Simulation of density-driven flow in fractured porous media

We study density-driven flow in a fractured porous medium in which the fractures are represented as manifolds of reduced dimensionality. Fractures are assumed to be thin regions of space filled with a porous material whose properties differ from those of the porous medium enclosing them. The interfaces separating the fractures from the embedding medium are assumed to be ideal. We consider two approaches: (i) the fractures have the same dimension, d, as the embedding medium and are said to be d-dimensional; (ii) the fractures are considered as (d-1)-dimensional manifolds, and the equations of density-driven flow are found by averaging the d-dimensional laws over the fracture width. We show that the second approach is a valid alternative to the first one. For this purpose, we perform numerical experiments using finite-volume discretization for both approaches. The results obtained by the two methods are in good agreement with each other.