Prediction of gypsum induction time to inform scaling kinetics using machine learning and Smoluchowski theory

Gypsum scaling remains a significant challenge in desalination and brine management systems, compromising operational efficiency, reducing equipment lifespan, and increasing chemical use. Predicting gypsum nucleation kinetics, reflected by the induction time, is essential for assessing the likelihood of scaling and selecting suitable mitigation strategies. Although many experimental studies have investigated gypsum crystallization under various conditions, no model has been developed to predict induction time across a wide range of solution compositions and operating temperatures. In this study, we compiled induction time data from the literature and recalculated the saturation index (SI) using the Pitzer model for thermodynamic consistency. To fill data gaps, additional induction time experiments were conducted across a range of temperatures (20–80 °C) and NaCl background concentrations (0–3M). A mechanistic model based on Smoluchowski aggregation theory was used to estimate induction time, and an empirical model of gypsum-solution interfacial energy as a function of temperature (20–80 °C) and NaCl concentration (0–5M) was developed. Finally, several machine learning (ML) models were trained to predict induction time and an integrated ML–Smoluchowski model that combines the physical model with data-driven learning was developed. The integrated model achieved the highest accuracy (R² = 0.93), outperforming both the standalone ML and Smoluchowski models (R² = 0.89 each). Results show that induction time decreases significantly with temperature and exhibits a non-monotonic trend with NaCl concentration. The integrated modeling approach offers a practical tool for estimating gypsum scaling risks in a variety of desalination and brine management scenarios.