Unit 26. Analysis of Steady State PFRs

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.

Reaction engineering of the third of the three ideal reactor types, the plug flow reactor (PFR), is the subject of Section D of Part III. The discussion parallels that of the previous two sections: typical reaction engineering tasks are defined, qualitative performance is examined and full mathematical analysis is described and illustrated. Similar to CSTRs, plug flow reactors are typically designed to operate at steady state, but their start-up and shut-down involves transient operation, so both modes of operation are considered in this section.

Unit 26 describes how to write an accurate mathematical model for a reactor that obeys the assumptions of a plug flow reactor and that operates at steady state. It also provides a general approach for solving the resulting set of coupled ordinary differential equations. That approach is analogous to the approach for batch reactors and transient CSTRs. While the approach will likely need to be adapted to match the particular task at hand, it will allow an accurate quantitative analysis of steady state plug flow reactor processes.

Learning Resources

• Archive (.zip) - Contains all learning resources listed below for this unit
• Documents to Read:
  • Unit 26 Informational Reading (.pdf)
  • Example 26.1 (.pdf)
  • Example 26.2 (.pdf)
  • Example 26.3 (.pdf)
• Videos to Watch (please right-click and save, then play back locally on your computer):
  • Unit 26 Informational Video (.mov)
  • Example 26.1 Video (.mov)
  • Example 26.2 Video (.mov)
  • Example 26.3 Video (.mov)
• Reference Files:
  • Unit 26 Definitions, Nomenclature and Equations (.pdf)
• Other Files:
  • Example_26_1.m - MATLAB file used in the solution of Example 26.1
  • Example_26_2.m - MATLAB file used in the solution of Example 26.2
  • Example_26_3.m - MATLAB file used in the solution of Example 26.3

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
  • 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 26.1 Solution (.pdf)
    • Activity_26_1.m - MATLAB file used in the solution of Activity 26.1

Practice Problems

1. Gas phase reaction (1a) occurs with negligible pressure drop in a 10 foot long tubular reactor with a 1 inch inside diameter. The heat of reaction (1a) is -24.7 kcal mol^-1, and the reaction is first order in A with a pre-exponential factor of 8.38 x 10⁸ min^-1 and an activation energy of 30.8 kcal mol^-1. The steady state feed to the adiabatic reactor is at 350 °C and 30 psia and contains 5% A and 13% B, the balance being an inert gas, I. The heat capacity of the gas is essentially equal to that of I: 7.12 cal mol^-1 K^-1 (independent of temperature). Calculate the conversion and outlet temperature if the space time is 10 min.

(Problem Statement as .pdf file)

2. The heat of reaction (2a) is 44.8 kJ mol^-1, and it is irreversible. The rate expression is equation (2b) where the pre-exponential factor is 7.22 x 10⁶ mol atm^-2 cm^-3 s^-1 and the activation energy is 84.1 kJ mol^-1. A 10 foot long tubular reactor with a diameter of 1 inch is heated by a fluid at 200 °C that is in contact with the outside of the tube wall. The overall heat transfer coefficient is 7.48 x 10⁴ J h^-1 ft^-2 K^-1. Pressure drop through the reactor is negligible. If a gas phase mixture of 60% A and 40% B enters the reactor at 282 L min^-1, 2.5 atm and 175 °C and if the heat capacities of A, B and Z are equal to 18.0, 12.25 and 21.2 cal mol^-1 K^-1, what steady state outlet temperature and conversion of B will result?

(Problem Statement as .pdf file)