Modelling aerobic granular sludge reactors through apparent half-saturation coefficients

During biological wastewater treatment, substrates undergo simultaneous diffusion and reactions inside microbial aggregates, creating microscale spatial substrate gradients and limiting the macroscale reaction rates. For flocculent and anaerobic granular sludge, this rate-limiting effect of diffusion is often lumped in model parameters, like the half-saturation coefficients of Monod kinetics in activated sludge models (ASM). Yet, an explicit description of the reaction-diffusion process with biofilm models is more common for aerobic granular sludge. This work investigates whether apparent half-saturation coefficients could have applications for aerobic granular sludge as well and examines the implications of this simplification. To this end, the macroscopic reaction rates predicted with a one-dimensional biofilm (1D) model were fitted with Monod kinetics. The results showed that the macroscale rates could indeed be described using apparent kinetics, at the very least over a time scale where the microbial population distribution stays fixed. However, the coefficients were sensitive to changes in the microbial population distribution, which can be affected by long-term changes in operating conditions. Also the activity of organisms that compete for the same substrates affect the parameter value. Be that as it may, apparent kinetics also depend on the operating conditions for flocculent and anaerobic granular sludge, but they have still been used successfully for design and optimization. Therefore, the last section of this work illustrates that they may also have applications for aerobic granular sludge. A simple model for ammonium removal using apparent half-saturation coefficients for oxygen and ammonium is applied to a full-scale reactor, taking advantage of the batch-wise operation and on-line monitoring data for regular recalibration.