Utilizing Buckingham Pi theorem and multiple regression analysis in scaling up direct contact membrane distillation processes

Predicting the performance of a full-scale direct contact membrane distillation (DCMD) module based on experimental lab-scale results is rather difficult, since the DCMD performance is dependent on many different process parameters. Hence, there is a need for a methodology to perform DCMD system up-scaling based on lab-scale experimental results. In this study, we devise an approach to scale up the performance of DCMD systems by using the Buckingham's Pi theorem to group the DCMD process parameters into eight relevant dimensionless groups. Experimental data obtained from literature at various module dimensions were used to evaluate the developed dimensionless groups. An experimentally validated computational fluid dynamics (CFD) model was also developed and used to extend the coverage of operational parameters beyond the available experimental data. Then, two empirical dimensionless correlations were created, using multiple nonlinear regression analysis, and then validated, to enable the prediction of flux and pressure drop in DCMD systems at any scale.