Efficiency of Conversion of Work of Drainage to Surface Energy for Sandstone and Carbonate

Abstract

Abstract The increase in surface energy resulting from drainage of a wetting phase from a porous medium is often equated to the work of displacement determined from the area under its capillary pressure curve. However, capillary pressure versus saturation relationships are not reversible and do not represent quasistatic displacement. The increase in surface energy is less than the work done because of inherent capillary instabilities that are the basic cause of capillary pressure hysteresis. Nevertheless, identification of the area under a capillary pressure curve with thermodynamic work of displacement can be justified by interpreting the curve as a series of alternating isons (reversible displacements) and rheons (spontaneous redistribution at constant saturation). The efficiency of conversion of work to surface energy, Ed, depends on the increase in surface area that accompanies drainage. Surface areas of non-wetting phase/solid and non-wetting phase/wetting phase have been determined through displacement of a colored low-viscosity liquid resin which can be solidified so that thin sections reveal the distribution of phases and surfaces within the pore space of the rock. Two dimensional images obtained from thin sections were analyzed using stereology to obtain estimates of saturations and interfacial areas in three dimensions. For drainage of Berea sandstone to 20% wetting phase saturation, Ed was 36% which was less than one half of the efficiency of 85% for the same range of change in saturation determined previously for random packings of equal spheres. Values of Ed for the tested carbonate were about one half of those for sandstone. The wide variation is explained in terms of a simple pore model that relates Ed to aspect ratio.