Analytical Model for Predicting Induction Times in Reverse Osmosis Systems with and without Antiscalants

Abstract

A simple predictive analytical model for induction times in reverse osmosis (RO), both with and without an antiscalant (AS), has been developed based on the fundamental principles of mass and momentum balance. The simplicity of the model arises from the very low Reynolds number in the vicinity of the cluster surface, enabling the use and derivation of exact equations. The main assumption of the induction time without AS, t0A, is that the net growth of the cluster size results from the difference between adhesion and shear forces. With AS, the induction time, tA, is extended due to the competition between the AS and the scaling molecules on the cluster’s surface ligands. The model was validated by fitting it to six independent datasets from experiments conducted with spiral-wound and tubular RO membranes under various operational conditions, resulting in an average difference of 8.0% (t0A) and 8.7% (tA) between predicted and experimental induction times. It was found that t0A is governed by three dimensionless parameters: supersaturation ratio (Sa), shear (Ku), and scalant saturation (κ). tA increases with t0A and the AS concentration.