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.