Model-Based Optimization of Multi-Stage Nanofiltration Using the Solution-Diffusion–Electromigration Model

Abstract

Nanofiltration is well suited to separate monovalent ions from multivalent ions, such as the separation of Li+ and Mg2+ from seawater, a potential lithium source for the production of lithium-ion batteries. To the best of our knowledge, there is no existing work on the optimization of a multi-stage membrane plant that differentiates between different ions and that is based on a validated transport model. This study presents a method for modeling predefined membrane interconnections using discretization along the membrane length and across the membrane thickness. The solution-diffusion–electromigration model was used as the transport model in a fundamental membrane flowsheet, and the model was employed to optimize a given flowsheet with a flexible objective function. The methodology was evaluated for three distinct separation tasks, and optimized operating points were found. These show that permeances and feed concentrations might cause negative rejections and positive rejections (especially for bivalent ions) depending on the ions’ properties and fluxes, thereby allowing for a favorable separation between the ions of different valence at optimized conditions. In an application-based case study for the separation of Li+ and Mg2+ from seawater, the method showed that under optimal conditions, the mol-based ratio of Mg2+/Li+ can be reduced from 2383 to 2.8 in three membrane stages.