Global optimization for accurate and efficient parameter estimation in nanofiltration

Abstract

One of the most well-established frameworks for modeling multicomponent transport in nanofiltration (NF) is the Donnan-Steric Pore Model with Dielectric Exclusion (DSPM-DE). Conventional DSPM-DE characterizes transport across NF membranes through four governing membrane parameters: (1) pore radius; (2) effective membrane thickness; (3) membrane charge density; and (4) the dielectric constant inside the membrane pores. The process for quantifying these parameters is typically sequential. First, neutral solute experiments are performed to determine pore radius and effective membrane thickness. Next, charged species experiments are conducted, and the data is used to regress out the remaining parameters. The resulting regressions are often performed using local search algorithms that can struggle to provide low residuals with robust fits. In addition, this two-step approach tends to: (1) require a substantial number of charged and uncharged solute experiments; and (2) introduce assumed relationships between pore size and water flux, such as the Hagen-Poiseuille equation, which may not be representative of transport through complex pore networks. To address these issues, we propose the use of metaheuristic global optimization techniques supplemented with gradient-free local search and maximum likelihood estimation to simultaneously regress all four membrane parameters directly from charged species experiments. We validate our approach against eight independent datasets across diverse input salinities, compositions, and membranes.