The role of sonic shocks between two- and three-phase states in porous media
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Flowof threefluids in porousmedia is governed by a systemof two conservation laws. Shock solutions are described by curves in state space, which is the saturation triangle of the fluids. We study a certain bifurcation locus of these curves, which is relevant for certain injection problems. Such structure arises, for instance, when water and gas are injected in a mature reservoir either to dislodge oil or to sequestrate CO2. The proof takes advantage of a certain wave curve to ensure that the waves in the flow are a rarefaction preceded by a shock, which is in turn preceded by a constant two-phase state (i.e., it lies at the boundary of the saturation triangle). For convex permeability models of Corey type, the analysis reveals further details, such as the number of possible two-phase states that correspond to the above mentioned shock, whatever the left state of the latter is within the saturation triangle.
Keywordsconservation laws Riemann problem umbilic point Petroleum Engineering flow in porous media permeability Corey model
Mathematical subject classificationPrimary: 35L65, 35L67 Secondary: 58J45, 76S05
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