e where Po is the product present at time zero (kg). As with Eq. (17.7), if Xo, Xm, and H are determined from the biomass profile, then the only unknowns in this equation are mP and YPX, and these can be determined by a least-squares fitting of Eq. 17.13) to the product profile.

Ooijkaas et al. (2000) used this approach to characterize spore production kinetics, with two minor differences. Firstly, the maintenance-associated spore production was assumed to be zero, meaning that the term involving mp disappeared from the equation and, secondly, there was a lag in the appearance of the first spores, which was taken into account by subtracting the lag phase from the total fermentation time. Additionally, the initial spore number was taken as zero. For a product that follows these conditions, the equation is:

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