Analyzing multicomponent permeation and coupling effects in pervaporation of Acetone-Butanol-Ethanol solutions using Maxwell-Stefan based modeling

The state-of-the-art research in pervaporation lacks a comprehensive understanding of the selective membrane permeation in real and multicomponent mixtures, a factor critical for its widespread commercial adoption. This work elucidates the contribution of various interaction effects, known as coupling phenomena, on the pervaporation of multicomponent Acetone-Butanol-Ethanol (ABE) solutions through a commercial PDMS membrane. Maxwell-Stefan (MS) diffusion formulations, combined with the UNIQUAC thermodynamic model, mostly restricted in literature to binary solutions permeating through a polymer membrane, are extended to multi- component feed solutions. The thermodynamic correction factor [Gamma] Gamma ] and correlation [B]- B ]- 1 matrices are analyzed to resolve coupling into its thermodynamic and kinetic (diffusive) constituents. A generalized and explicit analytical derivation for calculation of [Gamma] Gamma ] by UNIQUAC model is proposed, allowing estimation for any number of permeants. Subsequently, a significant inhibitory coupling of the component fluxes to the driving forces of its accompanying penetrants is revealed. In addition to the non-ideality arising from diagonal elements Gamma ii , the substantial negative off-diagonal elements Gamma ij in the thermodynamic correction matrices anticipate a decline in effective driving forces, butanol fluxes and permeation selectivity as we transition from binary butanol-water to multicomponent ABE mixtures. Following this, a detailed hit-and-trial based strategy is implemented to evaluate the relevance of membrane plasticization, cluster formation and interspecies frictional interactions towards the MS self and cross diffusivities within the [B]- B ]- 1 matrix. Existing semi-empirical expressions for self-diffusivities in binary alcohol-water systems incorporating plasticization and clustering constants are reformulated and compared for their ability to accurately describe fluxes in binary and ternary ABE solutions. Furthermore, the optimal model fit was found to be insensitive to variation in MS cross-diffusivities. This suggests that the contribution of correlation effects may be neglected altogether, provided the expressions for self-diffusivities are adequately tailored for membrane plasticization and clustering. Notably, while only butanol clustering suffices for binary mixtures, additional aggregates involving butanol-water, water-water, and butanol-acetone/ethanol are suggested to play a crucial role in steering diffusivities in ternary solutions. Consequently, the proposed models exhibit exceptional agreement with experimental data, achieving R2 2 values of approximately 0.96, 0.95, and 0.98 for butanol flux in binary butanol-water and ternary solutions containing acetone and ethanol, respectively. Besides providing a more cohesive fit to the overall experimental permeation data, the usefulness of this approach lies in significantly simplifying model computations, thus easing the potential modeling of even more complex mixtures.