ABSTRACT
We start our study with the basic unstructured model of the ideal chemostat. We consider the continuous bioreactor with cell recycle shown in Figure 4.1. The purge fraction W containing the biomass is operated directly from the bioreactor. Ideal conditions are assumed to prevail in the settler. The cell mass is assumed to be formed with a growth rate rx proportional to biomass concentration X, i.e., rx = rX, where r is the specific growth rate, assumed to depend only on the substrate. The substrate utilization rate rs is assumed to be a linear function of the cell growth rate rx, i.e., rs = −rx/Y where Y is the yield coefficient, assumed to be independent of the substrate and cell composition. In many cases, it is needed to account for the energy required for cell maintenance and cell death. An endogenous decay term kdX representing the rate of decay in the cell mass is used to correct the cell growth rate. The net cell growth rate is therefore, rX−kdX, where kd is the endogenous decay coefficient.
