Mathematical modeling of the membrane separation of nutmeg essential oil and dense CO2

This work presents the application of a mathematical model to describe the membrane separation of nutmeg essential oil from supercritical CO2 mixtures. The phenomenological analysis led to a mathematical description of the process based on the irreversible thermodynamics approach. The carbon dioxide permeate flux was modeled by associating the dependence of flux on the transmembrane pressure gradient to a mathematical equation which represents the concentration polarization phenomenon at the membrane surface. The thickness of the polarization layer was employed as fitting parameter, and the value which best-fitted the experimental data was 400 μm. The experimental observation of convective solvent transport mechanisms in the case of a such a dense membrane was related to the plasticization effect associated to an increase in the polymer chain mobility of the membrane due to the presence of dense CO2. The essential oil permeation was modeled by relating the proportionality between the essential oil permeate flux and the solvent permeate flux to the logarithmic mean concentration difference between the essential oil concentration in the feed and permeate sides.