Flux model for the membrane distillation process to treat wastewater: Effect of solids concentration

This study aims to develop a mathematical model to estimate the initial permeate flux of a direct contact membrane distillation process operated with various solids concentrations and Cross Flow Velocities (CFVs). Digestate produced from an anaerobic digestion of livestock wastewater was used as a feed solution for the laboratory scale membrane distillation. Heat transfer coefficients and Nusselt number constants were determined from the distillation experiments performed with various CFVs and feed solution temperatures. An empirical function was derived to reflect the effect of solids concentration on the flux prediction. A statistical analysis supported that the flux predicted by the model fitted very well with the observed flux. By using the developed model, numerical experiments were performed to simulate the flux according to various CFVs, feed solution temperatures, and solids concentrations (0–2200 mg/L). Also, Temperature Polarization Coefficient (TPC) values were calculated by using the results simulated from the numerical experiments. The developed model can be used to predict the initial flux of the membrane distillation process specifically to treat wastewater including high solids contents, and the modeling works can provide more insights on the relationship among flux, CFV, temperature difference, solids concentrations, and heat transfer efficiency.