It is clear that the obtained formulations for i (equations 14b, 14c, and 14d) all become the familiar Monod equation if mS = 0 (meaning Cs,min = 0 and kd = 0; see equations 15b and 15c). The Monod equation and equations 14c and 14d are very close for Cs > Ks, but substantial differences arise for Cs < Ks (see Fig. 8).

A final point to address is the implicit assumption (in equation 14a) that in the substrate-uptake process the substrate concentration can become zero. This is, in principle, not possible, because there always exists a substrate concentration where the catabolic reaction reaches a point where energy production in the form of ATP becomes impossible. This concentration is called the threshold concentration of substrate Cs thresh.

From published data it is known that imax can vary in a wide range (0.001-1 h_1) and that Ks is also covering an even wider range (10~8 to 10~3 mol/L). In the preceding sections mS and F^X have been studied from a thermody-namic point of view. In the following, we present correlations and points of view that allow the estimation kd, imax, Ks, and Cs thresh, all based on a thermodynamic point of view. Such relations are very relevant in, for example, considerations of waste-treatment processes where the threshold concentration determines the effluent quality, where kd determines the surplus sludge production, and where imax directly determines the reactor size or the type of reactor (suspended organisms or biomass retention systems). For batch-fermentation processes,imax is important because it determines the duration of a batch-growth process.

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