Mass Transfer from Fundamentals to Modern Industrial Applications By Koichi Asano

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Mass Transfer from Fundamentals to Modern Industrial Applications By Koichi Asano

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Contents

Preface XIII
1 Introduction 1
1.1 The Beginnings of Mass Transfer 1
1.2 Characteristics of Mass Transfer 2
1.3 Three Fundamental Laws of Transport Phenomena 3
1.3.1 Newton’s Law of Viscosity 3
1.3.2 Fourier’s Law of Heat Conduction 4
1.3.3 Fick’s Law of Diffusion 5
1.4 Summary of Phase Equilibria in Gas-Liquid Systems 6
References 7
2 Diffusion and Mass Transfer 9
2.1 Motion of Molecules and Diffusion 9
2.1.1 Diffusion Phenomena 9
2.1.2 Definition of Diffusional Flux and Reference Velocity
of Diffusion 10
2.1.3 Binary Diffusion Flux 12
2.2 Diffusion Coefficients 14
2.2.1 Binary Diffusion Coefficients in the Gas Phase 14
2.2.2 Multicomponent Diffusion Coefficients in the Gas Phase 15
Example 2.1 16
Solution 16
2.3 Rates of Mass Transfer 16
2.3.1 Definition of Mass Flux 16
2.3.2 Unidirectional Diffusion in Binary Mass Transfer 18
2.3.3 Equimolal Counterdiffusion 18
2.3.4 Convective Mass Flux for Mass Transfer in a Mixture of Vapors 20
Example 2.2 21
Solution 21
2.4 Mass Transfer Coefficients 21
Example 2.3 24
Solution 24
2.5 Overall Mass Transfer Coefficients 24
References 26
3 Governing Equations of Mass Transfer 27
3.1 Laminar and Turbulent Flow 27
3.2 Continuity Equation and Diffusion Equation 28
3.2.1 Continuity Equation 28
3.2.2 Diffusion Equation in Terms of Mass Fraction 29
3.2.3 Diffusion Equation in Terms of Mole Fraction 31
3.3 Equation of Motion and Energy Equation 33
3.3.1 The Equation of Motion (Navier–Stokes Equation) 33
3.3.2 The Energy Equation 33
3.3.3 Governing Equations in Cylindrical and Spherical Coordinates 33
3.4 Some Approximate Solutions of the Diffusion Equation 34
3.4.1 Film Model 34
3.4.2 Penetration Model 35
3.4.3 Surface Renewal Model 36
Example 3.1 37
Solution 37
3.5 Physical Interpretation of Some Important Dimensionless Numbers 38
3.5.1 Reynolds Number 38
3.5.2 Prandtl Number and Schmidt Number 39
3.5.3 Nusselt Number 41
3.5.4 Sherwood Number 42
3.5.5 Dimensionless Numbers Commonly Used in Heat and Mass
Transfer 44
Example 3.2 44
Solution 44
3.6 Dimensional Analysis 47
3.6.1 Principle of Similitude and Dimensional Homogeneity 47
3.6.2 Finding Dimensionless Numbers and Pi Theorem 48
References 51
4 Mass Transfer in a Laminar Boundary Layer 53
4.1 Velocity Boundary Layer 53
4.1.1 Boundary Layer Equation 53
4.1.2 Similarity Transformation 55
4.1.3 Integral Form of the Boundary Layer Equation 57
4.1.4 Friction Factor 58
4.2 Temperature and Concentration Boundary Layers 59
4.2.1 Temperature and Concentration Boundary Layer Equations 59
4.2.2 Integral Form of Thermal and Concentration Boundary Layer
Equations 60
Example 4.1 61
Solution 61
4.3 Numerical Solutions of the Boundary Layer Equations 62
4.3.1 Quasi-Linearization Method 62
4.3.2 Correlation of Heat and Mass Transfer Rates 64
Example 4.2 66
Solution 66
4.4 Mass and Heat Transfer in Extreme Cases 67
4.4.1 Approximate Solutions for Mass Transfer in the Case of Extremely Large
Schmidt Numbers 67
4.4.2 Approximate Solutions for Heat Transfer in the Case of Extremely Small
Prandtl Numbers 69
4.5 Effect of an Inactive Entrance Region on Rates of Mass Transfer 70
4.5.1 Polynomial Approximation of Velocity Profiles and Thickness
of the Velocity Boundary Layer 70
4.5.2 Polynomial Approximation of Concentration Profiles and Thickness
of the Concentration Boundary Layer 71
4.6 Absorption of Gases by a Falling Liquid Film 73
4.6.1 Velocity Distribution in a Falling Thin Liquid Film According
to Nusselt 73
4.6.2 Gas Absorption for Short Contact Times 75
4.6.3 Gas Absorption for Long Exposure Times 76
Example 4.3 77
Solution 78
4.7 Dissolution of a Solid Wall by a Falling Liquid Film 78
4.8 High Mass Flux Effect in Heat and Mass Transfer in Laminar Boundary
Layers 80
4.8.1 High Mass Flux Effect 80
4.8.2 Mickley’s Film Model Approach to the High Mass Flux Effect 81
4.8.3 Correlation of High Mass Flux Effect for Heat and Mass Transfer 83
Example 4.4 86
Solution 86
References 87
5 Heat and Mass Transfer in a Laminar Flow inside a Circular Pipe 89
5.1 Velocity Distribution in a Laminar Flow inside a Circular Pipe 89
5.2 Graetz Numbers for Heat and Mass Transfer 90
5.2.1 Energy Balance over a Small Volume Element of a Pipe 90
5.2.2 Material Balance over a Small Volume Element of a Pipe 92
5.3 Heat and Mass Transfer near the Entrance Region of a Circular Pipe 93
5.3.1 Heat Transfer near the Entrance Region at Constant
Wall Temperature 93
5.3.2 Mass Transfer near the Entrance Region at Constant Wall
Concentration 94
5.4 Heat and Mass Transfer in a Fully Developed Laminar Flow inside
a Circular Pipe 95
5.4.1 Heat Transfer at Constant Wall Temperature 95
5.4.2 Mass Transfer at Constant Wall Concentration 96
5.5 Mass Transfer in Wetted-Wall Columns 97
Example 5.1 98
Solution 98
References 100
6 Motion, Heat and Mass Transfer of Particles 101
6.1 Creeping Flow around a Spherical Particle 101
6.2 Motion of Spherical Particles in a Fluid 104
6.2.1 Numerical Solution of the Drag Coefficients of a Spherical Particle in the
Intermediate Reynolds Number Range 104
6.2.2 Correlation of the Drag Coefficients of a Spherical Particle 105
6.2.3 Terminal Velocity of a Particle 106
Example 6.1 107
Solution 107
6.3 Heat and Mass Transfer of Spherical Particles in a Stationary Fluid 109
6.4 Heat and Mass Transfer of Spherical Particles in a Flow Field 111
6.4.1 Numerical Approach to Mass Transfer of a Spherical Particle in a Laminar
Flow 111
6.4.2 The Ranz–Marshall Correlation and Comparison with Numerical
Data 112
Example 6.2 114
Solution 114
6.4.3 Liquid-Phase Mass Transfer of a Spherical Particle in Stokes’ Flow 115
6.5 Drag Coefficients, Heat and Mass Transfer of a Spheroidal Particle 115
6.6 Heat and Mass Transfer in a Fluidized Bed 117
6.6.1 Void Function 117
6.6.2 Interaction of Two Spherical Particles of the Same Size in a Coaxial
Arrangement 117
6.6.3 Simulation of the Void Function 118
References 120
7 Mass Transfer of Drops and Bubbles 121
7.1 Shapes of Bubbles and Drops 121
7.2 Drag Force of a Bubble or Drop in a Creeping Flow (Hadamard’s
Flow) 122
7.2.1 Hadamard’s Stream Function 122
7.2.2 Drag Coefficients and Terminal Velocities of Small Drops and
Bubbles 123
7.2.3 Motion of Small Bubbles in Liquids Containing Traces of
Contaminants 126
7.3 Flow around an Evaporating Drop 126
7.3.1 Effect of Mass Injection or Suction on the Flow around a Spherical
Particle 126
7.3.2 Effect of Mass Injection or Suction on Heat and Mass Transfer of a
Spherical Particle 128
Example 7.1 129
Solution 130
7.4 Evaporation of Fuel Sprays 131
7.4.1 Drag Coefficients, Heat and Mass Transfer of an Evaporating Drop 131
7.4.2 Behavior of an Evaporating Drop Falling Freely in the Gas Phase 132
Example 7.2 134
Solution 134
7.5 Absorption of Gases by Liquid Sprays 136
Example 7.3 137
Solution 138
7.6 Mass Transfer of Small Bubbles or Droplets in Liquids 140
7.6.1 Continuous-Phase Mass Transfer of Bubbles and Droplets in Hadamard
Flow 140
7.6.2 Dispersed-Phase Mass Transfer of Drops in Hadamard Flow 141
7.6.3 Mass Transfer of Bubbles or Drops of Intermediate Size in the Liquid
Phase 141
Example 7.4 142
Solution 142
References 143
8 Turbulent Transport Phenomena 145
8.1 Fundamentals of Turbulent Flow 145
8.1.1 Turbulent Flow 145
8.1.2 Reynolds Stress 146
8.1.3 Eddy Heat Flux and Diffusional Flux 147
8.1.4 Eddy Transport Properties 148
8.1.5 Mixing Length Model 149
8.2 Velocity Distribution in a Turbulent Flow inside a Circular Pipe and
Friction Factors 150
8.2.3 Friction Factors for Turbulent Flow inside a Smooth Circular Pipe 153
Example 8.1 155
Solution 155
8.3 Analogy between Momentum, Heat, and Mass Transfer 156
8.3.1 Reynolds Analogy 157
8.3.2 Chilton–Colburn Analogy 158
Example 8.2 160
Solution 160
8.3.3 Von Karman Analogy 161
8.3.4 Deissler Analogy 162
Example 8.3 164
Solution 164
8.4 Friction Factor, Heat, and Mass Transfer in a Turbulent Boundary
Layer 168
8.4.1 Velocity Distribution in a Turbulent Boundary Layer 168
8.4.2 Friction Factor 169
8.4.3 Heat and Mass Transfer in a Turbulent Boundary Layer 171
8.5 Turbulent Boundary Layer with Surface Mass Injection or Suction 172
Example 8.4 173
Solution 174
References 175
9 Evaporation and Condensation 177
9.1 Characteristics of Simultaneous Heat and Mass Transfer 177
9.1.1 Mass Transfer with Phase Change 177
9.1.2 Surface Temperatures in Simultaneous Heat and Mass Transfer 178
9.2 Wet-Bulb Temperatures and Psychrometric Ratios 179
Example 9.1 181
Solution 181
Example 9.2 182
Solution 182
9.3 Film Condensation of Pure Vapors 183
9.3.1 Nusselt’s Model for Film Condensation of Pure Vapors 183
9.3.2 Effect of Variable Physical Properties 187
Example 9.3 187
Solution 188
9.4 Condensation of Binary Vapor Mixtures 189
9.4.1 Total and Partial Condensation 189
9.4.2 Characteristics of the Total Condensation of Binary Vapor Mixtures 190
9.4.3 Rate of Condensation of Binary Vapors under Total Condensation 191
9.5 Condensation of Vapors in the Presence of a Non-Condensable Gas 192
9.5.1 Accumulation of a Non-Condensable Gas near the Interface 192
9.5.2 Calculation of Heat and Mass Transfer 193
9.5.3 Experimental Approach to the Effect of a Non-Condensable Gas 194
Example 9.4 195
Solution 196
9.6 Condensation of Vapors on a Circular Cylinder 200
9.6.1 Condensation of Pure Vapors on a Horizontal Cylinder 200
9.6.2 Heat and Mass Transfer in the case of a Cylinder with Surface
Mass Injection or Suction 201
9.6.3 Calculation of the Rates of Condensation of Vapors on a Horizontal Tube
in the Presence of a Non-Condensable Gas 203
Example 9.5 204
Solution 204
References 208
10 Mass Transfer in Distillation 209
10.1 Classical Approaches to Distillation and their Paradox 209
10.1.1 Tray Towers and Packed Columns 209
10.1.2 Tray Efficiencies in Distillation Columns 210
10.1.3 HTU as a Measure of Mass Transfer in Packed Distillation
Columns 211
10.1.4 Paradox in Tray Efficiency and HTU 212
Example 10.1 214
Solution 214
10.2 Characteristics of Heat and Mass Transfer in Distillation 216
10.2.1 Physical Picture of Heat and Mass Transfer in Distillation 216
10.2.2 Rate-Controlling Process in Distillation 217
10.2.3 Effect of Partial Condensation of Vapors on the Rates of Mass Transfer
in Binary Distillation 218
10.2.4 Dissimilarity of Mass Transfer in Gas Absorption and Distillation 221
Example 10.2 222
Solution 222
Example 10.3 222
Solution 222
10.3 Simultaneous Heat and Mass Transfer Model for Packed Distillation
Columns 225
10.3.1 Wetted Area of Packings 225
10.3.2 Apparent End Effect 227
10.3.3 Correlation of the Vapor-Phase Diffusional Fluxes in Binary
Distillation 228
10.3.4 Correlation of Vapor-Phase Diffusional Fluxes in Ternary
Distillation 230
10.3.5 Simulation of Separation Performance in Ternary Distillation on a Packed
Column under Total Reflux Conditions 231
Example 10.4 233
Solution 233
Example 10.5 239
Solution 239
10.4 Calculation of Ternary Distillations on Packed Columns under Finite Reflux
Ratio 239
10.4.1 Material Balance for the Column 239
10.4.2 Convergence of Terminal Composition 242
Example 10.6 244
Solution 244
10.5 Cryogenic Distillation of Air on Packed Columns 249
10.5.1 Air Separation Plant 249
10.5.2 Mass and Diffusional Fluxes in Cryogenic Distillation 249
10.5.3 Simulation of Separation Performance of a Pilot-Plant-Scale Air
Separation Plant 251
10.6 Industrial Separation of Oxygen-18 by Super Cryogenic Distillation 252
Contents XI
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10.6.1 Oxygen-18 as Raw Material for PET Diagnostics 252
10.6.2 A New Process for Direct Separation of Oxygen-18 from Natural
Oxygen 253
10.6.3 Construction and Operation of the Plant 255
References 257
Subject Index 271

Preface

The transfer of materials through interfaces in fluid media is called mass transfer.
Mass transfer phenomena are observed throughout Nature and in many fields of
industry. Today, fields of application of mass transfer theories have become widespread,
from traditional chemical industries to bioscience and environmental industries.
The design of new processes, the optimization of existing processes, and
solving pollution problems are all heavily dependent on a knowledge of mass
transfer.
This book is intended as a textbook on mass transfer for graduate students and
for practicing chemical engineers, as well as for academic persons working in the
field of mass transfer and related areas. The topics of the book are arranged so as
to start from fundamental aspects of the phenomena and then systematically and
in a step-by-step way proceed to detailed applications, with due consideration of
real separation problems. Important formulae and correlations are clearly described,
together with their basic assumptions and the limitations of the theories
in practical applications. Comparisons of the theories with numerical solutions or
observed data are also provided as far as possible. Each chapter contains some
illustrative examples to help readers to understand how to approach actual practical
problems.
The book consists of ten chapters. The first three chapters cover the fundamental
aspects of mass transfer. The next four chapters deal with laminar mass transfer
of various types. The fundamentals of turbulent transport phenomena and
mass transfer with phase change are then discussed in two further chapters. The
final chapter is a highlight of the book, wherein fundamental principles developed
in the previous chapters are applied to real industrial separation processes, and a
new model for the design of multi-component distillations on packed columns is
proposed, application of which has facilitated the industrial separation of a stable
isotope, oxygen-18, by super cryogenic distillation.