The process of cleaning microfiltration membranes contaminated with soybean oil, using pure supercritical carbon dioxide as cleaning fluid, was considered. A mathematical model of the process was developed, implemented into CFD software and validated using experimental results. The mathematical model is based on the Volume of Fluid approach and includes porous zone treatment, variable fluid phase composition due to mutual solubility of the contaminant and the solvent, as well as phase transition. The developed model was implemented into the OpenFOAM toolbox and validated using experimental results. The results of CFD simulations using the mathematical model show a good agreement with experimental results. CFD simulations were performed in order to analyze the effect of solvent flow rate and the effect of oil phase swelling on the course of the process. The mass transfer mechanisms were identified. The developed model is an efficient tool for process optimization, scale-up, and high-pressure equipment design.