Unit 24. Multiple Steady States in 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.

The design equations for a steady state CSTR are non-linear. Temperature appears in an exponential term in the design equations, and if the reaction is anything other than first order, the molar flow rates also appear in terms that are non-linear. In general, non-linear equations can have more than one solution. For example, a quadratic equation has two roots. Quite often in science and engineering problems, an equation may have multiple roots, but only one of the roots makes sense physically. When this type of equation is solved, the root that makes physical sense is chosen as the correct solution of the equation. Unit 24 shows that in the case of steady state CSTR, the equations can have more than one root, and more than one of those roots makes sense physically. That is, a CSTR with fixed inlet conditions may be capable of attaining more than one steady state outlet condition.

Learning Resources

• Archive (.zip) - Contains all learning resources listed below for this unit
• Documents to Read:
  • Unit 24 Informational Reading (.pdf)
  • Example 24.1 (.pdf)
  • Example 24.2 (.pdf)
• Videos to Watch (please right-click and save, then play back locally on your computer):
  • Unit 24 Informational Video (.mov)
  • Example 24.1 Video (.mov)
  • Example 24.2 Video (.mov)
• Reference Files:
  • Unit 24 Definitions, Nomenclature and Equations (.pdf)
• Other Files:
  • Example_24_1.m - MATLAB file used in the solution of Example 24.1

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
  • Learning Activity Files to make available to students before class
    • Activity 1 Handout (.xlsx)
  • 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
    • Final Activity 1 Handout (.xlsx)

Practice Problems

1. Suppose a steady state, 500 mL CSTR operates adiabatically at a space time of 0.4 min. The feed concentration is 5 M, and the feed temperature is 60 °C. The fluid heat capacity is constant and equal to 1 cal mL^-1 K^-1. In the reactor the feed, A, is converted to Z, reaction (1a). The heat released by the reaction is 30 kcal mol^-1. The reaction rate is first order in A, equation (1b), with a pre-exponential factor of 4.75 x 10¹³ min^-1 and an activation energy of 25 kcal mol^-1. At these conditions, multiple steady states are possible. Determine the conversion of A for each steady state.

(Problem Statement as .pdf file)