A discrete-domain approach to three-phase hysteresis in porous media

Abstract

An inherent challenge with multiphase flow processes in porous media, such as water-alternate-gas invasions for oil recovery or CO 2 injection for geologic storage, is that fluid displacements are irreversible, that is, they are history-dependent and exhibit hysteresis (Spiteri & Juanes, 2006). Hysteresis can be rate-dependent or rate-independent. Here, we examine rate-independent hysteresis in three-phase systems based on an energy landscape exhibiting metastability and barriers. Thus, we approach fluid displacements quasi-statically as a series of small changes of pressure or saturation. This is a reasonable approximation for slow displacement at pore scale where capillary forces typically dominate over viscous forces and gravity (Hilfer & Øren, 1996). At darcy (or, core) scale, hysteresis in two-phase systems emerges as the difference between drainage and imbibition capillary pressure curves (P αβ (S β )-curves), where capillary pressure is the difference in phase pressures p between nonwetting (α) and wetting (β) phases (i.e., P αβ = p α − p β ), and S β is wetting-phase saturation. Collectively, the shape of P αβ (S β )-curves depends on porous structure, pore-scale fluid displacements, saturation history, and wetting state. Morrow (1970) interpreted P αβ (S β )-curves thermodynamically as a sequence of reversible and irreversible pore-scale fluid displacements, termed "isons" and "rheons," respectively, that describe transitions between capillary equilibrium states (i.e., local energy