Title: Effective models of flow in highly heterogeneous fractured/vuggy porous media

Abstract:  The presence of vugs and fractures in porous media can significantly affect pressure and flow behavior of a fluid.

In this talk, I will present the effective models of flow in a porous medium including multi-scale fractures and  several vuggs of various spheroidal shapes.

The multiscale fractured porous medium is  an infinite set of self-similar double-porosity media. At each scale, the medium consists of a highly permeable network of connected channels and low-permeable blocks. The transition to the macroscale is performed by the means of two-scale homogenization technique.

The vuggy medium includes spheroidal fluid filled inclusions. The Stokes flow in the vug is coupled to Darcy’s law in the host matrix using the modified Beavers Joseph boundary condition for the curvy contact between vug and matrix. The pressure field and stream function inside and outside the vug is obtained analytically as a result of solution of harmonic and biharmonic equation inside and outside the vug.  The analytic form of equivalent permeability of one single vug is obtained in terms of Legendre polynomials. Then, the effective permeability of a vuggy medium including an arbitrary number of vuggs with different geometries is obtained.