Detailed modeling and simulation of an out-in configuration vacuum membrane distillation process

In this study, a detailed rigorous theoretical model was developed to predict the transmembrane flux of a shell-and-tube type vacuum membrane distillation (VMD) module for seawater desalination. Two modes of operation are used for performing the VMD, namely lumen-side feed (in-out) configuration and shell-side feed (out-in) configuration. In this study, detailed mathematical formulations are derived for an out-in configuration that is commonly used in seawater desalination applications. Experimental results and model predictions for mean permeate flux are compared and shown to be in good agreement. The results indicate that although the simple VMD model that maintains a constant permeate pressure is easy to use, it is likely to significantly overestimate the mean permeate flux when compared to the detailed model that considers the pressure build-up in the fiber lumen. The pressure build-up of water vapor in the fiber lumen is identified as the crucial factor that significantly affects the VMD performance because it directly reduces the driving force for vapor permeation through the membrane pores. Additionally, its effect is more pronounced at longer fiber lengths and higher permeate fluxes, and this is achieved at higher feed temperatures and velocities and at lower feed salinities. In conclusion, the results of the study are extremely important in module design for the practical applications of VMD processes.