A quasi steady state method for solving transient Darcy flow in complex 3D fractured networks accounting for matrix to fracture flow

In this paper, we generalize this approach in order to account for fluxes from matrix to fractures. The quasi steady state hypothesis at the fracture level is still kept. Then, we show that in the case of well separated time scales between matrix and fractures, the preceding model needs only to be slightly modified in order to incorporate these fluxes. The additional knowledge of the so-called matrix to fracture transfer function allows to modify the mass matrix that becomes a time convolution operator. This is reminiscent of existing space averaged transient dual porosity models.