Evaluation of empirical formulae for estimation of the longitudinal dispersion in activated sludge reactors

Tracer studies are widely applied to characterize the hydraulic properties of reactors. In the case of activated sludge reactors, however, tracer test results are difficult to interpret due to internal and returned activated sludge recirculation. Empirical formulae can be considered as an alternative method of estimating the hydraulic conditions within the activated sludge reactor. The aim of this study is to evaluate accuracy of four empirical formulae for the full-scale conditions based on the results of tracer studies performed at the Rock Creek Wastewater Treatment Plant (WWTP) in Hillsboro, OR (USA). Values of the dispersion coefficient, E(L), were first estimated using a 1-D advection-dispersion equation and setting a sum of squares of differences between the observed and calculated tracer concentrations to a minimum. The estimated values of E(L) coefficient remained within the range of 1043-1580 m2/h. The best approximation of dispersion was obtained from the formula of Fujie et al. (1983, J. Ferment. Technol. 63(3), 295). Also the formula of Murphy and Boyko (1970, J. San. Eng. ASCE 96(2), 211) generated E(L) values of the same order as the optimum E(L). The accuracy of these formulae was further confirmed based on the results of studies reported in the literature.