The cascade of perfectly mixed reactors

It follows from calculations in the proceeding section that the necessa reactor volume of a continuous stirred tank reactor (CSTR) needed to obtain a high degree of conversion is relatively large. A so-called cascade of CSTR s (a number of CSTR s in series) can be a practical alternative. Let us assume that we replace one CSTR with volume V by a series of n equal CSTR s that have the same total volume. The mean residence time in each reactor is then x/n. We can calculate the relative degree of conversion in each consecutive reactor, for any reaction order, with eq. (3.49), where X is replaced by x/n. We find then for 

Note that for reaction orders 1, the relative degree of conversion decreases along the cascade (jc. jc.), and for reaction orders 1 it increases 

For a first order reaction, the relative conversion in each reactor is the same, so that the calculation becomes much simpler  

The relation between the degree of conversion of a first order reaction, the number of CSTR s in a cascade, and the total mean residence time is shown in figure 3.8. We see that particularly for high desired degrees of conversion a cascade of several CSTR s appears attractive. 

Assume that a certain first order reaction (constant density) requires a mean residence time in one CSTR of 3 hours (10,800 s) to reach a degree of conversion of 0.99. If we would use three CSTR s in series, we find from equations (3.38) and (3.51) that the total mean residence time of the cascade to reach 0.99 conversion is only 1193 s, or approximately 20 min. This means that the total reactor volume needed to obtain the desired conversion is in this case 9 times smaller This ratio increases as the desired degree of conversion is higher. 

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In this chapter the most important operation modes of reactors are considered. Models are developed by combining simple reaction kinetics for single-phase reactions with mass balances for five ideal model reactors the ideal batch reactor the semi-batch reactor the plug flow reactor the perfectly mixed continuous reactor and the cascade of perfectly mixed reactors. For isothermal conditions, conversions can be calculated on the basis of chemical kinetics only. 

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