where De is the effective diffusivity (cm2
s-1), z is
the infinitesimal height of the substrate bed (cm),
C is the gas phase oxygen concentration (g cm-
3
), Ks is the substrate saturation constant (g cm-
3
), YX/S is the biomass yield coefficient and ε is
the porosity of the substrate bed.
The equations are subject to the following initial
and boundary conditions: