Application of the Buckingham Π Theorem to Model the Multiple Effect Vacuum Membrane Distillation

Abstract

Abstract This study aims to develop a dimensionless model of the vacuum multi-effect membrane distillation (V-MEMD) system through which a preliminary prediction of the most critical performance indicators can be attained. The Buckingham Π theorem was utilized to define dimensionless parameters that enable the predicted relationships associated with independent input parameters to describe the essential performance indicators of the V-MEMD system. The obtained simplified model reduces the design parameters from ten to two effective dimensionless parameters to realize the realistic and actual behavior of the designated system. The self-sustained model can be used as a short-cut tool for design and performance analysis to avoid time-consuming experimentations and complicated theoretical models. The compatibility of the generated model is assessed by matching the expected response of the output dimensionless parameters of recovery ratio (Π6) and gain output ratio (GOR, Π12) to variations in the pressure ratio and cooling process. The model is validated with other works, and discrepancies are found to be within ±8% and ±0.8 for the recovery ratio and GOR, respectively. Furthermore, the specific thermal energy consumption (STEC) is correlated to the GOR assuming constant vaporization enthalpy and density of the distillate water. The correlation can predict STEC within 5% accuracy over various operating conditions for the supplied hot water.