CONTENTSFront MatterCourse UnitsI. Chemical Reactions
II. Chemical Reaction Kinetics
A. Rate Expressions
B. Kinetics Experiments
C. Analysis of Kinetics Data
III. Chemical Reaction Engineering
A. Ideal Reactors
B. Perfectly Mixed Batch Reactors
C. Continuous Flow Stirred Tank Reactors
D. Plug Flow Reactors
E. Matching Reactors to Reactions
IV. Non-Ideal Reactions and Reactors
A. Alternatives to the Ideal Reactor Models
B. Coupled Chemical and Physical Kinetics
Supplemental Units |
Supplemental Unit S5. Solving Initial Value Differential EquationsKinetics and reaction engineering involve solving several different kinds of mathematics problems. In very simple cases these problems can be solved analytically, that is, using paper, pencil and hand-held calculator. In many cases, however, even very simple problems cannot be solved analytically. Instead they must be solved numerically using a computer. This supplement to “A First Course on Kinetics and Reaction Engineering” presents a very brief overview of numerical methods that are commonly used to solve kinetics and reaction engineering problems. The intent is not to provide comprehensive coverage of the methods; for that you should consult a book on numerical methods or take a course on the topic. Fortunately, there are several software packages that make it very easy to use numerical methods to solve these kinds of problems. However, each software package has its own unique user interface, data structure and coding format. These supplemental units do not try to describe how to use every available software package. No matter which specific software package one chooses to use, solving a particular type of problem will require that you provide certain information and input data. These supplemental units each begin with a concise statement of the problem followed by a listing of the information and data one will need to provide when solving such a problem, irrespective of what software is actually used. The form of the result that will be returned by the software is also described. That is followed by a general explanation of what the software does in order to obtain that result. Finally, for those with access to MATLAB and who choose to use it, generic template files that can be adapted to specific problems are provided. Examples from the main body of “A First Course on Kinetics and Reaction Engineering” are used to illustrate the use of the MATLAB template files.This supplemental unit describes how to numerically solve a set of coupled, initial-value ordinary differential equations (ODEs) of the following form, where the f's are algebraic functions of an independent variable, t, and the dependent variables, z1 through zn: dz1/dt = f1(t, z1, ..., zn); z1(t0) = z10 Notice that the boundary condition for every ODE in the set is specified at the same value, t0, of the independent variable. This is what makes them initial value ODEs. ODE sets of this type are solved by integrating from that initial value of the independent variable until some stopping criterion is satisfied. This unit shows how to solve sets of coupled, initial value ODEs with two kinds of stopping criteria: a specified value of the independent variable or a specified value of one of the dependent variables. Learning Resources
Teaching Resources
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