Application of the Buckingham ∏ theorem to model multiple effect vacuum membrane distillation
Abstract This study aims to develop a dimensionless model of the V-MEMD performance indicator through which a preliminary prediction of the most critical performance indicators can be attained. Buckingham ∏ theorem was utilized to define dimensionless parameters that allow the predicted relationships associating independent input parameters to describe the essential performance indicators of the V-MEMD system. The obtained compact 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 stands as a short-cut tool for design and performance analysis avoiding time consuming experimentations and/or complicated theoretical models. The compatibility of the generated model is assessed by matching the expected response of output dimensionless parameters (e.g., recovery ratio, R, and gain output ratio, GOR) to variation in pressure ratio and cooling process. The model is validated with other works, and discrepancies are remarked to be within ±10% and ±25% for recovery ratio and gain output ratio, respectively. Furthermore, the specific thermal energy consumption, STEC is correlated to GOR assuming constant vaporization enthalpy and density of the distillate water. The correlation can predict STEC within 5% accuracy over different operating conditions for the supplied hot water.