Steady-state analyses of activated sludge processes with plug-flow reactor

- Reduced model for activated sludge process in wastewater treatment.
- Plug-flow biological reactor with Monod growth kinetics.
- Two settler models: ideal (point) settler and one with compressive settling.
- Equations without derivatives obtained for steady-state operating conditions.

Activated sludge processes (ASPs) consisting of a plug-flow reactor (PFR) and a settler are analyzed in steady-state operation using a reduced model consisting of one soluble substrate and one particulate biomass component modelling the dominating biological process. Monod biomass growth rate is assumed. Two settler models are studied. One is the commonly used ideal settler, or point settler, which is assumed to never be overloaded and to have unlimited flux capacity. The other recently published steady-state settler model includes hindered and compressive settling, and models a realistic limiting flux capacity. Generally, the steady-state concentration profiles within the PFR and the settler are governed by nonlinear ordinary differential equations. It is shown that the steady-state behaviour of the ASP can, however, be captured by equations without derivatives. New theoretical results are given, such as conditions by means of inequalities on input variables and parameters for a steady-state solution to exist. Another novel finding is that, if the incoming substrate concentration is increased from a low or moderate stationary value and the solids residence time is kept fixed, then this results in a lower effluent concentration in the new steady state. The steady-state equations are solved numerically for different operating conditions. For common parameter values, numerical solutions reveal that an ASP having a PFR, instead of a continuously stirred tank reactor, is far more efficient in reducing the effluent substrate concentration and this can be obtained for much lower recycle ratios, which reduces the pumping energy considerably.