Chemostats concentration change equation

Many reviews and several books [61,62] have appeared on the theoretical and experimental aspects of the continuous, stirred tank reactor - the so-called chemostat. Properties of the chemostat are not discussed here. The concentrations of the reagents and products can not be calculated by the algebraic equations obtained for steady-state conditions, when ji = D (the left-hand sides of Eqs. 27-29 are equal to zero), because of the double-substrate-limitation model (Eq. 26) used. These values were obtained from the time course of the concentrations obtained by simulation of the fermentation. It was assumed that the dispersed organic phase remains in the reactor and the dispersed phase holdup does not change during the process. The inlet liquid phase does not contain either organic phase or biomass. 

Equation 3.93 can be compared with Equ. 3.91 for the true steady state in a CSTR. The two are formally identical. The difference is in the real meaning of the factor D in Equ. 3.90 it represents a dilution effect in the case of a chemostat. In the case of a semicontinuous stirred vessel with variable volume, the factor D x in Equ. 3.93 describes the decrease in cell concentration due to the change of the volume in the reactor (Dunn and Mor, 1975). Similar equations can be formulated for all other types of fed-batch processes using the appropriate modification of Equ. 3.86. 

It is instructive to compare the fed-batch model with the model for a constant-volume chemostat (see Equs. 3.90 and 3.91). Equation 6.3a,b is formally identical with Equ. 3.92a,b, but it is important to note that the physical meaning of the terms is not identical. Comparing the term x JV in Equs. 3.92 and 6.3 it can be seen that the origin of this term for the fed batch is the expression x -dV/dt it thus represents a decrease in cell concentration due to the volume change that arises from inlet flow rate On the other hand, —F x in Equ. 6.3, the chemostat, is a washout term expressing the mass flow rate of cells that leave with the outgoing stream. A fed batch can be compared with a constant-volume chemostat whose feed rate is decreasing slowly. 

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