The design formulas for the completely mixed activated sludge process as shown below are mass-balance applications of equations describing microbial growth and substrate decay. The final design equation Xw _ I (S-S)-k is derived VX VX assuming influent and effluent biomass concentration is negligible. The biomass balance max S S_QwX equation is = +k and the Monod equation which accounts for microbial K, +S VX dX SX growth kinetics is -kX. Modify the final design equation if the effluent dt K +S biomass concentration is no longer negligible. Influent Control volume (from primary clarifier) Secondary clarifier Qo. So, Xo = Aeration basin V, X, S Qo + Qr X, S Q, Xu Returned activated sludge (RAS) Effluent (to disinfection) Qo - Qw Xe, Se Qu. Xu Qw. Xw, Sw Waste activated sludge