Consider a bioreactor described by the set of balance equations

where x₁ and x₂ represent the biomass and substrate concentrations in the reactor. The growth rate depends on the substrate concentration. Different models have been proposed to represent this dependance.

• Monod kinetics:

• Substrate inhibition:

(a) Determine the steady states of the system and assess their stability properties using both the models for growth rate. The values of various parameters are: μ_max = 0.53, k_m = 0.12, k₁ = 0.4545, Y = 0.4, x_2f = 4, and D = 0.3.

(b) Generate the phase plot for each case in part (a).

Transcribed Image Text:

dx1 dt dx2 dt = (μ-D)x₁ = = D(x2f - x₂). - μι Y