A mathematical model for the fractionation of liquids with supercritical CO2 in a countercurrent packed column is presented. This model is based on the differential mass and energy balances over the height of the extractor, which are solved numerically. The phase behavior of the multicomponent systems of interest for this process is represented with the Peng-Robinson Equation of State. Volumetric and thermal properties of the fluids are also calculated with the PR-EOS. Transport properties are estimated applying suitable correlations. This model includes the coupled mass and heat transfer in the interface between the two fluid phases. Since the model includes the energy balance, it is possible to study the operation with a gradient of temperature over the height of the extractor. The model has been validated comparing the predictions with experimental data for the fractionation of edible oil mixtures and the separation of fish oil ethyl esters taken from the literature. The correlation between experimental and calculated results is reasonably good, and the model predicts correctly the trends of variation with the different operating and design parameters. (C) 2006 Elsevier B.V. All rights reserved.