Numerical techniques for the simulation of reverse osmosis systems with complicated geometries

Abstract

Reverse osmosis (RO) is a membrane desalination process with important applications to seawater desalination and advanced water treatment. RO, however, is an inherently energy intensive process due to the large pressures required to operate these systems. One major technical problem for RO that leads to further energy demands and performance losses is called concentration polarization. Concentration polarization refers to the accumulation of solutes near the membrane surface. The fundamentals of this process are complicated because of unsteady mixing and solute transport and because the flow regimes in RO systems are not fully understood. More recently, computational fluid dynamics (CFD) has been used as an investigative tool to study mass transport and polarization phenomena in RO. However, numerical challenges arise in RO systems due to complicated interactions between solute boundary layers and unsteady vortical flow structures generated by feed spacers. Feed spacers are mesh-like materials that support the membrane and separate the membrane sheets. Furthermore, these flow structures also interact with semipermeable membranes through which the permeate flow depends on the local pressure. Additionally, many simulations of spacers currently rely on body-fitted grids that require considerable time to generate.

This work addresses these challenges by developing a suite of numerical methods tailored to the efficient and accurate simulation of RO systems with feed spacers. We first develop an immersed boundary method capable of simulating spacers without body-fitted grids. We show that, using these methods, we can recover second-order spatial accuracy for both Dirichlet and Neumann type boundary conditions for the spacer filaments. We then explore the application of two projection methods to the accuracy of RO simulations. We found that traditional projection methods can produce lower temporal accuracy for the pressure field as well as the velocity fields. We then develop a modified projection method that recovers second-order accuracy. Using our methods, we perform a parametric CFD study of concentration polarization in RO system with three different spacer arrangements over a broad range of Reynolds numbers, $50 \le Re \le 500$. We then propose and investigate a reduced order model that mimics the impact of spacers on the near-membrane velocity field and demonstrate its ability to reproduce important CFD results to high accuracy.