Mineral salt scaling is a major impediment to high recovery operation of membrane desalination processes. When the concentrations of mineral salt ions near and at the membrane surface exceeds saturation, mineral salts may crystallize and scale the membrane surface, thereby leading to permeate flux decline and ultimately to a shorter membrane operational lifetime. Although various salts have been associated with membrane scaling, calcium sulfate dehydrate (gypsum), barium sulfate and calcium carbonate are most commonly encountered in inland water desalination. While calcium carbonate scale can be minimized by acid dosing of the RO, calcium sulfate and barium sulfate solubility is insensitive to pH. As part of a larger effort to mitigate mineral scaling, there is a considerable practical interest in developing a priori predictive models of membrane mineral salt scaling that provide detailed description of the temporal and axial development of surface scaling.

In the present study a comprehensive scale formation model is developed in which the crystallization induction time is considered such that the growth of crystals that are nucleated at different times is considered in a dynamic model. The number of crystals on the membrane surface is dependent on both time and the salt saturation index. The growth rate for a crystal is a function of the saturation index, the feed flow rate and the size of the crystal. Quantitative experimental data describing the progression of the surface crystal number density and the inherent kinetics of crystal growth for the development of mineral scale on a membrane surface was obtained using a high pressure transparent plate-and-frame RO cell that enabled observation of the real-time behavior of crystal growth on a membrane surface. Numerical model of the fluid dynamics and mass transfer in the brine channel was coupled with a detailed surface scale growth model to describe the development of mineral salt scaling on the membrane surface. This fully-coupled model was utilized to investigate the effect of operational parameters on the amount of surface crystal coverage and subsequent flux decline. Comparison of model simulations with experimental data demonstrated that the present modeling approach is an effective approach to describing the propagation of surface scale formation and the resulting flux decline. Finally, the application of the present modeling will be discussed with respect to assessing the adequacy of membrane module design for RO desalting applications with feed water of high scaling propensity.