WOLFRAM|DEMONSTRATIONS PROJECT

Dynamic Behavior of a Bioreactor

​
yield
6
feed substrate concentration
0.06
dilution rate
0.1
biomass
nutrient
The dynamic behavior of a chemostat can be described with the following system of ordinary differential equations:
dX
dt
=(μ-D)X
dS
dt
=
-μX
Y
+D(
S
in
-S)
where
D
is the dilution rate in
-1
s
,
X
is the biomass concentration in g/l,
S
is the substrate concentration in g/l,
S
in
is the feed substrate concentration,
Y=
dX
dS
is the yield, and
μ
is the specific growth rate given by the Monod function:
μ=
μ
max
S
K
S
+S
, where
K
S
is the half saturation constant and
μ
max
is the maximum value of the specific growth rate (
μ
max
=1 here).
This Demonstration lets you plot the substrate and biomass concentrations versus time and observe the washout (a phenomenon that occurs when the dilution rate,
D
, is so large that all micro-organisms will end up exiting the bioreactor). Another snapshot shows a situation where the biomass in the reactor reaches a steady-state value different from zero.