Cell growth with uncompetitive substrate inhibition is taking place in a CSTR. The cell gr...

Cell growth with uncompetitive substrate inhibition is taking place in a CSTR. The cell growth rate law for this system is

with µmax = 1.5 h−1, Ks = 1 g/dm3, KI, = 50 g/dm3, Cs0 = 30 g/dm3, Ycls = 0.08, Cco = 0.5 g/dm3, V = 500 dm3, and D = 0.75 h−1.

(a) Make a plot of the steady-state cell concentration Cc as a function of D. What is the volumetric flow rate (dm3/h) for which the cell production rate is a maximum?

(b) What would be the wash-out rate if Cc0 = 0? What is the maximum cell production rate and how does it compare with that in part (a)?

(c) Plot Cs as a function of D on the same graph as Cc vs. D? What do you observe?

(d) It is proposed to use the 500-dm3 batch reactor with Cs0 = 30 g/dm3 and C, o = 0.5 g/dm3. Plot Cc, Cs, rg, and -rs as a function of time? Describe what you find.

(e) It is proposed to operate the reactor in the fed-batch mode. A 10-dm3 solution is placed in the 500-dm3 reactor with CM = 2.0 g/dm3 and Cc0 = 0.5 g/dm3. Substrate is fed at a rate of 50 dm3/h and a concentration of 30 g/dm3. Plot Cs, Cr, rg, rs, and (VCe) as a function of time. Can you suggest a better volumetric feed rate? How do your results compare with part (d)?

(f) List ways you can work this problem incorrectly.

(g) How could you make this problem more difficult?