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 xiiiPreface xv1 Modeling the Kinetics of Hydrocracking of Heavy Oil with Mineral Catalyst 1Guillermo Félix, Fernando Trejo, and Jorge Ancheyta1.1 Introduction 11.1.1 Reserves and Production of Heavy Crude Oils 11.1.2 Heavy Crude Oil Upgrading Processes 21.1.3 Reactions During Slurry Phase Hydrocracking 61.1.4 Catalysts for Hydrocracking of Heavy Crude Oils in Slurry Phase 61.2 Kinetic Models 71.2.1 General Types of Kinetic Models 81.2.1.1 Lumping Kinetic Models 81.2.1.2 Continuous Lumping Kinetic Models 81.2.1.3 Single-Event Kinetic Models 101.2.2 Kinetic Models Reported in the Literature for Hydrocracking of Heavy Crude Oils Using Dispersed Catalysts 101.2.2.1 Kinetic Models Based on Distillation Curves 101.2.2.2 Kinetic Models Based on SARA Fractions 181.2.3 Kinetic Models Based on Continuous Lumping 211.2.4 Thermodynamic Model to Predict the Asphaltenes Flocculation and Sediments Formation 221.3 Kinetic Parameters Estimation 241.3.1 Assumptions 261.3.2 Initialization of Parameters 271.3.3 Nonlinear Optimization 281.3.4 Objective Function 281.3.5 Sensitivity and Statistical Analyses 291.3.5.1 Perturbations 291.3.5.2 Parity Plots 291.3.5.3 Residuals 291.3.5.4 AIC and BIC 301.4 Results and Discussion 301.4.1 Kinetic Parameters 301.4.1.1 Assumptions 301.4.1.2 Reaction Rate Coefficients 321.4.1.3 Activation Energies 381.4.2 Accuracy of the Kinetic Models 381.4.2.1 SARA-Based Models 381.4.2.2 Distillation Curves-Based Models 411.4.3 Reactions in Parallel and in Series 441.4.4 Thermodynamic Model 451.4.5 General Comments 481.5 Conclusion 50References 502 Modeling Catalyst Deactivation of Hydrotreating of Heavy Oils 56Javier Jurado, Vicente Samano, and Jorge Ancheyta2.1 Introduction 562.2 Mechanisms of Deactivation 572.2.1 Coking Deposition (Fouling) 592.2.2 Metal Deposition (Poisoning) 592.3 Deactivation Models 602.3.1 Deactivation Models by Coke Deposition 602.3.2 Deactivation Models by Metal Deposition 652.3.3 Deactivation Models by Coke and Metal Deposition 702.4 Development of Models for HDT Catalyst Deactivation 782.4.1 Important Issues 782.4.2 Final Remarks 822.5 Development of a Reactor Model for Heavy Oil Hydrotreating with Catalyst Deactivation Based on Vanadium and Coke Deposition 832.5.1 The Model 842.5.1.1 Description 842.5.1.2 Solution of the Model 862.5.1.3 Advantages of the Model 862.5.1.4 Procedure for Parameter Estimation 882.5.2 Results and Discussion 892.5.2.1 Profiles of Sulfur and Vanadium Concentration in Products 892.5.2.2 Comparison of Predictions with Literature and Proposed Model 902.5.2.3 Profiles of Coke and Vanadium on Catalyst 912.5.2.4 Final Remarks 932.5.3 Usefulness of the Model 952.5.4 Conclusion 962.6 Application of the Deactivation Model for Hydrotreating of Heavy Crude Oil in Bench-Scale Reactor 962.6.1 Properties of Heavy Oil 962.6.2 Properties of the Catalyst 962.6.3 Bench-Scale Reactor 982.6.4 Catalyst Activation 982.6.5 Operating Conditions 992.6.6 Characterization Methods 992.6.7 Parameter Estimation 1002.6.8 Results and Discussion 1012.6.8.1 Evolution of Sulfur and Metals Concentration in Products 1012.6.8.2 Coke and Metals on Catalyst 1022.6.9 Conclusion 105Nomenclature 105References 1113 Simulation of the Oxidative Regeneration of Coked Catalysts: Kinetics, Catalyst Pellet, and Bed Levels 116Sergey Zazhigalov, Osman Abdulla, and Andrey Zagoruiko3.1 Introduction 1163.2 Process Chemistry and Laboratory Experiments 1173.2.1 Catalyst and Proposed Reactions 1173.2.2 Reaction Kinetics 1193.2.3 Experimental Setup 1213.2.4 Experiments 1243.3 Mathematical Model 1263.4 Model Solution Method 1323.5 Modeling Results 1333.6 Conclusion 1343.7 Notation 136Abbreviations 136Acknowledgment 137References 1374 Modeling of Unsteady-State Catalytic and Adsorption–Catalytic Processes: Novel Reactor Designs 138Sergey Zazhigalov, Andrey Elyshev, and Andrey Zagoruiko4.1 Introduction 1384.2 Novel Reactor Designs for Catalytic Reverse-Flow and Adsorption–Catalytic Processes 1414.2.1 Unsteady-State Catalytic Reverse-Flow Process 1414.2.2 Adsorption–Catalytic Process 1424.3 Mathematical Models of the Processes 1454.3.1 Unsteady-State Catalytic Reverse-Flow Process 1454.3.2 Adsorption–Catalytic Process 1464.4 Results 1484.4.1 Unsteady-State Catalytic Reverse-Flow Process 1484.4.2 Adsorption–Catalytic Process 1534.4.2.1 Reactor with Truncated Cone Entrance 1534.4.2.2 Multisectional Reactor 1564.5 Conclusion 1644.6 Notation 165Abbreviations 165Acknowledgments 165References 1665 Molecular Reconstruction of Complex Hydrocarbon Mixtures for Modeling of Heavy Oil Processing 168Nikita Glazov and Andrey Zagoruiko5.1 Introduction 1685.2 The Problem 1685.3 Illustration 1695.4 Reconstruction by Entropy Maximization (REM) 1695.5 Stochastic Reconstruction (SR) 1745.6 Sr-em 1795.7 Structure-Oriented Lumping (SOL) Method 1815.8 State Space Representation Method 1825.9 Molecular Type-Homologous Series Matrix 1835.10 Conclusion 184Acknowledgment 184References 1846 Modeling of Catalytic Hydrotreating Reactor for Production of Green Diesel 187Alexis Tirado, Fernando Trejo, and Jorge Ancheyta6.1 Introduction 1876.2 Conversion of Vegetable Oils into Renewable Fuels 1876.2.1 Commercial Production of Renewable Diesel 1896.3 Hydrotreating Kinetic Models and Reaction Pathways 1906.3.1 Model Compounds 1906.3.2 Vegetable Oils 1976.4 Models for Catalytic Deactivation 2046.5 Reactor Modeling for Vegetable Oil Hydrotreating 2056.5.1 Deviation from Ideal Flow Pattern 2086.6 The Importance of Modelling Reactors for Vegetable Oil Hydrotreating 2106.7 Study Case for the Development of Dynamic Reactor Model 2106.7.1 Equations and Assumptions for Hydrotreating Reactor Modeling 2106.7.2 Kinetic Model for Hydrotreating of Vegetable Oil 2136.7.3 Hydrogen Consumption and Gas Generation 2136.7.4 Solution of Reactor Models 2156.8 Analysis and Discussion of Results 2176.8.1 Criteria to Ensure Ideal Behaviors in Trickle-Bed Reactor 2176.8.2 Dynamic Profiles of Feedstock and Products of a Bench-Scale Reactor for Catalytic Hydrotreating of Vegetable Oil 2196.8.3 Validation of Hydrotreating Reactor Model with Pilot Plant Data 2226.8.4 Dynamic Simulation of a Non-isothermal Reactor 2256.8.4.1 Comparison of Non-isothermal Model with Experimental Results in Isothermal Reactor 2256.8.4.2 Comparison of Bench-Scale and Pilot-Scale Reactor Under Non-isothermal Operating Condition 2276.8.5 Dynamic Simulation of an Adiabatic Commercial Reactor 2296.8.5.1 Configuration of Hydrogen Quenching 2326.8.5.2 Liquid-Phase Yields and Gas Composition 2326.9 Conclusions 235References 2367 Modeling of Slurry-Phase Hydrocracking Reactor 242Cristian Calderón and Jorge Ancheyta7.1 Introduction 2427.1.1 Characteristics of Slurry-Phase Reactors for Hydrocracking 2427.1.1.1 Type of Reactors 2427.1.1.2 Catalyst Properties 2457.1.2 SPR Modeling 2467.1.2.1 Classification 2467.1.2.2 Model Complexity 2497.1.2.3 Models for Slurry Reactors 2497.2 Proposed Generalized Model 2537.2.1 Equations for the Generalized Model 2537.2.2 Solids Concentration 2577.2.3 Initial and Boundary Conditions 2577.2.4 Estimation of Model Parameters 2607.2.5 Gas Holdup 2607.2.6 Gas–Liquid Mass Transfer Coefficients 2627.2.7 Gas–Liquid Equilibrium 2647.2.8 Liquid–Solid and Gas–Solid Mass Transfer Coefficients 2647.2.9 Dispersion Coefficients 2657.2.10 Heat Transfer Coefficients 2677.2.11 Example of Simplification of the Generalized Model 2677.3 Simplified Models 2687.3.1 SPR 1D Model 2687.3.2 SPR 2D Model 2697.3.3 Continous Stirred Tank Reactor Model 2707.3.4 Parameters 2707.3.5 Reaction Kinetics 2737.3.6 Solution Method 2747.4 Numerical Simulations 2757.4.1 Experimental Reactors 2757.4.1.1 Dynamic Simulations of CSTR and SPR 2757.4.1.2 Steady-State Simulations of a SPR 2787.4.2 Industrial-Scale Reactor 2807.4.2.1 Dynamic Simulations of the Industrial Slurry-Phase Reactor 2837.4.2.2 Sensitivity Analysis for the Industrial Slurry-Phase Reactor 2877.5 Conclusions 291Nomenclature 294References 2978 Modeling of Fischer–Tropsch Synthesis Reactor 303César I. Méndez and Jorge Ancheyta8.1 Fundamentals of the Fischer–Tropsch Synthesis to Produce Clean Fuels 3038.1.1 Fischer–Tropsch Synthesis Technology 3048.1.2 Fischer–Tropsch Synthesis Catalysts 3078.1.2.1 Cobalt-Based Catalysts 3078.1.2.2 Iron-Based Catalysts 3088.1.2.3 Catalyst Support 3098.1.3 Fischer–Tropsch Synthesis Kinetic Models 3098.1.3.1 Kinetic Models Developed with Iron Catalyst 3108.1.3.2 Kinetic Models Developed with Cobalt Catalyst 3108.1.4 General Aspects of Fischer–Tropsch Catalytic Mechanisms 3158.1.5 The Fischer–Tropsch Synthesis Product Distribution Models 3218.1.6 Final Remarks 3248.2 Modeling of Catalytic Fixed-Bed Reactors for Fuels Production by Fischer–Tropsch Synthesis 3248.2.1 Introduction 3248.2.2 Modeling of Fixed-Bed Fischer–Tropsch Reactors 3248.2.2.1 Classification of Fixed-Bed Fischer–Tropsch Reactor Models 3258.2.2.2 One- and Two-Dimensional Pseudohomogeneous Model 3258.2.2.3 One- and Two-Dimensional Heterogeneous Model 3268.2.3 Development of a Generalized Fixed-Bed Fischer–Tropsch Reactor Model 3268.2.3.1 General Equations of the Model 3268.2.3.2 Boundary Conditions of the Proposed Generalized Model 3348.2.3.3 Pressure Drop 3378.2.4 Model Parameters 3408.2.4.1 Mass Transfer Parameters 3408.2.4.2 Heat Transfer Parameters 3418.2.4.3 Phase Equilibrium 3438.2.4.4 Catalyst Particles Parameters 3458.2.4.5 Catalytic Bed Parameters 3528.2.5 Final Remarks 3548.3 Importance of Proper Hydrodynamics Modeling in Fixed-Bed Fischer–Tropsch Synthesis Reactor 3548.3.1 Introduction 3548.3.2 Mathematical Modeling of the Fixed-Bed Fischer–Tropsch Synthesis Reactor 3548.3.2.1 Reactor Model 3558.3.2.2 Kinetics 3568.3.2.3 Other Parameters and Correlations 3578.3.2.4 Numerical Method 3578.3.3 Results and Discussion 3588.3.3.1 Simulations for the One-Stage Reactor 3588.3.3.2 Simulations for the Two-Stage Reactor 3648.3.4 Final Remarks 3718.4 Dynamic One-Dimensional Pseudohomogeneous Model for Fischer–Tropsch Reactors 3718.4.1 Introduction 3718.4.2 Formulation of the Model 3718.4.2.1 Model Equations and Solution 3718.4.2.2 Model Parameters, Correlations, and Kinetics 3728.4.3 Results and Discussion 3738.4.3.1 Experimental Data 3738.4.3.2 Conversion of CO and H 2 3738.4.3.3 Temperature Profiles 3788.4.4 Product’s selectivity 3818.4.5 Final Remarks 3888.5 Modeling and Control of a Fischer–Tropsch Synthesis Reactor with a Novel Mechanistic Kinetic Approach 3908.5.1 Introduction 3908.5.2 Formulation of the Model 3928.5.2.1 Model Equations and Solution 3928.5.2.2 Model Parameters and Correlations 3948.5.2.3 The Mechanistic FTS Kinetic Model 3958.5.3 Implementation of the PI Controller 3968.5.4 Results and Discussion 3978.5.4.1 Experimental Data 3978.5.4.2 Simulations of the Syngas Conversion, Light Gases, and Heavy Liquid Selectivity 3978.5.4.3 Simulations of the Fischer–Tropsch Fixed-Bed Reactor and the Cooling Jacket Thermal Behavior 4048.5.4.4 Surfaces of the Syngas Conversion and the Heavy Liquids Selectivity as a Function of the FTS Reactor Temperature 4058.5.5 Final Remarks 4088.6 On the use of Steady-State Optimal Initial Operating Conditions for the Control Scheme Implementation of a Fixed-Bed Fischer–Tropsch Reactor 4088.6.1 Introduction 4088.6.2 Methodology 4088.6.2.1 Model Equations and Numerical Solution 4088.6.2.2 Model Parameters, Correlations, and Kinetics 4098.6.2.3 Steady-State Nonlinear Constrained Optimization Problem 4098.6.2.4 Implementation of the Control Scheme 4138.6.3 Results and discussion 4148.6.3.1 Experimental Data 4148.6.3.2 Simulations of the Steady-State Nonlinear Constrained Optimization Problem: CO Conversion, S C5+ Selectivity, and Temperature Profiles 4158.6.3.3 Simulations of the Control Scheme Implementation: CO Conversion, S C5+ Selectivity, and Temperature Profiles 4168.6.4 Final Remarks 420References 4219 Computational Fluid Dynamics Modeling of Mass Transfer Processes in Structured Beds of Microfibrous Catalysts 434Sergey Lopatin, Andrey Elyshev, and Andrey Zagoruiko9.1 Introduction 4349.2 Mathematical Model 4369.2.1 Model Description 4379.2.2 Computing Domain 4379.2.3 Simulation Object Geometry 4379.2.4 Reaction 4399.2.5 Model Parameters 4409.3 Simulation Results 4409.3.1 Cartridge Channel with Corrugated Structuring Mesh 4409.3.2 Influence of GFC Textile Shape 4439.3.3 Cartridge Channel Without Corrugated Structuring Mesh 4439.3.4 Two-Sided Washing of GFC Textiles 4479.3.5 Convective Flow Inside the GFC Thread 4499.3.6 The General Description of Mass Transfer in GFC 4519.4 Conclusion 452Abbreviations 453Acknowledgement 453References 453Index 456