Mathematical model of dynamic behavior of microbial desalination cells for simultaneous wastewater treatment and water desalination

Microbial desalination cells (MDCs) are an emerging concept for simultaneous wastewater treatment and water desalination. This work presents a mathematical model to simulate dynamic behavior of MDCs for the first time through evaluating multiple factors such as organic supply, salt loading, and current generation. Ordinary differential equations were applied to describe the substrate as well as bacterial concentrations in the anode compartment. Local sensitivity analysis was employed to select model parameters that needed to be re-estimated from the previous studies. This model was validated by experimental data from both a bench- and a large-scale MDC system. It could fit current generation fairly well and simulate the change of salt concentration. It was able to predict the response of the MDC with time under various conditions, and also provide information for analyzing the effects of different operating conditions. Furthermore, optimal operating conditions for the MDC used in this study were estimated to have an acetate flow rate of 0.8 mL·min^-1, influent salt concentration of 15 g·L^-1 and salt solution flow rate of 0.04 mL·min^-1, and to be operated with an external resistor less than 30 ω. The MDC model will be helpful with determining operational parameters to achieve optimal desalination in MDCs.