Analysis of a Singular Hyperbolic System of Conservation Laws
نویسنده
چکیده
models the water flooding of an oil reservoir [6]. Water flooding involves the injection of water, which is immiscible with oil, into certain wells of the reservoir to force oil out at others. In this case, s = s(x, t) is the saturation of water (i.e., the volume fraction of water in the total fluid, 0 < s d 1 ), and g= g(s) is the particle velocity of the water. Consequently, since the total volumetric flow rate is fixed [2, 6, 71, the fraction of the flow rate associated with the water is sg(s) =f(s). In this problem, the fractional flow curve f(.) is nonconvex: f increases from 0 to
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