Multiple Reactions in Batch Reactors

Obviously, va,i = 0 if component A does not participate in reaction I, and of course the rate of formation is negative for a reaction in which A is consumed. 

Determine the overall reaction rate for each component in the following set of reactions  

SOLUTION We begin with the stoichiometric coefficients for each component for each 

The various reactions are assumed to be elementary (as indicated by the rate constants over the 

Suppose there are N components involved in a set of Mreactions. Then Equation 1.22 can be written for each component using the rate expressions of Equation 2.7 or 2.8. 

This is a set of N ordinary differential equations, one for each component. The component reaction rates will have M terms, one for each reaction, although many of the terms may be zero. Equations (2.9) are subject to a set of N initial conditions of the form 

The number of simultaneous equations can usually be reduced to fewer than N using the methodology of Section 2.8. However, this reduction is typically more trouble than it is worth. 

Example 2.2 Derive the batch reactor design equations for the reaction set in Example 2.1. Assume a liquid-phase system with constant density. 

Solution The real work has already been done in Example 2.1, where lA, B-. c, were found. When density is constant, volume is constant, and the V terms in Equations (2.9) cancel. Substituting the reaction rates from Example 2.1 gives 

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