In this study, a predictive model was developed to describe the process of separation of volatile organic compounds. The model was based on solution–diffusion theory and computational fluid dynamics (CFD) was applied to model the pervaporation process for the separation of styrene–water in a PDMS membrane. Florry–Huggins-FV, Florry–Huggins and UNIFAC models were adopted to predict the equilibrium adsorption of styrene and water into the PDMS membrane and the results were compared. For the penetration, Duda's and Fujita's free volume theories were compared to estimate the diffusivity of penetration through the membrane. The conservation equations including the continuity and the momentum balance equations in membrane modulus were solved simultaneously using a finite element scheme. The studied system includes styrene–water solution which is adsorbed on a polydimethylsiloxane (PDMS, polydimethylsiloxane) nonporous polymer membrane. In this mass transfer model, diffusion coefficients through the membrane were taken into account as a function of concentration and they were estimated based on free volume theory. The proposed model was validated using experimental data obtained from pervaporation tests. The simulation results for various feed concentrations, feed temperatures and membrane thickness were in satisfactory agreement with experimental data. The CFD results showed that both the permeation flux and the styrene enrichment factor increased with the increase in concentration of styrene in the feed. By increasing membrane thickness the permeation flux decreased while the enrichment factor increased. The developed model can predict well the mass transfer process occurring in the feed and the membrane.