Gypsum scale formation and inhibition kinetics with implications in membrane system

•This model elucidates possible mechanisms of gypsum crystallization and inhibition.•The induction time of gypsum crystallization and inhibition is accurately predicted.•This model can help significantly improve the membrane treatment efficiency.•The new model has practical implications in various industries. Water desalination using membrane technology is one of the main technologies to resolve water pollution and scarcity issues. In the membrane treatment process, mineral scale deposition and fouling is a severe challenge that can lead to filtration efficiency decrease, permeate quality compromise, and even membrane damage. Multiple methods have been developed to resolve this problem, such as scale inhibitor addition, product recovery ratio adjustment, periodic membrane surface flushing. The performance of these methods largely depends on the ability to accurately predict the kinetics of mineral scale deposition and fouling with or without inhibitors. Gypsum is one of the most common and troublesome inorganic mineral scales in membrane systems, however, no mechanistic model is available to accurately predict the induction time of gypsum crystallization and inhibition. In this study, a new gypsum crystallization and inhibition model based on the classical nucleation theory and a Langmuir type adsorption isotherm has been developed. Through this model, it is believed that gypsum nucleation may gradually transit from homogeneous to heterogeneous nucleation when the gypsum saturation index (SI) decreases. Such transition is represented by a gradual decrease of surface tension at smaller SI values. This model assumes that the adsorption of inhibitors onto the gypsum nucleus can increase the nucleus superficial surface tension and prolong the induction time. Using the new model, this study accurately predicted the gypsum crystallization induction times with or without nine commonly used scale inhibitors over wide ranges of temperature (25–90 °C), SI (0.04–0.96), and background NaCl concentration (0–6 mol/L). The fitted affinity constants between scale inhibitors and gypsum show a good correlation with those between the same inhibitors and barite, indicating a similar inhibition mechanism via adsorption. Furthermore, by incorporating this model with the two-phase mineral deposition model our group developed previously, this study accurately predicts the gypsum deposition time on the membrane material surfaces reported in the literature. We believe that the mode