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please solve and explain all parts ( a - D ) . C . acetobutylicum is used for biobutanol production in a batch anaerobic fermenter,

please solve and explain all parts (a-D). C. acetobutylicum is used for biobutanol production in a batch anaerobic fermenter,
which is operated with a microbubble distillation sidearm that recycles the liquid
media completely. The sidearm distiller is designed to achieve a two-minute
contact time. In two minutes of contact, half of whatever concentration of butanol
is in the sidearm is stripped away. The distiller sidearm has a flowrate S=20Lmin.
The fermentation in a volume V=1m3 starts with an initial concentration of butanol
of c0=24.3gL-1. The distiller is sparged with bubbles of nitrogen. The system
initialisation is when the distiller sparge is turned on. Pure water flows into the
sidearm recycle stream after the distiller to maintain liquid flowrate returning to the
fermenter at the same rate as the sidearm flow S=20L(min).
(a) Draw a schematic of the system labelling all streams.
(b) Suppose there is no C. acetobutylicum metabolism to produce butanol. List your
assumptions, then write a butanol material balance for the no butanol
producing system, and solve it for an arbitrary time after the diluting feed stream
starts. What will the concentration c of butanol be after 30 minutes?
(c) Butanol attacks the cell membrane of C. acetobutylicum, inhibiting its metabolism and
therefore its production. This inhibition effect is modelled by a rate law for the
production of butanol r.
r=k(c0-c)
If k=0.2min-1, what is the rate of butanol production at the initial condition?
(d) Write a material balance on the system that takes into account the inhibition on the
fermenter. Does it have a steady state solution? If so, calculate the value of the
steady concentration c.

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