ABSTRACT
For type III models, the specific rates of cell growth and substrate utilization are related by the linear equation
σ = aµ (13.1)
where a is a positive stoichiometric constant. The model Equations (11.1-11.3) can be suitably rendered dimensionless by introducing the following variables,
S¯ = S
Sref , X¯ =
aX
Sref , P¯ =
P
Pref , D¯ =
D
µref (13.2)
t¯ = tµref , µ = µref µ¯, = ref ¯, α = refSref aµrefPref
(13.3)
where Pref , Sref , ref , and µref are reference quantities for P , S, , and µ, respectively. The model in dimensionless form is given by
dX¯
dt¯ = −D¯X¯ + µ¯X¯ (13.4)
dS¯
dt¯ = D¯(S¯f − S¯)− µ¯X¯ (13.5)
dP¯
dt¯ = α¯X¯ − D¯P¯ (13.6)
We assume that the rates µ¯ and ¯ are given by the following forms,
µ¯(S¯, P¯ ) = µ¯1(S¯)µ¯2(P¯ ) (13.7)
¯(S¯, P¯ ) = ¯1(S¯)¯2(P¯ ) (13.8)
As was mentioned in Chapter 11, this class of model was, for instance, used by Aiba and Shoda [10] and Aiba et al. [11] for ethanol production from glucose by Saccharomyces cerevisiae.
