Thermodynamic study of capillary pressure curves based on free energy minimization

This paper presents a new method for pore level network simulation of the distribution of two immiscible phases in a permeable medium. The method requires that the Helmholtz free energy of the system — the medium and the two phases contained within the pore space — be a minimum at all saturation states. We describe the method here and show some typical results from a computer algorithm that implements it. The results include (i) an explanation of the ‘scanning’ behaviour of capillary pressure curves based wholly on the free energy minimization, (ii) predictions of capillary pressure at arbitrary wetting states, including negative capillary pressures, and (iii) illustrations of how the minimized free energy changes along the scanning curves. The method also predicts the known dependency of the capillary pressure on the pore size distribution and interfacial tension. The current work is restricted to two‐dimensional networks, but the free energy minimization appears to be generalizable to three dimensions and to more than two fluid phases. Moreover, functions generated through the minimization, specifically contact areas between the medium surface and the phases, appear to have applications predicting other multiphase petrophysical properties.