Influence of the porous support on diffusion in composite membranes

Abstract

Composite membranes used in gas separation, pervaporation and reverse osmosis applications typically consist of at least one nonporous layer on top of a porous structure. The porous support restricts diffusion in the top layer because molecules can exit the layer only where a pore is present. This not only increases the path length for diffusion, but also increases the concentration gradient of the diffusing molecules as they approach the pore opening. These two effects combine to give the top layer a diffusion resistance that is greater than the intrinsic resistance of the layer, which is calculated as the actual thickness of the top layer, H, divided by the diffusion coefficient, D. In membrane terms, this means that the effective permeance of the composite membrane is smaller than the intrinsic permeance, which is calculated as the permeability coefficient, P, divided by H. The relative reduction in permeance is expressed by the restriction factor, Ψ, and is independent of the solubility and diffusion coefficients.We simulated the diffusion process using computational fluid dynamics (CFD) and determined the restriction factor, Ψ, as a function of the support porosity, ϕ, and a normalized dimension, τ, defined as the top layer thickness divided by the pore radius. By defining a dimensionless Restriction Number, NR, we were able to very accurately correlate the restriction factor data to the following equation:ψ=ϕ+1.6⋅NR1.11+1.6⋅NR1.1withNR=τ⋅ϕ1−ϕThe correlation predicts the restriction factor within 5% for all cases evaluated, which included three different pore distribution patterns and multiple pore size distributions with up to four different pore sizes. Our analysis suggests that the correlation is also applicable to porous supports with more realistic properties, such as random pore location and broader pore size distributions. The correlation is useful to evaluate the influence of the porous support on the permeance of composite membranes and shows that the effect can be significant in high-performance membranes.A limited number of CFD simulations were performed for composite membranes containing a gutter layer and show convincingly that a high permeability gutter layer can significantly improve the permeance of composite membranes while reducing selectivity by only a modest degree.