  We present a new model for two phase Darcy flows in fractured media, in which
fractures are modelled as submanifolds of codimension one with respect to the
surrounding domain (matrix). Fractures can act as drains or as barriers, since
pressure discontinuities at the matrix-fracture interfaces are permitted.
Additionally, a layer of damaged rock at the matrix-fracture interfaces is
accounted for. The numerical analysis is carried out in the general framework
of the Gradient Discretisation Method. Compactness techniques are used to
establish convergence results for a wide range of possible numerical schemes;
the existence of a solution for the two phase flow model is obtained as a
byproduct of the convergence analysis. A series of numerical experiments
conclude the paper, with a study of the influence of the damaged layer on the
numerical solution.
