Performance Equations of Recycle Reactors

Recycling cells from a CSTR effluent provides a means to continually inoculate the vessel and to add stability to the reactor, minimizing the effect of process perturbation. The productivity of a CSTR may be increased remarkably by recycling cells when the cells to be recycled are first concentrated by the factor P = XJX in a sedimentation unit. With a recycling stream and with r = FJF, the conservation of mass equations are 

In contrast to the CSTR with no recycling, where fi = D, the CSTR with cell recycling (rCSTR) realizes 

A schematic diagram of such a recycling system is shown in Fig. 6.37a. The equations are plotted in Fig. 6.37b together with the output of cells D Xg for 

An estimate of the effect of cell mass concentration and recycling on process economics may be obtained by plotting effluent substrate concentration for several different values of as shown in Fig. 6.38. Increasing has the effect of minimizing and also of making less sensitive or more stable with respect to variations in the flow rate of constant-volume reactors with residence times considerably below the washout value (Andrews, 1971). 

For the case of cascade of reactors with cell recycling, Powell and Lowe (1964) derived a performance equation that is analytically intractable. Nevertheless, a simple formula of the critical dilution rate Dcrit can be calculated in the case of a cascade of CSTRs as 

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