A reduced-order model of concentration boundary layers in reverse osmosis systems with vortical flow structures*

Reverse osmosis (RO) is a membrane desalination process that plays a central role in the energy-water-climate nexus due to its applications to desalinating seawater and treating complex wastewaters. RO operates by flowing a high-pressure feed solution (up to 80 bars) over a semipermeable membrane sheet that blocks solutes while allowing water to permeate. RO is energy intensive because the feed pressure must exceed the feed osmotic pressure to force permeate through the membrane. Moreover, the osmotic pressure at the membrane is much higher than that of the incoming feed due to the accumulation of solutes in a thin boundary layer growing along the membrane. This accumulation is not fully understood, and further complicated by the presence of "feed spacers," a plastic woven mesh that supports the membrane in the RO system. We perform a suite of time-resolved 2D CFD simulations of fluid flow and solute transport in an RO system with three different spacer geometries. We show that spacers generate vortical flow structures that generate regions of preferential solution accumulation within the concentration boundary. We then propose a reduced-order model that mimics the impact of spacers as a row of counter-rotating vortices near the membrane surface. We show that these vortices can be tuned to reproduce the key results of our CFD to high accuracy, for only a small fraction of the computational cost of CFD.