Abstract
A system of evolutionary partial differential equations (PDEs) describing the two-phase flow of immiscible fluids in one dimension is developed. In this formulation, the wetting and nonwetting phases are treated to be incompressible and compressible, respectively. This treatment is indeed necessary when a compressible nonwetting phase is subjected to compression during confinement. The system of PDEs consists of an evolution equation for the wetting-phase saturation and an evolution equation for the pressure in the nonwetting phase. This system is applied to the problem of unsaturated flows to assess the importance of air-phase compressibility. For those situations where air can move freely within the medium and ultimately escape through the boundaries without experiencing any compression, it is then reasonable to treat air as an incompressible phase so that the total volumetric flux becomes spatially invariant. As shown by Morel-Seytoux and Billica, this leads to a coupled evolution equation for water saturation and an integral expression for total volumetric flux. In the event that an air phase is subjected to confinement in some manner, the total volumetric flux cannot be assumed to be spatially invariant as did Morel-Seytouxet al.
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