Steady-state analysis of activated sludge processes with a settler model including sludge compression

A reduced model of a completely stirred-tank bioreactor coupled to a settling tank with recycle is analyzed in its steady states. In the reactor, the concentrations of one dominant particulate biomass and one soluble substrate component are modelled. While the biomass decay rate is assumed to be constant, growth kinetics can depend on both substrate and biomass concentrations, and optionally model substrate inhibition. Compressive and hindered settling phenomena are included using the Bürger-Diehl settler model, which consists of a partial differential equation. Steady-state solutions of this partial differential equation are obtained from an ordinary differential equation, making steady-state analysis of the entire plant difficult. A key result showing that the ordinary differential equation can be replaced with an approximate algebraic equation simplifies model analysis. This algebraic equation takes the location of the sludge-blanket during normal operation into account, allowing for the limiting flux capacity caused by compressive settling to easily be included in the steady-state mass balance equations for the entire plant system. This novel approach grants the possibility of more realistic solutions than other previously published reduced models, comprised of yet simpler settler assumptions. The steady-state concentrations, solids residence time, and the wastage flow ratio are functions of the recycle ratio. Solutions are shown for various growth kinetics; with different values of biomass decay rate, influent volumetric flow, and substrate concentration.