The role of capillary pumping on the course of cleaning porous materials containing liquid contaminants using supercritical fluids was investigated numerically. As a specific process to be modelled, cleaning of porous membranes, contaminated with soybean oil, using supercritical carbon dioxide as the cleaning fluid (solvent) was considered. A 3D pore-network model, developed as an extension of a 2D drying model, was used for performing pore scale simulations. The influence of various process parameters, including the coordination number of the pore network, the computational domain size, and the external flow mass transfer resistance, on the strength of the capillary pumping effect was investigated. The capillary pumping effect increases with increasing domain size and decreasing external flow mass transfer resistance. For low coordination numbers of the pore network, the capillary pumping effect is not noticeable at macro scale, while for high coordination numbers, the opposite trend is observed – capillary pumping may influence the process at macro scale. In the investigated system, the coordination number of the pore network seems to be low, as no capillary pumping effects were observed at macro scale during experimental investigation and macro-scale modelling of the membrane cleaning process.