Jorge Ancheyta, is Manager of Products for Transformation of the Crude Oil at the Mexican Petroleum Institute (IMP). He also has been a Professor in the School of Chemical Engineering and Extractive Industries at the National Polytechnic Institute of Mexico (ESIQIE-IPN) since 1992. Dr. Ancheyta works on the development and application of petroleum refining catalysts, kinetic and reactor models, and process technologies mainly in catalytic cracking, catalytic reforming, middle distillate hydrotreating and heavy oils upgrading.

About the Author xi

Preface xiii

1 Fundamentals of Chemical Reaction Kinetics 1

1.1 Concepts of Stoichiometry 1

1.1.1 Stoichiometric Number and Coefficient 1

1.1.2 Molecularity 2

1.1.3 Reaction Extent 3

1.1.4 Molar Conversion 4

1.1.5 Types of Feed Composition in a Chemical Reaction 5

1.1.6 Limiting Reactant 6

1.1.7 Molar Balance in a Chemical Reaction 7

1.1.8 Relationship between Conversion and Physical Properties of the Reacting System 8

1.2 Reacting Systems 11

1.2.1 Mole Fraction, Weight Fraction and Molar Concentration 11

1.2.2 Partial Pressure 13

1.2.3 Isothermal Systems at Constant Density 13

1.2.3.1 Relationship between Partial Pressure (pA) and Conversion (xA) 16

1.2.3.2 Relationship between Partial Pressure (pA) and Total Pressure (P) 16

1.2.3.3 Relationship between Molar Concentration (CA) and Total Pressure (P) 16

1.2.4 Isothermal Systems at Variable Density 18

1.2.5 General Case of Reacting Systems 22

1.2.6 Kinetic Point of View of the Chemical Equilibrium 22

1.3 Concepts of Chemical Kinetics 24

1.3.1 Rate of Homogeneous Reactions 24

1.3.2 Power Law 26

1.3.2.1 Relationship between kp and kc 27

1.3.2.2 Units of kc and kp 27

1.3.3 Elemental and Non-elemental Reactions 29

1.3.4 Comments on the Concepts of Molecularity and Reaction Order 30

1.3.5 Dependency of k with Temperature 30

1.3.5.1 Arrhenius Equation 30

1.3.5.2 Frequency Factor and Activation Energy 32

1.3.5.3 Evaluation of the Parameters of the Arrhenius Equation 32

1.3.5.4 Modified Arrhenius Equation 42

1.4 Description of Ideal Reactors 43

1.4.1 Batch Reactors 43

1.4.1.1 Modes of Operation 44

1.4.1.2 Data Collection 46

1.4.1.3 Mass Balance 48

1.4.2 Continuous Reactors 49

1.4.2.1 Space-Time and Space-Velocity 50

1.4.2.2 Plug Flow Reactor 50

1.4.2.3 Continuous Stirred Tank Reactor 52

2 Irreversible Reactions of One Component 55

2.1 Integral Method 56

2.1.1 Reactions of Zero Order 58

2.1.2 Reactions of the First Order 59

2.1.3 Reaction of the Second Order 61

2.1.4 Reactions of the nth Order 64

2.2 Differential Method 69

2.2.1 Numerical Differentiation 71

2.2.1.1 Method of Approaching the Derivatives (¿dCA/dt) to (¿CA/¿t) or (dxA/dt) to (¿xA/¿t) 71

2.2.1.2 Method of Finite Differences 72

2.2.1.3 Method of a Polynomial of the nth Order 74

2.2.2 Graphical Differentiation 74

2.2.2.1 Method of Area Compensation 74

2.2.2.2 Method of Approaching the Derivative (¿dCA/dt) to (¿CA/¿t) 76

2.2.2.3 Method of Finite Differences 77

2.2.2.4 Method of a Polynomial of the nth Order 78

2.2.2.5 Method of Area Compensation 80

2.2.2.6 Summary of Results 82

2.3 Method of Total Pressure 83

2.3.1 Reactions of Zero Order 84

2.3.2 Reactions of the First Order 85

2.3.3 Reactions of the Second Order 85

2.3.4 Reactions of the nth Order 86

2.3.5 Differential Method with Data of Total Pressure 88

2.4 Method of the Half-Life Time 91

2.4.1 Reactions of Zero Order 92

2.4.2 Reactions of the First Order 92

2.4.3 Reaction of the Second Order 93

2.4.4 Reaction of the nth Order 93

2.4.5 Direct Method to Calculate k and n with Data of t1/2 95

2.4.6 Extension of the Method of Half-Life Time (t1/2) to Any Fractional Life Time (t1/m) 97

2.4.7 Calculation of Activation Energy with Data of Half-Life Time 97

2.4.8 Some Observations of the Method of Half-Life Time 99

2.4.8.1 Calculation of n with Two Data of t1/2Measured with Different CAo 99

2.4.8.2 Generalization of the Method of Half-Life Time for Any Reaction Order 101

3 Irreversible Reactions with Two or Three Components 103

3.1 Irreversible Reactions with Two Components 103

3.1.1 Integral Method 103

3.1.1.1 Method of Stoichiometric Feed Composition 104

3.1.1.2 Method of Non-stoichiometric Feed Composition 109

3.1.1.3 Method of a Reactant in Excess 117

3.1.2 Differential Method 120

3.1.2.1 Stoichiometric Feed Composition 120

3.1.2.2 Feed Composition with a Reactant in Excess 120

3.1.2.3 Non-stoichiometric Feed Compositions 121

3.1.3 Method of Initial Reaction Rates 123

3.2 Irreversible Reactions between Three Components 127

3.2.1 Case 1: Stoichiometric Feed Composition 127

3.2.2 Case 2: Non-stoichiometric Feed Composition 129

3.2.3 Case 3: Feed Composition with One Reactant in Excess 130

3.2.4 Case 4: Feed Composition with Two Reactants in Excess 131

4 Reversible Reactions 135

4.1 Reversible Reactions of First Order 135

4.2 Reversible Reactions of Second Order 139

4.3 Reversible Reactions with Combined Orders 146

5 Complex Reactions 153

5.1 Yield and Selectivity 153

5.2 Simultaneous or Parallel Irreversible Reactions 155

5.2.1 Simultaneous Reactions with the Same Order 155

5.2.1.1 Case 1: Reactions with Only One Reactant 155

5.2.1.2 Case 2: Reactions with Two Reactants 161

5.2.2 Simultaneous Reactions with Combined Orders 163

5.2.2.1 Integral Method 165

5.2.2.2 Differential Method 166

5.3 Consecutive or In-Series Irreversible Reactions 167

5.3.1 Consecutive Reactions with the Same Order 167

5.3.1.1 Calculation of CR max and t¿ 171

5.3.1.2 Calculation of CR max and t¿ for k1= k2 172

5.3.2 Consecutive Reactions with Combined Orders 174

6 Special Topics in Kinetic Modelling 179

6.1 Data Reconciliation 180

6.1.1 Data Reconciliation Method 181

6.1.2 Results and Discussion 182

6.1.2.1 Source of Data 182

6.1.2.2 Global Mass Balances 185

6.1.2.3 Outlier Determination 187

6.1.2.4 Data Reconciliation 187

6.1.2.5 Analysis of Results 189

6.1.3 Conclusions 195

6.2 Methodology for Sensitivity Analysis of Parameters 196

6.2.1 Description of the Method 198

6.2.1.1 Initialization of Parameters 199

6.2.1.2 Non-linear Parameter Estimation 201

6.2.1.3 Sensitivity Analysis 201

6.2.1.4 Residual Analysis 202

6.2.2 Results and Discussion 202

6.2.2.1 Experimental Data and the Reaction Rate Model from the Literature 202

6.2.2.2 Initialization of Parameters 204

6.2.2.3 Results of Non-linear Estimation 206

6.2.2.4 Sensitivity Analysis 207

6.2.2.5 Analysis of Residuals 210

6.2.3 Conclusions 210

6.3 Methods for Determining Rate Coefficients in Enzymatic Catalysed Reactions 211

6.3.1 The Michaelis-Menten Model 213

6.3.1.1 Origin 213

6.3.1.2 Development of the Model 213

6.3.1.3 Importance of Vmax and Km 214

6.3.2 Methods to Determine the Rate Coefficients of the Michaelis-Menten Equation 214

6.3.2.1 Linear Regression 214

6.3.2.2 Graphic Method 215

6.3.2.3 Integral Method 215

6.3.2.4 Non-linear Regression 216

6.3.3 Application of the Methods 217

6.3.3.1 Experimental Data 217

6.3.3.2 Calculation of Kinetic Parameters 220

6.3.4 Discussion of Results 222

6.3.5 Conclusions 225

6.4 A Simple Method for Estimating Gasoline, Gas and Coke Yields in FCC Processes 226

6.4.1 Introduction 226

6.4.2 Methodology 227

6.4.2.1 Choosing the Kinetic Models 227

6.4.2.2 Reaction Kinetics 228

6.4.2.3 Estimation of Kinetic Parameters 229

6.4.2.4 Evaluation of Products Yields 230

6.4.2.5 Advantages and Limitations of the Methodology 230

6.4.3 Results and Discussion 231

6.4.4 Conclusions 234

6.5 Estimation of Activation Energies during Hydrodesulphurization of Middle Distillates 234

6.5.1 Introduction 234

6.5.2 Experiments 235

6.5.3 Results and Discussion 236

6.5.3.1 Experimental Results 236

6.5.3.2 Estimation of Kinetic Parameters 237

6.5.3.3 Effect of Feed Properties on Kinetic Parameters 240

6.5.4 Conclusions 241

Problems 243

Nomenclature 273

References 277

Index 283