Mathematical Modeling of Complex Reaction Systems in the Oil and Gas Industry

Jorge Ancheyta, PhD, is Manager of Products for the Transformation of Crude Oil at the Mexican Institute of Petroluem (IMP), as well as Professor in the School of Chemical Engineering, National Polytechnic Institute of Mexico, Mexico City. He has published prodigiously on petroleum refinement, heavy oil upgrading, and related subjects. Andrey Zagoruiko, PhD, is a researcher with the Boreskov Institute of Catalysis, Novosibirsk, Russia. He has published and lectured extensively on mathematical modelling and engineering of catalytic processes, and sits on the editoral board for Reviews in Chemical Engineering and Catalysis in Industry. Andrey Elyshev, PhD, is Director of the Centre for Nature-Inspired Engineering, University of Tyumen, Russia. He has received numerous scientific grants to design novel catalysts for environmental conversion of oil and gas.

List of Contributors xiii

Preface xv

1 Modeling the Kinetics of Hydrocracking of Heavy Oil with Mineral Catalyst 1
Guillermo Félix, Fernando Trejo, and Jorge Ancheyta

1.1 Introduction 1

1.1.1 Reserves and Production of Heavy Crude Oils 1

1.1.2 Heavy Crude Oil Upgrading Processes 2

1.1.3 Reactions During Slurry Phase Hydrocracking 6

1.1.4 Catalysts for Hydrocracking of Heavy Crude Oils in Slurry Phase 6

1.2 Kinetic Models 7

1.2.1 General Types of Kinetic Models 8

1.2.1.1 Lumping Kinetic Models 8

1.2.1.2 Continuous Lumping Kinetic Models 8

1.2.1.3 Single-Event Kinetic Models 10

1.2.2 Kinetic Models Reported in the Literature for Hydrocracking of Heavy Crude Oils Using Dispersed Catalysts 10

1.2.2.1 Kinetic Models Based on Distillation Curves 10

1.2.2.2 Kinetic Models Based on SARA Fractions 18

1.2.3 Kinetic Models Based on Continuous Lumping 21

1.2.4 Thermodynamic Model to Predict the Asphaltenes Flocculation and Sediments Formation 22

1.3 Kinetic Parameters Estimation 24

1.3.1 Assumptions 26

1.3.2 Initialization of Parameters 27

1.3.3 Nonlinear Optimization 28

1.3.4 Objective Function 28

1.3.5 Sensitivity and Statistical Analyses 29

1.3.5.1 Perturbations 29

1.3.5.2 Parity Plots 29

1.3.5.3 Residuals 29

1.3.5.4 AIC and BIC 30

1.4 Results and Discussion 30

1.4.1 Kinetic Parameters 30

1.4.1.1 Assumptions 30

1.4.1.2 Reaction Rate Coefficients 32

1.4.1.3 Activation Energies 38

1.4.2 Accuracy of the Kinetic Models 38

1.4.2.1 SARA-Based Models 38

1.4.2.2 Distillation Curves-Based Models 41

1.4.3 Reactions in Parallel and in Series 44

1.4.4 Thermodynamic Model 45

1.4.5 General Comments 48

1.5 Conclusion 50

References 50

2 Modeling Catalyst Deactivation of Hydrotreating of Heavy Oils 56
Javier Jurado, Vicente Samano, and Jorge Ancheyta

2.1 Introduction 56

2.2 Mechanisms of Deactivation 57

2.2.1 Coking Deposition (Fouling) 59

2.2.2 Metal Deposition (Poisoning) 59

2.3 Deactivation Models 60

2.3.1 Deactivation Models by Coke Deposition 60

2.3.2 Deactivation Models by Metal Deposition 65

2.3.3 Deactivation Models by Coke and Metal Deposition 70

2.4 Development of Models for HDT Catalyst Deactivation 78

2.4.1 Important Issues 78

2.4.2 Final Remarks 82

2.5 Development of a Reactor Model for Heavy Oil Hydrotreating with Catalyst Deactivation Based on Vanadium and Coke Deposition 83

2.5.1 The Model 84

2.5.1.1 Description 84

2.5.1.2 Solution of the Model 86

2.5.1.3 Advantages of the Model 86

2.5.1.4 Procedure for Parameter Estimation 88

2.5.2 Results and Discussion 89

2.5.2.1 Profiles of Sulfur and Vanadium Concentration in Products 89

2.5.2.2 Comparison of Predictions with Literature and Proposed Model 90

2.5.2.3 Profiles of Coke and Vanadium on Catalyst 91

2.5.2.4 Final Remarks 93

2.5.3 Usefulness of the Model 95

2.5.4 Conclusion 96

2.6 Application of the Deactivation Model for Hydrotreating of Heavy Crude Oil in Bench-Scale Reactor 96

2.6.1 Properties of Heavy Oil 96

2.6.2 Properties of the Catalyst 96

2.6.3 Bench-Scale Reactor 98

2.6.4 Catalyst Activation 98

2.6.5 Operating Conditions 99

2.6.6 Characterization Methods 99

2.6.7 Parameter Estimation 100

2.6.8 Results and Discussion 101

2.6.8.1 Evolution of Sulfur and Metals Concentration in Products 101

2.6.8.2 Coke and Metals on Catalyst 102

2.6.9 Conclusion 105

Nomenclature 105

References 111

3 Simulation of the Oxidative Regeneration of Coked Catalysts: Kinetics, Catalyst Pellet, and Bed Levels 116
Sergey Zazhigalov, Osman Abdulla, and Andrey Zagoruiko

3.1 Introduction 116

3.2 Process Chemistry and Laboratory Experiments 117

3.2.1 Catalyst and Proposed Reactions 117

3.2.2 Reaction Kinetics 119

3.2.3 Experimental Setup 121

3.2.4 Experiments 124

3.3 Mathematical Model 126

3.4 Model Solution Method 132

3.5 Modeling Results 133

3.6 Conclusion 134

3.7 Notation 136

Abbreviations 136

Acknowledgment 137

References 137

4 Modeling of Unsteady-State Catalytic and Adsorption–Catalytic Processes: Novel Reactor Designs 138
Sergey Zazhigalov, Andrey Elyshev, and Andrey Zagoruiko

4.1 Introduction 138

4.2 Novel Reactor Designs for Catalytic Reverse-Flow and Adsorption–Catalytic Processes 141

4.2.1 Unsteady-State Catalytic Reverse-Flow Process 141

4.2.2 Adsorption–Catalytic Process 142

4.3 Mathematical Models of the Processes 145

4.3.1 Unsteady-State Catalytic Reverse-Flow Process 145

4.3.2 Adsorption–Catalytic Process 146

4.4 Results 148

4.4.1 Unsteady-State Catalytic Reverse-Flow Process 148

4.4.2 Adsorption–Catalytic Process 153

4.4.2.1 Reactor with Truncated Cone Entrance 153

4.4.2.2 Multisectional Reactor 156

4.5 Conclusion 164

4.6 Notation 165

Abbreviations 165

Acknowledgments 165

References 166

5 Molecular Reconstruction of Complex Hydrocarbon Mixtures for Modeling of Heavy Oil Processing 168
Nikita Glazov and Andrey Zagoruiko

5.1 Introduction 168

5.2 The Problem 168

5.3 Illustration 169

5.4 Reconstruction by Entropy Maximization (REM) 169

5.5 Stochastic Reconstruction (SR) 174

5.6 Sr-em 179

5.7 Structure-Oriented Lumping (SOL) Method 181

5.8 State Space Representation Method 182

5.9 Molecular Type-Homologous Series Matrix 183

5.10 Conclusion 184

Acknowledgment 184

References 184

6 Modeling of Catalytic Hydrotreating Reactor for Production of Green Diesel 187
Alexis Tirado, Fernando Trejo, and Jorge Ancheyta

6.1 Introduction 187

6.2 Conversion of Vegetable Oils into Renewable Fuels 187

6.2.1 Commercial Production of Renewable Diesel 189

6.3 Hydrotreating Kinetic Models and Reaction Pathways 190

6.3.1 Model Compounds 190

6.3.2 Vegetable Oils 197

6.4 Models for Catalytic Deactivation 204

6.5 Reactor Modeling for Vegetable Oil Hydrotreating 205

6.5.1 Deviation from Ideal Flow Pattern 208

6.6 The Importance of Modelling Reactors for Vegetable Oil Hydrotreating 210

6.7 Study Case for the Development of Dynamic Reactor Model 210

6.7.1 Equations and Assumptions for Hydrotreating Reactor Modeling 210

6.7.2 Kinetic Model for Hydrotreating of Vegetable Oil 213

6.7.3 Hydrogen Consumption and Gas Generation 213

6.7.4 Solution of Reactor Models 215

6.8 Analysis and Discussion of Results 217

6.8.1 Criteria to Ensure Ideal Behaviors in Trickle-Bed Reactor 217

6.8.2 Dynamic Profiles of Feedstock and Products of a Bench-Scale Reactor for Catalytic Hydrotreating of Vegetable Oil 219

6.8.3 Validation of Hydrotreating Reactor Model with Pilot Plant Data 222

6.8.4 Dynamic Simulation of a Non-isothermal Reactor 225

6.8.4.1 Comparison of Non-isothermal Model with Experimental Results in Isothermal Reactor 225

6.8.4.2 Comparison of Bench-Scale and Pilot-Scale Reactor Under Non-isothermal Operating Condition 227

6.8.5 Dynamic Simulation of an Adiabatic Commercial Reactor 229

6.8.5.1 Configuration of Hydrogen Quenching 232

6.8.5.2 Liquid-Phase Yields and Gas Composition 232

6.9 Conclusions 235

References 236

7 Modeling of Slurry-Phase Hydrocracking Reactor 242
Cristian Calderón and Jorge Ancheyta

7.1 Introduction 242

7.1.1 Characteristics of Slurry-Phase Reactors for Hydrocracking 242

7.1.1.1 Type of Reactors 242

7.1.1.2 Catalyst Properties 245

7.1.2 SPR Modeling 246

7.1.2.1 Classification 246

7.1.2.2 Model Complexity 249

7.1.2.3 Models for Slurry Reactors 249

7.2 Proposed Generalized Model 253

7.2.1 Equations for the Generalized Model 253

7.2.2 Solids Concentration 257

7.2.3 Initial and Boundary Conditions 257

7.2.4 Estimation of Model Parameters 260

7.2.5 Gas Holdup 260

7.2.6 Gas–Liquid Mass Transfer Coefficients 262

7.2.7 Gas–Liquid Equilibrium 264

7.2.8 Liquid–Solid and Gas–Solid Mass Transfer Coefficients 264

7.2.9 Dispersion Coefficients 265

7.2.10 Heat Transfer Coefficients 267

7.2.11 Example of Simplification of the Generalized Model 267

7.3 Simplified Models 268

7.3.1 SPR 1D Model 268

7.3.2 SPR 2D Model 269

7.3.3 Continous Stirred Tank Reactor Model 270

7.3.4 Parameters 270

7.3.5 Reaction Kinetics 273

7.3.6 Solution Method 274

7.4 Numerical Simulations 275

7.4.1 Experimental Reactors 275

7.4.1.1 Dynamic Simulations of CSTR and SPR 275

7.4.1.2 Steady-State Simulations of a SPR 278

7.4.2 Industrial-Scale Reactor 280

7.4.2.1 Dynamic Simulations of the Industrial Slurry-Phase Reactor 283

7.4.2.2 Sensitivity Analysis for the Industrial Slurry-Phase Reactor 287

7.5 Conclusions 291

Nomenclature 294

References 297

8 Modeling of Fischer–Tropsch Synthesis Reactor 303
César I. Méndez and Jorge Ancheyta

8.1 Fundamentals of the Fischer–Tropsch Synthesis to Produce Clean Fuels 303

8.1.1 Fischer–Tropsch Synthesis Technology 304

8.1.2 Fischer–Tropsch Synthesis Catalysts 307

8.1.2.1 Cobalt-Based Catalysts 307

8.1.2.2 Iron-Based Catalysts 308

8.1.2.3 Catalyst Support 309

8.1.3 Fischer–Tropsch Synthesis Kinetic Models 309

8.1.3.1 Kinetic Models Developed with Iron Catalyst 310

8.1.3.2 Kinetic Models Developed with Cobalt Catalyst 310

8.1.4 General Aspects of Fischer–Tropsch Catalytic Mechanisms 315

8.1.5 The Fischer–Tropsch Synthesis Product Distribution Models 321

8.1.6 Final Remarks 324

8.2 Modeling of Catalytic Fixed-Bed Reactors for Fuels Production by Fischer–Tropsch Synthesis 324

8.2.1 Introduction 324

8.2.2 Modeling of Fixed-Bed Fischer–Tropsch Reactors 324

8.2.2.1 Classification of Fixed-Bed Fischer–Tropsch Reactor Models 325

8.2.2.2 One- and Two-Dimensional Pseudohomogeneous Model 325

8.2.2.3 One- and Two-Dimensional Heterogeneous Model 326

8.2.3 Development of a Generalized Fixed-Bed Fischer–Tropsch Reactor Model 326

8.2.3.1 General Equations of the Model 326

8.2.3.2 Boundary Conditions of the Proposed Generalized Model 334

8.2.3.3 Pressure Drop 337

8.2.4 Model Parameters 340

8.2.4.1 Mass Transfer Parameters 340

8.2.4.2 Heat Transfer Parameters 341

8.2.4.3 Phase Equilibrium 343

8.2.4.4 Catalyst Particles Parameters 345

8.2.4.5 Catalytic Bed Parameters 352

8.2.5 Final Remarks 354

8.3 Importance of Proper Hydrodynamics Modeling in Fixed-Bed Fischer–Tropsch Synthesis Reactor 354

8.3.1 Introduction 354

8.3.2 Mathematical Modeling of the Fixed-Bed Fischer–Tropsch Synthesis Reactor 354

8.3.2.1 Reactor Model 355

8.3.2.2 Kinetics 356

8.3.2.3 Other Parameters and Correlations 357

8.3.2.4 Numerical Method 357

8.3.3 Results and Discussion 358

8.3.3.1 Simulations for the One-Stage Reactor 358

8.3.3.2 Simulations for the Two-Stage Reactor 364

8.3.4 Final Remarks 371

8.4 Dynamic One-Dimensional Pseudohomogeneous Model for Fischer–Tropsch Reactors 371

8.4.1 Introduction 371

8.4.2 Formulation of the Model 371

8.4.2.1 Model Equations and Solution 371

8.4.2.2 Model Parameters, Correlations, and Kinetics 372

8.4.3 Results and Discussion 373

8.4.3.1 Experimental Data 373

8.4.3.2 Conversion of CO and H 2 373

8.4.3.3 Temperature Profiles 378

8.4.4 Product’s selectivity 381

8.4.5 Final Remarks 388

8.5 Modeling and Control of a Fischer–Tropsch Synthesis Reactor with a Novel Mechanistic Kinetic Approach 390

8.5.1 Introduction 390

8.5.2 Formulation of the Model 392

8.5.2.1 Model Equations and Solution 392

8.5.2.2 Model Parameters and Correlations 394

8.5.2.3 The Mechanistic FTS Kinetic Model 395

8.5.3 Implementation of the PI Controller 396

8.5.4 Results and Discussion 397

8.5.4.1 Experimental Data 397

8.5.4.2 Simulations of the Syngas Conversion, Light Gases, and Heavy Liquid Selectivity 397

8.5.4.3 Simulations of the Fischer–Tropsch Fixed-Bed Reactor and the Cooling Jacket Thermal Behavior 404

8.5.4.4 Surfaces of the Syngas Conversion and the Heavy Liquids Selectivity as a Function of the FTS Reactor Temperature 405

8.5.5 Final Remarks 408

8.6 On the use of Steady-State Optimal Initial Operating Conditions for the Control Scheme Implementation of a Fixed-Bed Fischer–Tropsch Reactor 408

8.6.1 Introduction 408

8.6.2 Methodology 408

8.6.2.1 Model Equations and Numerical Solution 408

8.6.2.2 Model Parameters, Correlations, and Kinetics 409

8.6.2.3 Steady-State Nonlinear Constrained Optimization Problem 409

8.6.2.4 Implementation of the Control Scheme 413

8.6.3 Results and discussion 414

8.6.3.1 Experimental Data 414

8.6.3.2 Simulations of the Steady-State Nonlinear Constrained Optimization Problem: CO Conversion, S C5+ Selectivity, and Temperature Profiles 415

8.6.3.3 Simulations of the Control Scheme Implementation: CO Conversion, S C5+ Selectivity, and Temperature Profiles 416

8.6.4 Final Remarks 420

References 421

9 Computational Fluid Dynamics Modeling of Mass Transfer Processes in Structured Beds of Microfibrous Catalysts 434
Sergey Lopatin, Andrey Elyshev, and Andrey Zagoruiko

9.1 Introduction 434

9.2 Mathematical Model 436

9.2.1 Model Description 437

9.2.2 Computing Domain 437

9.2.3 Simulation Object Geometry 437

9.2.4 Reaction 439

9.2.5 Model Parameters 440

9.3 Simulation Results 440

9.3.1 Cartridge Channel with Corrugated Structuring Mesh 440

9.3.2 Influence of GFC Textile Shape 443

9.3.3 Cartridge Channel Without Corrugated Structuring Mesh 443

9.3.4 Two-Sided Washing of GFC Textiles 447

9.3.5 Convective Flow Inside the GFC Thread 449

9.3.6 The General Description of Mass Transfer in GFC 451

9.4 Conclusion 452

Abbreviations 453

Acknowledgement 453

References 453

Index 456