Unit 30. Thermal Back-Mixing in a PFR

This website provides learning and teaching tools for a first course on kinetics and reaction engineering. Here, in Part III of the course, the focus is on the modeling of chemical reactors. In particular, it describes reaction engineering using the three ideal reactor types: perfectly mixed batch reactors, continuous flow stirred tank reactors and plug flow reactors. After considering each of the ideal reactor types in isolation, the focus shifts to ideal reactors that are combined with other reactors or equipment to better match the characteristics of the reactor to the reactions running within it.

The preceding sections of Part III examined reaction engineering using one of the three ideal reactor types in isolation. Section E considers the important topic of matching the reactions being run to the reactor that is best-suited to those reactions. It examines ways in which the ideal reactors can be modified or augmented so that their performance is further improved. In all cases considered in this section, each reactor is still one of the three ideal types, and it is still modeled as described in the preceding sections. The things that differ from prior analyses are the external connections to the reactor or reactors. These changes lead to improved performance for a selected class of reaction, but they can also affect the mathematical approach used to solve the reactor model equations.

One advantage offered by a CSTR when running an exothermic reaction is that the cool feed gets heated by mixing with the contents of the reactor. As a consequence the reaction takes place at the higher exit temperature where the rate is larger. Unit 30 shows how a PFR can be augmented by adding a heat exchanger that heats the feed using the product stream. By means of this augmentation, the PFR gains some of the thermal back-mixing benefits enjoyed by a CSTR.

Learning Resources

• Archive (.zip) - Contains all learning resources listed below for this unit
• Documents to Read:
  • Unit 30 Informational Reading (.pdf)
  • Example 30.1 (.pdf)
  • Example 30.2 (.pdf)
• Videos to Watch (please right-click and save, then play back locally on your computer):
  • Unit 30 Informational Video (.mov)
  • Example 30.1 Video (.mov)
  • Example 30.2 Video (.mov)
• Reference Files:
  • Unit 30 Definitions, Nomenclature and Equations (.pdf)
• Other Files:
  • Example_30_1_pfr.m - MATLAB file used to model the PFR in the solution of Example 30.1
  • Example_30_1.m - MATLAB file used to model the heat exchanger in the solution of Example 30.1
  • Example_30_2_pfr.m - MATLAB file used to model the PFR in the solution of Example 30.2
  • Example_30_1.m - MATLAB file used to model the heat exchanger in the solution of Example 30.2

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 30.1
  • 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_30_1.m - MATLAB file used in the solution of Activity 30.1
    • Activity_30_1_pfr.m - MATLAB file used to model the PFR in the solution of Activity 30.1

Practice Problems

1. Liquid phase reaction (1a) is exothermic with a constant heat of reaction of -75.6 kJ mol^-1. The second order (in A) rate coefficient has a pre-exponential factor of 5.22 x 10³ m³ mol^-1 min^-1 and an activation energy of 62.8 kJ mol^-1. A solution of 1 M A at 20 °C is fed to a counter-current heat exchanger at a rate of 1.25 L min^-1; after passing through the heat exchanger it is fed to a 0.5 m³ PFR operating adiabatically. The product of the heat transfer coefficient and the heat transfer area, UA, based on the arithmetic average temperature change is 5300 J K^-1 min^-1. If the heat capacity of the solution is constant and equal to 2 J mL K^-1, what percentage of the A in the feed will be converted and at what temperature will the final process stream leave the reactor?

(Problem Statement as .pdf file)