An extended bio-electrochemical model for wastewater treatment and water desalination: Insights into the performance of microbial desalination cells

Abstract

This paper presents an extended mathematical model for a microbial desalination cell (MDC), integrating Haldane kinetics for substrate inhibition and proton translocation theory for substrate dissociation under dynamic flow. The model is capable of predicting exoelectrogenic and methanogenic biomass dynamics, acetate removal efficiencies, salt concentration changes, and current production. Notably, it can be used to explore the influence of operational parameters such as dilution rates, temperatures, and external resistances. Our simulations reveal the optimal conditions for maximizing exoelectrogen concentration (500 mg/L) with minimal methanogen presence (50 mg/L) in the anode chamber at an anolyte dilution rate of 0.5 d−1, a temperature of 20 °C, and an influent acetate concentration of 1500 mg/L. The model accurately predicts the salt reduction in the middle chamber (from 0.2 to 0.09 mol/L) with a salt dilution rate of 0.5 d−1 and an external resistance of 20 Ohm. The model predicts a peak power output of 2.5 mW at external resistances between 20 and 50 Ohm. The model was validated against a suite of experimental literature data, including our previously published lab-scale studies, verifying its accuracy in predicting organic and salt removal rates, current production, and desalination efficiency. This extended model is a valuable tool for understanding the complex interactions between factors that influence MDC performance and can guide the optimization of MDC design for wastewater treatment and desalination.