Suppose that the fed-batch bioreactor in figure is converted to a continuous, stirred-tank bioreactor (also called a chemostat) by adding an exit stream. Assume that the inlet and exit streams have the same mass flow rate F and thus the volume of liquid Yin the chemostat is constant.

(a) Derive a dynamic model for this chemostat by modifying the fed-batch reactor model in Section 2.4.9.

(b) Derive the steady-state relationship between growth rate p. in Eq. 2-93 and dilution rate D where by definition, D = F/V. Suggest a simple control strategy for controlling the growth rate based on this result.

(c) An undesirable situation called washout occurs when all of the cells are washed out of the bioreactor and thus cell mass X becomes zero. Determine the 4alues of D that result in washout.

(d) For the numerical values given below, plot the steady-state cell production rate DX as a function of dilution rate D. Discuss the relationship between the values of D that result in washout and the value that provides the maximum production rate. The parameter values are: ?_m = 020 h^?1 K₅ = 1.0 g/1, and Y_X/S =0.5 g/g. The steady-state condition is D = 0.1 h^?1, X = 225 g/L, S = 1.0 g/L, and S_f = 10 g/L.

Stream 1 Wi Pure A Strean 2 Pure B To reacl