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Chemical Reactions and Chemical Reactors

Chemical Reactions and Chemical Reactors

George W. Roberts

ISBN: 978-0-471-74220-3

Mar 2008

480 pages

In Stock

$174.95

Description

Focused on the undergraduate audience, Chemical Reaction Engineering provides students with complete coverage of the fundamentals, including in-depth coverage of chemical kinetics.  By introducing heterogeneous catalysis early in the book, the text gives students the knowledge they need to solve real chemistry and industrial problems.  An emphasis on problem-solving and numerical techniques ensures students learn and practice the skills they will need later on, whether for industry or graduate work.

Related Resources

1. Reactions and Reaction Rates 1

1.1 Introduction 1

1.1.1 The Role of Chemical Reactions 1

1.1.2 Chemical Kinetics 2

1.1.3 Chemical Reactors 2

1.2 Stoichiometric Notation 3

1.3 Extent of Reaction and the Law of Definite Proportions 4

1.3.1 Stoichiometric Notation—Multiple Reactions 6

1.4 Definitions of Reaction Rate 8

1.4.1 Species-Dependent Definition 8

1.4.1.1 Single Fluid Phase 9

1.4.1.2 Multiple Phases 9

Heterogeneous Catalysis 9

Other Cases 10

1.4.1.3 Relationship between Reaction Rates of Various Species (Single Reaction) 10

1.4.1.4 Multiple Reactions 11

1.4.2 Species-Independent Definition 11

Summary of Important Concepts 12

Problems 12

2. Reaction Rates—Some Generalizations 16

2.1 Rate Equations 16

2.2 Five Generalizations 17

2.3 An Important Exception 33

Summary of Important Concepts 33

Problems 33

3. Ideal Reactors 36

3.1 Generalized Material Balance 36

3.2 Ideal Batch Reactor 38

3.3 Continuous Reactors 43

3.3.1 Ideal Continuous Stirred-Tank Reactor (CSTR) 45

3.3.2 Ideal Continuous Plug-Flow Reactor (PFR) 49

3.3.2.1 The Easy Way—Choose a Different Control Volume 51

3.3.2.2 The Hard Way—Do the Triple Integration 54

3.4 Graphical Interpretation of the Design Equations 54

Summary of Important Concepts 57

Problems 57

Appendix 3 Summary of Design Equations 60

4. Sizing and Analysis of Ideal Reactors 63

4.1 Homogeneous Reactions 63

4.1.1 Batch Reactors 63

4.1.1.1 Jumping Right In 63

4.1.1.2 General Discussion: Constant-Volume Systems 68

Describing the Progress of a Reaction 68

Solving the Design Equation 71

4.1.1.3 General Discussion: Variable-Volume Systems 74

4.1.2 Continuous Reactors 77

4.1.2.1 Continuous Stirred-Tank Reactors (CSTRs) 78

Constant-Density Systems 78

Variable-Density (Variable-Volume) Systems 80

4.1.2.2 Plug-Flow Reactors 82

Constant-Density (Constant-Volume) Systems 82

Variable-Density (Variable-Volume) Systems 84

4.1.2.3 Graphical Solution of the CSTR Design Equation 86

4.1.2.4 Biochemical Engineering Nomenclature 90

4.2 Heterogeneous Catalytic Reactions (Introduction to Transport Effects) 91

4.3 Systems of Continuous Reactors 97

4.3.1 Reactors in Series 98

4.3.1.1 CSTRs in Series 98

4.3.1.2 PFRs in Series 103

4.3.1.3 PFRs and CSTRs in Series 103

4.3.2 Reactors in Parallel 107

4.3.2.1 CSTRs in Parallel 107

4.3.2.2 PFRs in Parallel 109

4.3.3 Generalizations 110

4.4 Recycle 111

Summary of Important Concepts 114

Problems 114

Appendix 4 Solution to Example 4-10: Three Equal-Volume CSTRs in Series 122

5. Reaction Rate Fundamentals (Chemical Kinetics) 123

5.1 Elementary Reactions 123

5.1.1 Significance 123

5.1.2 Definition 125

5.1.3 Screening Criteria 126

5.2 Sequences of Elementary Reactions 129

5.2.1 Open Sequences 130

5.2.2 Closed Sequences 130

5.3 The Steady-State Approximation (SSA) 131

5.4 Use of the Steady-State Approximation 133

5.4.1 Kinetics and Mechanism 136

5.4.2 The Long-Chain Approximation 137

5.5 Closed Sequences with a Catalyst 138

5.6 The Rate-Limiting Step (RLS) Approximation 140

5.6.1 Vector Representation 141

5.6.2 Use of the RLS Approximation 142

5.6.3 Physical Interpretation of the Rate Equation 143

5.6.4 Irreversibility 145

5.7 Closing Comments 147

Summary of Important Concepts 147

Problems 148

6. Analysis and Correlation of Kinetic Data 154

6.1 Experimental Data from Ideal Reactors 154

6.1.1 Stirred-Tank Reactors (CSTRs) 155

6.1.2 Plug-Flow Reactors 156

6.1.2.1 Differential Plug-Flow Reactors 156

6.1.2.2 Integral Plug-Flow Reactors 157

6.1.3 Batch Reactors 158

6.1.4 Differentiation of Data: An Illustration 159

6.2 The Differential Method of Data Analysis 162

6.2.1 Rate Equations Containing Only One Concentration 162

6.2.1.1 Testing a Rate Equation 162

6.2.1.2 Linearization of Langmuir–Hinshelwood/Michaelis–Menten Rate Equations 165

6.2.2 Rate Equations Containing More Than One Concentration 166

6.2.3 Testing the Arrhenius Relationship 169

6.2.4 Nonlinear Regression 171

6.3 The Integral Method of Data Analysis 173

6.3.1 Using the Integral Method 173

6.3.2 Linearization 176

6.3.3 Comparison of Methods for Data Analysis 177

6.4 Elementary Statistical Methods 178

6.4.1 Fructose Isomerization 178

6.4.1.1 First Hypothesis: First-Order Rate Equation 179

Residual Plots 179

Parity Plots 180

6.4.1.2 Second Hypothesis: Michaelis–Menten Rate Equation 181

Constants in the Rate Equation: Error Analysis 184

Non-Linear Least Squares 186

6.4.2 Rate Equations Containing More Than One Concentration (Reprise) 186

Summary of Important Concepts 187

Problems 188

Appendix 6-A Nonlinear Regression for AIBN Decomposition 197

Appendix 6-B Nonlinear Regression for AIBN Decomposition 198

Appendix 6-C Analysis of Michaelis–Menten Rate Equation via

Lineweaver–Burke Plot Basic Calculations 199

7. Multiple Reactions 201

7.1 Introduction 201

7.2 Conversion, Selectivity, and Yield 203

7.3 Classification of Reactions 208

7.3.1 Parallel Reactions 208

7.3.2 Independent Reactions 208

7.3.3 Series (Consecutive) Reactions 209

7.3.4 Mixed Series and Parallel Reactions 209

7.4 Reactor Design and Analysis 211

7.4.1 Overview 211

7.4.2 Series (Consecutive) Reactions 212

7.4.2.1 Qualitative Analysis 212

7.4.2.2 Time-Independent Analysis 214

7.4.2.3 Quantitative Analysis 215

7.4.2.4 Series Reactions in a CSTR 218

Material Balance on A 219

Material Balance on R 219

7.4.3 Parallel and Independent Reactions 220

7.4.3.1 Qualitative Analysis 220

Effect of Temperature 221

Effect of Reactant Concentrations 222

7.4.3.2 Quantitative Analysis 224

7.4.4 Mixed Series/Parallel Reactions 230

7.4.4.1 Qualitative Analysis 230

7.4.4.2 Quantitative Analysis 231

Summary of Important Concepts 232

Problems 232

Appendix 7-A Numerical Solution of Ordinary Differential Equations 241

7-A.1 Single, First-Order Ordinary Differential Equation 241

7-A.2 Simultaneous, First-Order, Ordinary Differential Equations 245

8. Use of the Energy Balance in Reactor Sizing and Analysis 251

8.1 Introduction 251

8.2 Macroscopic Energy Balances 252

8.2.1 Generalized Macroscopic Energy Balance 252

8.2.1.1 Single Reactors 252

8.2.1.2 Reactors in Series 254

8.2.2 Macroscopic Energy Balance for Flow Reactors (PFRs and CSTRs) 255

8.2.3 Macroscopic Energy Balance for Batch Reactors 255

8.3 Isothermal Reactors 257

8.4 Adiabatic Reactors 261

8.4.1 Exothermic Reactions 261

8.4.2 Endothermic Reactions 262

8.4.3 Adiabatic Temperature Change 264

8.4.4 Graphical Analysis of Equilibrium-Limited Adiabatic Reactors 266

8.4.5 Kinetically Limited Adiabatic Reactors (Batch and Plug Flow) 268

8.5 Continuous Stirred-Tank Reactors (General Treatment) 271

8.5.1 Simultaneous Solution of the Design Equation and the Energy Balance 272

8.5.2 Multiple Steady States 276

8.5.3 Reactor Stability 277

8.5.4 Blowout and Hysteresis 279

8.5.4.1 Blowout 279

Extension 281

Discussion 282

8.5.4.2 Feed-Temperature Hysteresis 282

8.6 Nonisothermal, Nonadiabatic Batch, and Plug-Flow Reactors 284

8.6.1 General Remarks 284

8.6.2 Nonadiabatic Batch Reactors 284

8.7 Feed/Product (F/P) Heat Exchangers 285

8.7.1 Qualitative Considerations 285

8.7.2 Quantitative Analysis 286

8.7.2.1 Energy Balance—Reactor 288

8.7.2.2 Design Equation 288

8.7.2.3 Energy Balance—F/P Heat Exchanger 289

8.7.2.4 Overall Solution 291

8.7.2.5 Adjusting the Outlet Conversion 291

8.7.2.6 Multiple Steady States 292

8.8 Concluding Remarks 294

Summary of Important Concepts 295

Problems 296

Appendix 8-A Numerical Solution to Equation (8-26) 302

Appendix 8-B Calculation of G(T) and R(T) for ‘‘Blowout’’ Example 304

9. Heterogeneous Catalysis Revisited 305

9.1 Introduction 305

9.2 The Structure of Heterogeneous Catalysts 306

9.2.1 Overview 306

9.2.2 Characterization of Catalyst Structure 310

9.2.2.1 Basic Definitions 310

9.2.2.2 Model of Catalyst Structure 311

9.3 Internal Transport 311

9.3.1 General Approach—Single Reaction 311

9.3.2 An Illustration: First-Order, Irreversible Reaction in an Isothermal,Spherical Catalyst Particle 314

9.3.3 Extension to Other Reaction Orders and Particle Geometries 315

9.3.4 The Effective Diffusion Coefficient 318

9.3.4.1 Overview 318

9.3.4.2 Mechanisms of Diffusion 319

Configurational (Restricted) Diffusion 319

Knudsen Diffusion (Gases) 320

Bulk (Molecular) Diffusion 321

The Transition Region 323

Concentration Dependence 323

9.3.4.3 The Effect of Pore Size 325

Narrow Pore-Size Distribution 325

Broad Pore-Size Distribution 326

9.3.5 Use of the Effectiveness Factor in Reactor Design and Analysis 326

9.3.6 Diagnosing Internal Transport Limitations in Experimental Studies 328

9.3.6.1 Disguised Kinetics 328

Effect of Concentration 329

Effect of Temperature 329

Effect of Particle Size 330

9.3.6.2 The Weisz Modulus 331

9.3.6.3 Diagnostic Experiments 333

9.3.7 Internal Temperature Gradients 335

9.3.8 Reaction Selectivity 340

9.3.8.1 Parallel Reactions 340

9.3.8.2 Independent Reactions 342

9.3.8.3 Series Reactions 344

9.4 External Transport 346

9.4.1 General Analysis—Single Reaction 346

9.4.1.1 Quantitative Descriptions of Mass and Heat Transport 347

Mass Transfer 347

Heat Transfer 347

9.4.1.2 First-Order, Reaction in an Isothermal Catalyst Particle—The

Concept of a Controlling Step 348

hkvlc=kc _ 1 349

hkvlc=kc _ 1 350

9.4.1.3 Effect of Temperature 353

9.4.1.4 Temperature Difference Between Bulk Fluid and Catalyst Surface 354

9.4.2 Diagnostic Experiments 356

9.4.2.1 Fixed-Bed Reactor 357

9.4.2.2 Other Reactors 361

9.4.3 Calculations of External Transport 362

9.4.3.1 Mass-Transfer Coefficients 362

9.4.3.2 Different Definitions of the Mass-Transfer Coefficient 365

9.4.3.3 Use of Correlations 366

9.4.4 Reaction Selectivity 368

9.5 Catalyst Design—Some Final Thoughts 368

Summary of Important Concepts 369

Problems 369

Appendix 9-A Solution to Equation (9-4c) 376

10. ‘Nonideal’ Reactors 378

10.1 What Can Make a Reactor ‘‘Nonideal’’? 378

10.1.1 What Makes PFRs and CSTRs ‘‘Ideal’’? 378

10.1.2 Nonideal Reactors: Some Examples 379

10.1.2.1 Tubular Reactor with Bypassing 379

10.1.2.2 Stirred Reactor with Incomplete Mixing 380

10.1.2.3 Laminar Flow Tubular Reactor (LFTR) 380

10.2 Diagnosing and Characterizing Nonideal Flow 381

10.2.1 Tracer Response Techniques 381

10.2.2 Tracer Response Curves for Ideal Reactors

(Qualitative Discussion) 383

10.2.2.1 Ideal Plug-How Reactor 383

10.2.2.2 Ideal Continuous Stirred-Tank Reactor 384

10.2.3 Tracer Response Curves for Nonideal Reactors 385

10.2.3.1 Laminar Flow Tubular Reactor 385

10.2.3.2 Tubular Reactor with Bypassing 385

10.2.3.3 Stirred Reactor with Incomplete Mixing 386

10.3 Residence Time Distributions 387

10.3.1 The Exit-Age Distribution Function, E(t) 387

10.3.2 Obtaining the Exit-Age Distribution from Tracer Response Curves 389

10.3.3 Other Residence Time Distribution Functions 391

10.3.3.1 Cumulative Exit-Age Distribution Function, F(t) 391

10.3.3.2 Relationship between F(t) and E(t) 392

10.3.3.3 Internal-Age Distribution Function, I(t) 392

10.3.4 Residence Time Distributions for Ideal Reactors 393

10.3.4.1 Ideal Plug-Flow Reactor 393

10.3.4.2 Ideal Continuous Stirred-Tank Reactor 395

10.4 Estimating Reactor Performance from the Exit-Age Distribution—The Macrofluid Model 397

10.4.1 The Macrofluid Model 397

10.4.2 Predicting Reactor Behavior with the Macrofluid Model 398

10.4.3 Using the Macrofluid Model to Calculate Limits of Performance 403

10.5 Other Models for Nonideal Reactors 404

10.5.1 Moments of Residence Time Distributions 404

10.5.1.1 Definitions 404

10.5.1.2 The First Moment of E(t) 405

Average Residence Time 405

Reactor Diagnosis 406

10.5.1.3 The Second Moment of E(t)—Mixing 407

10.5.1.4 Moments for Vessels in Series 408

10.5.2 The Dispersion Model 412

10.5.2.1 Overview 412

10.5.2.2 The Reaction Rate Term 413

Homogeneous Reaction 413

Heterogeneous Catalytic Reaction 415

10.5.2.3 Solutions to the Dispersion Model 415

Rigorous 415

Approximate (Small Values of D/uL) 417

10.5.2.4 The Dispersion Number 417

Estimating D/uL from Correlations 417

Criterion for Negligible Dispersion 419

Measurement of D/uL 420

10.5.2.5 The Dispersion Model—Some Final Comments 422

10.5.3 CSTRs-In-Series (CIS) Model 422

10.5.3.1 Overview 422

10.5.3.2 Determining the Value of ‘‘N’’ 423

10.5.3.3 Calculating Reactor Performance 424

10.5.4 Compartment Models 426

10.5.4.1 Overview 426

10.5.4.2 Compartment Models Based on CSTRs and PFRs 427

Reactors in Parallel 427

Reactors in Series 429

10.5.4.3 Well-Mixed Stagnant Zones 431

10.6 Concluding Remarks 434

Summary of Important Concepts 435

Problems 435

Nomenclature 440

Index 446

Focused Audience: This text is focused on the undergraduate audience, with the goal of helping the student to master the course material