Problem Statement: The following equations describe the biomass and substrate concentrations in a continuous bioreactor with cell recycle operated at steady-state.
dx/dt = 0 = (m-*D)*x ... Biomass
ds/dt = 0 = D*(sf-s) - m*x/Yx ... Substrate
where m = mm*s/(K+s)
Yx = substrate-to-cell yield coefficient
D = dilution rate
sf = substrate concentration in the feed stream
Simulate microbial growth in an incompletely mixed bioreactor
by adding a second compartment. The fractional size of the first
compartment is a, and d=f/V is the
exchange "dilution" rate between two compartments, where f is
the flow rate between two compartments and V is the total
bioreactor volume.
+-----------------+
| Compartment #1 |
F, sf ---->| a*V x1 s1 |---> F, x1, s1
| |
+-----------------+
| ^
f, x1, s1 | | f, x2, s2
V |
+-----------------+
| Compartment #2 |
| (1-a)*V x2 s2 |
| |
+-----------------+
Solution:
Two-Compartmental Model for Incomplete Mixing, Dynamic Simulation
|
