$(14$ pts$)$ The data below were obtained for an organism in a $1-L$ chemostat with an inlet

substrate concentration $C_{Si}$ of $30\frac{g}{L}.$

a$.(7$ pts$)$ Now if the inlet substrate concentration is $25\frac{g}{L}$ and the cell concentration in the inlet

stream is $0\frac{g}{L},$ what dilution rate $D$ will give the maximum total rate of cell production? What

are the outlet cell and substrate concentrations at this dilution rate? $($Plotting $($or non$-$linear

regression$)$ and figuring out the kinetic parameters are worth $3$ pts$.$ You may use any of the

three linear plots or non$-$linear regression. Calculating the concentration and $D$ under

optimum condition is worth $4$ pts$.)$

b$.(7$ pts$)$ You are asked to design a continuous fermenter system with an inlet flow of $250\frac{L}{h}r$

and substrate concentration of $25\frac{g}{L}$ to produce $2100k\frac{g}{y}r$ of the product, given an operating

time of $300$ day$/$yr at $24h\frac{r}{?}$ day. Assume no cells or product in the inlet stream. Would you

HW $4$

CHBE$761/861$

recommend a single CSTF or two CSTFs in series? Design a system which will meet the

production constraints while minimizing total fermenter volume. Report reactor volumes and

effluent cell, substrate, and product concentrations for the proposed fermenter$($s$).($Converting

the given information to $Cx$ is worth $3$ pts$.$ Design of the reactors is worth $4pts.)$