Auxostat Math

Feedback control of nutrient or product concentrations in bioprocesses has been progressing in fits and starts for 40 years (Bryson, 1952), but has suffered from the lack of reliable equipment. Continuous bioprocessing permits the observation of microorganisms at steady state. Although chemostats are in common use, the advantages of auxostats have been recognized for sometime (Agrawal and Lim, 1984; Fraleigh et al., 1989). Auxostats can be operated in difficult or unstable conditions and can achieve steady state more quickly than can the open-loop chemostat. Operation near the maximum growth rate can be extremely unstable with a chemostat. The following equations are based on a bioprocess having Monod kinetics with mass balances for the liquid phase of the bioreactor:

X = biomass concentration (g l^-¹)
P = product concentration (g l^-¹)
D = dilution rate (h^-¹)
Y is usually Y_x/s,  biomass yield on nutrient (g g^-¹)
Other important yield coefficients are:
 Y_p/x = product yield on biomass (g g^-¹)
 Y_p/s = product yield on substrate (g g^-¹)
V_p = volumetric productivity (g l^-¹)