Models and simulations of variable-density flow in fractured porous media

We develop a numerical technique for variable-density flow in fractured porous media, in which fractures are (d - 1)-dimensional manifolds, with d being the dimension of the ambient space. The PDEs of variable-density flow are firstly presented in the same form for both the fractures and the enclosing medium. Then, the equations defined in the fractures are averaged along the fracture width and formulated in (d - 1)-dimensions. The resulting PDEs are solved together with those defined in the enclosing medium, which maintain their d-dimensional form. The discretisation of the coupled system of d- and (d - 1)-dimensional PDEs follows a finite-volume method requiring a special construction of the discretisation grid, obtained by the algorithm explained in this paper. The accuracy of our technique is tested by comparing the produced results with those obtained in simulations in which the fractures maintain dimension d. In all simulations the fractured medium is three-dimensional.