Asymptotic Analysis of a Nonlinear Parabolic Problem Modelling Miscible Compressible Displacement in Porous Media

Abstract

We study the asymptotic behavior, with respect to high Peclet numbers, of a model describing a compressible and miscible displacement in a porous medium. The transport of mass is then described by a nonlinear, fully coupled and degenerate parabolic system. Using non-classical estimates and renormalization tools, we prove existence of relevant weak solutions for the limit problem. Mathematics Subject Classification (2000). 35K60, 35K65, 35B40, 76S05, 35K57.

Partial regularity for an elliptic-parabolic system modeling miscible fluid flows in porous media

“…Amirat and Ziani [1] studied the asymptotic behavior of the weak solution as m goes to 0 and they proved an existence assertion when m = 0 and N = 2, or 3. Also see [6] for a related result. Existence with measure data was considered in [11].…”

“…Let (p, u) be a weak solution to (1)- (6). A point z 0 ∈ Ω T is called a regular point for the weak solution if for each > 1 there is a r > 0 such that…”

“…u(x, 0) = u 0 (x) on Ω, (6) where Ω T = Ω × (0, T ) and n is the unit outward normal to ∂Ω. This problem can be proposed as a mathematical model for the single-phase miscible displacement of one incompressible fluid by another in a porous medium [1,2,4,10,13].…”

Two-Component Two-Compressible Flow in a Porous Medium

“…This approach is also used in [8,9] to treat a homogenization problem of immiscible compressible water-gas flow in porous media. For miscible and compressible flow, we refer to [10,11] for more details.…”

Study of degenerate parabolic system modeling the hydrogen displacement in a nuclear waste repository

“…This approach is also used in [2,3] to treat a homogenization problem of immiscible compressible water-gas flow in porous media. For miscible and compressible flow, we refer to [9,10] for more details.…”