Unit 23. Analysis of Transient CSTRs

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.

Section C of Part III examines reaction engineering for continuous flow stirred tank reactors (CSTRs). As was done for batch reactors in the previous section of the course, common reaction engineering tasks are identified and the qualitative performance of CSTRs is examined. CSTRs are typically designed to operate at steady state, but getting them started and shutting them down involves transient operation. The mathematical analysis of transient reactors differs from that for steady state reactors, so these two situations are presented separately. In addition, CSTRs can display a phenomenon known as multiplicity of steady states which is discussed in this section.

It was noted in Unit 22 that CSTRs are usually designed to operate at steady state for extended periods of time. Nonetheless, analysis of transient behavior is an essential and critical part of the overall design of a system. In the case of CSTRs, transient analysis is used to determine the best way to start up the reactor and to shut it down. It is used to understand how the reactor system will respond to changes in its operating parameters, be they intentional or unexpected. Another use of transient analysis is in the design of control systems for the reactor system. Unit 23 describes setting up the transient CSTR design equations for a system, common simplifications of those equations, and a general approach to solving them for the purpose of performing some reaction engineering or reactor design task.

Learning Resources

• Archive (.zip) - Contains all learning resources listed below for this unit
• Documents to Read:
  • Unit 23 Informational Reading (.pdf)
  • Example 23.1 (.pdf)
  • Example 23.2 (.pdf)
• Videos to Watch (please right-click and save, then play back locally on your computer):
  • Unit 23 Informational Video (.mov)
  • Example 23.1 Video (.mov)
  • Example 23.2 Video (.mov)
• Reference Files:
  • Unit 23 Definitions, Nomenclature and Equations (.pdf)
• Other Files:
  • Example_23_1.m - MATLAB file used in the solution of Example 23.1
  • Example_23_1_ss.m - MATLAB file used in the solution of Example 23.1
  • Example_23_2.m - MATLAB file used in the solution of Example 23.2
  • Example_23_2_plot.m - MATLAB file used in the solution of Example 23.2

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
  • 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_23_2.m - MATLAB file used in the solution of Activity 23.2
• Alternative Questions (.pdf) that could be used in a pre-class quiz

Practice Problems

1. A 150 °C solution containing 2 mol L^-1 of A is fed to a 500 L CSTR at a rate of 250 L h^-1. A jacket surrounding the CSTR contains a fluid at a constant temperature of 180 °C. The contact area between the CSTR contents and the jacket is 2 m² and the overall heat transfer coefficient is equal to 500 kcal m^-2 h^-1 K^-1. Within the reactor reaction (2a) occurs at a rate given by equation (2b). The pre-exponential factor for the rate coefficient in equation (2) is 1.14 x 10⁹ L mol^-1 h^-1 and the activation energy is 16.2 kcal mol^-1. The reacting solution has a constant density and a constant heat capacity of 1.17 cal mL^-1 K^-1. The heat of reaction is 18.2 kcal mol^-1 and is independent of temperature. At steady state at these conditions, the outlet temperature is 167 °C and the conversion of A is 86%. Suppose that the temperature of the fluid in the jacket suddenly dropped to 160 °C. Calculate the temperature and conversion versus time until a new steady state is attained.

(Problem Statement as .pdf file)