefficient for the waterglycerol system as a function of the dimensionless Sherwood number 0.47 (ShW F E = 0.02859Re0.5105 Re0.6 P rL (D/L)0.48 Nb0.24 Sc0.5 ) and different conL N L f centrations of water in the feed 129 Figure 6.13: Predicted average mass transfer coefficient for the waterethylene glycol system as a function of the dimensionless Sherwood number 0.47 (ShW F E = 0.02859Re0.5105 Re0.6 P rL (D/L)0.48 Nb0.24 Sc0.5 ). L N L f 130 W Table 6.7: Predicted average mass transfer coefficient for the water-ethylene glycol system, kL F E 105 , m/s. Physical properties were calculated using DIPPR equations and Group Contribution Methods (GCM) W kL F E , DIPPR BS-AK BS-N BR-AK BR-N BS-AK 1.70 14720.0 30.6 0.78 1.70 1.27 2.76 0.79 2.74 16927.2 25.6 1.05 2.19 1.63 3.41 1.06 3.37 16664.8 26.1 1.15 2.37 1.71 3.51 1.17 1.57 13797.9 33.5 0.73 1.59 1.15 2.53 0.74 1.55 20582.9 33.8 0.92 2.02 1.36 2.99 0.94 2.09 20728.2 33.6 1.08 2.30 1.50 3.22 1.03 Feed kg/hr 1.125 1.495 1.871 1.121 1.118 1.498 Ref ReN Pr W kL F E , GCM BS-N BR-AK 1.72 1.30 2.21 1.67 2.38 1.75 1.61 1.19 2.05 1.41 2.20 1.44 BR-N 2.82 3.48 3.58 2.59 3.09 3.09 131 6.3 WFE-SRP Model Applied to Experimental Data The rigorous WFE-SRP computer program was used to analyze the experimental data. The program has the option of using actual, DIPPR equations and group contribution methods (GCM) to predict the physical properties. A comparison is presented for the three experimental systems. WFE-SRP has two models for the prediction of the process side heat transfer coefficient for a wiped film evaporator [11, 14] and two for the falling film evaporator [3, 75], thus giving four different combinations for the heat enhancement factor (h ), and predicting four different exiting concentrations of water. The following sections present the results when the computer program is applied to the experimental data for each system. 6.3.1 Water-Sucrose The WFE-SRP program was used with Equations 5.6-5.10 for the prediction of physical properties (fitted from experimental properties for water/sucrose solutions), and the modified UNIQUAC equations from Peres and Macedo [77] for the prediction of the activity coefficients (Equations 5.11-5.17), as well as the group contribution methods for physical properties and activity coefficient. Figure 6.14 shows the prediction of the concentration of water when using Bott and Romero [11] for the HTC of the wiped film evaporator and Ahmed and Kaparthi [3] for the falling film evaporator, while Figure 6.15 presents the relative error using the same equations. The average error for the combination of the equations was 0.15%, and for the GCM was 1.82%. 132 The experiments using water-sucrose were run at different inlet concentrations of sucrose, varying from 35 to 55 wt percent. They were not run at higher concentrations due to the solubility limit of sucrose in water at 20 C. Outlet concentrations varied from 40 to 66 wt percent of sucrose. From Figure 6.14 it can be seen that the computer program predicts the exiting concentration of water with good accuracy when using Equations 5.65.10 for physical properties and 5.11-5.17 for the activity coefficient. The GCM option is less accurate. This is primarily due to the estimation of viscosity and liquid enthalpies that are very different from the actual values. When the evaporation rate is low (i.e., concentration of water > 0.95) the prediction is more accurate than when the evaporation rate is high. Using the combination of equations with the Bott and Sheikh [14] correlation for the wiped film evaporator, gives a similar result as shown in Figure 6.16. The average error was 0.15% and 1.81%. Figure 6.17 depicts the relative error for this combination. From these plots, it can be seen than when using the Equations 5.65.10 for the prediction of physical properties, and the modified UNIQUAC equations from Peres and Macedo [77] for the prediction of the activity coefficients (Equations 5.11-5.17) in the WFE-SRP program, the prediction of exiting composition of water is very accurate. This confirms that the proposed model predicts the behavior of the water-sucrose system. 133 Figure 6.14: Predicted versus experimental exiting concentration of water using WFE-SRP for the water-sucrose system when using Equations 5.6-5.17 and GCM for physical properties and Bott and Romero-Ahmed and Kaparthi for HTC. 6.3.2 Water-Glycerol The WFE-SRP program was used with the DIPPR equations, as well as the group contribution methods, for the prediction of physical properties. 134 Figure 6.15: Relative error of the experimental exiting concentration of water using WFE-SRP for the water-sucrose system when using Equations 5.65.17 and GCM for physical properties and Bott and Romero-Ahmed and Kaparthi for HTC. Figure 6.18 shows the prediction of the concentration of water when using Bott and Romero [11] for the HTC of the wiped film evaporator and Ahmed and 135 Figure 6.16: Predicted versus experimental exiting concentration of water using WFE-SRP for the water-sucrose system when using Equations 5.6-5.17 and GCM for physical properties and Bott and Sheikh-Ahmed and Kaparthi for HTC. Kaparthi [3] for the falling film evaporator. Figure 6.19 presents the relative error using the same equations. The average error for the combination of the 136 Figure 6.17: Relative error of the experimental exiting concentration of water using WFE-SRP for the water-sucrose system when using Equations 5.65.17 and GCM for physical properties and Bott and Sheikh-Ahmed and Kaparthi for HTC. equations was 16.95%, and for the GCM was 5.14%. These experiments were also run at different inlet concentrations of 137 glycerol, varying from 38 to 75 wt percent. The outlet concentrations varied from 48 to 90 wt percent of glycerol. From Figure 6.18 it can be seen that the computer program predicts the exiting concentration of water with excellent accuracy for all the range of exiting water composition. The GCM method works even better than the DIPPR prediction for this system. Using the combination of equations with the Bott and Sheikh [14] correlation for wiped film evaporators, gives a similar result as shown in Figure 6.20. The average error was 16.89% and 5.09%. Figure 6.21 shows the relative error for this combination. 138 Figure 6.18: Predicted versus experimental exiting concentration of water using WFE-SRP for the water-glycerol system when using DIPPR and GCM for physical properties and Bott and Romero-Ahmed and Kaparthi for HTC. 6.3.3 Water-Ethylene Glycol These experiments were run at only one inlet concentration of ethylene glycol, around 75 wt percent. The outlet concentrations varied from 83 to 95 139 Figure 6.19: Relative error of the experimental exiting concentration of water using WFE-SRP for the water-glycerol system when using DIPPR and GCM for physical properties and Bott and Romero-Ahmed and Kaparthi for HTC. wt percent of glycerol. Physical properties for this system can be predicted using the equations 140 Figure 6.20: Predicted versus experimental exiting concentration of water using WFE-SRP for the water-glycerol system when using DIPPR and GCM for physical properties and Bott and Sheikh-Ahmed and Kaparthi for HTC. reported by M. Conde Engineering [57]. The equations for each property are as follows. 141 Figure 6.21: Relative error of the experimental exiting concentration of water using WFE-SRP for the water-glycerol system when using DIPPR and GCM for physical properties and Bott and Sheikh-Ahmed and Kaparthi for HTC. 142 Density, kg/m3 L = 658.49825 - 54.81501 wt + 664.71643 + 232.72605 wt 273.15 - 322.61661 T 273.15 + T 2 273.15 T (6.15) Heat Capacity, kJ/kg-K CpL = 5.36449 + 0.78863 wt - 2.59001 - 2.73187 wt 273.15 + 1.43759 T 273.15 + T 2 273.15 T (6.16) Thermal Conductivity, W/m-K L = 0.83818 - 1.3762 wt - 0.07629 + 1.0772 wt 273.15 - 0.20174 T 273.15 + T 2 273.15 T 273.15 + T 2 273.15 T (6.17) Viscosity, Pas ln(L ) = -4.63024 - 2.14817 wt - 12.70106 + 5.40536 wt 273.15 + 10.9899 T (6.18) In the previous equations, wt is the weight fraction of ethylene glycol in the solution and T is the temperature in K. The WFE-SRP computer program was also used with the DIPPR equations, group contribution methods, and previous equations for the actual physical properties for the experimental data points. Figure 6.22 shows the prediction of the concentration of water when using Bott and Romero [11] for the HTC of the wiped film evaporator and Ahmed and Kaparthi [3] for the 143 falling film evaporator, while Figure 6.23 presents the relative error using the same equations. The average error for the combination of the equations was 61.95%, for the GCM was 29.58%, and when using actual physical properties the error was 14.59% From Figure 6.22, it can be seen that the computer program predicts the exiting concentration of water with good accuracy for the range of exiting water composition. The GCM method works better than the DIPPR prediction for this system, but using the correlations for the prediction of physical properties is even better: the average error was lower. This was also the case for the water/sucrose system. Using the combination of equations with the Bott and Sheikh [14] correlation for a wiped film evaporator, gives a similar result as shown in Figure 6.24. The average error was 62.13%, 25.99%, and 12.01%. Figure 6.25 shows the relative error for this combination. 144 Figure 6.22: Predicted versus experimental exiting concentration of water using WFE-SRP for the water-ethylene glycol system when using DIPPR, GCM, and actual correlations for physical properties and Bott and RomeroAhmed and Kaparthi for HTC. 145 Figure 6.23: Relative error of the experimental exiting concentration of water using WFE-SRP for the water-ethylene glycol system when using DIPPR and GCM for physical properties and Bott and Romero-Ahmed and Kaparthi for HTC. 146 Figure 6.24: Predicted versus experimental exiting concentration of water using WFE-SRP for the water-ethylene glycerol system when using DIPPR, GCM, and actual correlations for physical properties and Bott and SheikhAhmed and Kaparthi for HTC. 147 Figure 6.25: Relative error of the experimental exiting concentration of water using WFE-SRP for the water-ethylene glycol system when using DIPPR and GCM for physical properties and Bott and Sheikh-Ahmed and Kaparthi for HTC. 148 Chapter 7 Conclusions and Future Work 7.1 Wiped Film Evaporator as an Isothermal Flash The results of this study reveal that a wiped film evaporator (WFE) can be treated as an isothermal flash in a process simulator. Some deviations can be expected for systems where high evaporation rates are expected. Figures 6.1, 6.3, and 6.5 show the good agreement of the experimental exiting concentration of water for the three systems when the wiped film evaporator is treated as an isothermal flash. When any of the mentioned conditions are met, the WFE can be treated as an isothermal flash in a process simulator. It should be pointed out that when using the simulator, the results will only provide required heat duty and product distribution of vapor and liquid. The effect of the number of blades or the rotational speed on the heat duty and product distribution could not be evaluated. 149 7.2 Proposed Model: Simultaneous Heat and Mass Transfer The proposed rigorous model for considering the simultaneous heat and mass transfer in the wiped film evaporator is appropriate, from the results presented in Chapter 6, especially when the physical properties are predicted with good accuracy, like the fitted equations from experimental data for the water-sucrose system [60]. The agreement of the proposed model with the experimental data is shown in Figures 6.14 and 6.16 for water-sucrose, 6.18 and 6.20 for water-glycerol, and 6.22...
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