Mathematical Modeling of Hollow-fiber Membrane System in Biological Wastewater Treatment

A set of mathematical models were derived based on the biokinetics and material balance principles to describe the performance of membrane system in this research. A synthetic wastewater and a meat packing wastewater were processed through a lab-scale membrane bioreactor system to generate experimental data for calibration and verification of the derived models. For the synthetic wastewater treatment, a high and stable Total Organic Carbon (TOC) removal was achieved with volumetric organic loading from 0.2 to 24.2 kg TOC/md). It was found that the derived system models fit the experimental data well. The bio-kinetic coefficients of k, Ks, Y and kd in the models were found to be 0.16 d, 1.0 mg/L, 1.75 mg Mixed Liquor Volatile Suspended Solids (MLVSS)/mg TOC and 0.11 d, respectively. For the meat packing wastewater treatment, the bio-kinetic coefficients of k, Ks, Y and kd were found to be 0.48 d, 56.3 mg/L, 0.53 mg MLVSS/mg COD and 0.04 d, respectively. F/M ratio of 0.08 was found to be the proper operating condition for the system. Based on the proposed system models, the optimum MLSS concentration and F/M ratio can be computed to yield minimum cost of a membrane bioreactor system without excess biomass production.