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

Fernando A. Morales

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arXiv · 1312.4033

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

Fernando A. Morales

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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 $\epsilon \rightarrow 0$ which yields an analogous system hosting only tangential flow in the fissures. Finally the fissures are collapsed into two dimensional manifolds.

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Fernando A. Morales. 2013-12-14. On the Homogenization of Geological Fissured Systems With Curved non-periodic Cracks. https://arxiv.org/abs/1312.4033

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