Machine learning-based analysis of calcium sulfate scaling-induced permeability decline in semi-batch reverse osmosis

Semi-batch reverse osmosis (SBRO) increases water recovery while producing high-quality permeate for water reuse. However, SBRO operation is often constrained by calcium sulfate (CaSO₄) scaling during the treatment of industrial and municipal effluents for water reuse. Because permeability decline under scaling conditions arises from complex interactions between feed and hydrodynamic conditions, its interpretation remains challenging. This study analyzes CaSO₄ scaling-induced permeability decline in SBRO using machine learning (ML). A 7307 × 16 dataset comprising 12 experimental sets was obtained using a pilot-scale SBRO unit equipped with a 2.5-in. spiral-wound RO element and operated at 90% water recovery. Correlation analysis indicated that feed variables exhibited strong negative correlations (up to r = −0.87) with normalized temperature-corrected water permeability (A_TC/A_TC,0). In contrast, the effects of operating variables, such as feed hydraulic pressure (P_f), feed flow rate (Q_f), and permeate flow rate (Q_p), on A_TC/A_TC,0 were not clearly identified by correlation analysis because these variables were controlled discretely. To identify the main variables associated with CaSO₄ scaling-induced A_TC/A_TC,0 decline in SBRO, several ML models were trained without temporal variables. The Matern 5/2 Gaussian process regression model (R² = 0.998), coupled with Shapley additive explanations, indicated greater contributions of operating variables than feed variables to the predicted A_TC/A_TC,0 within the investigated dataset. These statistical relationships are consistent with the non-ideal flow behavior of the spiral-wound RO module and the dynamic operating characteristics of SBRO. Finally, increasing Q_f and Q_p was proposed as a process strategy to limit CaSO₄ scaling-induced A_TC/A_TC,0 decline in SBRO.