Impact of large-scale effects on mass transfer and concentration polarization in Reverse Osmosis membrane systems

We present well-resolved computational fluid dynamics simulations of a large-scale reverse osmosis membrane -spacer configuration (- 1 m). Our computational model solves the flow and transport equations with variable solute-dependent properties. We utilize a high resolution computational mesh to resolve all relevant length scales associated with spacer-induced mixing and thin concentration boundary layers. An important contribution of this work is the development of a modified mass-transfer correlation that accounts for the development of the concentration boundary layer along the channel. A set of 2D axisymmetric simulations were performed for a spiral wound module layer with varying cross-flow conditions and spacer diameters which indicate a significant entrance length effect for concentration profile development at lower flow rates while mixing effects dominate at higher flow rates. The mass-transfer correlations at higher flow rates compare well with published correlations while a surrogate model for Sherwood number was obtained that depends on an additional similarity variable that accounted for entrance length effects at lower flow rates. Finally, a large-scale membrane-spacer design relevant to high-pressure reverse osmosis is studied with a non-uniform arrangement of spacers, which indicate a substantial saving in pressure drop (- 40%) compared to traditional uniformly spaced pattern with minor variations (- 2%) in concentration polarization, product water quality (- 1%) and water recovery (- 7%) compared to a uniform spacer pattern.