A New Model for Microbial Desalination Cells: Model Formulation and Validation under Different Operating Conditions

Abstract

In this paper, a dynamic mathematical model was developed to simulate the processes in Microbial Desalination Cells (MDCs) operated in cyclic batch flow mode using ordinary differential equations found in the literature. In contrast to previous models, the proposed model was developed for fed-batch operations and considers the effects of temperature and substrate inhibition using simple equations for quick simulation. Local sensitivity analysis was performed to determine the parameters with the least impact on current, COD, and salt removal, which were then eliminated from the simplified model. These parameters were found to be the decay rates of anodophilic and methanogenic microorganisms ( $k_{d,a}$ and $k_{d,m}$ ) and the internal resistance parameters ( $R_{\text{anolyte}}$ and $R_{\text{membrane}}$ ). In addition, the best-performing parameters based on the sensitivity analysis results were selected for reestimation for model fitting. The reestimated parameters were mediator yield ( $Y$ ), membrane salt transfer coefficient ( $d$ ), maximum substrate utilization rate by methanogenic microorganisms ( ${\mu }_{\text{s}}$ , ${}_{\text{m}}$ , max), and maximum anodophilic growth rate ( ${\mu }_{\text{a}}$ , max). The predictions of the model were consistent with both our previous experimental data and experimental studies found in the literature and can be easily used by experimentalists for the rapid simulation and prediction of an MDC’s performance under different operating conditions.