A mathematical model for mass transfer in hydrophobic pervaporation for organic compounds separation from aqueous solutions

In this study, a numerical predictive model was developed based on the solution–diffusion theory to describe the mass transfer of the pervaporation process through the PDMS membrane taking into account fluxes coupling. The Flory–Huggins model was used to predict equilibrium sorption of ethanol and water into the PDMS membrane. The transport of penetrants through the membrane was described with generalized Fick’s law which is able to calculate the mass fluxes and selectivities as well as the concentration profile of components inside the membrane. Three modeling cases were considered: (I) constant diffusion coefficient inside the membrane, (II) concentration dependent diffusion coefficient and (III) concentration and temperature dependent diffusion coefficient. For estimating the diffusion coefficients of penetrants through the membrane, the Duda’s free volume theory was applied. The resulting nonlinear transport equations were solved simultaneously by formulating the weak form Galerkin finite element method. The model was then validated using the experimental data obtained from the pervaporative separation of ethanol from aqueous solutions. Finally, the effect of operating parameters such as feed concentration and temperature on the permeation flux and penetrant selectivities were investigated via both the model prediction and experiments. The results showed that the penetrant diffusion coefficient dependencies on the component concentrations must be taken into account.

► A numerical model was developed to describe the mass transfer of the pervaporation.
► The nonlinear transport equations were solved by finite element method.
► The concentration and temperature profiles through the membrane were predicted.
► The model enables to predict the flux and selectivity through the membrane.
► The concentration dependency of diffusion coefficient must be taken into account.