Modeling of organic solvent nanofiltration : a study of the parameters which affect permeation properties

This doctoral thesis is focused on understanding the transport mechanism of nanofiltration processes when a non-ideal mixture permeates through the membrane, with the ultimate vision of addressing a general modeling for nanofiltration industrial processes. Here, the comprehension of the properties which affect the permeation behavior in membrane separation processes is investigated. A study of the theories related with membrane separation processes has been done, as well as of the methods employed to describe the properties involved in the process. The pursued goal was successfully achieved by the use of the so-called “solution-diffusion with imperfections model”. The system chosen for the modeling consists of a PDMS membrane (polymer) industrially used for the separation of glycols (TEG, TEGDME or PEGDME) from ketones (MEK or DEK). In order to estimate the concentration inside the membrane, it was necessary to estimate the activities of the systems by the UNIFAC group contribution method, which demonstrated the non-ideality of the used systems. By combining the calculation of the activities with the Flory-Huggins-Staverman (FHS) solution theory applied for free-standing polymer swelling experiments, it was possible to investigate the dependence of the FHS interaction parameter with the change of solution concentration in ternary polymer–solvent–solvent systems. The presence of a second permeant induced variations in the interaction parameters when this is calculated by Hildebrand solubility parameters and by the FHS equation. The possible arrangement of ketone molecules inside the lattice is hindered by the presence of EGDME molecules. A simulation routine to model the permeation behavior of the nanofiltration experiments based on the solution-diffusion with imperfections model consisting of three different stages was done, where the different values involved were theoretically estimated and compared to experimental measurements. First, the estimation of self-diffusion coefficients of pure substances has been done by the use of the Dullien equation. As expected, higher self-diffusivities were obtained for smaller substances than those values obtained for bigger ones, as long as the substances in question present comparable activities. The low self-diffusivity found for the TEG has been attributed to the formation of hydrogen bonds between TEG molecules, which hinders the mobility and increases the viscosity. As a second stage in the developed simulation routine, tracer diffusivities were experimentally modeled by the use of the Vrentas & Duda diffusion theory and the Wesselingh & Bollen multicomponent diffusion model. For substances with similar activities, lower mobility and lesser possibilities of configuration inside the polymer lattice have been observed for bigger molecules than for smaller ones. The last simulation stage consisted of the estimation of thermodynamic diffusion coefficients by the use of Maxwell-Stefan friction factors. The concentration of the permeants inside the actual membrane has been estimated with the FHS equation under the conditions stated by the solution-diffusion model. The modeled permeation fluxes were directly compared with the experimental nanofiltration results in order to evaluate the quality of the simulation routine. Good correlations were found for all ketone/EGDME systems when both concentration and diffusion coefficients were estimated as previously described. Particularly, it is worth noticing the importance of a good estimation of the diffusion coefficient values and, even more, a reliable estimation of the actual concentration of the permeants inside the membrane.