Derivation of -rAM1

The derivation of -r_AM1 as a function of conversion is shown below:

Where, v₀ is the entering volumetric flow rate (m³/kg), m_AO is the entering mass flow rate (kg/day), C_AO is the entering concentration of hippo feed in (kg/m³), Θ_B is the ratio of microbes to hippo feed, Y_M is the yield coefficient (dimensionless) and K_M is the Monod constant (kg/m³). Substituting for the concentrations C_A and C_B:

This function can then be written as:

Where a, b, c and e are all positive constants.