CONTENTS

Front Matter

Title Page, Preface and Acknowledgements
About the Author
Status, History, Issues and Updates
Complementary Textbooks
Teaching Notes and Resources
A Note about Numerical Solutions

Course Units

I. Chemical Reactions
1. Stoichiometry and Reaction Progress
2. Reaction Thermochemistry
3. Reaction Equilibrium
II. Chemical Reaction Kinetics
A. Rate Expressions
4. Reaction Rates and Temperature Effects
5. Empirical and Theoretical Rate Expressions
6. Reaction Mechanisms
7. The Steady State Approximation
8. Rate-Determining Step
9. Homogeneous and Enzymatic Catalysis
10. Heterogeneous Catalysis
B. Kinetics Experiments
11. Laboratory Reactors
12. Performing Kinetics Experiments
C. Analysis of Kinetics Data
13. CSTR Data Analysis
14. Differential Data Analysis
15. Integral Data Analysis
16. Numerical Data Analysis
III. Chemical Reaction Engineering
A. Ideal Reactors
17. Reactor Models and Reaction Types
B. Perfectly Mixed Batch Reactors
18. Reaction Engineering of Batch Reactors
19. Analysis of Batch Reactors
20. Optimization of Batch Reactor Processes
C. Continuous Flow Stirred Tank Reactors
21. Reaction Engineering of CSTRs
22. Analysis of Steady State CSTRs
23. Analysis of Transient CSTRs
24. Multiple Steady States in CSTRs
D. Plug Flow Reactors
25. Reaction Engineering of PFRs
26. Analysis of Steady State PFRs
27. Analysis of Transient PFRs
E. Matching Reactors to Reactions
28. Choosing a Reactor Type
29. Multiple Reactor Networks
30. Thermal Back-Mixing in a PFR
31. Back-Mixing in a PFR via Recycle
32. Ideal Semi-Batch Reactors
IV. Non-Ideal Reactions and Reactors
A. Alternatives to the Ideal Reactor Models
33. Axial Dispersion Model
34. 2-D and 3-D Tubular Reactor Models
35. Zoned Reactor Models
36. Segregated Flow Models
37. Overview of Multi-Phase Reactors
B. Coupled Chemical and Physical Kinetics
38. Heterogeneous Catalytic Reactions
39. Gas-Liquid Reactions
40. Gas-Solid Reactions

Supplemental Units

S1. Identifying Independent Reactions
S2. Solving Non-differential Equations
S3. Fitting Linear Models to Data
S4. Numerically Fitting Models to Data
S5. Solving Initial Value Differential Equations
S6. Solving Boundary Value Differential Equations

Unit 33. Axial Dispersion Model

This website provides learning and teaching tools for a first course on kinetics and reaction engineering. In the preceding parts of the course, the reacting fluid was always treated as if it was homogeneous, and only ideal reactor types were considered. The knowledge gained to this point is sufficient for reaction engineering for many commercial processes. Nonetheless, there are situations where the reactor does not conform to one of the ideal types and/or the rates are affected by the kinetics of physical processes in addition to the chemical reaction rate. Part IV of the course surveys a few such situations. It does not provide an in-depth analysis of any of them, but the information provided should serve as a good foundation for further study.

The first section of Part IV considers reactors that do not satisfy the assumptions of any of the ideal reactor types. It touches upon three approaches to modeling such reactors. One approach is to increase the rigor of the ideal reactor models by changing one of more of the assumptions that define the ideal reactor, but retaining most of the original model. A second approach is to effectively abandon rigor in favor of a quantitatively accurate description of the reactor behavior. The last approach uses statistical methods to describe the performance of a reactor. Section A then concludes by considering changes that are necessary when modeling reactors wherein two phases are involved in the reaction(s) taking place, and presenting with an overview of reactors that are used when the reaction involves two or more phases.

In the plug flow reactor model, concentration only varies in the axial direction, and the sole cause of that variation is convection plus reaction. Unit 33 describes axial dispersion models where a diffusion-like phenomenon in the z direction is added to the model. In real reactors, axial diffusion is almost never significant. Nonetheless, the axial dispersion model can still be useful because in effect, it can add a variable amount of backmixing to a PFR. As such, axial dispersion models sometimes offer an accurate description of a tubular reactor that does not fully conform to the assumptions of an ideal PFR.

Learning Resources

Teaching Resources

Practice Problems

1. Gas phase A, at 10 atm and 100 °C is fed at a rate of 23,000 L min-1 to a 2 in diameter, isothermal tubular reactor that is 8 ft long. The reactor temperature is 100 °C and pressure drop in the reactor is negligible. Reversible reaction (1a) takes place at a rate described by equation (1b). At the operating temperature, kf = 4750 min-1 and kr = 4300 min-1. Calculate the conversion of A if the axial dispersion coefficient is equal to 5.5 x 105 dm-2 min-1.

  A ↔ Z (1a)  
  r = kfCA-krCZ (1b)  

(Problem Statement as .pdf file)