This paper deals with a mathematical model for oil filtration in a porous
medium and its self-similar and traveling wave regimes. The model consists of
the equation for conservation mass and dependencies for porosity, permeability,
and oil density on pressure. The oil viscosity is considered to be the
experimentally expired parabolic relationship on pressure. To close the model,
two types of Darcy law are used: the classic one and the dynamic one describing
the relaxation processes during filtration. In the former case, self-similar
solutions are studied, while in the latter case, traveling wave solutions are
the focus. Using the invariant solutions, the initial model is reduced to the
nonlinear ordinary differential equations possessing the trajectories vanishing
at infinity and representing the moving liquid fronts in porous media. To
approximate these solutions, we elaborate the semi-analytic procedure based on
modified Pade approximants. In fact, we calculate sequentially Pade
approximants up to 3d order for a two-point boundary value problem on the
semi-infinite domain. A good agreement of evaluated Pade approximants and
numerical solutions is observed. The approach provides relatively simple
quasi-rational expressions of solutions and can be easily adapted for other
types of model’s nonlinearity.

Dieser Artikel untersucht Zeitreisen und deren Auswirkungen.

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