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

• Archive (.zip) - Contains all learning resources listed below for this unit
• Documents to Read:
  • Unit 33 Informational Reading (.pdf)
  • Example 33.1 (.pdf)
  • Example 33.2 (.pdf)
• Videos to Watch (please right-click and save, then play back locally on your computer):
  • Unit 33 Informational Video (.mov)
  • Example 33.1 Video (.mov)
  • Example 33.2 Video (.mov)
• Reference Files:
  • Unit 33 Definitions, Nomenclature and Equations (.pdf)
• Other Files:
  • Example_33_1.m - MATLAB file used to coordinate the calculations and make the plot for Example 33.1
  • Example_33_1_pfr.m - MATLAB file used to perform the PFR calculations for Example 33.1
  • Example_33_1_ad.m - MATLAB file used to perform the axial dispersion model calculations for Example 33.1
  • Example_33_2.m - MATLAB file used to perform the calculations for Example 33.2

Teaching Resources

• Archive (.zip) - Contains all teaching resources listed below for this unit
• Sample Class
  • Online Pre-class Quiz (.pdf file)
  • Redacted slides to make available to students before class
    • Keynote 09
    • PowerPoint
  • Other files to make available to students before class
    • Worksheet for Activity 33.1
  • Class Lesson Plan (.pdf)
  • Complete slides to make available to students after class
    • Keynote 09
    • PowerPoint
  • Other files to make available to students after class
    • Activity_33_1.m - MATLAB file used to coordinate the calculations and make the plot for Activity 33.1
    • Activity_33_1_ad.m - MATLAB file used to perform the axial dispersion model calculations for Activity 33.1

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, k_f = 4750 min^-1 and k_r = 4300 min^-1. Calculate the conversion of A if the axial dispersion coefficient is equal to 5.5 x 10⁵ dm^-2 min^-1.

(Problem Statement as .pdf file)