Similarity Scaling of Fully Developed Mass Transport and Pressure Drop in Oriented Spacer-Filled Channels in Spiral-Wound Membrane Modules

Abstract

Feed spacers in reverse osmosis membrane modules enhance mass transport but simultaneously increase flow resistance. The quantitative dependence of both on spacer orientation remains poorly understood despite its importance for optimal module design. This work introduces an analytic least-square method for deriving scaling laws governing Sherwood number ($Sh$) and friction factor ($f$) as functions of spacer orientation and Reynolds number ($Re$) through high-resolution computational fluid dynamics simulations. The analytical least-square fitting method provides a systematic approach for extracting transport coefficients. Physical similarity analyses on industrial spacers reveal that mass transport follows $Sh = 3.595(1 + 0.244 \sin(2α)) Re^{1/2}$ while pressure drop scales as $f = 11.63(1 + 0.19 \sin(2α)) Re^{-1/2}$, enabling quantification of orientation-dependent transport efficiency across the full operating range. A novel RO performance analysis scheme shows that the trade-off between water flux and pressure drop crucially depends on the spacer orientation. $45^\circ$-oriented spacers improve the water flux marginally, while increasing the pressure drop significantly, compared to $0^\circ$-oriented spacers.