Chemical Reaction Kinetics

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 xiPreface xiii1 Fundamentals of Chemical Reaction Kinetics 11.1 Concepts of Stoichiometry 11.1.1 Stoichiometric Number and Coefficient 11.1.2 Molecularity 21.1.3 Reaction Extent 31.1.4 Molar Conversion 41.1.5 Types of Feed Composition in a Chemical Reaction 51.1.6 Limiting Reactant 61.1.7 Molar Balance in a Chemical Reaction 71.1.8 Relationship between Conversion and Physical Properties of the Reacting System 81.2 Reacting Systems 111.2.1 Mole Fraction, Weight Fraction and Molar Concentration 111.2.2 Partial Pressure 131.2.3 Isothermal Systems at Constant Density 131.2.3.1 Relationship between Partial Pressure (pA) and Conversion (xA) 161.2.3.2 Relationship between Partial Pressure (pA) and Total Pressure (P) 161.2.3.3 Relationship between Molar Concentration (CA) and Total Pressure (P) 161.2.4 Isothermal Systems at Variable Density 181.2.5 General Case of Reacting Systems 221.2.6 Kinetic Point of View of the Chemical Equilibrium 221.3 Concepts of Chemical Kinetics 241.3.1 Rate of Homogeneous Reactions 241.3.2 Power Law 261.3.2.1 Relationship between kp and kc 271.3.2.2 Units of kc and kp 271.3.3 Elemental and Non-elemental Reactions 291.3.4 Comments on the Concepts of Molecularity and Reaction Order 301.3.5 Dependency of k with Temperature 301.3.5.1 Arrhenius Equation 301.3.5.2 Frequency Factor and Activation Energy 321.3.5.3 Evaluation of the Parameters of the Arrhenius Equation 321.3.5.4 Modified Arrhenius Equation 421.4 Description of Ideal Reactors 431.4.1 Batch Reactors 431.4.1.1 Modes of Operation 441.4.1.2 Data Collection 461.4.1.3 Mass Balance 481.4.2 Continuous Reactors 491.4.2.1 Space–Time and Space–Velocity 501.4.2.2 Plug Flow Reactor 501.4.2.3 Continuous Stirred Tank Reactor 522 Irreversible Reactions of One Component 552.1 Integral Method 562.1.1 Reactions of Zero Order 582.1.2 Reactions of the First Order 592.1.3 Reaction of the Second Order 612.1.4 Reactions of the nth Order 642.2 Differential Method 692.2.1 Numerical Differentiation 712.2.1.1 Method of Approaching the Derivatives (−dCA/dt) to (ΔCA/Δt) or (dxA/dt) to (ΔxA/Δt) 712.2.1.2 Method of Finite Differences 722.2.1.3 Method of a Polynomial of the nth Order 742.2.2 Graphical Differentiation 742.2.2.1 Method of Area Compensation 742.2.2.2 Method of Approaching the Derivative (−dCA/dt) to (ΔCA/Δt) 762.2.2.3 Method of Finite Differences 772.2.2.4 Method of a Polynomial of the nth Order 782.2.2.5 Method of Area Compensation 802.2.2.6 Summary of Results 822.3 Method of Total Pressure 832.3.1 Reactions of Zero Order 842.3.2 Reactions of the First Order 852.3.3 Reactions of the Second Order 852.3.4 Reactions of the nth Order 862.3.5 Differential Method with Data of Total Pressure 882.4 Method of the Half-Life Time 912.4.1 Reactions of Zero Order 922.4.2 Reactions of the First Order 922.4.3 Reaction of the Second Order 932.4.4 Reaction of the nth Order 932.4.5 Direct Method to Calculate k and n with Data of t1/2 952.4.6 Extension of the Method of Half-Life Time (t1/2) to Any Fractional Life Time (t1/m) 972.4.7 Calculation of Activation Energy with Data of Half-Life Time 972.4.8 Some Observations of the Method of Half-Life Time 992.4.8.1 Calculation of n with Two Data of t1/2Measured with Different CAo 992.4.8.2 Generalization of the Method of Half-Life Time for Any Reaction Order 1013 Irreversible Reactions with Two or Three Components 1033.1 Irreversible Reactions with Two Components 1033.1.1 Integral Method 1033.1.1.1 Method of Stoichiometric Feed Composition 1043.1.1.2 Method of Non-stoichiometric Feed Composition 1093.1.1.3 Method of a Reactant in Excess 1173.1.2 Differential Method 1203.1.2.1 Stoichiometric Feed Composition 1203.1.2.2 Feed Composition with a Reactant in Excess 1203.1.2.3 Non-stoichiometric Feed Compositions 1213.1.3 Method of Initial Reaction Rates 1233.2 Irreversible Reactions between Three Components 1273.2.1 Case 1: Stoichiometric Feed Composition 1273.2.2 Case 2: Non-stoichiometric Feed Composition 1293.2.3 Case 3: Feed Composition with One Reactant in Excess 1303.2.4 Case 4: Feed Composition with Two Reactants in Excess 1314 Reversible Reactions 1354.1 Reversible Reactions of First Order 1354.2 Reversible Reactions of Second Order 1394.3 Reversible Reactions with Combined Orders 1465 Complex Reactions 1535.1 Yield and Selectivity 1535.2 Simultaneous or Parallel Irreversible Reactions 1555.2.1 Simultaneous Reactions with the Same Order 1555.2.1.1 Case 1: Reactions with Only One Reactant 1555.2.1.2 Case 2: Reactions with Two Reactants 1615.2.2 Simultaneous Reactions with Combined Orders 1635.2.2.1 Integral Method 1655.2.2.2 Differential Method 1665.3 Consecutive or In-Series Irreversible Reactions 1675.3.1 Consecutive Reactions with the Same Order 1675.3.1.1 Calculation of CR max and t∗ 1715.3.1.2 Calculation of CR max and t∗ for k1= k2 1725.3.2 Consecutive Reactions with Combined Orders 1746 Special Topics in Kinetic Modelling 1796.1 Data Reconciliation 1806.1.1 Data Reconciliation Method 1816.1.2 Results and Discussion 1826.1.2.1 Source of Data 1826.1.2.2 Global Mass Balances 1856.1.2.3 Outlier Determination 1876.1.2.4 Data Reconciliation 1876.1.2.5 Analysis of Results 1896.1.3 Conclusions 1956.2 Methodology for Sensitivity Analysis of Parameters 1966.2.1 Description of the Method 1986.2.1.1 Initialization of Parameters 1996.2.1.2 Non-linear Parameter Estimation 2016.2.1.3 Sensitivity Analysis 2016.2.1.4 Residual Analysis 2026.2.2 Results and Discussion 2026.2.2.1 Experimental Data and the Reaction Rate Model from the Literature 2026.2.2.2 Initialization of Parameters 2046.2.2.3 Results of Non-linear Estimation 2066.2.2.4 Sensitivity Analysis 2076.2.2.5 Analysis of Residuals 2106.2.3 Conclusions 2106.3 Methods for Determining Rate Coefficients in Enzymatic Catalysed Reactions 2116.3.1 The Michaelis–Menten Model 2136.3.1.1 Origin 2136.3.1.2 Development of the Model 2136.3.1.3 Importance of Vmax and Km 2146.3.2 Methods to Determine the Rate Coefficients of the Michaelis–Menten Equation 2146.3.2.1 Linear Regression 2146.3.2.2 Graphic Method 2156.3.2.3 Integral Method 2156.3.2.4 Non-linear Regression 2166.3.3 Application of the Methods 2176.3.3.1 Experimental Data 2176.3.3.2 Calculation of Kinetic Parameters 2206.3.4 Discussion of Results 2226.3.5 Conclusions 2256.4 A Simple Method for Estimating Gasoline, Gas and Coke Yields in FCC Processes 2266.4.1 Introduction 2266.4.2 Methodology 2276.4.2.1 Choosing the Kinetic Models 2276.4.2.2 Reaction Kinetics 2286.4.2.3 Estimation of Kinetic Parameters 2296.4.2.4 Evaluation of Products Yields 2306.4.2.5 Advantages and Limitations of the Methodology 2306.4.3 Results and Discussion 2316.4.4 Conclusions 2346.5 Estimation of Activation Energies during Hydrodesulphurization of Middle Distillates 2346.5.1 Introduction 2346.5.2 Experiments 2356.5.3 Results and Discussion 2366.5.3.1 Experimental Results 2366.5.3.2 Estimation of Kinetic Parameters 2376.5.3.3 Effect of Feed Properties on Kinetic Parameters 2406.5.4 Conclusions 241Problems 243Nomenclature 273References 277Index 283