Unit 13. CSTR Data Analysis

This website provides learning and teaching tools for a first course on kinetics and reaction engineering. The course is divided into four parts (I through IV). Here, in Part II of the course, the focus is on chemical reaction kinetics, and more specifically, on rate expressions, which are mathematical models of reaction rates. As you progress through Part II, you will learn how rate expressions are generated from experimental kinetics data.

Part II of the course concludes with Section C which describes how to test a rate expression (Section A) using experimental data (Section B). The testing of a rate expression entails its substitution into the model for the experimental reactor and the subsequent fitting of that model to the experimental data. The end result will reveal whether the selected rate expression offers a sufficiently accurate representation of the rate of the reaction under consideration. If it does, the fitting process also will yield the best values for the parameters that appear in the selected rate expression.

Unit 13 describes the analysis of kinetics data that have been generated using an isothermal, steady state CSTR. When only one reaction takes place in the reactor, the model for any one experiment in an isothermal, steady state CSTR is an algebraic equation. In this unit, the model equation is re-written in the form of a linear equation (if necessary), linear least squares is used to fit the resulting linear model to the data, the accuracy of the fitted model is assessed, and if the accuracy is acceptable, the kinetic parameters and their uncertainties are calculated from the slope(s) and intercept of the linear model that was fit to the data.

Learning Resources

• Archive (.zip) - Contains all learning resources listed below for this unit
• Documents to Read:
  • Unit 13 Informational Reading (.pdf)
  • Example 13.1 (.pdf)
  • Example 13.2 (.pdf)
  • Example 13.3 (.pdf)
• Videos to Watch (please right-click and save, then play back locally on your computer):
  • Unit 13 Informational Video (.mov)
  • Example 13.1 Video (.mov)
  • Example 13.2 Video (.mov)
  • Example 13.3 Video (.mov)
• Reference Files:
  • Unit 13 Definitions, Nomenclature and Equations (.pdf)
• Other Files:
  • 13_How_To.pdf - How to test a rate expression using CSTR data and linear least squares
  • Example_13_1a.m, Example_13_1b.m and Example_13_1c.m - MATLAB files used in the solution of Example 13.1
  • Example_13_2.m - MATLAB file used in the solution of Example 13.2
  • Example_13_3.m - MATLAB file used in the solution of Example 13.3

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
  • 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
  • Learning Activity Files to make available to students after class
    • Activity 1 Results (.xlsx)
    • Activity_13_1a.m - MATLAB file used in the solution of Activity 13.1a
    • Activity_13_1b.m - MATLAB file used in the solution of Activity 13.1b

Practice Problems

1. Suppose you wish to test equation (1a) to determine whether it is satisfactory as a rate expression for liquid phase reaction (1b). To do so you used a 3 gal. reactor that had been tested and shown to behave as an ideal CSTR. You made 15 steady state experimental runs using the inlet flow rates and compositions shown in this Table (.xlsx file), and in each run you recorded the steady state conversion, also shown in the table. Determine whether equation (1a) is an acceptable rate expression, and if it is, estimate the values and uncertainties for the two rate coefficients.

(Problem Statement as .pdf file)

2. Suppose that the liquid-phase decomposition of isobutyl iodide (1-Iodo-3-methylpropane) according to reaction (2a) was studied in hexachlorobutadiene solution using a CSTR. At the temperature studied, 160 °C, the reaction is effectively irreversible. In a series of experiments using a feed containing iodine and isobutyl iodide in varying concentrations, the space time was varied and the steady state conversion of isobutyl iodide was measured. Using the resulting data in this Excel© file, determine whether the rate expression in equation (2b) accurately predicts the reaction kinetics. If it does, determine the best value for the rate coefficient, including 95% confidence limits.

(Problem Statement as .pdf file)