This book is accompanied by a CD-ROM containing computer software that can be used to provide numerical solutions to many of the examples and problems in the book. Our treatment of chemical kinetics in Chapters 2 through 10 is such that no prior knowledge is assumed on the part of the student.
Contents
Nature and Scope of Chemical Kinetics 1
Nature and Scope of Chemical Reaction Engineering 1.3 Kinetics and Chemical Reaction Engineering 2
Aspects of Chemical Reaction Engineering 15 .1 Reactor Design and Analysis of Performance 15
Plan of Treatment in Following Chapters 21 .1 Organization of Topics 21
Batch Reactor (BR) 26 .1 General Features 26
Smnmary of Results for Ideal Reactor Models 38 2.7 Stoichiometric Table 39
Problems for Chapter 2 40
Experimental Measurements: General Considerations 4 5 3.3 Experimental Methods to Follow the Extent of Reaction 46
Experimental Strategies for Determining Rate Parameters 48 .1 Concentration-Related Parameters: Order of Reaction 49
Problems for Chapter 3 6 1
4 . DEVELOPMENT OF THE RATE LAW FOR A SIMPLE SYSTEM 64
The Rate Law 6 4
Gas-Phase Reactions: Choice of Concentration Units 66 .1 Use of Partial Pressure 66
Problems for Chapter 4 80
5 . COMPLEXSYSTEMS 87 -
Types and Examples of Complex Systems 8 7 51.1 Reversible (Opposing) Reactions 87
Series Reactions 103
6 . FUNDAMENTALS OF REACTION RATES 115
Prelhninary Considerations 115
Simple Collision Theory of Reaction Rates 128
Elementary Reactions Involving Other Than Gas-Phase Neutral Species 146 .1 Reactions in Condensed Phases 146
Problems for Chapter 6 152
7 . HOMOGENEOUS REACTION MECHANISMS AND RATE LAWS 154
Simple Homogeneous Reactions 155 .1 Types of Mechanisms 155
8 . CATALYSIS AND CATALYTIC REACTIONS 176
Catalysis and Catalysts 176 81.1 Nature and Concept 176
Surface Catalysis: Intrinsic Kinetics 191 .1 Surface-Reaction Steps 191
Heterogeneous Catalysis: Kinetics in Porous Catalyst Particles 198 .1 General Considerations 198
Catalyst Deactivation and Regeneration 214 .1 Fouling 214
9 0’ MULTIPHASE REACTING SYSTEMS 224 9.1 Gas-Solid (Reactant) Systems 224
Intrinsic Kinetics of Heterogeneous Reactions Involving Solids 255 9.4 Problems for Chapter 9 257
10 . BIOCHEMICAL REACTIONS: ENZYME KINETICS 261
Enzyme Catalysis 261
Models of Enzyme Kinetics 264 .1 Michaelis-Menten Model 264
Inhibition and Activation in Enzyme Reactions 269 .1 Substrate Effects 270
11 . PRELIMINARY CONSIDERATIONS IN CHEMICAL REACTION ENGINEERING 279
Process Design and Mechanical Design 279 .1 Process Design 279
Batch Versus Continuous Operation 295 12.3 Design Equations for a Batch Reactor 296
13 . IDEALFLOW 317
Terminology 317
Types of Ideal Flow; Closed and Open Vessels 318 .1 Backmix Flow (BMF) 318
Age-Distribution Functions for Ideai Fiow 325 .1 Backmix Flow (BMF) 325
Problems for Chapter 13 333
14 . CONTINUOUS STIRRED-TANK REACTORS (CSTR) 335
Uses of a CSTR 336
Advantages and Disadvantages of a CSTR 336 14.3 Design Equations for a Single-Stage CSTR 336
Problems for Chapter 14 361
Design Equations for a PFR 366
Combinations of PFRs: Configurational Effects 387 15.5 Problems for Chapter 15 389
- Design Equations for an LFR 394
- Parallel Reactions 426 18.3 Series Reactions 429
- Choice of Reactor and Design Considerations 432 .1 Reactors for Reversible Reactions 433
- General Features of Nonideal Flow 453 19.2 Miig: Macromixing and Micromixing 454
- Characterization of Nonideal Flow in Terms of RTD 455 .1 Applications of RTD Measurements 455
- Problems for Chapter 19 490
- Axial Dispersion Reactor Model 499 20.3 Segregated-Plow Reactor Model (SPM) 501
- Examples of Reactions 512
- Types of Reactors and Modes of Operation 514 .1 Reactors for Two-Phase Reactions 514
- Pseudohomogeneous, One-Dimensional, Plug-Plow Model 527 1 Continuity Equation 527
- Reactor Models 553
- Moving-Particle Reactors 570 .1 Some Types 570
- Hydrodynamic Models of Fluidization 579 .1 Two-Region Model (Class (1)) 579
24 l REACTORS FOR FLUID-FLUID REACTIONS 599 24.1 Types of Reactions 599
Choice of Tower or Tank Reactor 602 24.4 Tower Reactors 603
APPENDIX A 623
Common Conversion Factors for Non-S1 Units to SI Units A.2 Values of Physicochemical Constants 623
Standard SI Prefixes 624
APPENDIX B: BIBLIOGRAPHY 625 B.l Books on Chemical Reactors 625
Books on Chemical Kinetics and Catalysis 626
APPENDIX C: ANSWERS TO SELECTED PROBLEMS 627
APPENDIX D: USE OF E-Z SOLVE FOR EQUATION SOLVING AND PARAMETER ESTIMATION 635
NOMENCLATURE 643
INDEXES 657
Introduction
- NATURE AND SCOPE OF CHEMICAL KINETICS
- NATURE AND SCOPE OF CHEMICAL REACTION ENGINEERING
- KINETICS AND CHEMICAL REACTION ENGINEERING
- ASPECTS OF KINETICS .1 Rate of Reaction-Definition
- Parameters Affecting Rate of Reaction: The Rate Law
- Measurement of Rate of Reaction-Preliminary
- Kinetics and Chemical Reaction Stoichiometry
Although great strides have been made in recent decades towards meeting this target, in many cases the best guide is to base it, to some extent, on the performance of the "last built". We illustrate the procedure in the following two examples, as implemented by the computer algebra software Muthematica3 (Smith and Missen, 1997).4 (The systems in these examples are small enough that matrix reduction can alternatively be done by manipulating hand.) As shown in these examples, and also in Example 1-2, the maximum number of linearly independent chemical equations required is 5.
SOLUTION
- Kinetics and Thermodynamics/Equilibrium
- Kinetics and Tkansport Processes
- ASPECTS OF CHEMICAL REACTION ENGINEERING 1 Reactor Design and Analysis of Performance
- Parameters Affecting Reactor Performance
- Balance Equations
- An Example of an Industrial Reactor
- DIMENSIONS AND UNITS
- PLAN OF TREATMENT IN FOLLOWING CHAPTERS .1 Organization of Topics
- Use of Computer Software for Problem Solving
- PROBLEMS FOR CHAPTER 1
This matrix can be rearranged by permuting the columns so that it is in the usual form for A*;. the order of species changes accordingly. The important consequence is that the maximum number of steps in a kinetic scheme is the same as the number (R) of chemical equations (the number of steps in a kinetic mechanism is usually larger), and therefore stoichiometry tells us the maximum number. of independent rate laws that we need to obtain experimentally (one for each step in the scheme) to fully describe the macroscopic behavior of the system. 3) The canonical form of equation 1.4-10, or its corresponding conventional form, is suitable for relating the reaction rates of substances in a complex system, corresponding to equation 1.4-8 for a simple system.
Kinetics and Ideal Reactor Models
TIME QUANTITIES
That is, r is the time required for a volume of feed equal to the volume of the container (V) to flow through the container. V is the volume of the container accessible to the liquid. r can be used as a scaling quantity for reactor performance, but the reaction conditions must be the same, point-for-point, in the scaling.
BATCH REACTOR (BR) .1 General Features
- Material Balance; Interpretation of ri
The general balance equation, 1.51, can then be written as a material balance for A with reference to a specified control volume (in Figure 2.1 this is the volume of the liquid). Whether A is the limiting reactant or not, it may be convenient to normalize by means of the degree of reaction, 5, defined for any species involved in the reaction by.
CONTINUOUS STIRRED-TANK REACTOR (CSTR) .1 General Features
- Material Balance; Interpretation of ri
2] As a consequence of [l], the exit stream has the same properties as the liquid inside the vessel. 2 For comparison with the "definition" of the species-independent rate, I, in note 1 of Chapter 1 (corresponding to equation 2.2-2 for a BR),.
PLUG-FLOW REACTOR (PFR) .1 General Features
- Material Balance; Interpretation of ri
If the density is constant, Equation 2.4-6 takes the form of Equation 2.2-10 for constant density in BR. Using Equation 2.4-4 in integrated form, V = 1 FAodfAl( -I*), together with the stoichiometry of the reaction, from which the total molar flow rate at any point. and the ideal gas equation of state from which the volumetric flow at any point is q = F,RTIP.
LAMINAR-FLOW REACTOR (LFR)
However, in this case density is not constant through the PFR, and the result for r differs from that for t obtained in (a). For simplicity in this case, we only consider steady-state behavior, despite the more general situation.
SUMMARY OF RESULTS FOR IDEAL REACTOR MODELS
3] A cylindrical LFR can be physically represented as consisting of a large number of thin cylindrical shells (each of thickness dr) with increasing radius (from center to wall) which move or slide past each other with decreasing velocity (from center to wall) ; is the residence time of a thin cylindrical shell at radius r.
STOICHIOMETRIC TABLE
PROBLEMS FOR CHAPTER 2
The primary application of chemical kinetics in CRE is the development of a rate law (for a simple system) or a set of rate laws (for a kinetics scheme of a complex system). This requires experimental measurement of reaction rate and its dependence on concentration, temperature, etc.
FEATURES OF A RATE LAW: INTRODUCTION .1 Separation of Effects
- Effect of Concentration: Order of Reaction
- Effect of Temperature: Arrhenius Equation; Activation Energy
Such changes do not change the form of Equation 3.1-2 or the values of (Y, p, and y; it is a matter of convenience which type is chosen. Establishing the form of Equation 3.1-2, including the values of the various parameters , is a matter of experiment.
EXPERIMENTAL MEASUREMENTS: GENERAL CONSIDERATIONS
EXPERIMENTAL METHODS TO FOLLOW THE EXTENT OF REACTION
- Ex-situ and In-situ Measurement Techniques
- Chemical Methods
- Physical Methods
- Other Measured Quantities
As the chemical reaction proceeds in a system, the physical properties of the system change due to the change in the chemical composition. If an appropriate property changes in a measurable way that can be related to composition, then the rate of change of the property is a measure of the rate of reaction.
EXPERIMENTAL STRATEGIES FOR DETERMINING RATE PARAMETERS
- Concentration-Related Parameters: Order of Reaction .1 Use of Constant-Volume BR
From Equation 2.2-10 and differentiation of the c*(t) data (numerically or graphically), values of (-Y*) can be generated as a function of cA. The equation to be integrated follows from the tariff law and the material balance equation 2.2-10.
NOTES ON METHODOLOGY FOR PARAMETER ESTIMATION
A function is linear with respect to its parameters, if, for example, doubling the values of all parameters doubles the value of the function; otherwise it is non-linear. There are a number of statistical and spreadsheet software packages available for linear regression, as well as for nonlinear regression of algebraic expressions (e.g. the Arrhenius equation).
PROBLEMS FOR CHAPTER 3
3-7 What is the expression corresponding to Equation 3.4-13 for the same type of reaction (I VA[A + I V~/B + products, constant density) occurring in a CSTR of volume V with a steady-state flow rate of q . Use a spreadsheet or equivalent computer program to calculate the concentration of product C as the reaction proceeds with time (t) in a constant volume batch reactor (try the parameter values below).
Development of the Rate Law for a Simple System
THE RATE LAW
- Form of Rate Law Used
- Empirical versus Fundamental Rate Laws
- Separability versus Nonseparability of Effects
The values of (Y~, A and EA must be determined from experimental data to establish the form of the rate law for a specific reaction. Any mathematical function that adequately represents experimental rate data can be used in the rate law.
GAS-PHASE REACTIONS: CHOICE OF CONCENTRATION UNITS .1 Use of Partial Pressure
- Rate and Rate Constant in Terms of Partial Pressure
- Rate Defined by - dpildt
- Arrhenius Parameters in Terms of Partial Pressure
If pi is used in the rate law instead of ci, there are two ways to interpret ri and thus ki. Alternatively, we can redefine the rate of reaction in terms of the rate of change of the partial pressure of a substance.
DEPENDENCE OF RATE ON CONCENTRATION
- First-Order Reactions
- Second-Order Reactions
- Third-Order Reactions
- Other Orders of Reaction
- Comparison of Orders of Reaction
- Product Species in the Rate Law
Determine the order of this reaction with respect to ethylene oxide at 20°C and the value of the rate constant. From equation 4.2-6, we write the assumed combined form of the rate law and the material balance equation (for constant volume), in terms of CHsCHO (A), as
DEPENDENCE OF RATE ON TEMPERATURE .1 Determination of Arrhenius Parameters
- Arrhenius Parameters and Choice of Concentration Units for Gas-Phase Reactions
In experiments 2 and 3, cu or co is approximately constant, and (- rA) doubles as CA doubles. From the given data we cannot say which of these three possibilities correctly accounts for the inhibition by product(s).
PROBLEMS FOR CHAPTER 4
From these results, determine the order of the reaction and the value of the rate constant (specify its units). Use (a) the differential method and (b) the integral method to determine the order of the reaction and the value of the rate constant.
Complex Systems
TYPES AND EXAMPLES OF COMPLEX SYSTEMS
Reversible (Opposing) Reactions
- Reactions in Parallel
Reactions in Series
- Combinations of Complexities
- Compartmental or Box Representation of Reaction Network
MEASURES OF REACTION EXTENT AND SELECTIVITY .1 Reaction Stoichiometry and Its Significance
- Fractional Conversion of a Reactant
- Yield of a Product
- Overall and Instantaneous Fractional Yield
The yield of a product is a measure of the magnitude of the reaction at a given point (time or position) in terms of a specified product and reactant. For the stoichiometric scheme in section 5.2.3, the total fractional yield of D with respect to A is,S,.
Extent of Reaction
- Stoichiometric Table for Complex System
Using the chemical system and equations (l), (2), and (3) of Example 5-1, construct a stoichiometric table, based on the use of tj, to represent the molar flow rates of all six species. Assume that experimental data are available for the flow rates (or equivalent) of CO, CO and HCHO as non-components.
REVERSIBLE REACTIONS .1 Net Rate and Forms of Rate Law
- Thermodynamic Restrictions on Rate and on Rate Laws
- Determination of Rate Constants
- Optimal T for Exothermic Reversible Reaction
The table can be represented as Table 5.1, where both sj and Fi obtained from equation 5.2-11 are applied alternately to non-components and components. This behavior can be represented graphically by constructing the rD-T-fA relationship from equation 5.3-16, where kf, k, and Ke4 depend on T.
SERIES REACTIONS
Values of the rate constants kI and b can be obtained from experimental measurements of cA and cn at different times in a BR. A simpler procedure is to first obtain k, from Equation 3.4-10, and then to obtain h from k, and one of the coordinates of the maximum value of cB (t, or cn,max).
Concept of Rate-Determining Step (rds)
- Determination of Reaction Network
The increase in partial yield of A may be due to it being a byproduct of the reaction that produces C (such as CO, formed in each step in selective oxidation reactions), or it may be due to different rate laws for the formation of A and B. The corresponding rate laws (tested using experimental measurements from differential PFR) are:. The values of the rate constants together with the values of the corresponding activation energies are given by the authors.).
PROBLEMS FOR CHAPTER 5
In their study of the kinetics of the partial oxidation of methane to HCHO, along with CO, CO, and H,O (Example 5-1), Spencer and Pereira (1987) observed the following: The kinetics of liquid-phase oxidation of anthracene (AN) in AQ by NO2 in acetic acid as a solvent was studied by Rodriguez and Tijero (1989) in a semi-solid reactor (batch vs. liq. phase) under conditions such that the kinetics of the overall gas-liq. process is controlled by the liq.-phase reaction rate.
Fundamentals of Reaction Rates
PRELIMINARY CONSIDERATIONS .1 Relating to Reaction-Rate Theories
- Relating to Reaction Mechanisms and Elementary Reactions
For example, the formation of ammonia, represented by the simple reaction N, + 3H, + 2NH, does not proceed in the way implied by this chemical statement, that is, by the simultaneous union of one molecule of N and three molecules of H to form two of NH ,. Molecularity of the reaction: number of reacting partners in an elementary reaction: unimolecular (one), bimolecular (two) or thermomolecular (three); in the above mechanism, the first and third steps are unimolecular as written, while the others are bimolecular.
DESCRIPTION OF ELEMENTARY CHEMICAL REACTIONS
6.2.1 ‘Ijpes of Elementary Reactions
General Requirements for Elementary Chemical Reactions
The simple theories of reaction rates involve applying basic physical-chemical knowledge to calculate or estimate the rate of successful molecular encounters. In section 6.3 we present important results from physical chemistry; in the following sections we show how they are used to establish rate theories, construct rate laws, and estimate the values of rate constants for elementary reactions.
ENERGY IN MOLECULES
- Potential Energy in Molecules-Requirements for Reaction
- Triatomic Systems: Potential Energy Surface and Transition State
- Kinetic Energy in Molecules
The notion of the transition state is central to both theories discussed in this chapter. The r,-distance after the transition is the same as before, although this is not the most stable configuration of the molecule in the excited state.
SIMPLE COLLISION THEORY OF REACTION RATES
- Simple Collision Theory (SCT) of Bimolecular Gas-Phase Reactions
A simple estimate of the frequency of A-B collisions can be obtained by assuming that the molecules are hard spheres of finite size, and that, like billiard balls, a collision occurs if the center of the B molecule is within the . Therefore, the best representation of the "necessary" amount of energy is somewhat higher than the barrier height.
- Collision Theory of Unimolecular Reactions
- Collision Theory of Bimolecular Combination Reactions; Termolecular Reactions
- TRANSITION STATE THEORY (TST) 1 General Features of the TST
- Thermodynamic Formulation
- Quantitative Estimates of Rate Constants Using TST with Statistical Mechanics
- Comparison of TST with SCT
- ELEMENTARY REACTIONS INVOLVING OTHER THAN GAS-PHASE NEUTRAL SPECIES
- Reactions in Condensed Phases
- Surface Phenomena
- Photochemical Elementary Reactions
- Reactions in Plasmas
- Summary 151
- SUMMARY
- PROBLEMS FOR CHAPTER 6
In the TST, molecularity (m) is the number of reactant molecules that form one molecule of the transition state. Nevertheless, the ratio of partition functions (thermodynamics) tells how easy (likely) reaching the transition state is.
Homogeneous Reaction
Mechanisms and Rate Laws
SIMPLE HOMOGENEOUS REACTIONS .1 Types of Mechanisms
- Open-Sequence Mechanisms: Derivation of Rate Law from Mechanism
- Closed-Sequence Mechanisms; Chain Reactions
- Photochemical Reactions
In these cases, the equilibrium constant for each of the fast steps appears as a multiplying factor in the rate law. This can be demonstrated by considering the following simplified chain mechanism for reaction A.
COMPLEX REACTIONS .1 Derivation of Rate Laws
- Computer Modeling of Complex Reaction Kinetics
If the reactive species in the chemical activation step initiates a radical chain with chain length CL, then the total quantum yield based on the final product is Q, X CL and can be greater than 1. The individual absorption characteristics of molecules exposed to radiation in the ultraviolet and visible range lead to greater specificities.
POLYMERIZATION REACTIONS
- Chain-Reaction Polymerization
- Step-Change Polymerization
For the rate law is the rate of polymerization, the rate of disappearance of monomer. Each step is a second-order elementary reaction, and the rate constant k (defined for each step)' is the same for all steps.
PROBLEMS FOR CHAPTER 7
A possible free radical chain mechanism for the thermal decomposition of acetaldehyde (to CH4 and CO) is the Rice-Herzfeld mechanism (Laidler and Liu, 1967):. b) Classify each step in the mechanism. How many of the reactions in this mechanism can be affected by the rate of energy transfer.
Catalysis and Catalytic Reactions
CATALYSIS AND CATALYSTS .1 Nature and Concept
- Types of Catalysis
- General Aspects of Catalysis
The nature of the catalytic cycle is illustrated in Figure 8.1 for the catalytic reaction used commercially to make propene oxide (with MO as catalyst), cited above. Homogeneous catalysis is responsible for about 20% of the production of commercial catalytic reactions in the chemical industry.
MOLECULAR CATALYSIS .1 Gas-Phase Reactions
