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 of width $\mathcal{O}(\epsilon)$, generated by the rigid translation of continuous piecewise $C^{1}$ functions in a fixed direction. The phenomenon is modeled in mixed variational formulation, using the stationary Darcy's law and coefficients of low resistance $\mathcal{O}(\epsilon)$ on the network. The singularities are removed by 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.

Keywords

• Fissured media
• tangential flow
• interface geometry
• coupled Darcy flow system
• upscaling
• mixed formulation