Macroscopic properties of fractured porous media

The macroscopic properties of fractured porous media locally governed by a Laplace equation are determined by several methods. The first one consists in discretizing the porous medium and the fractures and in solving the Laplace equation in the discretized structure. The other methods consist in successive upscalings. The first upscaling replaces the porous medium by a continuum with a given transport property. The second upscaling replaces the fractures by surfaces with equivalent properties. The results of the various methods give very close results. They suggest a simple approximation which is successful when the properties of the fluid and of the continuous porous medium are not too different.