2. The substrate concentration in a batch bioreactor is maintained at a constant concentration of 5 kg/m³ by continuous addition of substrate. The volume of the liquid is not altered by this addition and growth can be expressed by Monod kinetics and death of microorganisms is negligible.
Data:
Maximum specific rate of substrate uptake, $q_{s,max} = 0.6$ kg substrate/kg cells-h
Inoculum concentration, $X_0 = 0.5$ kg/m³
Liquid medium volume, $V = 10$ m³
Yield of biomass on substrate, $Y_{xs} = 0.5$ kg biomass/kg substrate
Assume: When $\mu = \mu_{max}$, then $q_s = q_{s,max}$
a) What is the specific growth rate?
b) What is the time required to obtain a biomass concentration of 20 kg/m³?
c) What is the total amount of substrate consumed during this time?
[20 marks]