Unit 31. Back-Mixing in a PFR via Recycle

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.

Unit 30 showed how augmenting a PFR with a heat exchanger can impart thermal backmixing to the PFR, similar to that enjoyed naturally by a CSTR. Unit 31 extends the augmentation to include backmixing of both heat and mass. This is accomplished by adding a recycle stream to an ideal PFR. The unit shows that by adjusting the amount of material that is backmixed, the augmented PFR can span a range of performance characteristics from being a pure PRF to being a being essentially a pure CSTR.

Learning Resources

• Archive (.zip) - Contains all learning resources listed below for this unit
• Documents to Read:
  • Unit 31 Informational Reading (.pdf)
  • Example 31.1 (.pdf)
  • Example 31.2 (.pdf)
• Videos to Watch (please right-click and save, then play back locally on your computer):
  • Unit 31 Informational Video (.mov)
  • Example 31.1 Video (.mov)
  • Example 31.2 Video (.mov)
• Reference Files:
  • Unit 31 Definitions, Nomenclature and Equations (.pdf)
• Other Files:
  • Example_31_1_pfr.m - MATLAB file used to model the PFR in the solution of Example 31.1
  • Example_31_1.m - MATLAB file used to model the mixing point in the solution of Example 31.1
  • Example_31_2_pfr.m - MATLAB file used to model the PFR in the solution of Example 31.2
  • Example_31_2.m - MATLAB file used to model the mixing point in the solution of Example 31.2

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 31.1
  • 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_31_1_pfr.m - MATLAB file used to model the PFR in Activity 31.1
    • Activity_31_1.m - MATLAB file used to model the mixing point in Activity 31.1

Practice Problems

1. Problem 30.1 described a thermally backmixed PFR. Suppose that instead of passing the effluent from that reactor through a heat exchanger to heat the feed, part of the feed was recycled at a recycle ratio of 1.0. How does the conversion compare to that of the thermally backmixed PFR (72%)? Specifically, 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 the process at a rate of 1.25 L min^-1. It is mixed with the recycle stream from the outlet of a 0.5 m³ PFR operating adiabatically with a recycle ratio of 1.0. 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)