Steady‐State Analysis for Biological Treatment of Inhibitory Substrates

A steady‐state approach for designing biological wastewater treatment systems is developed for inhibitory substrates using the Haldane rate expression. Steady‐state solutions are derived for a continuous‐flow completely mixed reactor with recycle of the biomass. It is determined that two steady‐state operating regions exist at any one mean cell residence time; an unstable region, where the substrate concentration increases and the biomass concentration decreases as the mean cell residence time increases, and a stable region, where the substrate concentration decreases and the biomass concentration increases with mean cell residence time. A critical mean cell residence time, ${\theta }_c^{*}\text{,}$ is established as a design parameter, for inhibitory substrates, to maintain a biological reactor in the stable operating region. A survey of published data for phenol exhibits an excellent logprobability relationship for ${\theta }_c^{*}\text{.}$ For design purposes, the hydraulic residence time, ${\theta }_h\text{,}$ is set equal to ${\theta }_c^{*}\text{,}$ This restricts the mean cell residence time, ${\theta }_c\text{,}$ to values higher than ${\theta }_h\text{,}$ i.e., ${\theta }_c\ge {\theta }_h\text{,}$ and maintains a reactor in the stable operating region at all times (based on steady‐state analysis). For phenol, a very biodegradable inhibitory substrate, the data indicate a log‐mean ${\theta }_c^{*}$ of 0.29 days, ${\theta }_c^{*}\text{.}$ However, values of ${\theta }_c^{*}$ guaranteeing a less‐than‐1% chance that ${\theta }_c^{*}$ will be exceeded are in excess of one day.