Unit 19. Analysis of Batch Reactors

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 B of Part III examines reaction engineering for perfectly mixed batch reactors. Typical reaction engineering tasks involving batch reactors are identified and described. In order to become a proficient reaction engineer, one must develop an intuitive appreciation of how a reactor responds to changes in operational procedures. For this reason a detailed discussion of the qualitative analysis of batch reactors is presented in this section along with the full mathematical analysis of their behavior.

As noted in Unit 18, batch reactor processing often follows an operational protocol that involves sequential steps much like a cooking recipe. In general, each step in the operational protocol must be analyzed separately. Unit 19 describes and illustrates how to quantitatively analyze a step in the operational protocol using the batch reactor design equations that were derived in Unit 17. In particular, Unit 19 discusses which of the mole and energy balances are needed to accurately model different types of processing steps. It also describes how to identify zero-valued and insignificant terms that can be dropped from the design equations. Finally, it considers a few of the more common ways of modeling heat transfer between the reactor contents and either a submerged heat transfer coil or an external heat transfer jacket.

Learning Resources

• Archive (.zip) - Contains all learning resources listed below for this unit
• Documents to Read:
  • Unit 19 Informational Reading (.pdf)
  • Example 19.1 (.pdf)
  • Example 19.2 (.pdf)
  • Example 19.3 (.pdf)
• Videos to Watch (please right-click and save, then play back locally on your computer):
  • Unit 19 Informational Video (.mov)
  • Example 19.1 Video (.mov)
  • Example 19.2 Video (.mov)
  • Example 19.2 Video (.mov)
• Reference Files:
  • Unit 19 Definitions, Nomenclature and Equations (.pdf)
• Other Files:
  • Example_19_1.m - MATLAB file used in the solution of Example 19.1
  • Example_19_2.m - MATLAB file used in the solution of Example 19.2
  • Example_19_3.m - MATLAB file used in the solution of Example 19.3

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
  • Other files to make available to students before class
    • Activity 19.1 Handout (.pdf)
  • 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_19_1.m - MATLAB file used in the solution of Activity 19.1
    • Activity_19_2.m - MATLAB file used in the solution of Activity 19.2

Practice Problems

1. The conversion of A to B takes place in an aqueous solution in an adiabatic batch reactor. The reactor is charged with 1200 L of a 2 M solution of A at 300 K. The heat capacity of the solution as a whole can be taken to equal 1.0 cal mL^-1 K^-1. The heats of formation of A and B may be taken to equal -75 and -82 kcal mol^-1, respectively, and the heat of reaction may be assumed to be independent of temperature. Calculate the time required to reach 80% conversion and the final temperature. The reaction is first order in A and the rate coefficient obeys the Arrhenius expression with a pre-exponential term equal to 2.4 x 10⁸ s^-1 and an activation energy of 15.3 kcal mol^-1.

(Problem Statement as .pdf file)

2. An adiabatic batch reactor with a volume of 15 ft³ is initially charged with a 650 °R solution containing A at a concentration of 0.125 lbmol ft^-3 and B at a concentration of 3 lbmol ft^-3. Reaction (2a) occurs with a rate given by equation (2b) wherein k₀ = 1.2 x 10¹⁴ ft³ lbmol^-1 min^-1, E/R = 23000 °R, K₀ = 6.5 x 10^-13 ft³ lbmol^-1 and ΔH/R = -20000 °R. The heat of reaction (2a) is constant and equal to -170,000 BTU lbmol^-1. The heat capacity of the solution may be taken to equal 135 BTU °R^-1 ft^-3, independent of temperature. The density of the liquid may be assumed to be constant. Calculate the concentration of Z and the temperature after 2 h of operation.

(Problem Statement as .pdf file)