The Flow of Fluids in Porous Media
نویسنده
چکیده
This lecture will outline the developments over the past two years of Todd Dupont and the author on problems of flow of fluids in porous media arising from petroleum reservoir engineering. Two specific problems will be discussed and a third mentioned. The first is the single-phase flow of a non-ideal gas. This flow can be described by a nonlinear parabolic equation. The second is the two-phase flow of water and oil. If the fluids are assumed incompressible (this is the more difficult situation mathematically) and immiscible, a degenerate nonlinear parabolic system in two dependent variables results. The time derivative of only one appears explicitly. The third problem comes from a so-called "beta factor" description of three-phase (oil, gas, water) flow. Again a very strongly nonlinear parabolic system is generated.
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