Cover
Preface
Nomenclature
Part I: Reactor Analysis, Design, and Scale‐up
1. 1 Nonideal Flow
  1. 1.1 Introduction
  2. 1.2 Residence Time Distribution (RTD) Function
  3. 1.3 RTD in Ideal Reactors
  4. 1.4 Modeling the Reactor with the RTD
  5. 1.5 Other Models of Real Reactors Using CSTR and PFR
  6. Bibliography
2. 2 Convolution and Deconvolution of Residence Time Distribution Curves in Reactors
  1. 2.1 Introduction
  2. 2.2 Convolution
  3. 2.3 Deconvolution
  4. 2.4 Computer Program Using Matlab® (Convolution)
  5. 2.5 Computer Program Using MATLAB (Deconvolution)
  6. 2.6 Convolution of Signals in Reactors Connected in Series
  7. Bibliography
3. 3 Use of Transfer Function for Convolution and Deconvolution of Complex Reactor Systems
  1. 3.1 Introduction
  2. 3.2 Definition and Properties of the Transfer Function
  3. 3.3 Laplace Transform
  4. 3.4 Use of Laplace Transform in Chemical Reactor Characterization
  5. 3.5 Complex Network of Ideal Reactors
  6. 3.6 Transfer Function for the Dispersion Model
  7. Bibliography
4. 4 Partial Differential Equations in Reactor Design
  1. 4.1 Introduction
  2. 4.2 Classification of Partial Differential Equations
  3. 4.3 Approximations by Finite Differences
  4. 4.4 Approaching the Problem Using Finite Differences
  5. 4.5 Other Applications of PDE – Numerical Methods
  6. Bibliography
5. 5 Unsteady State Regime Simulation in Reactor Design
  1. 5.1 Introduction
  2. 5.2 CSTR Working in Unsteady State
  3. 5.3 PFR Working in Dynamic Regime (No Dispersion)
  4. 5.4 PFR Working in Dynamic Regime (with Dispersion)
  5. 5.5 Multiple Steady States in CSTR with Exothermal Reaction
  6. Bibliography
6. 6 Scaling and Stability of Chemical Reactors
  1. 6.1 Introduction
  2. 6.2 Scaling the Batch Tank Stirred Reactor
  3. 6.3 Rapid Exothermic Reaction in a Tubular Reactor
  4. Bibliography
7. 7 Forced Unsteady State Operation of Chemical Reactors
  1. 7.1 Introduction
  2. 7.2 Objectives and Types of FUSO
  3. 7.3 Periodic Variation of the Input
  4. 7.4 Periodic Flow Reversal
  5. 7.5 Operation with Variable Volume (VVO)
  6. 7.6 Oscillating Pressure
  7. Bibliography
Part II: Catalytic, Multiphase and Biochemical Reactor Design
1. 8 Industrial Catalysis
  1. 8.1 Introduction
  2. 8.2 Industrial Preparation of Catalysts
  3. 8.3 Main Catalytic Processes in Industry
  4. Bibliography
2. 9 Catalytic and Multiphase Reactor Design
  1. 9.1 Introduction
  2. 9.2 Rate Equation in Catalytic Systems
  3. 9.3 Rate Equation When Chemical Step Is Limiting Reaction Rate
  4. 9.4 Rate Expression for External Diffusion as a Limiting Step
  5. 9.5 Reaction Rate When Internal Diffusion Is Slow
  6. 9.6 Combination of Resistances
  7. 9.7 Monolithic Catalytic Reactors
  8. 9.8 Fluid–Fluid Reactions (Catalyzed and Noncatalyzed)
  9. 9.9 Design of Multiphase Reactors
  10. Bibliography
3. 10 Biochemical Reactors
  1. 10.1 Introduction
  2. 10.2 Enzymatic Catalysis
  3. 10.3 Microbial Kinetics
  4. 10.4 Immobilization of Enzymes and Cells: Mass Transfer Effects
  5. 10.5 Bioreactors
  6. Bibliography
Index
End User License Agreement

List of Tables

Chapter 3
1. Table 3.1 Properties of the Laplace transform.
2. Table 3.2 Laplace transform of basic functions.
Chapter 4
1. Table 4.1 First‐order approximations of the first and second derivative.
2. Table 4.2 Second‐order approximation of the first and second derivative.
Chapter 5
1. Table 5.1 Steady‐state conditions of the example, without considering their stab...
Chapter 6
1. Table 6.1 Maximum typical values of the scale factor of several equipment.
2. Table 6.2 Standards for scaling based on residence time.
3. Table 6.3 Results in the batch and semibatch reactor after 600 seconds.
4. Table 6.4 Optimum length, conversion and performance for tubular reactors.
Chapter 8
1. Table 8.1 Characteristics of some support materials.
2. Table 8.2 Use of zeolite in a modern oil refinery.
3. Table 8.3 Examples of space velocity.
4. Table 8.4 Important industrial catalyzed reactions with the corresponding cataly...
5. Table 8.5 Catalytic processes in the syngas production.
6. Table 8.6 Typical composition of the exhaust gases of diesel and gasoline engine...
Chapter 9
1. Table 9.1 Different properties used for defining reaction rate and their corresp...
Chapter 10
1. Table 10.1 Yield definitions.

List of Illustrations

Chapter 1
1. Figure 1.1 Measurement of the RTD.
2. Figure 1.2 Two E(t) functions are needed to characterize a reactor with two mo...
3. Figure 1.3 Interpretation of the cumulative distribution curve, F(t).
4. Figure 1.4 Effect of the second moment of the RTD in the curve shape. Both dis...
5. Figure 1.5 Form of the RTD curve for positive and negative skewness.
6. Figure 1.6 Dirac delta function, i.e. response of an ideal PFR to a pulse trac...
7. Figure 1.7 Response of a CSTR to a pulse tracer input.
8. Figure 1.8 Real reactor modeled as a CSTR and a PFR in series.
9. Figure 1.9 RTD for a CSTR and a PFR in series.
10. Figure 1.10 Tanks‐in‐series model.
11. Figure 1.11 Response to a pulse tracer input in function of the number from ta...
12. Figure 1.12 Effect of the dispersion on the velocity profile.
13. Figure 1.13 Real reactor and modeling using two CSTR.
14. Figure 1.14 Real reactor and modeling using a single CSTR with dead volume and...
15. Figure 1.15 E(t) predicted by this model with different values of the paramete...
16. Figure 1.16 Combinations of ideal reactors used to model real reactors.
17. Figure 1.17 (a) Concentration of tracer obtained in a step input experiment an...
Chapter 2
1. Figure 2.1 Visual example of the convolution of two functions.
2. Figure 2.2 Input signal to a reactor, RTD, and output convoluted signal.
3. Figure 2.3 Solution to Example 2.3. Convolution of two given signals.
4. Figure 2.4 Solution to Example 2.4. Convolution of a given signal with the RTD...
5. Figure 2.5 Solution to Example 2.5. Convolution of a given signal with the RTD...
6. Figure 2.6 Solution to Example 2.6. Deconvolution.
7. Figure 2.7 Set of three reactors connected in series.
Chapter 3
1. Figure 3.1 Step input of tracer to a CSTR.
2. Figure 3.2 Series of coupled systems and signals.
3. Figure 3.3 System of CSTRs connected in series.
4. Figure 3.4 Branches in parallel with the split “S“ and mix “M“ points.
5. Figure 3.5 Two continuous stirred tanks in parallel.
6. Figure 3.6 Combination of systems showing internal or external recycle current...
Chapter 4
1. Figure 4.1 Diffusion of a gas inside a plane catalyst particle.
2. Figure 4.2 Resolution scheme for the explicit method.
3. Figure 4.3 Graphical representation of the concentration of gas in the solid p...
4. Figure 4.4 Scheme of the model proposed for an electrochemical reactor with a ...
5. Figure 4.5 RTD calculated in the reactor, for (a) β _dyn = 0.38 and (b) β...
6. Figure 4.6 Catalytic flat wall.
7. Figure 4.7 Concentration profile obtained with different values of the constan...
Chapter 5
1. Figure 5.1 Continuous stirred tank reactor (CSTR).
2. Figure 5.2 CSTR working in unsteady state regime. The concentration at the exi...
3. Figure 5.3 The mole balance in a PFR.
4. Figure 5.4 PFR working in unsteady state regime (without dispersion) at differ...
5. Figure 5.5 PFR working in unsteady state regime (with dispersion) at different...
6. Figure 5.6 CSTR with cooling jacked. T is the temperature of the reactor; T _c i...
7. Figure 5.7 Three possible steady states in the exothermal cooled CSTR.
8. Figure 5.8 Temperature evolution with time in the system starting at different...
9. Figure 5.9 Small changes in the input temperature will move the Q _removed and d...
Chapter 6
1. Figure 6.1 Conventional scaling process.
2. Figure 6.2 Temperature control in batch reactors manipulates the temperature o...
3. Figure 6.3 Concentration and temperature profiles in the small and the large r...
4. Figure 6.4 Concentration of reactive A (a), product P, and reactor temperature...
5. Figure 6.5 Concentration of P (a) and reactor temperature (b) in adiabatic and...
6. Figure 6.6 (a) Concentration of P as a function of the temperature of the reac...
7. Figure 6.7 Temperature increase for exothermic reactions in a tubular reactor....
8. Figure 6.8 Geometric place of the maximum temperature differences for several ...
9. Figure 6.9 System behavior for N _c/N _ad = 5 and N _ad = 8.
10. Figure 6.10 Solution of Example 6.4.
Chapter 7
1. Figure 7.1 Effect of regulation in unsteady operations.
2. Figure 7.2 Flow variation of reagentsA and B periodically between two values.
3. Figure 7.3 Comparison of the input signals of a steady‐ state operation with a...
4. Figure 7.4 Island model. (a) Steady‐ state operation, (b) FUSO..
5. Figure 7.5 Operation diagram of an operation in adiabatic stages and one of “r...
6. Figure 7.6 Development of a temperature profile during operation in “reverse f...
7. Figure 7.7 Reverse flow in a reactor with a simple combination of two three‐wa...
8. Figure 7.8 Mode of operation of a variable volume operation.
9. Figure 7.9 System for a periodic separation reactor.
Chapter 8
1. Figure 8.1 Trickle‐bed reactor.
2. Figure 8.2 Catalyst key points.
3. Figure 8.3 Typical distribution profiles of active phase in a spherical suppor...
4. Figure 8.4 Structure of sodalite unit and superstructure of the zeolites. Sour...
5. Figure 8.5 Catalyst structure and active components.
6. Figure 8.6 Scheme of the production of zeolites.
7. Figure 8.7 Scheme of the FCC process.
8. Figure 8.8 Flowchart of the ethylbenzene production process. V‐1, V‐2, and V‐4...
9. Figure 8.9 Ethylene recirculation diagram.
10. Figure 8.10 Complete process for energy production from biomass.
11. Figure 8.11 Some catalytic processes present in the gas exhaust of diesel and ...
12. Figure 8.12 Variation of the conversion of the three‐way catalyst reactions as...
13. Figure 8.13 Flow dynamics in a DPF and general aspect. Source: Adapted from ht...
Chapter 9
1. Figure 9.1 Representation of the action of a catalyst.
2. Figure 9.2 Porosity and void volumes in catalyst. Reaction steps in catalytic ...
3. Figure 9.3 Variation of the proportion of active centers bonding to the ligand...
4. Figure 9.4 Porous catalyst pellet with reagent A entry on both sides.
5. Figure 9.5 Variation of the concentration of A vs. distance x.
6. Figure 9.6 Porous cylindrical catalyst pellet with reagent A entry on the exte...
7. Figure 9.7 Error implied in the use of the approximation Eq. (9.50) instead of...
8. Figure 9.8 Monolithic catalyst structure.
9. Figure 9.9 Solution to Example 9.7.
10. Figure 9.10 Double‐layer (two‐film) model.
11. Figure 9.11 Concentration of components being transferred between phases. The ...
12. Figure 9.12 General rate equation for different values of M _H and E _i.
13. Figure 9.13 Membrane reactor.
14. Figure 9.14 Nomenclature used.
15. Figure 9.15 Schematic showing the resistances involved in the gas–liquid react...
16. Figure 9.16 Scheme of a multiphase system with the nomenclature used.
17. Figure 9.17 Summary of cases and situations studied for the design of multipha...
Chapter 10
1. Figure 10.1 Biochemical route in catalyzed enzymatic reactions.
2. Figure 10.2 Reaction rate and value of K′ obtained vs. concentration of one of...
3. Figure 10.3 K′ vs. concentration of substrate in a bisusbtrate ordered mechani...
4. Figure 10.4 Exemplification of K′ vs. concentration for the different mechanis...
5. Figure 10.5 Phases of the cell growth.
6. Figure 10.6Figure 10.6 Scheme of immobilization of enzymes in different struct...
7. Figure 10.7 Scheme of a continuous stirred tank bioreactor (CSTB).
8. Figure 10.8 Variation of substrate, biomass, and cell production concentration...
9. Figure 10.9 Continuous agitated tank fermenter with recirculation of microorga...
10. Figure 10.10 Scheme of a tubular bioreactor.
11. Figure 10.11 Scheme of a tubular bioreactor with recycle.
12. Figure 10.12 Solution of Example 10.5.

Copyright

Author

Prof. Juan A. Conesa

Universidad de Alicante

Ingenieria Quimica

Carr. San Vicente del Raspeig

s/n

03690 Alicante

Spain

Cover

All books published by Wiley‐VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

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Print ISBN: 978‐3‐527‐34630‐1

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Preface

The main objective of this book is to introduce the reader to the analysis of complex chemical reactors. In them, reactions with complex kinetics will be carried out and/or they will work in unusual situations, such as unsteady state operation. The mathematical tools necessary for the characterization of flow and kinetic models that can solve complex problems in the design of reactors are given in the book. Reactors operating in a transitory regime are also described, and their design equations are analyzed. Special attention is paid to the description and design of catalytic reaction systems, in which the presence of two or more phases makes their analysis and design complex.

Throughout the book there are many examples of application of the concepts and equations studied, to strengthen the content treated. In the examples, complex reactors are solved in terms of the characterization of their flow, and other situations that are not usually dealt with in textbooks.

For the resolution of many examples, programming in Matlab® (or its equivalent in freeware, GNU Octave) is used. The necessary level of knowledge of this program is very low. The use of big programs that link two or more Matlab scripts is avoided, and simple programs are offered as alternatives, which, although more rudimentary, are capable of performing complex calculations.

The book covers some aspects that are not treated in any textbook dedicated to the reactor design. There are some chapters with material similar to other texts but in many facets the work presents aspects that are not treated at all in any other book, as is the use of numerical methods for solving engineering problems (unsteady state regime included), the use of transfer functions to study residence time distributions, the convolution and deconvolution curves for reactor characterization, forced‐unsteady‐state‐operation, scale‐up of chemical reactors, design of multiphasic reactors, and biochemical reactors design (not only Michaelis–Menten nor Monod kinetics). Other aspects considered, mainly in part two, are the design of multiphase gas–liquid–solid reactors, including bubble reactors, agitated and trickle flow reactors.

A special emphasis is done to the numerical solution of differential equations using the finite differences approximation. I know there are available more complex tools for solving such situations, but in my opinion, it is important that students have in mind this simple system for solving PDE. This would give a background for understanding other more complex methods.

At the University of Alicante, the text is the basis for a course of 4.5 credit points in the last year of ChemEng MS. The course is complemented with the study of electrochemical, photochemical, and sonochemical reactors.

Alicante, Spain

May 2019

Juan A. Conesa

Nomenclature

Suggested units are indicated for each variable.

N: Amount of substance (mol)
Q: Volumetric flow rate (m³/s)
C: Concentration (usually mol/m³, or kg/m³)
E: (in the RTD context) → residence time distribution function, RTD (–)
F: Integral form of the residence time distribution function (–)
t _m: First moment of the RTD; mean value of time (s)
: Average residence time (=V/Q) (s)
V: Volume (m³)
σ: Standard deviation (s)
s: (in the RTD context) → skewness (s)
s: (in the LT context) → main variable in the Laplace space
δ: Dirac delta function (–)
n _t: Number of tanks in the tanks‐in‐series model (–)
k: Kinetic constant (units depend on the kinetic law)
D _e: Effective diffusion coefficient (m²/s)
n _T: Total molar flow (mol/s)
S: Section (m²)
C _T: Total concentration (mol/m³)
u: Linear velocity (m/s)
L: Characteristic length (m)
M: Tracer mass (kg or kmol)
V _p: Volume with piston flow regime (m³)
V _d: Dead volume (m³)
X _A: Molar conversion of reactant A (–)
r _A: Reaction (or process) rate based on the external catalyst surface (mol/(s m²))
r′_A: Reaction (or process) rate based on the weight of catalyst (mol/(s kg))
r″ _A: Reaction (or process) rate based on the volume of reacting species (mol/(s m³))
r‴ _A: Reaction (or process) rate based on the volume of catalyst particles (mol/(s m³))
C _As: Concentration of A in the surface (mol/m³)
D _AB: Diffusion coefficient (diffusivity) of A in B (m²/s)
q _s: Heat flow in the surface (J/s)
h: Heat transfer coefficient (J/K s)
T: Temperature (K)
k _L: Mass transfer coefficient in the liquid phase (mol/(s m²)/(mol/m³) = m/s)
Q _c: Flow rate in the cooling zone (m³/s)
ΔH _r: Enthalpy of a reaction (kJ/mol)
U: Global heat transfer coefficient (J/K s)
E: (in the reaction rates context) → activation energy (J/mol)
H(s): Transfer function (–) (Laplace space)
X(s): Stimulus function (–) (Laplace space)
Y(s): Response to stimulus function (–)(Laplace space)
h(t): Time‐dependent transfer function (–)
y(t): Time‐dependent response to stimulus function (–)
x(t): Time‐dependent stimulus function (–)
L{h(t)}: Laplace transform of function h(t)
α: Fraction of flow rate (–)
β: Fraction of volume (–)
Cp: Concentration of product “P” (mol/m³)
c _p: Calorific capacity of the reacting flow (J/K g)
c _Pc: Calorific capacity of the cooling fluid (J/K g)
N _c: Dimensionless cooling capacity (–)
N _ad: Dimensionless adiabatic heat increment (–)
Δυ: Dimensionless temperature difference (–)
k _h: Kinetic constant at the temperature of the cooling medium (units depend on the reaction order)
k ₀: Pre‐exponential factor of the kinetic constant (units depend on the reaction order)
Φ: Thiele modulus (–)
We: Weisz modulus (–)
m: kinetics to diffusion ratio in catalytic reactions (1/m)
K _M: Michaelis constant (g/l)
K _S: Monod constant (g/l)
W: Weight of catalyst (g)
μ: Growth rate per unit of cell (1/s)
φ: Tortuosity factor (–)
η: Effectiveness (–)
η _e: Effectiveness (related to external diffusion) (–)
J ₀: Bessel function of zero order (–)
J ₁: Bessel function of first order (–)
α: Fraction of volume of a subsystem (–)
β: Fraction of flow passing through a subsystem (–)
q: Heat flux (J/s)
q _C: Heat flux in cooling media (J/s)
u: Linear velocity (m/s)
T _C: Temperature of the cooling media (K)
A _m×n: Matrix of convolution
g _A: Generation term of a mole balance (mol/s)
n _A: Molar flow of component “A” (mol/s or mol/(s m²))

Subscripts:

i: Actual position
i+1: Position of the following interval
i−1: Position of the preceding interval
S: Surface
0: Inlet conditions
mm: Maximum of the maxima curve (critical point)

Superscripts

t: Actual time
t+1: Time of the following interval
t−1: Time of the previous interval

Chemical Reactor Design

Mathematical Modeling and Applications