The bacteria X-II can be described by a simple Monod equation with µmax = 0.8 h−1 and KM = 4 g/dm3, Yp/c. = 0.2 g/g, and Ys/c = 2 g/g. The process is carried out in a CSTR in which the feed rate is 1000 dm3/h at a substrate concentration of 10 g/dm3.
(a) What size fermentor is needed to achieve 90% conversion of the substrate? What is the exiting cell concentration?
(b) How would your answer to (a) change if all the cells were filtered out and returned to the feed stream?
(c) Consider now two 5000 dm3 CSTRs connected in series. What are the exiting concentrations Cv, C(., and Cp from each of the reactors?
(d) Determine, if possible, the volumetric flow rate at which wash-out occurs and also the flow rate at which the cell production rate (Cc v0) in grams per day is a maximum.
(e) Suppose you could use the two 5000-dm3 reactors as batch reactors that take two hours to empty, clean, and fill. What would your production rate be in (grams per day) if your initial cell concentration is 0.5 g/dm3? How many 500-dm3 reactors would you need to match the CSTR production rate?
(f) List ways you can work this problem incorrectly.
(g) How could you make this problem more difficult?
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