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8.01.2023 - 07:21 |
Dynamics of Structures (6e) - Anil K. Chopra
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Dynamics of Structures, 5/e
https://ipfs.io/ipfs/bafykbzacecc32mjncgs7gpcifzuc5peheudxq54wmpyhk5pkroaiubtmwuh3g?filename=Anil%20K.%20Chopra%20-%20Dynamics%20of%20Structures%2C%205_e-Pearson%20%282016%29.epub |
Kaneki Ken, netsonicyxf, ronyleonel, totolemoco, |
6.06.2021 - 18:02 |
Looking for ACI 318-19 related technical documents
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https://mega.nz/file/XcMQmD4Z#BG7cHfnpY5_jZ016TGeKVb39y1kCXGDEAfAgVxUugDc ACI 318-19 Building Code Requirements for Structural Concrete
https://mega.nz/file/nUFmnZSK#StfDoNHAMzhM1TUW_hKIo5RcPqM-2c2nG7wdMWOLvG4 MNL-17 |
en_boy, netsonicyxf, |
30.01.2020 - 06:20 |
[Request] ISO Graphycal Symbols
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ISO 3864-1:2011 - Graphical symbols — Safety colours and safety signs — Part 1: Design principles for safety signs and safety markings
[attachment=24706:ISO_3864_1_2011.zip] ISO 3864-2:2016 - Graphical symbols — Safety colours and safety signs — Part 2: Design principles for product safety labels
[attachment=24707:ISO_3864_2_2004.zip] ISO 3864-3:2012 - Graphical symbols — Safety colours and safety signs — Part 3: Design principles for graphical symbols for use in safety signs
[attachment=24708:ISO_3864_3_2012.zip] ISO 3864-4:2011 - Graphical symbols — Safety colours and safety signs — Part 4: Colorimetric and photometric properties of safety sign materials
[attachment=24709:ISO_3864_4_2011.zip] ISO 7010:2019 - Graphical symbols — Safety colours and safety signs — Registered safety signs
[attachment=24710:ISO_7010....zip.001.zip]
[attachment=24711:ISO_7010....zip.002.zip]
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2ak2, acier, Capricorn, dizz, ioncube, nephrops, |
24.12.2019 - 15:52 |
Fluid Conveyance Spreadsheets
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[attachment=24599:API_and_..._Excel_1.zip]
[attachment=24600:API_and_..._Excel_2.zip]
[attachment=24601:API_and_..._Excel_3.zip] |
2ak2, ashraf_1969, bakti, camiqmex, cinder, ioncube, muwlla, NikolasDaktilas, Ал1965, |
23.06.2019 - 07:50 |
Perry's Chemical Engineers' Handbook, 9th Edition
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[attachment=23991:0071834087_1.jpg]
https://www.mhprofessional.com/9780071834087-usa-perrys-chemical-engineers-handbook-9th-edition-group
Table of Contents A. About the Editors B. Contributors C. Preface to the Ninth Edition 1. Section 1: Unit Conversion Factors and Symbols CHAPTER PRELIMINARIES UNITS AND SYMBOLS CONVERSION FACTORS 2. Section 2: Physical and Chemical Data CHAPTER PRELIMINARIES GENERAL REFERENCES PHYSICAL PROPERTIES OF PURE SUBSTANCES VAPOR PRESSURES VAPOR PRESSURES OF SOLUTIONS SOLUBILITIES DENSITIES DENSITIES OF AQUEOUS INORGANIC SOLUTIONS AT 1 ATM DENSITIES OF MISCELLANEOUS MATERIALS LATENT HEATS SPECIFIC HEATS PROPERTIES OF FORMATION AND COMBUSTION REACTIONS HEATS OF SOLUTION THERMAL EXPANSION AND COMPRESSIBILITY THERMODYNAMIC PROPERTIES TRANSPORT PROPERTIES PREDICTION AND CORRELATION OF PHYSICAL PROPERTIES* 3. Section 3: Mathematics CHAPTER PRELIMINARIES GENERAL REFERENCES MATHEMATICS MENSURATION FORMULAS ELEMENTARY ALGEBRA ANALYTIC GEOMETRY PLANE TRIGONOMETRY DIFFERENTIAL AND INTEGRAL CALCULUS INFINITE SERIES COMPLEX VARIABLES DIFFERENTIAL EQUATIONS DIFFERENCE EQUATIONS INTEGRAL EQUATIONS INTEGRAL TRANSFORMS (OPERATIONAL METHODS) MATRIX ALGEBRA AND MATRIX COMPUTATIONS NUMERICAL APPROXIMATIONS TO SOME EXPRESSIONS NUMERICAL ANALYSIS AND APPROXIMATE METHODS NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS AS INITIAL-VALUE PROBLEMS OPTIMIZATION STATISTICS DIMENSIONAL ANALYSIS PROCESS SIMULATION 4. Section 4: Thermodynamics CHAPTER PRELIMINARIES INTRODUCTION GENERAL BALANCES PROPERTY CALCULATIONS FROM EQUATIONS OF STATE SYSTEMS OF VARIABLE COMPOSITION TRENDS IN PHASE BEHAVIOR TEMPERATURE DEPENDENCE OF INFINITE-DILUTION ACTIVITY COEFFICIENTS THERMODYNAMICS FOR CONCEPTUAL DESIGN REACTING SYSTEMS 5. Section 5: Heat and Mass Transfer CHAPTER PRELIMINARIES HEAT TRANSFER HEAT TRANSFER BY CONDUCTION HEAT TRANSFER BY CONVECTION HEAT TRANSFER WITH CHANGE OF PHASE HEAT TRANSFER BY RADIATION MASS TRANSFER 6. Section 6: Fluid and Particle Dynamics CHAPTER PRELIMINARIES FLUID DYNAMICS PARTICLE DYNAMICS 7. Section 7: Reaction Kinetics CHAPTER PRELIMINARIES REFERENCES INTRODUCTION BASIC CONCEPTS IDEAL REACTORS KINETICS OF COMPLEX HOMOGENEOUS REACTIONS INTRINSIC KINETICS FOR FLUID-SOLID CATALYTIC REACTIONS FLUID-SOLID REACTIONS WITH MASS AND HEAT TRANSFER GAS-LIQUID REACTIONS GAS-LIQUID-SOLID REACTIONS DETERMINATION OF MECHANISM AND KINETICS 8. Section 8: Process Control CHAPTER PRELIMINARIES FUNDAMENTALS OF PROCESS DYNAMICS AND CONTROL ADVANCED CONTROL SYSTEMS UNIT OPERATIONS CONTROL BATCH PROCESS CONTROL BIOPROCESS CONTROL TELEMETERING AND TRANSMISSION DIGITAL TECHNOLOGY FOR PROCESS CONTROL PROCESS MEASUREMENTS CONTROLLERS, FINAL CONTROL ELEMENTS, AND REGULATORS 9. Section 9: Process Economics CHAPTER PRELIMINARIES GENERAL COMMENTS ACCOUNTING AND FINANCIAL CONSIDERATIONS CAPITAL COST ESTIMATION MANUFACTURING/OPERATING EXPENSES FACTORS THAT AFFECT PROFITABILITY PROFITABILITY OTHER ECONOMIC TOPICS CAPITAL PROJECT EXECUTION AND ANALYSIS GLOSSARY 10. Section 10: Transport and Storage of Fluids CHAPTER PRELIMINARIES MEASUREMENT OF FLOW PUMPS AND COMPRESSORS COMPRESSORS PROCESS PLANT PIPING STORAGE AND PROCESS VESSELS 11. Section 11: Heat-Transfer Equipment CHAPTER PRELIMINARIES THERMAL DESIGN OF HEAT-TRANSFER EQUIPMENT TEMA-STYLE SHELL-AND-TUBE HEAT EXCHANGERS HAIRPIN/DOUBLE-PIPE HEAT EXCHANGERS AIR-COOLED HEAT EXCHANGERS COMPACT AND NONTUBULAR HEAT EXCHANGERS HEAT EXCHANGERS FOR SOLIDS THERMAL INSULATION AIR CONDITIONING REFRIGERATION EVAPORATORS 12. Section 12: Psychrometry, Evaporative Cooling, and Solids Drying CHAPTER PRELIMINARIES PSYCHROMETRY EVAPORATIVE COOLING SOLIDS-DRYING FUNDAMENTALS 13. Section 13: Distillation CHAPTER PRELIMINARIES INTRODUCTION TO DISTILLATION OPERATIONS THERMODYNAMIC DATA AND MODELS SINGLE-STAGE EQUILIBRIUM FLASH CALCULATIONS GRAPHICAL METHODS FOR BINARY DISTILLATION APPROXIMATE MULTICOMPONENT DISTILLATION METHODS SIMULATION OF DISTILLATION PROCESSES DEGREES OF FREEDOM AND DESIGN VARIABLES DISTILLATION SYSTEMS ENHANCED DISTILLATION PETROLEUM AND COMPLEX-MIXTURE DISTILLATION BATCH DISTILLATION 14. Section 14: Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation CHAPTER PRELIMINARIES INTRODUCTION DESIGN OF GAS ABSORPTION SYSTEMS EQUIPMENT FOR DISTILLATION AND GAS ABSORPTION: TRAY COLUMNS EQUIPMENT FOR DISTILLATION AND GAS ABSORPTION: PACKED COLUMNS OTHER TOPICS FOR DISTILLATION AND GAS ABSORPTION EQUIPMENT PHASE DISPERSION PHASE SEPARATION 15. Section 15: Liquid-Liquid Extraction and Other Liquid-Liquid Operations and Equipment CHAPTER PRELIMINARIES INTRODUCTION AND OVERVIEW THERMODYNAMIC BASIS FOR LIQUID-LIQUID EXTRACTION SOLVENT SCREENING METHODS LIQUID DENSITY, VISCOSITY, AND INTERFACIAL TENSION LIQUID-LIQUID DISPERSION FUNDAMENTALS PROCESS FUNDAMENTALS AND BASIC CALCULATION METHODS CALCULATION PROCEDURES LIQUID-LIQUID EXTRACTION EQUIPMENT PROCESS CONTROL CONSIDERATIONS LIQUID-LIQUID PHASE SEPARATION EQUIPMENT EMERGING DEVELOPMENTS 16. Section 16: Adsorption and Ion Exchange CHAPTER PRELIMINARIES DESIGN CONCEPTS ADSORBENTS AND ION EXCHANGERS SORPTION EQUILIBRIUM CONSERVATION EQUATIONS RATE AND DISPERSION FACTORS BATCH ADSORPTION FIXED-BED TRANSITIONS CHROMATOGRAPHY PROCESS CYCLES EQUIPMENT 17. Section 17: Gas–Solid Operations and Equipment CHAPTER PRELIMINARIES FLUIDIZED-BED SYSTEMS GAS–SOLIDS SEPARATIONS 18. Section 18: Liquid-Solid Operations and Equipment CHAPTER PRELIMINARIES MIXING AND PROCESSING OF LIQUIDS AND SOLIDS MIXING OF VISCOUS FLUIDS, PASTES, AND DOUGHS CRYSTALLIZATION FROM SOLUTION CRYSTALLIZATION FROM THE MELT LEACHING GRAVITY SEDIMENTATION OPERATIONS FILTRATION CENTRIFUGES EXPRESSION SELECTION OF A SOLIDS-LIQUID SEPARATOR 19. Section 19: Reactors CHAPTER PRELIMINARIES INTRODUCTION REACTOR CONCEPTS RESIDENCE TIME DISTRIBUTION AND MIXING SINGLE-PHASE REACTORS FLUID–SOLID REACTORS FLUID–FLUID REACTORS SOLIDS REACTORS MULTIPHASE REACTORS SOME CASE STUDIES 20. Section 20: Bioreactions and Bioprocessing CHAPTER PRELIMINARIES BIOENGINEERING OVERVIEW AND CONCEPTS BIOREACTORS AND UPSTREAM PROCESSES DOWNSTREAM PROCESSING: SEPARATION AND PURIFICATION PRODUCT QUALITY ATTRIBUTE CONTROL EMERGING BIOPHARMACEUTICAL AND BIOPROCESS TECHNOLOGIES AND TRENDS 21. Section 21: Solids Processing and Particle Technology CHAPTER PRELIMINARIES PARTICLE CHARACTERIZATION BULK SOLIDS FLOW AND HOPPER DESIGN SOLIDS MIXING PNEUMATIC CONVEYING OF SOLIDS SCREENING SIZE REDUCTION MODELING AND SIMULATION OF GRINDING PROCESSES CRUSHING AND GRINDING EQUIPMENT: DRY GRINDING—IMPACT AND ROLLER MILLS CRUSHING AND GRINDING EQUIPMENT: FLUID-ENERGY OR JET MILLS CRUSHING AND GRINDING EQUIPMENT: WET/DRY GRINDING—MEDIA MILLS SIZE ENLARGEMENT FEEDING, METERING, AND DOSING 22. Section 22: Waste Management CHAPTER PRELIMINARIES INTRODUCTION TO WASTE MANAGEMENT AND REGULATORY OVERVIEW POLLUTION PREVENTION GREEN CHEMISTRY AND GREEN ENGINEERING AIR POLLUTION MANAGEMENT OF STATIONARY SOURCES INDUSTRIAL WASTEWATER MANAGEMENT MANAGEMENT OF SOLID WASTES 23. Section 23: Process Safety CHAPTER PRELIMINARIES INTRODUCTION TO PROCESS SAFETY CASE HISTORIES HAZARDOUS MATERIALS AND CONDITIONS INHERENTLY SAFER DESIGN AND RELATED CONCEPTS PROCESS SAFETY ANALYSIS CONSEQUENCE MODELS SAFETY EQUIPMENT, PROCESS DESIGN, AND OPERATION 24. Section 24: Energy Resources, Conversion, and Utilization CHAPTER PRELIMINARIES INTRODUCTION FUELS HEAT GENERATION PINCH ANALYSIS ENERGY RECOVERY THERMAL ENERGY CONVERSION AND UTILIZATION 25. Section 25: Materials of Construction CHAPTER PRELIMINARIES INTRODUCTION CORROSION FUNDAMENTALS CORROSION PREVENTION CORROSION-TESTING METHODS ALLOY DESIGNATIONS FERRITIC STEELS STAINLESS STEELS NICKEL ALLOYS REACTIVE METALS OTHER METALS AND ALLOYS LOW-TEMPERATURE AND CRYOGENIC MATERIALS NONMETALLIC MATERIALS FOR CORROSION CONTROL
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ioncube, ivanushka1, knight282009, laminars, silkem, Williams, |
15.07.2018 - 01:21 |
Physical and Chemical Engineering Sciences
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Fluid Mechanics for Chemical Engineers: with Microfluidics, CFD, and COMSOL Multiphysics 5, 3rd EditionJames O. Wilkes, University of Michigan
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Table of Contents Preface xv
Part I: Macroscopic Fluid Mechanics 1
Chapter 1: Introduction to Fluid Mechanics 3
1.1 Fluid Mechanics in Chemical Engineering 3
1.2 General Concepts of a Fluid 3
1.3 Stresses, Pressure, Velocity, and the Basic Laws 5
1.4 Physical Properties—Density, Viscosity, and Surface Tension 10
1.5 Units and Systems of Units 21
1.6 Hydrostatics 26
1.7 Pressure Change Caused by Rotation 39
Problems for Chapter 1 42
Chapter 2: Mass, Energy, and Momentum Balances 55
2.1 General Conservation Laws 55
2.2 Mass Balances 57
2.3 Energy Balances 61
2.4 Bernoulli’s Equation 67
2.5 Applications of Bernoulli’s Equation 70
2.6 Momentum Balances 78
2.7 Pressure, Velocity, and Flow Rate Measurement 92
Problems for Chapter 2 96
Chapter 3: Fluid Friction in Pipes 120
3.1 Introduction 120
3.2 Laminar Flow 123
3.3 Models for Shear Stress 129
3.4 Piping and Pumping Problems 133
3.5 Flow in Noncircular Ducts 150
3.6 Compressible Gas Flow in Pipelines 156
3.7 Compressible Flow in Nozzles 159
3.8 Complex Piping Systems 163
Problems for Chapter 3 168
Chapter 4: Flow in Chemical Engineering Equipment 185
4.1 Introduction 185
4.2 Pumps and Compressors 188
4.3 Drag Force on Solid Particles in Fluids 194
4.4 Flow Through Packed Beds 204
4.5 Filtration 210
4.6 Fluidization 215
4.7 Dynamics of a Bubble-Cap Distillation Column 216
4.8 Cyclone Separators 219
4.9 Sedimentation 222
4.10 Dimensional Analysis 224
Problems for Chapter 4 230
Part II: Microscopic Fluid Mechanics 247
Chapter 5: Differential Equations of Fluid Mechanics 249
5.1 Introduction to Vector Analysis 249
5.2 Vector Operations 250
5.3 Other Coordinate Systems 263
5.4 The Convective Derivative 266
5.5 Differential Mass Balance 267
5.6 Differential Momentum Balances 271
5.7 Newtonian Stress Components in Cartesian Coordinates 274
Problems for Chapter 5 285
Chapter 6: Solution Of Viscous-Flow Problems 292
6.1 Introduction 292
6.2 Solution of the Equations of Motion in Rectangular Coordinates 294
6.3 Alternative Solution Using a Shell Balance 301
6.4 Poiseuille and Couette Flows in Polymer Processing 313
6.5 Solution of the Equations of Motion in Cylindrical Coordinates 325
6.6 Solution of the Equations of Motion in Spherical Coordinates 330
Problems for Chapter 6 336
Chapter 7: Laplace’s Equation, Irrotational and Porous-Media Flows 357
7.1 Introduction 357
7.2 Rotational and Irrotational Flows 359
7.3 Steady Two-Dimensional Irrotational Flow 364
7.4 Physical Interpretation of the Stream Function 367
7.5 Examples of Planar Irrotational Flow 369
7.6 Axially Symmetric Irrotational Flow 382
7.7 Uniform Streams and Point Sources 384
7.8 Doublets and Flow Past a Sphere 388
7.9 Single-Phase Flow in a Porous Medium 391
7.10 Two-Phase Flow in Porous Media 394
7.11 Wave Motion in Deep Water 400
Problems for Chapter 7 404
Chapter 8: Boundary-Layer and Other Nearly Unidirectional Flows 418
8.1 Introduction 418
8.2 Simplified Treatment of Laminar Flow Past a Flat Plate 419
8.3 Simplification of the Equations of Motion 426
8.4 Blasius Solution for Boundary-Layer Flow 429
8.5 Turbulent Boundary Layers 432
8.6 Dimensional Analysis of the Boundary-Layer Problem 434
8.7 Boundary-Layer Separation 437
8.8 The Lubrication Approximation 448
8.9 Polymer Processing by Calendering 457
8.10 Thin Films and Surface Tension 463
Problems for Chapter 8 466
Chapter 9: Turbulent Flow 480
9.1 Introduction 480
9.2 Physical Interpretation of the Reynolds Stresses 487
9.3 Mixing-Length Theory 488
9.4 Determination of Eddy Kinematic Viscosity and Mixing Length 491
9.5 Velocity Profiles Based on Mixing-Length Theory 493
9.6 The Universal Velocity Profile for Smooth Pipes 495
9.7 Friction Factor in Terms of Reynolds Number for Smooth Pipes 497
9.8 Thickness of the Laminar Sublayer 499
9.9 Velocity Profiles and Friction Factor for Rough Pipe 501
9.10 Blasius-Type Law and the Power-Law Velocity Profile 502
9.11 A Correlation for the Reynolds Stresses 503
9.12 Computation of Turbulence by the k–ε Method 506
9.13 Analogies Between Momentum and Heat Transfer 520
9.14 Turbulent Jets 524
Problems for Chapter 9 532
Chapter 10: Bubble Motion, Two-Phase Flow, and Fluidization 542
10.1 Introduction 542
10.2 Rise of Bubbles in Unconfined Liquids 542
10.3 Pressure Drop and Void Fraction in Horizontal Pipes 547
10.4 Two-Phase Flow in Vertical Pipes 554
10.5 Flooding 566
10.6 Introduction to Fluidization 570
10.7 Bubble Mechanics 572
10.8 Bubbles in Aggregatively Fluidized Beds 577
Problems for Chapter 10 586
Chapter 11: Non-Newtonian Fluids 602
11.1 Introduction 602
11.2 Classification of Non-Newtonian Fluids 603
11.3 Constitutive Equations for Inelastic Viscous Fluids 606
11.4 Constitutive Equations for Viscoelastic Fluids 626
11.5 Response to Oscillatory Shear 633
11.6 Characterization of the Rheological Properties of Fluids 636
Problems for Chapter 11 644
Chapter 12: Microfluidics and Electrokinetic Flow Effects 653
12.1 Introduction 653
12.2 Physics of Microscale Fluid Mechanics 654
12.3 Pressure-Driven Flow Through Microscale Tubes 655
12.4 Mixing, Transport, and Dispersion 656
12.5 Species, Energy, and Charge Transport 658
12.6 The Electrical Double Layer and Electrokinetic Phenomena 661
12.7 Measuring the Zeta Potential 676
12.8 Electroviscosity 678
12.9 Particle and Macromolecule Motion in Microfluidic Channels 678
Problems for Chapter 12 683
Chapter 13: An Introduction to Computational Fluid Dynamics and ANSYS Fluent 688
13.1 Introduction and Motivation 688
13.2 Numerical Methods 690
13.3 Learning CFD by Using ANSYS Fluent 699
13.4 Practical CFD Examples 703
References for Chapter 13 719
Chapter 14: COMSOL Multiphysics for Solving Fluid Mechanics Problems 720
14.1 COMSOL Multiphysics—An Overview 720
14.2 The Steps for Solving Problems in COMSOL 723
14.3 How to Run COMSOL 725
14.4 Variables, Constants, Expressions, and Units 741
14.5 Boundary Conditions 742
14.6 Variables Used by COMSOL 743
14.7 Wall Functions in Turbulent-Flow Problems 744
14.8 Streamline Plotting in COMSOL 747
14.9 Special COMSOL Features Used in the Examples 749
14.10 Drawing Tools 754
14.11 Fluid Mechanics Problems Solvable by COMSOL 756
14.12 Conclusion—Problems and Learning Tools 761
Appendix A: Useful Mathematical Relationships 762
Appendix B: Answers to the True/False Assertions 768
Appendix C: Some Vector and Tensor Operations 771
General Index 773
Comsol Multiphysics Index 782
The Authors 784
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camiqmex, ioncube, knight282009, sebaversa, tygra123, |
13.07.2018 - 17:48 |
Physical and Chemical Engineering Sciences
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Analysis, Synthesis, and Design of Chemical Processes, 5th Edition - Richard Turton, Joseph A. Shaeiwitz, Debangsu Bhattacharyya
» Click to show Spoiler - click again to hide... «
Table of Contents
Preface xxv
About the Authors xxix
List of Nomenclature xxxi
Chapter 0: Outcomes Assessment 1
0.1 Student Self-Assessment 2
0.2 Assessment by Faculty 4
0.3 Summary 6
References 6
Section I: Conceptualization and Analysis of Chemical Processes 7
Chapter 1: Diagrams for Understanding Chemical Processes 9
1.1 Block Flow Diagram (BFD) 11
1.2 Process Flow Diagram (PFD) 14
1.3 Piping and Instrumentation Diagram (P&ID) 27
1.4 Additional Diagrams 32
1.5 Three-Dimensional Representation of a Process 34
1.6 The 3-D Plant Model 41
1.7 Operator and 3-D Immersive Training Simulators 43
1.8 Summary 48
References 49
Short Answer Questions 49
Problems 50
Chapter 2: The Structure and Synthesis of Process Flow Diagrams 55
2.1 Hierarchy of Process Design 55
2.2 Step 1—Batch versus Continuous Process 56
2.3 Step 2—The Input/Output Structure of the Process 60
2.4 Step 3—The Recycle Structure of the Process 70
2.5 Step 4—General Structure of the Separation System 83
2.6 Step 5—Heat-Exchanger Network or Process Energy Recovery System 83
2.7 Information Required and Sources 83
2.8 Summary 83
References 85
Short Answer Questions 86
Problems 86
Chapter 3: Batch Processing 91
3.1 Design Calculations for Batch Processes 91
3.2 Gantt Charts and Scheduling 97
3.3 Nonoverlapping Operations, Overlapping Operations, and Cycle Times 98
3.4 Flowshop and Jobshop Plants 101
3.5 Product and Intermediate Storage and Parallel Process Units 106
3.6 Design of Equipment for Multiproduct Batch Processes 111
3.7 Summary 113
References 114
Short Answer Questions 114
Problems 114
Chapter 4: Chemical Product Design 123
4.1 Strategies for Chemical Product Design 124
4.2 Needs 125
4.3 Ideas 127
4.4 Selection 128
4.5 Manufacture 130
4.6 Batch Processing 131
4.7 Economic Considerations 131
4.8 Summary 132
References 132
Chapter 5: Tracing Chemicals through the Process Flow Diagram 135
5.1 Guidelines and Tactics for Tracing Chemicals 135
5.2 Tracing Primary Paths Taken by Chemicals in a Chemical Process 136
5.3 Recycle and Bypass Streams 142
5.4 Tracing Nonreacting Chemicals 145
5.5 Limitations 145
5.6 Written Process Description 146
5.7 Summary 147
Problems 147
Chapter 6: Understanding Process Conditions 149
6.1 Conditions of Special Concern for the Operation of Separation and Reactor Systems 150
6.2 Reasons for Operating at Conditions of Special Concern 152
6.3 Conditions of Special Concern for the Operation of Other Equipment 155
6.4 Analysis of Important Process Conditions 158
6.5 Summary 165
References 165
Short Answer Questions 165
Problems 166
Section II: Engineering Economic Analysis of Chemical Processes 169
Chapter 7: Estimation of Capital Costs 171
7.1 Classifications of Capital Cost Estimates 172
7.2 Estimation of Purchased Equipment Costs 175
7.3 Estimating the Total Capital Cost of a Plant 182
7.4 Estimation of Plant Costs Based on Capacity Information 206
7.5 Summary 208
References 208
Short Answer Questions 209
Problems 210
Chapter 8: Estimation of Manufacturing Costs 213
8.1 Factors Affecting the Cost of Manufacturing a Chemical Product 213
8.2 Cost of Operating Labor 218
8.3 Utility Costs 219
8.4 Raw Material Costs 234
8.5 Yearly Costs and Stream Factors 237
8.6 Estimating Utility Costs from the PFD 238
8.7 Cost of Treating Liquid and Solid Waste Streams 240
8.8 Evaluation of Cost of Manufacture for the Production of Benzene via the Hydrodealkylation of Toluene 241
8.9 Summary 242
References 243
Short Answer Questions 243
Problems 244
Chapter 9: Engineering Economic Analysis 247
9.1 Investments and the Time Value of Money 248
9.2 Different Types of Interest 251
9.3 Time Basis for Compound Interest Calculations 254
9.4 Cash Flow Diagrams 255
9.5 Calculations from Cash Flow Diagrams 259
9.6 Inflation 266
9.7 Depreciation of Capital Investment 268
9.8 Taxation, Cash Flow, and Profit 274
9.9 Summary 277
References 277
Short Answer Questions 278
Problems 278
Chapter 10: Profitability Analysis 285
10.1 A Typical Cash Flow Diagram for a New Project 285
10.2 Profitability Criteria for Project Evaluation 287
10.3 Comparing Several Large Projects: Incremental Economic Analysis 295
10.4 Establishing Acceptable Returns from Investments: The Concept of Risk 298
10.5 Evaluation of Equipment Alternatives 299
10.6 Incremental Analysis for Retrofitting Facilities 305
10.7 Evaluation of Risk in Evaluating Profitability 309
10.8 Profit Margin Analysis 325
10.9 Summary 326
References 327
Short Answer Questions 327
Problems 328
Section III: Synthesis and Optimization of Chemical Processes 343
Chapter 11: Utilizing Experience-Based Principles to Confirm the Suitability of a Process Design 347
11.1 The Role of Experience in the Design Process 348
11.2 Presentation of Tables of Technical Heuristics and Guidelines 351
11.3 Summary 354
List of Informational Tables 354
References 368
Problems 368
Chapter 12: Synthesis of the PFD from the Generic BFD 369
12.1 Information Needs and Sources 370
12.2 Reactor Section 372
12.3 Separator Section 373
12.4 Reactor Feed Preparation and Separator Feed Preparation Sections 388
12.5 Recycle Section 389
12.6 Environmental Control Section 389
12.7 Major Process Control Loops 390
12.8 Flow Summary Table 390
12.9 Major Equipment Summary Table 390
12.10 Summary 391
References 391
General Reference 392
Problems 392
Chapter 13: Synthesis of a Process Using a Simulator and Simulator Troubleshooting 397
13.1 The Structure of a Process Simulator 398
13.2 Information Required to Complete a Process Simulation: Input Data 401
13.3 Handling Recycle Streams 413
13.4 Choosing Thermodynamic Models 415
13.5 Case Study: Toluene Hydrodealkylation Process 426
13.6 Electrolyte Systems Modeling 428
13.7 Solids Modeling 440
Appendix 13.1 445
Appendix 13.2 447
13.8 Summary 450
References 451
Short Answer Questions 454
Problems 455
Chapter 14: Process Optimization 463
14.1 Background Information on Optimization 463
14.2 Strategies 469
14.3 Topological Optimization 473
14.4 Parametric Optimization 479
14.5 Lattice Search, Response Surface, and Mathematical Optimization Techniques 489
14.6 Process Flexibility and the Sensitivity of the Optimum 489
14.7 Optimization in Batch Systems 490
14.8 Summary 497
References 498
Short Answer Questions 498
Problems 498
Chapter 15: Pinch Technology 509
15.1 Introduction 509
15.2 Heat Integration and Network Design 510
15.3 Composite Temperature-Enthalpy Diagram 523
15.4 Composite Enthalpy Curves for Systems without a Pinch 524
15.5 Using the Composite Enthalpy Curve to Estimate Heat-Exchanger Surface Area 525
15.6 Effectiveness Factor (F) and the Number of Shells 529
15.7 Combining Costs to Give the EAOC for the Network 534
15.8 Other Considerations 536
15.9 Heat-Exchanger Network Synthesis Analysis and Design (HENSAD) Program 540
15.10 Mass-Exchange Networks 541
15.11 Summary 550
References 550
Short Answer Questions 551
Problems 552
Chapter 16: Advanced Topics Using Steady-State Simulators 561
16.1 Why the Need for Advanced Topics in Steady-State Simulation? 562
16.2 User-Added Models 562
16.3 Solution Strategy for Steady-State Simulations 571
16.4 Studies with the Steady-State Simulation 589
16.5 Estimation of Physical Property Parameters 601
16.6 Summary 605
References 605
Short Answer Questions 607
Problems 607
Chapter 17: Using Dynamic Simulators in Process Design 617
17.1 Why Is There a Need for Dynamic Simulation? 618
17.2 Setting Up a Dynamic Simulation 619
17.3 Dynamic Simulation Solution Methods 633
17.4 Process Control 639
17.5 Summary 647
References 647
Short Answer Questions 648
Problems 649
Chapter 18: Regulation and Control of Chemical Processes with Applications Using Commercial Software 655
18.1 A Simple Regulation Problem 656
18.2 The Characteristics of Regulating Valves 657
18.3 Regulating Flowrates and Pressures 660
18.4 The Measurement of Process Variables 662
18.5 Common Control Strategies Used in Chemical Processes 663
18.6 Exchanging Heat and Work between Process and Utility Streams 674
18.7 Logic Control 680
18.8 Advanced Process Control 682
18.9 Case Studies 683
18.10 Putting It All Together: The Operator Training Simulator (OTS) 688
18.11 Summary 689
References 690
Problems 690
Section IV: Chemical Equipment Design and Performance Process Equipment Design and Performance 695
Chapter 19: Process Fluid Mechanics 697
19.1 Basic Relationships in Fluid Mechanics 697
19.2 Fluid Flow Equipment 703
19.3 Frictional Pipe Flow 709
19.4 Other Flow Situations 723
19.5 Performance of Fluid Flow Equipment 736
References 755
Short Answer Questions 756
Problems 757
Chapter 20: Process Heat Transfer 771
20.1 Basic Heat-Exchanger Relationships 771
20.2 Heat-Exchange Equipment Design and Characteristics 779
20.3 LMTD Correction Factor for Multiple Shell and Tube Passes 789
20.4 Overall Heat Transfer Coefficients—Resistances in Series 798
20.5 Estimation of Individual Heat Transfer Coefficients and Fouling Resistances 800
20.6 Extended Surfaces 828
20.7 Algorithm and Worked Examples for the Design of Heat Exchangers 837
20.8 Performance Problems 846
References 859
Appendix 20.A Heat-Exchanger Effectiveness Charts 861
Appendix 20.B Derivation of Fin Effectiveness for a Rectangular Fin 864
Short Answer Questions 866
Problems 866
Chapter 21: Separation Equipment 875
21.1 Basic Relationships in Separations 876
21.2 Illustrative Diagrams 883
21.3 Equipment 911
21.4 Extraction Equipment 942
21.5 Gas Permeation Membrane Separations 947
References 951
Short Answer Questions 952
Problems 954
Chapter 22: Reactors 961
22.1 Basic Relationships 962
22.2 Equipment Design for Nonisothermal Conditions 980
22.3 Performance Problems 1003
Chapter 23: Other Equipment 1015
23.1 Pressure Vessels 1016
23.2 Knockout Drums or Simple Phase Separators 1024
23.3 Steam Ejectors 1049
References 1058
Short Answer Questions 1059
Problems 1060
Chapter 24: Process Troubleshooting and Debottlenecking 1065
24.1 Recommended Methodology 1067
24.2 Troubleshooting Individual Units 1071
24.3 Troubleshooting Multiple Units 1076
24.4 A Process Troubleshooting Problem 1081
24.5 Debottlenecking Problems 1085
24.6 Summary 1091
References 1091
Problems 1091
Section V: The Impact of Chemical Engineering Design on Society 1101
Chapter 25: Ethics and Professionalism 1103
25.1 Ethics 1104
25.2 Professional Registration 1121
25.3 Legal Liability [13] 1125
25.4 Business Codes of Conduct [14, 15] 1126
25.5 Summary 1127
References 1128
Problems 1129
Chapter 26: Health, Safety, and the Environment 1131
26.1 Risk Assessment 1131
26.2 Regulations and Agencies 1134
26.3 Fires and Explosions 1143
26.4 Process Hazard Analysis 1145
26.5 Chemical Safety and Hazard Investigation Board 1153
26.6 Inherently Safe Design 1153
26.7 Summary 1154
26.8 Glossary 1154
References 1156
Problems 1157
Chapter 27: Green Engineering 1159
27.1 Environmental Regulations 1159
27.2 Environmental Fate of Chemicals 1160
27.3 Green Chemistry 1163
27.4 Pollution Prevention during Process Design 1164
27.5 Analysis of a PFD for Pollution Performance and Environmental Performance 1166
27.6 An Example of the Economics of Pollution Prevention 1167
27.7 Life Cycle Analysis 1168
27.8 Summary 1169
Section VI: Interpersonal and Communication Skills 1173
Chapter 28: Teamwork 1175
28.1 Groups 1175
28.2 Group Evolution 1184
28.3 Teams and Teamwork 1186
28.4 Misconceptions 1189
28.5 Learning in Teams 1189
28.6 Other Reading 1190
28.7 Summary 1191
References 1192
Problems 1192
Chapter 29: Written and Oral Communication 1195
29.1 Audience Analysis 1196
29.2 Written Communication 1196
29.3 Oral Communication 1209
29.4 Software and Author Responsibility 1215
29.5 Summary 1218
References 1218
Problems 1219
Chapter 30: A Report-Writing Case Study 1221
30.1 The Assignment Memorandum 1221
30.2 Response Memorandum 1222
30.3 Visual Aids 1224
30.4 Example Reports 1230
30.5 Checklist of Common Mistakes and Errors 1244
Appendix A: Cost Equations and Curves for the CAPCOST Program 1247
A.1 Purchased Equipment Costs 1247
A.2 Pressure Factors 1264
A.3 Material Factors and Bare Module Factors 1267
References 1275
Appendix B: Information for the Preliminary Design of Fifteen Chemical Processes 1277
B.1 Dimethyl Ether (DME) Production, Unit 200 1278
B.2 Ethylbenzene Production, Unit 300 1283
B.3 Styrene Production, Unit 400 1291
B.4 Drying Oil Production, Unit 500 1299
B.5 Production of Maleic Anhydride from Benzene, Unit 600 1305
B.6 Ethylene Oxide Production, Unit 700 1311
B.7 Formalin Production, Unit 800 1317
B.8 Batch Production of L-Phenylalanine and L-Aspartic Acid, Unit 900 1323
B.9 Acrylic Acid Production via the Catalytic Partial Oxidation of Propylene [1–5], Unit 1000 1329
B.10 Production of Acetone via the Dehydrogenation of Isopropyl Alcohol (IPA) [1–4], Unit 1100 1338
B.11 Production of Heptenes from Propylene and Butenes [1], Unit 1200 1344
B.12 Design of a Shift Reactor Unit to Convert CO to CO2, Unit 1300 1352
B.13 Design of a Dual-Stage Selexol Unit to Remove CO2 and H2S From
B.14 Design of a Claus Unit for the Conversion of H2S to Elemental Sulfur, Unit 1500 1363
B.15 Modeling a Downward-Flow, Oxygen-Blown, Entrained-Flow Gasifier, Unit 1600 1371
Appendix C: Design Projects 1379
Project 1 Increasing the Production of 3-Chloro-1-Propene (Allyl Chloride) in Unit 600 1381
Project 2 Design and Optimization of a New 20,000-Metric-Tons-per-Year Facility to Produce Allyl Chloride at La Nueva Cantina, Mexico 1394
Project 4 The Design of a New 100,000-Metric-Tons-per-Year Phthalic Anhydride Production Facility 1412
Project 5 Problems at the Cumene Production Facility, Unit 800 1417
Project 6 Design of a New, 100,000-Metric-Tons-per-Year Cumene Production Facility 1430
Index 1433
Essentials of Chemical Reaction Engineering, 2nd Edition - H. Scott Fogler
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Table of Contents Preface xv
About the Author xxxi
Chapter 1: Mole Balances 1
1.1 The Rate of Reaction, –rA 4
1.2 The General Mole Balance Equation 8
1.3 Batch Reactors (BRs) 10
1.4 Continuous-Flow Reactors 12
1.5 Industrial Reactors 23
Chapter 2: Conversiona and Reactor Sizing 33
2.1 Definition of Conversion 34
2.2 Batch Reactor Design Equations 34
2.3 Design Equations for Flow Reactors 37
2.4 Sizing Continuous-Flow Reactors 40
2.5 Reactors in Series 49
2.6 Some Further Definitions 60
Chapter 3: Rate Laws 71
3.1 Basic Definitions 72
3.2 The Rate Law 74
3.3 The Reaction Rate Constant 85
3.4 Molecular Simulations 95
3.5 Present Status of Our Approach to Reactor Sizing and Design 99
Chapter 4: Stoichiometry 111
4.1 Batch Systems 113
4.2 Flow Systems 119
4.3 Reversible Reactions and Equilibrium Conversion 132
Chapter 5: Isothermal Reactor Design: Conversion 147
5.1 Design Structure for Isothermal Reactors 148
5.2 Batch Reactors (BRs) 152
5.3 Continuous-Stirred Tank Reactors (CSTRs) 160
5.4 Tubular Reactors 170
5.5 Pressure Drop in Reactors 177
5.6 Synthesizing the Design of a Chemical Plant 199
Chapter 6: Isothermal Reactor Design: Moles and Molar Flow Rates 217
6.1 The Molar Flow Rate Balance Algorithm 218
6.2 Mole Balances on CSTRs, PFRs, PBRs, and Batch Reactors 218
6.3 Application of the PFR Molar Flow Rate Algorithm to a Microreactor 222
6.4 Membrane Reactors 227
6.5 Unsteady-State Operation of Stirred Reactors 236
6.6 Semibatch Reactors 237
Chapter 7: Collection and Analysis of Rate Data 255
7.1 The Algorithm for Data Analysis 256
7.2 Determining the Reaction Order for Each of Two Reactants Using the Method of Excess 258
7.3 Integral Method 259
7.4 Differential Method of Analysis 263
7.5 Nonlinear Regression 271
7.6 Reaction-Rate Data from Differential Reactors 276
7.7 Experimental Planning 283
Chapter 8: Multiple Reactions 293
8.1 Definitions 294
8.2 Algorithm for Multiple Reactions 297
8.3 Parallel Reactions 300
8.4 Reactions in Series 309
8.5 Complex Reactions 319
8.6 Membrane Reactors to Improve Selectivity in Multiple Reactions 327
8.7 Sorting It All Out 332
8.8 The Fun Part 332
Chapter 9: Reaction Mechanisms, Pathways, Bioreactions, and Bioreactors 349
9.1 Active Intermediates and Nonelementary Rate Laws 350
9.2 Enzymatic Reaction Fundamentals 359
9.3 Inhibition of Enzyme Reactions 372
9.4 Bioreactors and Biosynthesis 380
Chapter 10: Catalysis and Catalytic Reactors 419
10.1 Catalysts 419
10.2 Steps in a Catalytic Reaction 425
10.3 Synthesizing a Rate Law, Mechanism, and Rate-Limiting Step 441
10.4 Heterogeneous Data Analysis for Reactor Design 457
10.5 Reaction Engineering in Microelectronic Fabrication 467
10.6 Model Discrimination 472
10.7 Catalyst Deactivation 475
10.8 Reactors That Can Be Used to Help Offset Catalyst Decay 485
Chapter 11: Nonisothermal Reactor Design–The Steady-State Energy Balance and Adiabatic PFR Applications 515
11.1 Rationale 516
11.2 The Energy Balance 517
11.3 The User-Friendly Energy Balance Equations 525
11.4 Adiabatic Operation 531
11.5 Adiabatic Equilibrium Conversion 541
11.6 Reactor Staging with Interstage Cooling or Heating 546
11.7 Optimum Feed Temperature 550
Chapter 12: Steady-State Nonisothermal Reactor Design—Flow Reactors with Heat Exchange 565
12.1 Steady-State Tubular Reactor with Heat Exchange 566
12.2 Balance on the Heat-Transfer Fluid 569
12.3 Algorithm for PFR/PBR Design with Heat Effects 572
12.4 CSTR with Heat Effects 592
12.5 Multiple Steady States (MSS) 602
12.6 Nonisothermal Multiple Chemical Reactions 609
12.7 Radial and Axial Variations in a Tubular Reactor 624
12.8 Safety 632
Chapter 13: Unsteady-State Nonisothermal Reactor Design 661
13.1 The Unsteady-State Energy Balance 662
13.2 Energy Balance on Batch Reactors (BRs) 664
13.3 Batch and Semibatch Reactors with a Heat Exchanger 679
13.4 Nonisothermal Multiple Reactions 690
Appendix A: Numerical Techniques 715
A.1 Useful Integrals in Reactor Design 715
A.2 Equal-Area Graphical Differentiation 716
A.3 Solutions to Differential Equations 718
A.4 Numerical Evaluation of Integrals 719
A.5 Semilog Graphs 721
A.6 Software Packages 721
Appendix B: Ideal Gas Constant and Conversion Factors 723
Appendix C: Thermodynamic Relationships Involving the Equilibrium Constant 727
Appendix D: Software Packages 733
D.1 Polymath 733
D.2 Wolfram 735
D.3 MATLAB 735
D.4 Excel 736
D.5 COMSOL (http://www.umich.edu/~elements/5e/12chap/comsol.html) 736
D.6 Aspen 737
D.7 Visual Encyclopedia of Equipment—Reactors Section 738
D.8 Reactor Lab 738
Appendix E: Rate-Law Data 739
Appendix F: Nomenclature 741
Appendix G: Open-Ended Problems 745
G.1 Design of Reaction Engineering Experiment 745
G.2 Effective Lubricant Design 745
G.3 Peach Bottom Nuclear Reactor 745
G.4 Underground Wet Oxidation 746
G.5 Hydrodesulfurization Reactor Design 746
G.6 Continuous Bioprocessing 746
G.7 Methanol Synthesis 746
G.8 Cajun Seafood Gumbo 746
G.9 Alcohol Metabolism 747
G.10 Methanol Poisoning 748
Appendix H: Use of Computational Chemistry Software Packages 749
H.1 Computational Chemical Engineering 749
Appendix I: How to Use the CRE Web Resources 751
I.1 CRE Web Resources Components 751
I.2 How the Web Can Help Your Learning Style 754
I.3 Navigation 755
Index 757
Web Chapters (available on companion Web site)
Chapter 14: Mass Transfer Limitations in Reacting Systems
Chapter 15: Diffusion and Reaction
Chapter 16: Residence Time Distributions of Chemical Reactors
Chapter 17: Predicting Conversion Directly from the Residence Time Distribution
Chapter 18: Models for Nonideal Reactors
Mass Transfer Processes: Modeling, Computations, and Design - P. A. Ramachandran
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Table of Contents Preface xxix
About the Author xxxvii
Notation xxxix
Part I: Fundamentals of Mass Transfer Modeling 1
Chapter 1: Introduction to Modeling of Mass Transfer Processes 3
1.1 What Is Mass Transfer? 5
1.2 Preliminaries: Continuum and Concentration 7
1.3 Flux Vector 10
1.4 Concentration Jump at Interface 15
1.5 Application Examples 20
1.6 Basic Methodology of Model Development 28
1.7 Conservation Principle 29
1.8 Differential Models 30
1.9 Macroscopic Scale 32
1.10 Mesoscopic or Cross-Section Averaged Models 37
1.11 Compartmental Models 43
Chapter 2: Examples of Differential (1-D) Balances 51
2.1 Cartesian Coordinates 52
2.2 Cylindrical Coordinates 67
2.3 Spherical Coordinates 73
Chapter 3: Examples of Macroscopic Models 85
3.1 Macroscopic Balance 87
3.2 The Batch Reactor 90
3.3 Reactor–Separator Combination 96
3.4 Sublimation of a Spherical Particle 101
3.5 Dissolved Oxygen Concentration in a Stirred Tank 104
3.6 Continuous Stirred Tank Reactor 106
3.7 Tracer Experiments: Test for Backmixed Assumption 110
3.8 Liquid–Liquid Extraction 112
Chapter 4: Examples of Mesoscopic Models 123
4.1 Solid Dissolution from a Wall 124
4.2 Tubular Flow Reactor 129
4.3 Mass Exchangers 134
Chapter 5: Equations of Mass Transfer 151
5.1 Flux Form 153
5.2 Frame of Reference 156
5.3 Properties of Diffusion Flux 163
5.4 Pseudo-Binary Diffusivity 165
5.5 Concentration Form 166
5.6 Common Boundary Conditions 171
5.7 Macroscopic Models: Single-Phase Systems 172
5.8 Multiphase Systems: Local Volume Averaging 175
Chapter 6: Diffusion-Dominated Processes and the Film Model 185
6.1 Steady State Diffusion: No Reaction 186
6.2 Diffusion-Induced Convection 193
6.3 Film Concept in Mass Transfer Analysis 198
6.4 Surface Reactions: Role of Mass Transfer 206
6.5 Gas–Liquid Interface: Two-Film Model 212
Chapter 7: Phenomena of Diffusion 223
7.1 Diffusion Coeffcients in Gases 224
7.2 Diffusion Coeffcients in Liquids 237
7.3 Non-Ideal Liquids 243
7.4 Solid–Solid Diffusion 246
7.5 Diffusion of Fluids in Porous Solids 248
7.6 Heterogeneous Media 254
7.7 Polymeric Membranes 256
7.8 Other Complex Effects 257
Chapter 8: Transient Diffusion Processes 265
8.1 Transient Diffusion Problems in 1-D 266
8.2 Solution for Slab: Dirichlet Case 267
8.3 Solutions for Slab: Robin Condition 276
8.4 Solution for Cylinders and Spheres 278
8.5 Transient Non-Homogeneous Problems 283
8.6 2-D Problems: Product Solution Method 285
8.7 Semi-Infinite Slab Analysis 287
8.8 Penetration Theory of Mass Transfer 294
8.9 Transient Diffusion with Variable Diffusivity 295
8.10 Eigenvalue Computations with CHEBFUN 297
8.11 Computations with PDEPE Solver 299
Chapter 9: Basics of Convective Mass Transport 309
9.1 Definitions for External and Internal Flows 310
9.2 Relation to Differential Model 311
9.3 Key Dimensionless Groups 313
9.4 Mass Transfer in Flows in Pipes and Channels 315
9.5 Mass Transfer in Flow over a Flat Plate 316
9.6 Mass Transfer for Film Flow 318
9.7 Mass Transfer from a Solid Sphere 320
9.8 Mass Transfer from a Gas Bubble 321
9.9 Mass Transfer in Mechanically Agitated Tanks 325
9.10 Gas–Liquid Mass Transfer in a Packed Bed Absorber 327
Chapter 10: Convective Mass Transfer: Theory for Internal Laminar Flow 335
10.1 Mass Transfer in Laminar Flow in a Pipe 336
10.2 Wall Reaction: The Robin Problem 344
10.3 Entry Region Analysis 348
10.4 Channel Flows with Mass Transfer 350
10.5 Mass Transfer in Film Flow 353
10.6 Numerical Solution with PDEPE 358
Chapter 11: Mass Transfer in Laminar Boundary Layers 365
11.1 Flat Plate with Low Flux Mass Transfer 366
11.2 Integral Balance Approach 376
11.3 High Flux Analysis 383
11.4 Mass Transfer for Flow over Inclined and Curved Surfaces 388
11.5 Bubbles and Drops 396
Chapter 12: Convective Mass Transfer in Turbulent Flow 403
12.1 Properties of Turbulent Flow 404
12.2 Properties of Time Averaging 406
12.3 Time-Averaged Equation of Mass Transfer 408
12.4 Closure Models 411
12.5 Velocity and Turbulent Diffusivity Profiles 413
12.6 Turbulent Mass Transfer in Channels and Pipes 417
12.7 Van Driest Model for Large Sc 425
12.8 Turbulent Mass Transfer at Gas–Liquid Interface 427
Chapter 13: Macroscopic and Compartmental Models 435
13.1 Stirred Reactor: The Backmixing Assumption 436
13.2 Transient Balance: Tracer Studies 438
13.3 Moment Analysis of Tracer Data 444
13.4 Tanks in Series Models: Reactor Performance 449
13.5 Macrofluid Models 450
13.6 Variance-Based Models for Partial Micromixing 453
13.7 Compartmental Models 454
13.8 Compartmental Models for Environmental Transport 459
13.9 Fluid–Fluid Systems 462
13.10 Models for Multistage Cascades 465
Chapter 14: Mesoscopic Models and the Concept of Dispersion 475
14.1 Plug Flow Idealization 476
14.2 Dispersion Model 478
14.3 Dispersion Coeffcient: Tracer Response Method 484
14.4 Taylor Model for Dispersion in Laminar Flow 488
14.5 Segregated Flow Model 491
14.6 Dispersion Coe[1]cient Values for Some Common Cases 493
14.7 Two-Phase Flow: Models Based on Ideal Flow Patterns 495
14.8 Tracer Response in Two-Phase Systems 503
Chapter 15: Mass Transfer: Multicomponent Systems 517
15.1 Constitutive Model for Multicomponent Transport 518
15.2 Computations for a Reacting System 520
15.3 Heterogeneous Reactions 525
15.4 Non-Reacting Systems 528
15.5 Multicomponent Diffusivity Matrix 535
Chapter 16: Mass Transport in Electrolytic Systems 543
16.1 Transport of Charged Species: Preliminaries 544
16.2 Charge Neutrality 547
16.3 General Expression for the Electric Field 548
16.4 Electrolyte Transport across Uncharged Membrane 551
16.5 Transport across a Charged Membrane 553
16.6 Transfer Rate in Diffusion Film near an Electrode 556
Part II: Reacting Systems 565
Chapter 17: Laminar Flow Reactor 567
17.1 Model Equations and Key Dimensionless Groups 568
17.2 Two Limiting Cases 572
17.3 Mesoscopic Dispersion Model 575
17.4 Other Examples of Flow Reactors 577
Chapter 18: Mass Transfer with Reaction: Porous Catalysts 585
18.1 Catalyst Properties and Applications 586
18.2 Diffusion-Reaction Model 588
18.3 Multiple Species 605
18.4 Three-Phase Catalytic Reactions 607
18.5 Temperature Effects in a Porous Catalyst 610
18.6 Orthogonal Collocation Method 615
18.7 Finite Difference Methods 617
18.8 Linking with Reactor Models 622
Chapter 19: Reacting Solids 635
19.1 Shrinking Core Model 636
19.2 Volume Reaction Model 644
19.3 Other Models for Gas–Solid Reactions 651
19.4 Solid–Solid Reactions 654
Chapter 20: Gas–Liquid Reactions: Film Theory Models 661
20.1 First-Order Reaction of Dissolved Gas 662
20.2 Bulk Concentration and Bulk Reactions 668
20.3 Bimolecular Reactions 672
20.4 Simultaneous Absorption of Two Gases 684
20.5 Coupling with Reactor Models 688
20.6 Absorption in Slurries 692
20.7 Liquid–Liquid Reactions 697
Chapter 21: Gas–Liquid Reactions: Penetration Theory Approach 705
21.1 Concepts of Penetration Theory 706
21.2 Bimolecular Reaction 712
21.3 Instantaneous Reaction Case 714
21.4 Ideal Contactors 717
Chapter 22: Reactive Membranes and Facilitated Transport 727
22.1 Single Solute Diffusion 729
22.2 Co- and Counter-Transport 736
22.3 Equilibrium Model: A Computational Scheme 739
22.4 Reactive Membranes in Practice 742
Chapter 23: Biomedical Applications 749
23.1 Oxygen Uptake in Lungs 751
23.2 Transport in Tissues: Krogh Model 757
23.3 Compartmental Models for Pharmacokinetics 760
23.4 Model for a Hemodialyzer 763
Chapter 24 Electrochemical Reaction Engineering 775
24.1 Basic Definitions 776
24.2 Thermodynamic Considerations: Nernst Equation 781
24.3 Kinetic Model for Electrochemical Reactions 786
24.4 Mass Transfer Eects 791
24.5 Voltage Balance 793
24.6 Copper Electrowinning 795
24.7 Hydrogen Fuel Cell 798
24.8 Li-Ion Battery Modeling 800
Part III: Mass Transfer–Based Separations 809
Chapter 25: Humidification and Drying 811
25.1 Wet and Dry Bulb Temperature 812
25.2 Humidification: Cooling Towers 815
25.3 Model for Counterflow 817
25.4 Cross-Flow Cooling Towers 825
25.5 Drying 827
25.6 Constant Rate Period 830
25.7 Falling Rate Period 833
Chapter 26: Condensation 845
26.1 Condensation of Pure Vapor 846
26.2 Condensation of a Vapor with a Non-Condensible Gas 850
26.3 Fog Formation 855
26.4 Condensation of Binary Gas Mixture 857
26.5 Condenser Model 861
26.6 Ternary Systems 864
Chapter 27: Gas Transport in Membranes 871
27.1 Gas Separation Membranes 872
27.2 Gas Translation Model 879
27.3 Gas Permeator Models 881
27.4 Reactor Coupled with a Membrane Separator 890
Chapter 28: Liquid Separation Membranes 897
28.1 Classification Based on Pore Size 898
28.2 Transport in Semi-Permeable Membranes 900
28.3 Forward Osmosis 907
28.4 Pervaporation 908
Chapter 29: Adsorption and Chromatography 919
29.1 Applications and Adsorbent Properties 920
29.2 Isotherms 921
29.3 Model for Batch Slurry Adsorber 924
29.4 Fixed Bed Adsorption 931
29.5 Chromatography 938
Chapter 30: Electrodialysis and Electrophoresis 945
30.1 Technological Aspects 946
30.2 Preliminary Design of an Electrodialyzer 951
30.3 Principle of Electrophoresis 955
30.4 Electrophoretic Separation Devices 957
References 965
Index 979
Transport Processes and Separation Process Principles, 5th Edition - Christie John Geankoplis, Allen H. Hersel, Daniel H. Lepek
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Table of Contents Preface to the Fifth Edition xxvii
About the Authors xxxi
Part 1: Transport Processes: Momentum, Heat, and Mass
Chapter 1: Introduction to Engineering Principles and Units 3
1.0 Chapter Objectives 3
1.1 Classification of Transport Processes and Separation Processes (Unit Operations) 3
1.2 SI System of Basic Units Used in This Text and Other Systems 6
1.3 Methods of Expressing Temperatures and Compositions 8
1.4 Gas Laws and Vapor Pressure 10
1.5 Conservation of Mass and Material Balances 13
1.6 Energy and Heat Units 17
1.7 Conservation of Energy and Heat Balances 23
1.8 Numerical Methods for Integration 28
1.9 Chapter Summary 29
Chapter 2: Introduction to Fluids and Fluid Statics 36
2.0 Chapter Objectives 36
2.1 Introduction 36
2.2 Fluid Statics 37
2.3 Chapter Summary 47
Chapter 3: Fluid Properties and Fluid Flows 50
3.0 Chapter Objectives 50
3.1 Viscosity of Fluids 50
3.2 Types of Fluid Flow and Reynolds Number 54
3.3 Chapter Summary 58
Chapter 4: Overall Mass, Energy, and Momentum Balances 61
4.0 Chapter Objectives 61
4.1 Overall Mass Balance and Continuity Equation 62
4.2 Overall Energy Balance 68
4.3 Overall Momentum Balance 81
4.4 Shell Momentum Balance and Velocity Profile in Laminar Flow 90
4.5 Chapter Summary 96
Chapter 5: Incompressible and Compressible Flows in Pipes 105
5.0 Chapter Objectives 105
5.1 Design Equations for Laminar and Turbulent Flow in Pipes 106
5.2 Compressible Flow of Gases 125
5.3 Measuring the Flow of Fluids 129
5.4 Chapter Summary 138
Chapter 6: Flows in Packed and Fluidized Beds 145
6.0 Chapter Objectives 145
6.1 Flow Past Immersed Objects 146
6.2 Flow in Packed Beds 150
6.3 Flow in Fluidized Beds 156
6.4 Chapter Summary 161
Chapter 7: Pumps, Compressors, and Agitation Equipment 166
7.0 Chapter Objectives 166
7.1 Pumps and Gas-Moving Equipment 166
7.2 Agitation, Mixing of Fluids, and Power Requirements 176
7.3 Chapter Summary 192
Chapter 8: Differential Equations of Fluid Flow 196
8.0 Chapter Objectives 196
8.1 Differential Equations of Continuity 196
8.2 Differential Equations of Momentum Transfer or Motion 202
8.3 Use of Differential Equations of Continuity and Motion 207
8.4 Chapter Summary 216
Chapter 9: Non-Newtonian Fluids 220
9.0 Chapter Objectives 220
9.1 Non-Newtonian Fluids 221
9.2 Friction Losses for Non-Newtonian Fluids 226
9.3 Velocity Profiles for Non-Newtonian Fluids 229
9.4 Determination of Flow Properties of Non-Newtonian Fluids Using a Rotational Viscometer 232
9.5 Power Requirements in Agitation and Mixing of Non-Newtonian Fluids 234
9.6 Chapter Summary 235
Chapter 10: Potential Flow and Creeping Flow 239
10.0 Chapter Objectives 239
10.1 Other Methods for Solution of Differential Equations of Motion 239
10.2 Stream Function 240
10.3 Differential Equations of Motion for Ideal Fluids (Inviscid Flow) 241
10.4 Potential Flow and Velocity Potential 241
10.5 Differential Equations of Motion for Creeping Flow 246
10.6 Chapter Summary 247
Chapter 11: Boundary-Layer and Turbulent Flow 250
11.0 Chapter Objectives 250
11.1 Boundary-Layer Flow 251
11.2 Turbulent Flow 254
11.3 Turbulent Boundary-Layer Analysis 260
11.4 Chapter Summary 263
Chapter 12: Introduction to Heat Transfer 265
12.0 Chapter Objectives 265
12.1 Energy and Heat Units 265
12.2 Conservation of Energy and Heat Balances 271
12.3 Conduction and Thermal Conductivity 277
12.4 Convection 282
12.5 Radiation 284
12.6 Heat Transfer with Multiple Mechanisms/Materials 287
12.7 Chapter Summary 292
Chapter 13: Steady-State Conduction 299
13.0 Chapter Objectives 299
13.1 Conduction Heat Transfer 299
13.2 Conduction Through Solids in Series or Parallel with Convection 305
13.3 Conduction with Internal Heat Generation 313
13.4 Steady-State Conduction in Two Dimensions Using Shape Factors 315
13.5 Numerical Methods for Steady-State Conduction in Two Dimensions 318
13.6 Chapter Summary 326
Chapter 14: Principles of Unsteady-State Heat Transfer 332
14.0 Chapter Objectives 332
14.1 Derivation of the Basic Equation 332
14.2 Simplified Case for Systems with Negligible Internal Resistance 334
14.3 Unsteady-State Heat Conduction in Various Geometries 337
14.4 Numerical Finite-Difference Methods for Unsteady-State Conduction 355
14.5 Chilling and Freezing of Food and Biological Materials 366
14.6 Differential Equation of Energy Change 372
14.7 Chapter Summary 376
Chapter 15: Introduction to Convection 385
15.0 Chapter Objectives 385
15.1 Introduction and Dimensional Analysis in Heat Transfer 385
15.2 Boundary-Layer Flow and Turbulence in Heat Transfer 389
15.3 Forced Convection Heat Transfer Inside Pipes 394
15.4 Heat Transfer Outside Various Geometries in Forced Convection 402
15.5 Natural Convection Heat Transfer 408
15.6 Boiling and Condensation 415
15.7 Heat Transfer of Non-Newtonian Fluids 424
15.8 Special Heat-Transfer Coefficients 427
15.9 Chapter Summary 436
Chapter 16: Heat Exchangers 444
16.0 Chapter Objectives 444
16.1 Types of Exchangers 444
16.2 Log-Mean-Temperature-Difference Correction Factors 447
16.3 Heat-Exchanger Effectiveness 450
16.4 Fouling Factors and Typical Overall U Values 453
16.5 Double-Pipe Heat Exchanger 454
16.6 Chapter Summary 458
Chapter 17: Introduction to Radiation Heat Transfer 461
17.0 Chapter Objectives 461
17.1 Introduction to Radiation Heat-Transfer Concepts 461
17.2 Basic and Advanced Radiation Heat-Transfer Principles 465
17.3 Chapter Summary 482
Chapter 18: Introduction to Mass Transfer 487
18.0 Chapter Objectives 487
18.1 Introduction to Mass Transfer and Diffusion 487
18.2 Diffusion Coefficient 493
18.3 Convective Mass Transfer 508
18.4 Molecular Diffusion Plus Convection and Chemical Reaction 508
18.5 Chapter Summary 512
Chapter 19: Steady-State Mass Transfer 519
19.0 Chapter Objectives 519
19.1 Molecular Diffusion in Gases 519
19.2 Molecular Diffusion in Liquids 528
19.3 Molecular Diffusion in Solids 531
19.4 Diffusion of Gases in Porous Solids and Capillaries 537
19.5 Diffusion in Biological Gels 544
19.6 Special Cases of the General Diffusion Equation at Steady State 546
19.7 Numerical Methods for Steady-State Molecular Diffusion in Two Dimensions 550
19.8 Chapter Summary 557
Chapter 20: Unsteady-State Mass Transfer 568
20.0 Chapter Objectives 568
20.1 Unsteady-State Diffusion 568
20.2 Unsteady-State Diffusion and Reaction in a Semi-Infinite Medium 575
20.3 Numerical Methods for Unsteady-State Molecular Diffusion 577
20.4 Chapter Summary 582
Chapter 21: Convective Mass Transfer 586
21.0 Chapter Objectives 586
21.1 Convective Mass Transfer 586
21.2 Dimensional Analysis in Mass Transfer 594
21.3 Mass-Transfer Coefficients for Various Geometries 595
21.4 Mass Transfer to Suspensions of Small Particles 610
21.5 Models for Mass-Transfer Coefficients 613
21.6 Chapter Summary 617
Part 2: Separation Process Principles
Chapter 22: Absorption and Stripping 627
22.0 Chapter Objectives 627
22.1 Equilibrium and Mass Transfer Between Phases 627
22.2 Introduction to Absorption 645
22.3 Pressure Drop and Flooding in Packed Towers 649
22.4 Design of Plate Absorption Towers 654
22.5 Design of Packed Towers for Absorption 656
22.6 Efficiency of Random-Packed and Structured Packed Towers 672
22.7 Absorption of Concentrated Mixtures in Packed Towers 675
22.8 Estimation of Mass-Transfer Coefficients for Packed Towers 679
22.9 Heat Effects and Temperature Variations in Absorption 682
22.10 Chapter Summary 685
Chapter 23: Humidification Processes 694
23.0 Chapter Objectives 694
23.1 Vapor Pressure of Water and Humidity 694
23.2 Introduction and Types of Equipment for Humidification 703
23.3 Theory and Calculations for Cooling-Water Towers 704
23.4 Chapter Summary 712
Chapter 24: Filtration and Membrane Separation Processes (Liquid–Liquid or Solid–Liquid Phase) 716
24.0 Chapter Objectives 716
24.1 Introduction to Dead-End Filtration 716
24.2 Basic Theory of Filtration 722
24.3 Membrane Separations 732
24.4 Microfiltration Membrane Processes 733
24.5 Ultrafiltration Membrane Processes 734
24.6 Reverse-Osmosis Membrane Processes 738
24.7 Dialysis 747
24.8 Chapter Summary 751
Chapter 25: Gaseous Membrane Systems 759
25.0 Chapter Objectives 759
25.1 Gas Permeation 759
25.2 Complete-Mixing Model for Gas Separation by Membranes 765
25.3 Complete-Mixing Model for Multicomponent Mixtures 770
25.4 Cross-Flow Model for Gas Separation by Membranes 773
25.5 Derivation of Equations for Countercurrent and Cocurrent Flow for Gas Separation by Membranes 779
25.6 Derivation of Finite-Difference Numerical Method for Asymmetric Membranes 787
25.7 Chapter Summary 798
Chapter 26: Distillation 805
26.0 Chapter Objectives 805
26.1 Equilibrium Relations Between Phases 805
26.2 Single and Multiple Equilibrium Contact Stages 808
26.3 Simple Distillation Methods 813
26.4 Binary Distillation with Reflux Using the McCabe–Thiele and Lewis Methods 818
26.5 Tray Efficiencies 836
26.6 Flooding Velocity and Diameter of Tray Towers Plus Simple Calculations for Reboiler and Condenser Duties 839
26.7 Fractional Distillation Using the Enthalpy–Concentration Method 841
26.8 Distillation of Multicomponent Mixtures 851
26.9 Chapter Summary 862
Chapter 27: Liquid–Liquid Extraction 874
27.0 Chapter Objectives 874
27.1 Introduction to Liquid–Liquid Extraction 874
27.2 Single-Stage Equilibrium Extraction 878
27.3 Types of Equipment and Design for Liquid–Liquid Extraction 880
27.4 Continuous Multistage Countercurrent Extraction 889
27.5 Chapter Summary 901
Chapter 28: Adsorption and Ion Exchange 907
28.0 Chapter Objectives 907
28.1 Introduction to Adsorption Processes 907
28.2 Batch Adsorption 910
28.3 Design of Fixed-Bed Adsorption Columns 912
28.4 Ion-Exchange Processes 918
28.5 Chapter Summary 924
Chapter 29: Crystallization and Particle Size Reduction 928
29.0 Chapter Objectives 928
29.1 Introduction to Crystallization 928
29.2 Crystallization Theory 935
29.3 Mechanical Size Reduction 942
29.4 Chapter Summary 947
Chapter 30: Settling, Sedimentation, and Centrifugation 952
30.0 Chapter Objectives 952
30.1 Settling and Sedimentation in Particle–Fluid Separation 953
30.2 Centrifugal Separation Processes 966
30.3 Chapter Summary 979
Chapter 31: Leaching 984
31.0 Chapter Objectives 984
31.1 Introduction and Equipment for Liquid–Solid Leaching 984
31.2 Equilibrium Relations and Single-Stage Leaching 990
31.3 Countercurrent Multistage Leaching 994
31.4 Chapter Summary 999
Chapter 32: Evaporation 1002
32.0 Chapter Objectives 1002
32.1 Introduction 1002
32.2 Types of Evaporation Equipment and Operation Methods 1004
32.3 Overall Heat-Transfer Coefficients in Evaporators 1008
32.4 Calculation Methods for Single-Effect Evaporators 1010
32.5 Calculation Methods for Multiple-Effect Evaporators 1016
32.6 Condensers for Evaporators 1026
32.7 Evaporation of Biological Materials 1028
32.8 Evaporation Using Vapor Recompression 1029
32.9 Chapter Summary 1030
Chapter 33: Drying 1035
33.0 Chapter Objectives 1035
33.1 Introduction and Methods of Drying 1035
33.2 Equipment for Drying 1036
33.3 Vapor Pressure of Water and Humidity 1040
33.4 Equilibrium Moisture Content of Materials 1049
33.5 Rate-of-Drying Curves 1052
33.6 Calculation Methods for a Constant-Rate Drying Period 1057
33.7 Calculation Methods for the Falling-Rate Drying Period 1062
33.8 Combined Convection, Radiation, and Conduction Heat Transfer in the Constant-Rate Period 1065
33.9 Drying in the Falling-Rate Period by Diffusion and Capillary Flow 1068
33.10 Equations for Various Types of Dryers 1074
33.11 Freeze-Drying of Biological Materials 1084
33.12 Unsteady-State Thermal Processing and Sterilization of Biological Materials 1088
33.13 Chapter Summary 1096
Part 3: Appendixes
Appendix A.1 Fundamental Constants and Conversion Factors 1107
Appendix A.2 Physical Properties of Water 1113
Appendix A.3 Physical Properties of Inorganic and Organic Compounds 1124
Appendix A.4 Physical Properties of Foods and Biological Materials 1147
Appendix A.5 Properties of Pipes, Tubes, and Screens 1151
Appendix A.6 Lennard-Jones Potentials as Determined from Viscosity Data 1154
Notation 1156
Index 1166
Chemical Process Equipment Design - Richard Turton, Joseph A. Shaeiwitz
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Table of Contents Preface xi
Acknowledgments xiii
About the Authors xv
Chapter 1: Process Fluid Mechanics 1
1.0 Introduction 1
1.1 Basic Relationships in Fluid Mechanics 1
1.2 Fluid Flow Equipment 7
1.3 Frictional Pipe Flow 13
1.4 Other Flow Situations 28
1.5 Performance of Fluid Flow Equipment 41
Chapter 2: Process Heat Transfer 77
2.0 Introduction 77
2.1 Basic Heat-Exchanger Relationships 77
2.2 Heat-Exchange Equipment Design and Characteristics 84
2.3 LMTD Correction Factor for Multiple Shell and Tube Passes 95
2.4 Overall Heat Transfer Coefficients–Resistances in Series 104
2.5 Estimation of Individual Heat Transfer Coefficients and Fouling Resistances 106
2.6 Extended Surfaces 135
2.7 Algorithm and Worked Examples for the Design of Heat Exchangers 144
2.8 Performance Problems 154
Chapter 3: Separation Equipment 185
3.0 Introduction 185
3.1 Basic Relationships in Separations 186
3.2 Illustrative Diagrams 193
3.3 Equipment 221
3.4 Extraction Equipment 251
3.5 Gas Permeation Membrane Separations 253
Chapter 4: Reactors 275
4.0 Introduction 275
4.1 Basic Relationships 276
4.2 Equipment Design for Nonisothermal Conditions 294
4.3 Performance Problems 317
Chapter 5: Other Equipment 331
5.0 Introduction 331
5.1 Pressure Vessels 332
5.2 Knockout Drums or Simple Phase Separators 340
5.3 Steam Ejectors 365
Index 383
Fundamental Concepts and Computations in Chemical Engineering Vivek Utgika
Table of Contents Preface xiii
Acknowledgments xvii
About the Author xix
Chapter 1: The Chemical Engineering Profession 1
1.1 Engineering and Engineers 2
1.2 Engineering Disciplines 8
1.3 Defining Chemical Engineering 12
1.4 Roles and Responsibilities of a Chemical Engineer 14
1.5 Employment of Chemical Engineers 19
1.6 Summary 22
Chapter 2: Chemical and Allied Industries 27
2.1 Classification of Industries 27
2.2 The Chemical Industry 29
2.3 Related Industries 34
2.4 Top 50 Chemical Companies 36
2.5 Important Chemical Products 40
2.6 Characteristics of Chemical Industries 50
2.7 Summary 53
Chapter 3: Making of a Chemical Engineer 57
3.1 A Chemical Process Plant: Synthesis of Ammonia 57
3.2 Responsibilities and Functions of a Chemical Engineer 61
3.3 Chemical Engineering Curriculum 63
3.4 Summary 87
Chapter 4: Introduction to Computations in Chemical Engineering 91
4.1 Nature of Chemical Engineering Computational Problems 91
4.2 Solution Algorithms 102
4.3 Computational Tools—Machines and Software 107
4.4 Summary 113
Chapter 5: Computations in Fluid Flow 117
5.1 Qualitative Description of Flow in Conduits 117
5.2 Quantitative Analysis of Fluid Flow 119
5.3 Basic Computational Problems 124
5.4 Summary 140
Chapter 6: Material Balance Computations 143
6.1 Quantitative Principles of Material Balance 143
6.2 Material Balances in Nonreacting Systems 146
6.3 Material Balances in Reacting Systems 151
6.4 Material Balances over Multiple Process Units 159
6.5 Summary 163
Chapter 7: Energy Balance Computations 167
7.1 Quantitative Principles of Energy Balance 167
7.2 Basic Energy Balance Problems 175
7.3 Summary 186
Chapter 8: Computations in Chemical Engineering Thermodynamics 191
8.1 Fundamental Concepts of Thermodynamics 192
8.2 Basic Computational Problems 204
8.3 Summary 211
Chapter 9: Computations in Chemical Engineering Kinetics 217
9.1 Fundamental Concepts of Chemical Engineering Kinetics 218
9.2 Basic Computational Problems 229
9.3 Summary 240
Epilogue 245
Appendix A: Introduction to Mathematical Software Packages 247
Appendix B: Computations Using Process Simulation Software 259
Index 273
Elements of Chemical Reaction Engineering, 5th Edition - H. Scott Fogler
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Table of Contents
Preface xvii
About the Author xxxiii
Chapter 1: Mole Balances 1
1.1 The Rate of Reaction, –rA 4
1.2 The General Mole Balance Equation 8
1.3 Batch Reactors (BRs) 10
1.4 Continuous-Flow Reactors 12
1.5 Industrial Reactors 22
Chapter 2: Conversion and Reactor Sizing 31
2.1 Definition of Conversion 32
2.2 Batch Reactor Design Equations 32
2.3 Design Equations for Flow Reactors 35
2.4 Sizing Continuous-Flow Reactors 38
2.5 Reactors in Series 47
2.6 Some Further Definitions 58
Chapter 3: Rate Laws 69
3.1 Basic Definitions 70
3.2 The Reaction Order and the Rate Law 72
3.3 Rates and the Reaction Rate Constant 83
3.4 Present Status of Our Approach to Reactor Sizing and Design 93
Chapter 4: Stoichiometry 105
4.1 Batch Systems 107
4.2 Flow Systems 113
4.3 Reversible Reactions and Equilibrium Conversion 126
Chapter 5: Isothermal Reactor Design: Conversion 139
5.1 Design Structure for Isothermal Reactors 140
5.2 Batch Reactors (BRs) 144
5.3 Continuous-Stirred Tank Reactors (CSTRs) 152
5.4 Tubular Reactors 162
5.5 Pressure Drop in Reactors 169
5.6 Synthesizing the Design of a Chemical Plant 190
Chapter 6: Isothermal Reactor Design: Moles and Molar Flow Rates 207
6.1 The Molar Flow Rate Balance Algorithm 208
6.2 Mole Balances on CSTRs, PFRs, PBRs, and Batch Reactors 208
6.3 Application of the PFR Molar Flow Rate Algorithm to a Microreactor 212
6.4 Membrane Reactors 217
6.5 Unsteady-State Operation of Stirred Reactors 225
6.6 Semibatch Reactors 227
Chapter 7: Collection and Analysis of Rate Data 243
7.1 The Algorithm for Data Analysis 244
7.2 Determining the Reaction Order for Each of Two Reactants Using the Method of Excess 246
7.3 Integral Method 247
7.4 Differential Method of Analysis 251
7.5 Nonlinear Regression 258
7.6 Reaction-Rate Data from Differential Reactors 264
7.7 Experimental Planning 271
Chapter 8: Multiple Reactions 279
8.1 Definitions 280
8.2 Algorithm for Multiple Reactions 282
8.3 Parallel Reactions 285
8.4 Reactions in Series 294
8.5 Complex Reactions 304
8.6 Membrane Reactors to Improve Selectivity in Multiple Reactions 312
8.7 Sorting It All Out 317
8.8 The Fun Part 317
Chapter 9: Reaction Mechanisms, Pathways, Bioreactions, and Bioreactors 333
9.1 Active Intermediates and Nonelementary Rate Laws 334
9.2 Enzymatic Reaction Fundamentals 343
9.3 Inhibition of Enzyme Reactions 356
9.4 Bioreactors and Biosynthesis 364
Chapter 10: Catalysis and Catalytic Reactors 399
10.1 Catalysts 399
10.2 Steps in a Catalytic Reaction 405
10.3 Synthesizing a Rate Law, Mechanism, and Rate-Limiting Step 421
10.4 Heterogeneous Data Analysis for Reactor Design 436
10.5 Reaction Engineering in Microelectronic Fabrication 446
10.6 Model Discrimination 451
10.7 Catalyst Deactivation 454
Chapter 11: Nonisothermal Reactor Design—The Steady-State Energy Balance and Adiabatic PFR Applications 493
11.1 Rationale 494
11.2 The Energy Balance 495
11.3 The User-Friendly Energy Balance Equations 502
11.4 Adiabatic Operation 508
11.5 Adiabatic Equilibrium Conversion 518
11.6 Reactor Staging 522
11.7 Optimum Feed Temperature 526
Chapter 12: Steady-State Nonisothermal Reactor Design—Flow Reactors with Heat Exchange 539
12.1 Steady-State Tubular Reactor with Heat Exchange 540
12.2 Balance on the Heat-Transfer Fluid 543
12.3 Algorithm for PFR/PBR Design with Heat Effects 545
12.4 CSTR with Heat Effects 564
12.5 Multiple Steady States (MSS) 574
12.6 Nonisothermal Multiple Chemical Reactions 581
12.7 Radial and Axial Variations in a Tubular Reactor 595
12.8 Safety 603
Chapter 13: Unsteady-State Nonisothermal Reactor Design 629
13.1 Unsteady-State Energy Balance 630
13.2 Energy Balance on Batch Reactors 632
13.3 Semibatch Reactors with a Heat Exchanger 646
13.4 Unsteady Operation of a CSTR 651
13.5 Nonisothermal Multiple Reactions 656
Chapter 14: Mass Transfer Limitations in Reacting Systems 679
14.1 Diffusion Fundamentals 680
14.2 Binary Diffusion 684
14.3 Diffusion Through a Stagnant Film 688
14.4 The Mass Transfer Coefficient 690
14.5 What If . . . ? (Parameter Sensitivity) 705
Chapter 15: Diffusion and Reaction 719
15.1 Diffusion and Reactions in Homogeneous Systems 720
15.2 Diffusion and Reactions in Spherical Catalyst Pellets 720
15.3 The Internal Effectiveness Factor 730
15.4 Falsified Kinetics 737
15.5 Overall Effectiveness Factor 739
15.6 Estimation of Diffusion- and Reaction-Limited Regimes 743
15.7 Mass Transfer and Reaction in a Packed Bed 744
15.8 Determination of Limiting Situations from Reaction-Rate Data 750
15.9 Multiphase Reactors in the Professional Reference Shelf 751
15.10 Fluidized Bed Reactors 753
15.11 Chemical Vapor Deposition (CVD) 753
Chapter 16: Residence Time Distributions of Chemical Reactors 767
16.1 General Considerations 767
16.2 Measurement of the RTD 770
16.3 Characteristics of the RTD 777
16.4 RTD in Ideal Reactors 784
16.5 PFR/CSTR Series RTD 789
16.6 Diagnostics and Troubleshooting 793
Chapter 17: Predicting Conversion Directly from the Residence Time Distribution 807
17.1 Modeling Nonideal Reactors Using the RTD 808
17.2 Zero-Adjustable-Parameter Models 810
17.3 Using Software Packages 827
17.4 RTD and Multiple Reactions 830
Chapter 18: Models for Nonideal Reactors 845
18.1 Some Guidelines for Developing Models 846
18.2 The Tanks-in-Series (T-I-S) One-Parameter Model 848
18.3 Dispersion One-Parameter Model 852
18.4 Flow, Reaction, and Dispersion 854
18.5 Tanks-in-Series Model versus Dispersion Model 869
18.6 Numerical Solutions to Flows with Dispersion and Reaction 870
18.7 Two-Parameter Models—Modeling Real Reactors with Combinations of Ideal Reactors 871
18.8 Use of Software Packages to Determine the Model Parameters 880
18.9 Other Models of Nonideal Reactors Using CSTRs and PFRs 882
18.10 Applications to Pharmacokinetic Modeling 883
Appendix A: Numerical Techniques 897
A.1 Useful Integrals in Reactor Design 897
A.2 Equal-Area Graphical Differentiation 898
A.3 Solutions to Differential Equations 900
A.4 Numerical Evaluation of Integrals 901
A.5 Semilog Graphs 903
A.6 Software Packages 903
Appendix B: Ideal Gas Constant and Conversion Factors 905
Appendix C: Thermodynamic Relationships Involving the Equilibrium Constant 909
Appendix D: Software Packages 915
D.1 Polymath 915
D.2 MATLAB 916
D.3 Aspen 916
D.4 COMSOL Multiphysics 917
Appendix E: Rate Law Data 919
Appendix F: Nomenclature 921
Appendix G: Open-Ended Problems 925
G.1 Design of Reaction Engineering Experiment 925
G.2 Effective Lubricant Design 925
G.3 Peach Bottom Nuclear Reactor 925
G.4 Underground Wet Oxidation 926
G.5 Hydrodesulfurization Reactor Design 926
G.6 Continuous Bioprocessing 926
G.7 Methanol Synthesis 926
G.8 Cajun Seafood Gumbo 926
G.9 Alcohol Metabolism 927
G.10 Methanol Poisoning 928
Appendix H: Use of Computational Chemistry Software Packages 929
Appendix I: How to Use the CRE Web Resources 931
I.1 CRE Web Resources Components 931
I.2 How the Web Can Help Your Learning Style 933
I.3 Navigation 934
Index 937
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20.05.2018 - 15:17 |
Physical and Chemical Engineering Sciences
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[attachment=22051:0134181026.jpg] Transport Processes and Separation Process Principles (5th Edition)
Series: Prentice Hall International Series in the Physical and Chemical Engineering Sciences Hardcover: 1248 pages Publisher: Prentice Hall; 5 edition (May 3, 2018) Language: English ISBN-10: 0134181026 ISBN-13: 978-0134181028
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Table of Contents Preface to the Fifth Edition xxvii
About the Authors xxxi
Part 1: Transport Processes: Momentum, Heat, and Mass
Chapter 1: Introduction to Engineering Principles and Units 3
1.0 Chapter Objectives 3
1.1 Classification of Transport Processes and Separation Processes (Unit Operations) 3
1.2 SI System of Basic Units Used in This Text and Other Systems 6
1.3 Methods of Expressing Temperatures and Compositions 8
1.4 Gas Laws and Vapor Pressure 10
1.5 Conservation of Mass and Material Balances 13
1.6 Energy and Heat Units 17
1.7 Conservation of Energy and Heat Balances 23
1.8 Numerical Methods for Integration 28
1.9 Chapter Summary 29
Chapter 2: Introduction to Fluids and Fluid Statics 36
2.0 Chapter Objectives 36
2.1 Introduction 36
2.2 Fluid Statics 37
2.3 Chapter Summary 47
Chapter 3: Fluid Properties and Fluid Flows 50
3.0 Chapter Objectives 50
3.1 Viscosity of Fluids 50
3.2 Types of Fluid Flow and Reynolds Number 54
3.3 Chapter Summary 58
Chapter 4: Overall Mass, Energy, and Momentum Balances 61
4.0 Chapter Objectives 61
4.1 Overall Mass Balance and Continuity Equation 62
4.2 Overall Energy Balance 68
4.3 Overall Momentum Balance 81
4.4 Shell Momentum Balance and Velocity Profile in Laminar Flow 90
4.5 Chapter Summary 96
Chapter 5: Incompressible and Compressible Flows in Pipes 105
5.0 Chapter Objectives 105
5.1 Design Equations for Laminar and Turbulent Flow in Pipes 106
5.2 Compressible Flow of Gases 125
5.3 Measuring the Flow of Fluids 129
5.4 Chapter Summary 138
Chapter 6: Flows in Packed and Fluidized Beds 145
6.0 Chapter Objectives 145
6.1 Flow Past Immersed Objects 146
6.2 Flow in Packed Beds 150
6.3 Flow in Fluidized Beds 156
6.4 Chapter Summary 161
Chapter 7: Pumps, Compressors, and Agitation Equipment 166
7.0 Chapter Objectives 166
7.1 Pumps and Gas-Moving Equipment 166
7.2 Agitation, Mixing of Fluids, and Power Requirements 176
7.3 Chapter Summary 192
Chapter 8: Differential Equations of Fluid Flow 196
8.0 Chapter Objectives 196
8.1 Differential Equations of Continuity 196
8.2 Differential Equations of Momentum Transfer or Motion 202
8.3 Use of Differential Equations of Continuity and Motion 207
8.4 Chapter Summary 216
Chapter 9: Non-Newtonian Fluids 220
9.0 Chapter Objectives 220
9.1 Non-Newtonian Fluids 221
9.2 Friction Losses for Non-Newtonian Fluids 226
9.3 Velocity Profiles for Non-Newtonian Fluids 229
9.4 Determination of Flow Properties of Non-Newtonian Fluids Using a Rotational Viscometer 232
9.5 Power Requirements in Agitation and Mixing of Non-Newtonian Fluids 234
9.6 Chapter Summary 235
Chapter 10: Potential Flow and Creeping Flow 239
10.0 Chapter Objectives 239
10.1 Other Methods for Solution of Differential Equations of Motion 239
10.2 Stream Function 240
10.3 Differential Equations of Motion for Ideal Fluids (Inviscid Flow) 241
10.4 Potential Flow and Velocity Potential 241
10.5 Differential Equations of Motion for Creeping Flow 246
10.6 Chapter Summary 247
Chapter 11: Boundary-Layer and Turbulent Flow 250
11.0 Chapter Objectives 250
11.1 Boundary-Layer Flow 251
11.2 Turbulent Flow 254
11.3 Turbulent Boundary-Layer Analysis 260
11.4 Chapter Summary 263
Chapter 12: Introduction to Heat Transfer 265
12.0 Chapter Objectives 265
12.1 Energy and Heat Units 265
12.2 Conservation of Energy and Heat Balances 271
12.3 Conduction and Thermal Conductivity 277
12.4 Convection 282
12.5 Radiation 284
12.6 Heat Transfer with Multiple Mechanisms/Materials 287
12.7 Chapter Summary 292
Chapter 13: Steady-State Conduction 299
13.0 Chapter Objectives 299
13.1 Conduction Heat Transfer 299
13.2 Conduction Through Solids in Series or Parallel with Convection 305
13.3 Conduction with Internal Heat Generation 313
13.4 Steady-State Conduction in Two Dimensions Using Shape Factors 315
13.5 Numerical Methods for Steady-State Conduction in Two Dimensions 318
13.6 Chapter Summary 326
Chapter 14: Principles of Unsteady-State Heat Transfer 332
14.0 Chapter Objectives 332
14.1 Derivation of the Basic Equation 332
14.2 Simplified Case for Systems with Negligible Internal Resistance 334
14.3 Unsteady-State Heat Conduction in Various Geometries 337
14.4 Numerical Finite-Difference Methods for Unsteady-State Conduction 355
14.5 Chilling and Freezing of Food and Biological Materials 366
14.6 Differential Equation of Energy Change 372
14.7 Chapter Summary 376
Chapter 15: Introduction to Convection 385
15.0 Chapter Objectives 385
15.1 Introduction and Dimensional Analysis in Heat Transfer 385
15.2 Boundary-Layer Flow and Turbulence in Heat Transfer 389
15.3 Forced Convection Heat Transfer Inside Pipes 394
15.4 Heat Transfer Outside Various Geometries in Forced Convection 402
15.5 Natural Convection Heat Transfer 408
15.6 Boiling and Condensation 415
15.7 Heat Transfer of Non-Newtonian Fluids 424
15.8 Special Heat-Transfer Coefficients 427
15.9 Chapter Summary 436
Chapter 16: Heat Exchangers 444
16.0 Chapter Objectives 444
16.1 Types of Exchangers 444
16.2 Log-Mean-Temperature-Difference Correction Factors 447
16.3 Heat-Exchanger Effectiveness 450
16.4 Fouling Factors and Typical Overall U Values 453
16.5 Double-Pipe Heat Exchanger 454
16.6 Chapter Summary 458
Chapter 17: Introduction to Radiation Heat Transfer 461
17.0 Chapter Objectives 461
17.1 Introduction to Radiation Heat-Transfer Concepts 461
17.2 Basic and Advanced Radiation Heat-Transfer Principles 465
17.3 Chapter Summary 482
Chapter 18: Introduction to Mass Transfer 487
18.0 Chapter Objectives 487
18.1 Introduction to Mass Transfer and Diffusion 487
18.2 Diffusion Coefficient 493
18.3 Convective Mass Transfer 508
18.4 Molecular Diffusion Plus Convection and Chemical Reaction 508
18.5 Chapter Summary 512
Chapter 19: Steady-State Mass Transfer 519
19.0 Chapter Objectives 519
19.1 Molecular Diffusion in Gases 519
19.2 Molecular Diffusion in Liquids 528
19.3 Molecular Diffusion in Solids 531
19.4 Diffusion of Gases in Porous Solids and Capillaries 537
19.5 Diffusion in Biological Gels 544
19.6 Special Cases of the General Diffusion Equation at Steady State 546
19.7 Numerical Methods for Steady-State Molecular Diffusion in Two Dimensions 550
19.8 Chapter Summary 557
Chapter 20: Unsteady-State Mass Transfer 568
20.0 Chapter Objectives 568
20.1 Unsteady-State Diffusion 568
20.2 Unsteady-State Diffusion and Reaction in a Semi-Infinite Medium 575
20.3 Numerical Methods for Unsteady-State Molecular Diffusion 577
20.4 Chapter Summary 582
Chapter 21: Convective Mass Transfer 586
21.0 Chapter Objectives 586
21.1 Convective Mass Transfer 586
21.2 Dimensional Analysis in Mass Transfer 594
21.3 Mass-Transfer Coefficients for Various Geometries 595
21.4 Mass Transfer to Suspensions of Small Particles 610
21.5 Models for Mass-Transfer Coefficients 613
21.6 Chapter Summary 617
Part 2: Separation Process Principles
Chapter 22: Absorption and Stripping 627
22.0 Chapter Objectives 627
22.1 Equilibrium and Mass Transfer Between Phases 627
22.2 Introduction to Absorption 645
22.3 Pressure Drop and Flooding in Packed Towers 649
22.4 Design of Plate Absorption Towers 654
22.5 Design of Packed Towers for Absorption 656
22.6 Efficiency of Random-Packed and Structured Packed Towers 672
22.7 Absorption of Concentrated Mixtures in Packed Towers 675
22.8 Estimation of Mass-Transfer Coefficients for Packed Towers 679
22.9 Heat Effects and Temperature Variations in Absorption 682
22.10 Chapter Summary 685
Chapter 23: Humidification Processes 694
23.0 Chapter Objectives 694
23.1 Vapor Pressure of Water and Humidity 694
23.2 Introduction and Types of Equipment for Humidification 703
23.3 Theory and Calculations for Cooling-Water Towers 704
23.4 Chapter Summary 712
Chapter 24: Filtration and Membrane Separation Processes (Liquid–Liquid or Solid–Liquid Phase) 716
24.0 Chapter Objectives 716
24.1 Introduction to Dead-End Filtration 716
24.2 Basic Theory of Filtration 722
24.3 Membrane Separations 732
24.4 Microfiltration Membrane Processes 733
24.5 Ultrafiltration Membrane Processes 734
24.6 Reverse-Osmosis Membrane Processes 738
24.7 Dialysis 747
24.8 Chapter Summary 751
Chapter 25: Gaseous Membrane Systems 759
25.0 Chapter Objectives 759
25.1 Gas Permeation 759
25.2 Complete-Mixing Model for Gas Separation by Membranes 765
25.3 Complete-Mixing Model for Multicomponent Mixtures 770
25.4 Cross-Flow Model for Gas Separation by Membranes 773
25.5 Derivation of Equations for Countercurrent and Cocurrent Flow for Gas Separation by Membranes 779
25.6 Derivation of Finite-Difference Numerical Method for Asymmetric Membranes 787
25.7 Chapter Summary 798
Chapter 26: Distillation 805
26.0 Chapter Objectives 805
26.1 Equilibrium Relations Between Phases 805
26.2 Single and Multiple Equilibrium Contact Stages 808
26.3 Simple Distillation Methods 813
26.4 Binary Distillation with Reflux Using the McCabe–Thiele and Lewis Methods 818
26.5 Tray Efficiencies 836
26.6 Flooding Velocity and Diameter of Tray Towers Plus Simple Calculations for Reboiler and Condenser Duties 839
26.7 Fractional Distillation Using the Enthalpy–Concentration Method 841
26.8 Distillation of Multicomponent Mixtures 851
26.9 Chapter Summary 862
Chapter 27: Liquid–Liquid Extraction 874
27.0 Chapter Objectives 874
27.1 Introduction to Liquid–Liquid Extraction 874
27.2 Single-Stage Equilibrium Extraction 878
27.3 Types of Equipment and Design for Liquid–Liquid Extraction 880
27.4 Continuous Multistage Countercurrent Extraction 889
27.5 Chapter Summary 901
Chapter 28: Adsorption and Ion Exchange 907
28.0 Chapter Objectives 907
28.1 Introduction to Adsorption Processes 907
28.2 Batch Adsorption 910
28.3 Design of Fixed-Bed Adsorption Columns 912
28.4 Ion-Exchange Processes 918
28.5 Chapter Summary 924
Chapter 29: Crystallization and Particle Size Reduction 928
29.0 Chapter Objectives 928
29.1 Introduction to Crystallization 928
29.2 Crystallization Theory 935
29.3 Mechanical Size Reduction 942
29.4 Chapter Summary 947
Chapter 30: Settling, Sedimentation, and Centrifugation 952
30.0 Chapter Objectives 952
30.1 Settling and Sedimentation in Particle–Fluid Separation 953
30.2 Centrifugal Separation Processes 966
30.3 Chapter Summary 979
Chapter 31: Leaching 984
31.0 Chapter Objectives 984
31.1 Introduction and Equipment for Liquid–Solid Leaching 984
31.2 Equilibrium Relations and Single-Stage Leaching 990
31.3 Countercurrent Multistage Leaching 994
31.4 Chapter Summary 999
Chapter 32: Evaporation 1002
32.0 Chapter Objectives 1002
32.1 Introduction 1002
32.2 Types of Evaporation Equipment and Operation Methods 1004
32.3 Overall Heat-Transfer Coefficients in Evaporators 1008
32.4 Calculation Methods for Single-Effect Evaporators 1010
32.5 Calculation Methods for Multiple-Effect Evaporators 1016
32.6 Condensers for Evaporators 1026
32.7 Evaporation of Biological Materials 1028
32.8 Evaporation Using Vapor Recompression 1029
32.9 Chapter Summary 1030
Chapter 33: Drying 1035
33.0 Chapter Objectives 1035
33.1 Introduction and Methods of Drying 1035
33.2 Equipment for Drying 1036
33.3 Vapor Pressure of Water and Humidity 1040
33.4 Equilibrium Moisture Content of Materials 1049
33.5 Rate-of-Drying Curves 1052
33.6 Calculation Methods for a Constant-Rate Drying Period 1057
33.7 Calculation Methods for the Falling-Rate Drying Period 1062
33.8 Combined Convection, Radiation, and Conduction Heat Transfer in the Constant-Rate Period 1065
33.9 Drying in the Falling-Rate Period by Diffusion and Capillary Flow 1068
33.10 Equations for Various Types of Dryers 1074
33.11 Freeze-Drying of Biological Materials 1084
33.12 Unsteady-State Thermal Processing and Sterilization of Biological Materials 1088
33.13 Chapter Summary 1096
Part 3: Appendixes
Appendix A.1 Fundamental Constants and Conversion Factors 1107
Appendix A.2 Physical Properties of Water 1113
Appendix A.3 Physical Properties of Inorganic and Organic Compounds 1124
Appendix A.4 Physical Properties of Foods and Biological Materials 1147
Appendix A.5 Properties of Pipes, Tubes, and Screens 1151
Appendix A.6 Lennard-Jones Potentials as Determined from Viscosity Data 1154
Notation 1156
Index 1166
http://seizefile.net/702715 |
ioncube, |
19.04.2018 - 18:10 |
Practical Thermal Design of Air-Cooled Heat Exchangers
|
QUOTE (knight282009 @ 19.04.2018 - 18:52) ioncube, Forums are good for briefly understanding the practical nature of equipment based on experience but are no match for the books which provide in-depth comprehensive details related to design. I would recommend VDI Heat Atlas for exchangers. VDI Heat Atlas |
alexxxxss, camiqmex, Capricorn, czk, ioncube, knight282009, tanbqtb03, |
16.04.2018 - 15:24 |
Practical Thermal Design of Air-Cooled Heat Exchangers
|
https://www.slideshare.net/menjung1/practical-thermal-design-of-air-cooled-heat-exchangers |
alexxxxss, |
29.11.2016 - 20:05 |
GB 150 pressure vessel
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QUOTE (gogu252 @ 29.11.2016 - 19:40) THX, however it is in chinese and unfortuneltly for me : i have no idea about how to read it GB 150-2011 reference ASME VIII standard |
gogu252, |
29.11.2016 - 10:42 |
GB 150 pressure vessel
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https://mega.nz/#!HYMwWKgL!oEbRaAV1eCyMDl0dHiLfSkD6nwudyGnT4VJx5hmKTtg
GB 150-2011 |
2ak2, |
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