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

摘要

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 vs. 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, relating the area under a capillary pressure curve to the 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, E_d, depends on the increase in surface area that accompanies drainage. Surface areas of nonwetting phase/ solid and nonwetting phase/wetting phase have been determined through displacement of a colored low-viscosity liquid resin that 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, E_d 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 E_d for the tested carbonate were approximately one-half of those for sandstone. The wide variation is explained in terms of a simple pore model that relates E_d to aspect ratio.