Archive | 2019
Deformable Porous Medium Saturated by Three Immiscible Fluids
Abstract
A number of processes in civil, environmental, and hydrocarbon engineering involve the co-existence of three non-miscible fluids, typically water, a nonaqueous phase liquid (NAPL), e.g. a chlorinated solvent, oil, supercritical CO\\(_2\\), and a gas, e.g. air, methane, CO\\(_2\\) in gaseous phase. Immiscibility is accompanied by the presence of a meniscus and endows each fluid with its own pressure. The relative wettability characteristics of the three fluids are complex and depend on the physical properties and chemical content of the fluids and on the mineralogy of the rock. In water wet rocks, water is more wetting than oil which is more wetting than gas, because the water–oil contact angle is smaller than 90\\(^{\\circ }\\); thus, water keeps preferentially in contact with the rock matrix and oil tends to spread spontaneously. As a consequence, small pores are mostly filled by water, oil may invade intermediate pores, and gas tends to occupy the middle of large pores only. The presence of three immiscible fluid phases implies the formulation of the capillary pressures and relative permeabilities to be significantly distinct from the two-fluid phase context. Moreover, specific issues, like the regime of the equations of mass conservation, deserve attention.