Modeling Water Movement and Flux from Membrane Pervaporation Systems for Wastewater Microirrigation

A mathematical model to predict the performance of a membrane pervaporation unit directly placed in the soil to reuse wastewater for agricultural microirrigation was presented. The model was formulated by combining the solution–diffusion and the resistance-in-series model for mass transport across the membrane thickness, the Richard’s equation for soil water movement and the van Genuchten function for soil hydraulic properties to predict the water permeate flux for different types of test soil over a wide range of process operating conditions. Its applicability was assessed by comparing to the experimental data collected using both hollow fiber (HF) bundles and corrugated sheets (CS) membrane modules made of a hydrophilic dense polymer. A good agreement was observed between the model predictions and the experimental measurements. Further analysis concluded that the water permeate flux were mainly controlled by the porosity, the particle-size distribution, and the residual water of the soil. The overall mass transfer resistances were estimated to be $1.2\times {10}^{14}$ and $5.6\times {10}^{13}\mathrm{s}\mathrm{Pa}∕\mathrm{m}$ for the HF and CS modules buried in loam soil, respectively, which are different from those measured in sweeping air pervaporation tests. The soil resistance for water transport was $7.1\times {10}^{13}\mathrm{s}\mathrm{Pa}∕\mathrm{m}$ . It is believed that the model could be a valuable tool to refine the design and optimize the operation of the proposed membrane pervaporation system.