The concentrations of phenol and biomass during methanogenic degradation in a laboratory experiment are shown in the figure (Bekins et al., 1998, GW 36, 261). The phenol concentration decreases linearly with time (characteristic for a zeroth order degradation rate), but the degradation declines at very small concentrations.

The breakdown was modeled with the Monod kinetic rate equation:
where S is the concentration of phenol (mg/L), t is time (s), kmax is the maximal rate (mg/L/s), and k½ is the half-saturation constant (mg/L).

The PHREEQC input file given in Example 10.7 calculates the line in the graph. Note that the rate is zero order when the phenol concentration is above 5 mg/L (about 3 times higher than k½, the slope d S / dt is constant), but that it becomes first order with respect to phenol (= S) at lower concentrations.