On the Homogenization of Geological Fissured Systems With Curved non-periodic Cracks

Abstract

We analyze the steady fluid flow in a porous medium containing a network of thin fissures i.e. width $\mathcal{O}(\epsilon )$, where all the cracks are generated by the rigid translation of a continuous piecewise $C^1$ functions in a fixed direction. The phenomenon is modeled in mixed variational formulation, using the stationary Darcy's law and setting coefficients of low resistance $\mathcal{O}(\epsilon )$ on the network. The singularities are removed performing asymptotic analysis as $\epsilon \to 0$ which yields an analogous system hosting only tangential flow in the fissures. Finally the fissures are collapsed into two dimensional manifolds.

24 pages, 4 figures

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• The asymptotic analysis of a Darcy-Stokes system coupled through a curved interface
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• On the Construction of Geometric Parameters for Preferential Fluid Flow Information in Fissured Media