Several experimental studies revealed multiphase behavior that is not accounted for in standard models. In heterogeneous oil-water laboratory experiments, Illangasekare et al. [1992] observed lateral spreading of a plume when it reached the boundary between finer and coarser layers. The plume would not penetrate the fine layer until it attained a sufficient ponded depth, an apparent result of different capillary pressure-saturation relationships in the two sands. The oil preferentially filled the coarse lens and developed a sharp interface with the fine sand, in contrast to simulations with constitutive models used in typical numerical codes, which would show it diffusing through. Oldenburg and Pruess [1993] developed a numerical model using harmonic-average relative conductivities at capillary interfaces to avoid this type of diffusion caused by standard upstream weighting. With detailed cross-sectional characterization of saturations in an oil body floating on the water table at a spill site, Essaid et al. [1993] similarly found that migration of oil at the capillary fringe was not reproduced in simulations. To match the observed asymmetrical oil body with high saturation at its center, it was necessary to include hysteresis with oil entrapment in the model used, as well as heterogeneity to account for observed fingering. Lenhard et al. [1991] used an empirical correlation to obtain trapped saturation from imbibition residual nonwetting-phase saturation and other standard data, developing a hysteretic model that compared better to experiments than did a nonhysteretic model. This model included contact angles and irregular pore geometry to incorporate entrapment. Subsequent three-phase experiments [ Lenhard, 1992; Lenhard et al., 1993] extended the case for inclusion of hysteresis in models.
Kaluarachchi and Parker [1992] modeled effects of oil entrapment on three-phase relative permeability-saturation-capillary pressure relations. A non-hysteretic model, using data on air-water saturation-capillary pressure, residual oil saturation, and ratios of water surface tension to oil surface tension and to water-oil interfacial tension, proved to be more efficient than a full hysteretic model.
Seeking to predict capillary pressure-saturation curves from interfacial tensions, Demond and Roberts [1991] surprisingly found that residual water saturation increased as interfacial tension decreased. They explained this on the basis of the range of pore sizes, with decreasing interfacial tension leading to an increased drainage rate and hence to increased channeling and bypassing of pores. The authors found that capillary pressure had to be defined as a function of effective saturation, potentially a difficult matter without possibly unjustified assumptions about residual water saturation.
Accurate representation of these capillarity-related phenomena is important for modeling in appropriate situations, as evidence mounts that models should account for hysteresis in particular. As a practical matter, these phenomena introduce additional model complications of a modular nature involving evaluation of coefficients in equations. Unlike nonequilibrium phase behavior, they do not affect the basic structure, such as the set of primary variables.