The growth of bacteria to form a product, P, is carried out in a 25 dm3 CSTR (chemostat)....

The growth of bacteria to form a product, P, is carried out in a 25 dm3 CSTR (chemostat). The bacteria (e.g., Zymononas) consumes the nutrient substrate (e.g., to generate more cells and the desired product—ethanol)

The CSTR was initially inoculated with bacteria and now has reached steady state. Only substrate (nutrient) is fed to the reactor at a volumetric rate of 5 dmh and a concentration of 30 g/dm3. The growth law rg (g/hr dm3) is

and the rate of substrate consumption is related to growth rate by

with the stoichiometric relationship

(a) Write a mass balance on the cells and the substrate in the CSTR operated at steady state.

(b) Solve the cell mass balance for the substrate concentration and calculate Cs.

(c) Calculate the cell concentration, Cc.

(d) How would your answers to (b) and (c) change if the volumetric feed rate were cut in half?

(e) How would your answers to (b) and (c) change if the CSTR volume were reduced by a factor of three?

(f) The reaction is now carried out in a 10 dm3 batch reactor with initial concentrations of substrate Cso = 30 g/dm3 and cells of Cco = 0.1 g/dm3. Plot Cs, Cc, rg, and -rs as a function of time. Repeat (f) for a 100 dm3 reactor.

(g) Additional Information:

Try to work the California problems in 30 minutes.