Coupled 3-D hydrodynamics and mass transfer analysis of mineral scaling-induced flux decline in a laboratory plate-and-frame reverse osmosis membrane module

A 3-D (3-dimensional) numerical modeling approach to analyze the coupling of mineral scale, concentration polarization and permeate flux was developed and demonstrated for a gypsum membrane scaling test in a plate-and-frame RO membrane module geometry. The impact of concentration polarization on mineral gypsum scaling, and in turn the impact of mineral scale on the concentration polarization field, were explored via 3-D finite-element numerical solutions of the coupled fluid hydrodynamics and solute mass transfer equations, along with detailed experimental data on the extent and location of mineral scale. Numerical simulations of the concentration field for a scale-free membrane revealed that the regions of highest supersaturation with respect to calcium sulfate corresponded to regions of highest gypsum scale density, as observed through real-time imaging of the membrane surface in the gypsum scaling test. 3-D simulations of the concentration field in the presence of mineral scale revealed that the concentration polarization modulus and permeate flux were largely unaffected in contiguous scale-free regions of the membrane. However, near and just downstream of individual crystal formations, the local concentration polarization modulus decreased (by ∼5%) and the permeate flux increased (by ∼2%) relative to the same positions in the absence of scale. The model-calculated and experimental permeate flux decline agreed closely with an average absolute error of 1.8%. The present study suggests that flux decline due to mineral scaling can be reasonably described by the surface blockage mechanism.