Penetration theory assumes that turbulent eddies travel from the bulk of the phase to the interface where they remain constant for a constant exposure time (t_{e}). The model correlating K_{L}, mass transfer coefficient and D_{AB}, diffusivity can be expressed as

The oxygen uptake requirements of a microbial population is characterized by the following parameters: μ_{m }= 0.2 h^{-1}, K_{0} = 0.2 mg O_{2}.l^{-1}, Y_{0} = 0.5 mg dry weight/mg O_{2} and C_{0,crit}=0.8 mg.l^{-1} The required concentration of cells is 1000 mg.l^{-1} and the saturation oxygen concentration of the medium is 5.8 mg.l^{-1}. The required K_{L}a must be greater than