Cell growth can be calculated from the cell yield on the growth-limiting substrate and the initial concentration of substrate, again assuming cell maintenance and product formation are negligible.

Subsequently, the ratio of biomass productivities in the CSTR at Dm, (Rcstr)m, and in the batch fermentor is given by equation 15, in which it is assumed that S0 > KS (as it often is).

+ i max "TURNAROUD

Equation 15 often appears as a measure of relative biomass productivity, in which the CSTR is favored over batch operation at high growth rates and long turnaround times. However, equations 10 and 11, associated with maximum productivity, do not reflect the ultimate limitation posed by heat and mass transfer in industrial aerobic processes. Given that productivity has a limit dictated by the system, the independent parameters, D and S0, can be adjusted so that the maximum productivity is attained during operation. Recognizing that (Rcstr) is ultimately limited by the maximum oxygen transfer rate, equation 12 can be rearranged to give the biomass productivity.

(D + mQ2 • Yx/O) Notice that the cell concentration is fixed once an operating

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