Problem Statement: The following equations describe the biomass and substrate concentrations in a continuous bioreactor with cell recycle operated at steady-state.
Cell
Separator
F -->--+---<---O----------> F, s
| a*F |
v C*x ^(1+a)*F
| | | |
| | | |
| |
| Fermentor |
| |
| V, x, s, p |
| |
+--------------+
Biomass: dx/dt = (μ-(1+a-a*C)*D)*x
Substrate: ds/dt = D*(sf-s) - μ*x/Yx - (α*μ*x+β*x)/Yp
where m = mm*s/(K+s)
Yx = substrate-to-cell yield coefficient
D = dilution rate
sf = substrate concentration in the feed stream
a = relative fraction of recycle stream to feed stream
C = cell concentration factor in cell separator
Solution:
Solution:
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