Pressure-driven polymeric membrane performance prediction, new membrane dimensionless number, and considerations for effective membrane design, selection, testing, and operation

The demand for polymeric membranes in industries such as fine chemicals, petroleum, and pharmaceuticals underscores the need to optimize organic separation systems. This involves enhancing performance, longevity, and cost-efficiency while tackling chemical and mechanical instabilities. A model is here developed which relates membrane performance, indicated by the permeate solute concentration (Cpi) of species i, to the real-time compressive Young’s modulus (E) during compaction with permeation under a transmembrane pressure (ΔP) or compressive stress. Lower Cpi values indicate better performance. The model integrates solvent densities (ρi), solubility parameters of the membrane (δ M ), solute (δ So ), solvent (δ Sv ), and the extent of membrane constraint (ϕ). It also considers membrane swelling (Ls) and compaction (Lc) with the associated Poisson ratio (γ), providing a comprehensive framework for predicting membrane performance. A key feature is the dimensionless parameter β, defined as ln (Ls/Lc), which describes different operational regimes (β < 1, β = 1, β > 1). This parameter connects membrane affinity characteristics with mechanical properties. The model’s capabilities were demonstrated using three organic separation systems (A, B, and C) which separated isoleucine from DMF, methanol, and hexane solutions, respectively, using nanofiltration (NF) membranes with low, medium, and high E values. The transmembrane pressure ranged from 0.069 to 5.52 MPa (10–800 psi) for β < 1. The performance results indicate that the trend of System B (medium E) > System A (low E) > System C (high E), correlating to decreasing solvent–solute interactions (Δδ SoSv ) and compaction levels. Moderate compaction, resulting in moderate membrane resistance and densification, proved beneficial. Cpi–β plots revealed three distinct slopes, corresponding to elastic deformation, plastic deformation, and the densification of membrane polymers, thus guiding optimal ΔP ranges for operation. This model paves the way for advancing polymeric pressure-driven membrane research and offers new insights into membrane selection, testing, design, and operation.