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Introduction to the surface renewal model of mass transfer for the analysis and design of gas-liquid contacting equipment and membrane filters Applications of the Surface Renewal Model of Mass Transfer provides a rigorous application of the surface renewal theory of mass transfer to describe physical and chemical gas absorption and membrane filtration. This book demonstrates that the surface renewal model can predict the experimentally measured liquid-side physical mass-transfer coefficient in gas absorption with a fair degree of accuracy, shows that the surface renewal model can…mehr
Introduction to the surface renewal model of mass transfer for the analysis and design of gas-liquid contacting equipment and membrane filters
Applications of the Surface Renewal Model of Mass Transfer provides a rigorous application of the surface renewal theory of mass transfer to describe physical and chemical gas absorption and membrane filtration. This book demonstrates that the surface renewal model can predict the experimentally measured liquid-side physical mass-transfer coefficient in gas absorption with a fair degree of accuracy, shows that the surface renewal model can correlate permeate flux and transmembrane pressure drop data in constant pressure and constant flux microfiltration, and contains numerous examples of the application of the model to real-world situations.
This book includes information on:
Applications of the surface renewal model in fields like chemical engineering and oceanography
The complex nature of the surface renewal model as a better description of the turbulent hydrodynamics that prevail at the gas-liquid interface compared to the film model
Measurements of the liquid-side physical mass-transfer coefficient in gas absorption studies and surface-age distributions in wind-wave tanks
Flow instabilities induced by wall roughness or spacers or by their deliberate introduction into the main flow in membrane filtration
Analysis and design of gas-liquid contactors (stirred tanks and packed towers) and membrane filters using a mass-transfer approach
Applications of the Surface Renewal Model of Mass Transfer is an excellent, first-of-its-kind reference for researchers in academia and industry, along with advanced students in chemical engineering, environmental engineering, bioprocess/biological engineering, paper engineering, and related programs of study.
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Autorenporträt
Dr. Hengshuo Huang is a dedicated researcher specializing in chemical engineering and environmental biotechnology. His postdoctoral research at Peking University, where he is Assistant Research Fellow under Professor Shaojun Guo, focuses on gas diffusion electrode modeling via finite element analysis and machine learning for electrochemical applications.
Dr. Siddharth G. Chatterjee is Associate Professor Emeritus in the Department of Chemical Engineering at SUNY College of Environmental Science and Forestry in Syracuse, New York, USA.
Inhaltsangabe
Preface xiii About the Companion Website xv 1 The Surface Renewal Model of Mass Transfer 1 1.1 Introduction 1 1.2 Literature Review 2 References 8 2 Age-Distribution Function of the Surface Renewal Model 15 2.1 Introduction 15 2.2 Danckwerts Age Distribution 15 2.2.1 Case 1 16 2.2.2 Case 2 17 2.3 Generalized Danckwerts Age Distribution 19 Notation 23 Greek Letters 24 Homework Exercises 24 References 24 3 Physical Gas Absorption in a Large Volume of Liquid 27 3.1 Introduction 27 3.2 Rates of Absorption and Dissolved-Gas Transfer 27 3.3 Comparison of the Surface Renewal Model with Experimental Data 32 Notation 34 Greek Letters 35 Homework Exercises 35 References 35 4 Physical Gas Absorption in a Stirred Batch Cell 37 4.1 Introduction 37 4.2 Interfacial Mass-Transfer Model 38 4.2.1 Zero Gas-Phase Mass-Transfer Resistance 38 4.2.2 Finite Gas-Phase Mass-Transfer Resistance 42 4.3 Philosophical Interlude 45 4.4 Bulk Mass-Transfer Model 46 4.4.1 Zero Gas-Phase Mass-Transfer Resistance 47 4.4.2 Finite Gas-Phase Mass-Transfer Resistance 47 4.5 Analytical Expressions for the Rates of Absorption and Dissolved-Gas Transfer Using the Laplace Transform Method 48 4.5.1 Gaver-Stehfest Algorithm 48 4.5.2 Zero Gas-Phase Mass-Transfer Resistance 49 4.5.3 Finite Gas-Phase Mass-Transfer Resistance 50 4.6 Conventional Pseudo-Steady-State LDF Model 52 4.7 Absorption of Oxygen and Hydrogen in Water 52 Notation 64 Greek Letters 66 Homework Exercises 66 References 67 5 Gas Absorption with First-Order Reaction in a Stirred Batch Cell 69 5.1 Introduction 69 5.2 Interfacial Mass-Transfer Model 72 5.2.1 Zero Gas-Phase Mass-Transfer Resistance 72 5.2.2 Finite Gas-Phase Mass-Transfer Resistance 78 5.3 Bulk Mass-Transfer Model 83 5.3.1 Zero Gas-Phase Mass-Transfer Resistance 84 5.3.2 Finite Gas-Phase Mass-Transfer Resistance 85 5.4 Analytical Expressions for the Rates of Absorption and Dissolved-Gas Transfer Using the Laplace Transform Method 85 5.4.1 Gaver-Stehfest Algorithm 85 5.4.2 Zero Gas-Phase Mass-Transfer Resistance 86 5.4.3 Finite Gas-Phase Mass-Transfer Resistance 88 5.5 Pseudo-Steady-State (PSS) Model 89 5.5.1 Zero Gas-Phase Mass-Transfer Resistance 89 5.5.2 Finite Gas-Phase Mass-Transfer Resistance 91 5.6 Absorption of Oxygen in Water Containing a Liquid-Phase Reagent (e.g., Na 2 SO 3) 91 Notation 100 Greek Letters 102 Acronyms 102 Homework Exercises 103 References 103 6 Gas Absorption with First-Order Reaction in a Packed Tower 107 6.1 Introduction 107 6.2 Surface Renewal Model 109 6.2.1 Physical Absorption 115 6.2.2 Liquid-Phase Control 116 6.2.3 Gas-Phase Control 117 6.3 Film Model 118 6.3.1 Physical Absorption 120 6.3.2 Liquid-Phase Control 120 6.3.3 Gas-Phase Control 120 6.4 Mass-Transfer and Hydraulic Correlations 121 6.5 Illustrative Calculations 122 6.5.1 System 1 124 6.5.2 System 2 126 6.5.3 System 3 128 6.5.4 Outlet Gas- and Liquid-Phase Concentrations as Functions of Hatta Number 129 6.5.5 Effect of Operational Gas and Liquid Mass Velocities on Gas Concentration Profile 131 6.5.6 Effect of Hatta Number on the Height and Number of Overall Gasand Liquid-Phase Mass-Transfer Units 133 Notation 135 Greek Letters 137 Homework Exercises 137 Acknowledgment 138 References 138 7 Gas Absorption with Instantaneous Reaction in a Packed Tower 141 7.1 Introduction 141 7.2 Theoretical Analysis 144 7.2.1 Film Model 145 7.2.1.1 Zero Gas-Phase Mass-Transfer Resistance 147 7.2.1.2 Finite Gas-Phase Mass-Transfer Resistance 152 7.2.2 Surface Renewal Model 153 7.2.2.1 Zero Gas-Phase Mass-Transfer Resistance 154 7.2.2.2 Finite Gas-Phase Mass-Transfer Resistance 160 7.3 Illustrative Calculations 166 7.3.1 Zero Gas-Phase Mass-Transfer Resistance 166 7.3.1.1 Tower Concentration Profiles 168 7.3.1.2 Movement of Reaction Front 170 7.3.2 Finite Gas-Phase Mass-Transfer Resistance 171 7.3.2.1 Validity of the Solution of the Surface Renewal Model 171 7.3.2.2 Tower Concentration Profiles 173 7.3.2.3 Effect of Concentration of B in the Incoming Liquid on Tower Performance 175 Notation 179 Greek Letters 182 Acronyms 182 Homework Exercises 182 References 183 8 Constant Pressure Crossflow Ultrafiltration (UF) 187 8.1 Introduction 187 8.2 Surface Renewal Model 188 8.2.1 Empirical Equation 190 8.2.2 Diffusion Equation 191 8.3 Film Model 196 8.4 Mass-Transfer Coefficient 196 8.5 Relation Between Limiting Flux and Transmembrane Pressure (tmp) 197 8.6 Application of the Surface Renewal and Film Models 197 8.6.1 UF of Cheese Whey 197 8.6.2 UF of Dextran Solutions 200 8.6.3 UF of Skim Milk 204 Notation 207 Greek Letters 208 Acronyms 209 Homework Exercises 209 Acknowledgment 209 References 210 9 Constant Pressure Crossflow Microfiltration 213 9.1 Introduction 213 9.2 Surface Renewal Model of Crossflow Microfiltration 216 9.2.1 Complete Model 216 9.2.2 Approximate Model 221 9.3 Correlation of the Surface Renewal Model with Experimental Permeate Flux Data 224 9.3.1 Data of Hasan et al. (2013) 224 9.3.1.1 Fermentation 224 9.3.1.2 Membrane Characteristics 224 9.3.1.3 Experimental Runs 225 9.3.1.4 Model Validation 225 9.3.2 Dependence of the Surface Renewal Frequency on Feed Velocity 229 9.3.3 Data of Mallubhotla and Belfort (1997) 231 9.3.3.1 Model Validation 232 Notation 242 Greek Letters 243 Acronyms 244 Homework Exercises 244 References 245 10 Constant Flux Crossflow Microfiltration 249 10.1 Introduction 249 10.2 Surface Renewal Model of Crossflow Microfiltration 252 10.2.1 Complete Model: Compressible Cake (n ¿ 0) 254 10.2.1.1 Variation of TMP with Process Time 255 10.2.1.2 Variation of TMP with Permeate Flux 255 10.2.2 Subsidiary Model: Incompressible Cake (n = 0) 257 10.3 Correlation of the Surface Renewal Model with Experimental TMP Data 258 10.3.1 Data of Ho and Zydney (2002) 258 10.3.2 Data of Kovalsky et al. (2009) 262 10.3.3 Data of Miller et al. (2014) 263 Notation 271 Greek Letters 272 Acronyms 272 Homework Exercises 273 References 274 Index 277
Preface xiii About the Companion Website xv 1 The Surface Renewal Model of Mass Transfer 1 1.1 Introduction 1 1.2 Literature Review 2 References 8 2 Age-Distribution Function of the Surface Renewal Model 15 2.1 Introduction 15 2.2 Danckwerts Age Distribution 15 2.2.1 Case 1 16 2.2.2 Case 2 17 2.3 Generalized Danckwerts Age Distribution 19 Notation 23 Greek Letters 24 Homework Exercises 24 References 24 3 Physical Gas Absorption in a Large Volume of Liquid 27 3.1 Introduction 27 3.2 Rates of Absorption and Dissolved-Gas Transfer 27 3.3 Comparison of the Surface Renewal Model with Experimental Data 32 Notation 34 Greek Letters 35 Homework Exercises 35 References 35 4 Physical Gas Absorption in a Stirred Batch Cell 37 4.1 Introduction 37 4.2 Interfacial Mass-Transfer Model 38 4.2.1 Zero Gas-Phase Mass-Transfer Resistance 38 4.2.2 Finite Gas-Phase Mass-Transfer Resistance 42 4.3 Philosophical Interlude 45 4.4 Bulk Mass-Transfer Model 46 4.4.1 Zero Gas-Phase Mass-Transfer Resistance 47 4.4.2 Finite Gas-Phase Mass-Transfer Resistance 47 4.5 Analytical Expressions for the Rates of Absorption and Dissolved-Gas Transfer Using the Laplace Transform Method 48 4.5.1 Gaver-Stehfest Algorithm 48 4.5.2 Zero Gas-Phase Mass-Transfer Resistance 49 4.5.3 Finite Gas-Phase Mass-Transfer Resistance 50 4.6 Conventional Pseudo-Steady-State LDF Model 52 4.7 Absorption of Oxygen and Hydrogen in Water 52 Notation 64 Greek Letters 66 Homework Exercises 66 References 67 5 Gas Absorption with First-Order Reaction in a Stirred Batch Cell 69 5.1 Introduction 69 5.2 Interfacial Mass-Transfer Model 72 5.2.1 Zero Gas-Phase Mass-Transfer Resistance 72 5.2.2 Finite Gas-Phase Mass-Transfer Resistance 78 5.3 Bulk Mass-Transfer Model 83 5.3.1 Zero Gas-Phase Mass-Transfer Resistance 84 5.3.2 Finite Gas-Phase Mass-Transfer Resistance 85 5.4 Analytical Expressions for the Rates of Absorption and Dissolved-Gas Transfer Using the Laplace Transform Method 85 5.4.1 Gaver-Stehfest Algorithm 85 5.4.2 Zero Gas-Phase Mass-Transfer Resistance 86 5.4.3 Finite Gas-Phase Mass-Transfer Resistance 88 5.5 Pseudo-Steady-State (PSS) Model 89 5.5.1 Zero Gas-Phase Mass-Transfer Resistance 89 5.5.2 Finite Gas-Phase Mass-Transfer Resistance 91 5.6 Absorption of Oxygen in Water Containing a Liquid-Phase Reagent (e.g., Na 2 SO 3) 91 Notation 100 Greek Letters 102 Acronyms 102 Homework Exercises 103 References 103 6 Gas Absorption with First-Order Reaction in a Packed Tower 107 6.1 Introduction 107 6.2 Surface Renewal Model 109 6.2.1 Physical Absorption 115 6.2.2 Liquid-Phase Control 116 6.2.3 Gas-Phase Control 117 6.3 Film Model 118 6.3.1 Physical Absorption 120 6.3.2 Liquid-Phase Control 120 6.3.3 Gas-Phase Control 120 6.4 Mass-Transfer and Hydraulic Correlations 121 6.5 Illustrative Calculations 122 6.5.1 System 1 124 6.5.2 System 2 126 6.5.3 System 3 128 6.5.4 Outlet Gas- and Liquid-Phase Concentrations as Functions of Hatta Number 129 6.5.5 Effect of Operational Gas and Liquid Mass Velocities on Gas Concentration Profile 131 6.5.6 Effect of Hatta Number on the Height and Number of Overall Gasand Liquid-Phase Mass-Transfer Units 133 Notation 135 Greek Letters 137 Homework Exercises 137 Acknowledgment 138 References 138 7 Gas Absorption with Instantaneous Reaction in a Packed Tower 141 7.1 Introduction 141 7.2 Theoretical Analysis 144 7.2.1 Film Model 145 7.2.1.1 Zero Gas-Phase Mass-Transfer Resistance 147 7.2.1.2 Finite Gas-Phase Mass-Transfer Resistance 152 7.2.2 Surface Renewal Model 153 7.2.2.1 Zero Gas-Phase Mass-Transfer Resistance 154 7.2.2.2 Finite Gas-Phase Mass-Transfer Resistance 160 7.3 Illustrative Calculations 166 7.3.1 Zero Gas-Phase Mass-Transfer Resistance 166 7.3.1.1 Tower Concentration Profiles 168 7.3.1.2 Movement of Reaction Front 170 7.3.2 Finite Gas-Phase Mass-Transfer Resistance 171 7.3.2.1 Validity of the Solution of the Surface Renewal Model 171 7.3.2.2 Tower Concentration Profiles 173 7.3.2.3 Effect of Concentration of B in the Incoming Liquid on Tower Performance 175 Notation 179 Greek Letters 182 Acronyms 182 Homework Exercises 182 References 183 8 Constant Pressure Crossflow Ultrafiltration (UF) 187 8.1 Introduction 187 8.2 Surface Renewal Model 188 8.2.1 Empirical Equation 190 8.2.2 Diffusion Equation 191 8.3 Film Model 196 8.4 Mass-Transfer Coefficient 196 8.5 Relation Between Limiting Flux and Transmembrane Pressure (tmp) 197 8.6 Application of the Surface Renewal and Film Models 197 8.6.1 UF of Cheese Whey 197 8.6.2 UF of Dextran Solutions 200 8.6.3 UF of Skim Milk 204 Notation 207 Greek Letters 208 Acronyms 209 Homework Exercises 209 Acknowledgment 209 References 210 9 Constant Pressure Crossflow Microfiltration 213 9.1 Introduction 213 9.2 Surface Renewal Model of Crossflow Microfiltration 216 9.2.1 Complete Model 216 9.2.2 Approximate Model 221 9.3 Correlation of the Surface Renewal Model with Experimental Permeate Flux Data 224 9.3.1 Data of Hasan et al. (2013) 224 9.3.1.1 Fermentation 224 9.3.1.2 Membrane Characteristics 224 9.3.1.3 Experimental Runs 225 9.3.1.4 Model Validation 225 9.3.2 Dependence of the Surface Renewal Frequency on Feed Velocity 229 9.3.3 Data of Mallubhotla and Belfort (1997) 231 9.3.3.1 Model Validation 232 Notation 242 Greek Letters 243 Acronyms 244 Homework Exercises 244 References 245 10 Constant Flux Crossflow Microfiltration 249 10.1 Introduction 249 10.2 Surface Renewal Model of Crossflow Microfiltration 252 10.2.1 Complete Model: Compressible Cake (n ¿ 0) 254 10.2.1.1 Variation of TMP with Process Time 255 10.2.1.2 Variation of TMP with Permeate Flux 255 10.2.2 Subsidiary Model: Incompressible Cake (n = 0) 257 10.3 Correlation of the Surface Renewal Model with Experimental TMP Data 258 10.3.1 Data of Ho and Zydney (2002) 258 10.3.2 Data of Kovalsky et al. (2009) 262 10.3.3 Data of Miller et al. (2014) 263 Notation 271 Greek Letters 272 Acronyms 272 Homework Exercises 273 References 274 Index 277
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