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

Summary 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, Ed, 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, 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 approximately one-half of those for sandstone. The wide variation is explained in terms of a simple pore model that relates Ed to aspect ratio. Introduction Changes in fluid saturations during multiphase displacements in porous media are accompanied by changes in interfacial surface area between the phases. Interfacial areas are directly related to surface energy and are fundamental to spontaneous-imbibition phenomena, to multiphase transport properties such as relative permeability, and to processes that involve mass transfer between phases (Haines 1930; Leverett 1941; Rapoport and Leas 1951; Payne 1953; Rootare and Prenzlow 1967; Hassanizadeh and Gray 1993; Reeves and Celia 1996; Kim et al. 1997; Alpak et al. 1999; Schaefer et al. 2000a, 2000b; Beliaev and Hassanizadeh 2001; Wan and Tokunaga 2002; Jain et al. 2003; Cheng et al. 2004). The relationship between work of displacement from capillary pressure data to changes in surface energy from direct measurements of surface areas has been reported in detail for drainage, imbibition, and secondary drainage for random packings of equal spheres (Morrow 1970a). The first measurements of relationships between work and increase in surface energy for porous rocks are reported here for primary drainage of a sandstone and a limestone.