Theoretical model for a submerged biological filter

A mathematical model was developed for percent removal of a pure, non‐adsorbable, biodegradable substrate in a submerged biological filter using the nonlinear Monod expression for the substrate utilization rate. Analytical solutions were obtained using zero and first order linearizations of the Monod expression and were compared to the numerical solution of the nonlinear system. The relevant dimensionless parameter groups describing the system were identified and their effects on substrate flux into the biolayer, effectiveness factor, and percent removal were also examined. Criteria were established for determining the relative accuracy of the two biokinetic approximations and for determining values of “limiting” biolayer thickness.