Single Phase Flow in Partially Fissured Media

Totally ssured media in which the individual cells are isolated by the ssure system are eeectively described by double porosity models with microstructure. Such models contain the geometry of the individual cells in the medium and the ux across their interface with the ssure system which surrounds them. We extend these results to a dual-permeability model which accounts for the secondary ux arising from direct cell-to-cell diiusion within the solid matrix. Homogenization techniques are used to construct a new macroscopic model for the ow of a single phase compressible uid through a partially ssured medium from an exact but highly singular microscopic model, and it is shown that this macroscopic model is mathematically well posed. Preliminary numerical experiments illustrate diierences in the behaviour of solutions to the partially ssured from that of the totally ssured case.