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.

Dataset of reverse osmosis membrane transport properties calculated with and without assumptions about concentration polarization and solute rejection and the errors associated with each assumption.

The data shared in this work represent aspects of the performance of reverse osmosis membranes during filtration. We present pressure, permeate flux, and solute rejection data gathered during cross-flow filtration experiments, which were used to (i) model water and solute permeation through the membranes and (ii) calculate concentration polarization moduli and a suite of transport properties, including water permeance, solute permeance, and water-solute selectivity. Membrane transport properties were calculated with the different approaches commonly used to simplify transport property calculations. Typical calculations of these transport properties often use simplifying assumptions (e.g., negligible concentration polarization and solute rejection close to 100%). However, the extent of the errors associated with using simplifying assumptions in this context were not previously known or quantified. This publication and corresponding dataset pertain to figures presented in the accompanying work (Armstrong et al., 2022) [1].

Molecular Methods for Assessing the Morphology, Topology, and Performance of Polyamide Membranes.

The molecular-scale morphology and topology of polyamide composite membranes determine the performance characteristics of these materials. However, molecular-scale simulations are computationally expensive and morphological and topological characterization of molecular structures are not well developed. Molecular dynamics simulation and analysis methods for the polymerization, hydration, and quantification of polyamide membrane structures were developed and compared to elucidate efficient approaches for producing and analyzing the polyamide structure. Polymerization simulations that omitted the reaction-phase solvent did not change the observed hydration, pore-size distribution, or water permeability, while improving the simulation efficiency. Pre-insertion of water into the aggregate pores (radius ≈ 4 Å) of dry domains enabled shorter hydration simulations and improved simulation scaling, without altering pore structure, properties, or performance. Medial axis and Minkowski functional methods were implemented to identify permeation pathways and quantify the polyamide morphology and topology, respectively. Better agreement between simulations and experimentally observed systems was accomplished by increasing the domain size rather than increasing the number of ensemble realizations of smaller systems. The largest domain hydrated was an order of magnitude larger by volume than the largest domain previously reported. This work identifies methods that can enable more efficient and meaningful fundamental modeling of membrane materials.

Effect of Feed Water pH on the Partitioning of Alkali Metal Salts from Aqueous Phase into the Polyamide Active Layers of Reverse Osmosis Membranes.

The partitioning of solutes into the polyamide active layers of reverse osmosis (RO) membranes is a key membrane property determining solute permeation. Quantification of partition coefficients and their dependence on feedwater pH would contribute to the development of predictive transport models of contaminant transport through RO membranes; however, neither solute partitioning nor the effect of feed solution pH on partitioning has been thoroughly characterized in the literature. Accordingly, we characterized the partitioning of all chloride salts of alkali metals (CsCl, RbCl, KCl, NaCl, and LiCl) from the aqueous phase into the polyamide active layers of five polyamide RO membranes, including one prepared in-house and four commercial membranes. We evaluated the effect of pH on the partitioning of alkali metal salts and whether the effect of pH on salt partitioning and rejection is consistent with Donnan theory predictions. Results showed that for all membranes, the partition coefficients of all salts were less than one and did not differ substantially among RO membranes. Results also indicated that for all membranes tested, Donnan theory provided an appropriate theoretical framework to estimate the effect of pH on salt partitioning (evaluated for all chloride salts of alkali metals) and salt rejection (evaluated for NaCl). Thus, we conclude that changes in salt rejection resulting from feed solution pH are primarily driven by changes in salt partitioning with comparatively small changes in salt diffusion coefficients.