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FINITE ANALYTIC METHOD FOR 2D FLUID FLOW IN POROUS MEDIA WITH PERMEABILITY IN TENSOR FORM

Volumen 19, Edición 6, 2016, pp. 539-555
DOI: 10.1615/JPorMedia.v19.i6.50
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SINOPSIS

The finite analytic method is developed to solve the two-dimensional fluid flow in heterogeneous porous media with permeability in tensor form. A local nodal analytic solution around the grid node joining the different permeability areas is derived. In general, the pressure follows the power-law distribution with gradient divergence as approaching the grid node, rather than having piecewise linear distribution. This nodal solution is employed to construct a finite analytic numerical scheme with a discretized boundary condition. It is interesting that the velocity on the boundary exhibits the power-law divergence behaviors in the case of permeability in tensor form because of the crossflow effects, which is different from that of the scalar permeability. Numerical examples show that, only with 2 × 2 or 3 × 3 subdivisions, our scheme can provide rather accurate solutions, and the convergence rate of the scheme is independent of the permeability heterogeneity, while a dramatic increase of the refinement ratio is needed when using the traditional method, especially for strong heterogeneous porous medium.

CITADO POR
  1. Wang Min, Wang Yan-Feng, Liu Zhi-Feng, Wang Xiao-Hong, Wang Yong, Cao Wei-Dong, Finite analytic numerical method for three-dimensional quasi-laplace equation with conductivity in tensor form, Numerical Methods for Partial Differential Equations, 33, 5, 2017. Crossref

  2. Cao Zhi-Wei, Liu Zhi-Feng, Wang Yi-Zhou, Wang Xiao-Hong, Noetinger Benoît, Power series analytical solution for 2D quasi-Laplace equation with piecewise constant conductivities, Communications in Nonlinear Science and Numerical Simulation, 62, 2018. Crossref

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