Problem Statement: The following Contois equation of growth describes high-density cell fermentation where cell growth is suppressed when the fermentor becomes too crowded.
u=um*s/(K*x+s)
In the above equation, x is the cell concentration,
s is the limiting substrate concentration, and u is
the specific growth rate. The kinetics of formation of the
desired product is mixed (i.e., partially cell growth related and
partially nongrowth related). A cell-free feed stream
continuously enters the fermentor, and the fermentor content is
also continuously withdrawn. Assume that the limiting substrate
is utilized only for cell growth but not for product formation.
Solution:
Solution:
Set each of the above dynamic equations to 0:
dx/dt=ds/dt=dp/dt=0.
Solution:
In addition to dx/dt=ds/dt=dp/dt=0 from the last part,
add d(D*p)/dD=d(D*P)/dsf=0. In practical
cases, both D and f are constrained
between 0 and an upper limit.
Solution:
No. Product productivity is proportional to cell concentration
and cell growth rate. A distinct advantage of a continuous
bioreactor is that it is more productive. Remember that a
fed-batch fermentor utilizes only a fraction of the available
volume, especially at the beginning. You can also convince
yourself through dynamic simulation.
Solution:
Note that normally only the cells are concentrated (with
centrifugation, filtration, or sedimentation) and returned back
to the bioreactor. Soluble substrate and product are not
concentrated, and their dynamic equations remain unchanged from
Part (a.
Solution:
Cell concentration: up (See the Mathcad worksheet below to be exact.)
Substrate concentration: down
Product concentration: up
Solution:
Cell recycle increases cell concentration in the bioreactor and
pushes the washout dilution rate to a higher level. Remember
that the product is synthesized by cells; thus, more cells,
more product (both concentration and productivity) -- whether
or not cell growth is suppressed at high cell concentration.
Contois Equation of Growth
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