Abstract
An abstract result is proved for the convergence of Adomian decomposition method for partial differential equations that model porous medium equation. Moreover, we prove that this decomposition scheme applied to a porous medium equation arising in instability phenomena in double phase flow through porous media is convergent in a suitable Hilbert space. Furthermore, this technique is utilized to find closed-form solutions for the problem under consideration.
Highlights
The oil-water movement in a porous medium is an important problem of petroleum technology and water hydrology (Scheidegger [1])
Scheidegger [1] analyzed the statistical behavior of instability in a displacement process through a homogeneous porous medium with capillary pressure and pressure-dependent phase densities
We investigate the applicability of Adomian decomposition method to the nonlinear partial differential equation arising in instability phenomena in double phase flow through porous media in order to obtain the analytical solution
Summary
The oil-water movement in a porous medium is an important problem of petroleum technology and water hydrology (Scheidegger [1]). Scheidegger [1] analyzed the statistical behavior of instability in a displacement process through a homogeneous porous medium with capillary pressure and pressure-dependent phase densities. This problem has great importance for oil production in petroleum technology. Venkateswar [5] has discussed on the flow of immiscible liquids in a heterogeneous porous medium with capillary pressure and connate water saturation. We investigate the applicability of Adomian decomposition method to the nonlinear partial differential equation arising in instability phenomena in double phase flow through porous media in order to obtain the analytical solution.
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