Impact of Three-Phase Relative Permeability Model on Recovery in Mixed Media: Miscibility, IFT, and Hysteresis Issues

This paper explores the importance of proper choice of three-phase relative permeability model for mixed-wet media, in contrast with commonly available water-wet rock models, that is, Stone! and Baker. The mixed-wet condition is likely the most frequently encountered wetting condition worldwide. Two formulations are available under these conditions. Blunt(3) developed a model that is somewhat complex to employ in simulators. In contrast, Jerauld(4-6) formulated a model that is relatively easier to implement. Jerauld's model incorporates the effect of interfacial tension (I FT) between phase pairs, as well as the ability to model mixed wettability. In this paper, to evaluate the effect of three-phase relative formulation, Stone I is used as a paradigm of strong wetting and serves as a base comparison for a mixed-wet formulation, namely, Jerauld's model. We illustrate the differences in performance prediction in three-phase oil relative permeability (km) for the same two-phase relative permeability data sets. We show how Jerauld's formulation can be used in commercial simulators, though in a limited fashion. Recovery prediction differences as well as the effect of gas miscibility on oil relative permeability to water (km.) are shown, Results show that three-phase k(ro) values, based on Jerauld's model, can be up to 2 times lower than those predicted by using Stone I and consequently the calculated recovery using Stone I model might be overestimated by 21% at immiscible condition. Gas miscibility affects gas-oil relative permeability and oil water relative permeability as well. Miscibility diminishes the oil-to-water relative permeability (k(row)), resulting in lower recovery. The recovery predicted using, Stone I model is overestimated by 13% at 80% miscibility with respect to Jerauld's model, if the effect of miscibility is only accounted For oil gas relative permeability. We show the importance of using an adequate three-phase model in mixed-wet system in addition to accounting for the effect of gas miscibility on oil water relative permeability.