Trends and errors in reverse osmosis membrane performance calculations stemming from test pressure and simplifying assumptions about concentration polarization and solute rejection

A primary goal in the design of reverse osmosis (RO) membranes is to improve water-solute selectivity and water permeance. These transport properties are commonly calculated in the literature using the solution-diffusion model with selectivity (A/B, bar^-1) defined as the ratio between water permeance (A, L.m^-2.h^-1.bar^-1) and solute permeance (B, L.m^-2.h^-1). In calculating transport properties, researchers often use simplifying assumptions about concentration polarization (CP; i.e., assuming negligible CP or a certain extent of CP) and solute rejection (i.e., assuming solute rejection is approximately 1 to enable the explicit use of the CP modulus in solute permeance calculations). Although using these assumptions to calculate transport properties is common practice, we could not find a study that evaluated the errors associated with using them. The uncertainty in these errors could impede unequivocally identifying manufacturing approaches that break through the commonly plotted trade-off frontier between selectivity and water permeance (A/B vs. A); however, we did not find in the literature a study that quantified such errors. Accordingly, we aimed to: (1) quantify the error in transport properties (A, B, and A/B) calculated using common simplifying assumptions about CP and rejection; and (2) determine if using simplifying assumptions affects conclusions drawn about membrane performance or trends concerning the trade-off frontier. Results show that compared with the case where no simplifying assumptions were made, simplified calculations were least accurate at low pressures for water permeance (up to 78% overestimation) and high pressures for solute permeance (up to 188% overestimation). Accordingly, the corresponding selectivities were least accurate at low pressure (up to 111% overestimation) and high pressure (up to 66% underestimation), and conclusions drawn about membrane performance and trade-off trends were pressure-dependent. Importantly, even in the absence of simplifying assumptions, selectivity results were pressure-dependent, indicating the importance of standardizing test conditions for the continued use of current performance metrics (i.e., A/B and A). We propose a two-pressure approach-collecting data for A and B at a high and a low pressure, respectively-combined with simplifying assumptions for more accurate simplified estimations of selectivity (< 10% absolute error). Our work contributes to a better understanding of the effects of operating pressure and key simplifying assumptions commonly used in calculating RO membrane performance metrics and interpretation of corresponding results.