Applications of Ideal Reactor Models

In each case of Section 4.3 the reactor models obtained on the basis of the mixing models were left in general form, with specific results for concentration or conversion versus reactor size depending on the type of rate law to be used. In the following we shall derive a number of expressions for particular rate laws which relate conversion, reactor size, and residence time for the particular case of homogeneous, isothermal ideal reactors. 

For the plug-flow reactor there is a formal analogy with the batch reactor equations derived in Chapter 1 if there is no volume change on reaction. As an example, consider the PFR design equation, (4-45), written for first-order irreversible kinetics (A B). 

Now we have the following relationships among the various molal flow rates and the constant total flow 

The left side of equation (4-62) is just the residence time, so that 

Corresponding derivations for the second-order irreversible cases 2A C + D orA + B C + D yield (assuming equimolal amounts of A and B in the feed in the second case) 

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