Application of mathematical models to predict permeate water quality in pilot- and full-scale reverse osmosis processes

Abstract

An evaluation that investigated the accuracy and precision of various mathematical models in predicting permeate water quality for pilot- and full-scale reverse osmosis (RO) membrane processes treating brackish ground water containing scale inhibitors has been completed. Process feed, permeate and concentrate were monitored for flow, pressure, and water quality at operating pilot- and full-scale facilities that employed polyamide-based thin-film composite spiral-wound element configurations. The collected information was used to predict water and solute mass transfer using common porous and non-porous mechanistic-based mathematical models. Overall, this study demonstrated the application of 27 models (or model modifications) for predicting the permeate water quality of pilot- and full-scale RO processes using operation information taken directly from utilities' SCADA output data. The solution friction model was observed to be the most accurate in predicting permeate TDS and chloride, partially attributed to its' accurate estimation of the water mass transfer coefficient (MTC) and supported by t-test and Monte Carlo analysis. The solution diffusion method of determining k_w-SD, which used the water flux and net driving pressure, was further refined with power and exponential functions to account for performance decline. These functions were generally accurate in predicting the observed water MTC; however, the k_w-SD approach proved to be more reliable. The solute mass transfer coefficients were determined experimentally and empirically using the Sherwood number correlation. The constants used for Sherwood number correlations under laminar or turbulent flow conditions typically failed to accurately predict actual solute mass transfer values unless a model-fitting approach was used.