ABSTRACT
In this part of the book, we revisit the unstructured model, already studied in Chapter 4, by including the dynamics associated with the formation of a metabolic product. The continuous bioreactor is described by the following unstructured model for the biomass X, a limiting substrate S, and a desired nonbiomass product P,
dX
dt = µX −DX (11.1)
dS
dt = D(Sf − S) − σX (11.2)
dP
dt = X −DP (11.3)
µ is the specific cell growth rate, σ is the cell mass specific net utilization rate of limiting substrate, and is the cell mass specific net production rate. We also assume clean feed conditions, i.e., no cells or product enter the bioreactor through the feed. In its most general form defined by Equations (11.111.3), the rates µ, σ, and may, theoretically, depend on the process state variables X, S, and P , and may not be related. However, as pointed out by Parulekar [272], the general unstructured model described by Equations (11.111.3) can be classified in a practical way based on eventual relations among the specific growth rates µ, , and σ. In this part of the book, we examine the stability behavior of three large classes of models derived from the general Equations (11.1-11.3). The classification is inspired, but different from the one proposed in [272].
