Convergence of a dual-porosity model for two-phase flow in fractured reservoirs

A dual-porosity model describing two-phase, incompressible, immiscible flows in a fractured reservoir is considered. Indeed, relations among fracture mobilities, fracture capillary pressure, matrix mobilities, and matrix capillary pressure of the model are mainly concerned. Roughly speaking, proper relations for these functions are (1) Fracture mobilities go to zero slower than matrix mobilities as fracture and matrix saturations go to their limits, (2) Fracture mobilities times derivative of fracture capillary pressure and matrix mobilities times derivative of matrix capillary presure are both integrable functions. Galerkin's method is used to study this problem. Under above two conditions, convergence of discretized solutions obtained by Galerkin's method is shown by using compactness and monotonicity methods. Uniqueness of solutions is studied by a duality argument.