Numerical simulation of water injection in fractured media using the discrete-fracture model and the Galerkin method

Numerical simulation of water injection in discrete fractured media with capillary pressure is a challenge. Dual-porosity models, in view of their strength and simplicity, can be used mainly for sugar-cube representation of fractured media. In such a representation, the transfer function between the fracture and the matrix block can be calculated readily for water-wet media. For a mixed-wet system, the evaluation of the transfer function becomes complicated because of the effect of gravity. In this work, we use a discrete-fracture model in which the fractures are discretized as 1D entities to account for fracture thickness by an integral form of the flow equations. This simple step greatly improves the numerical solution. Then, the discrete-fracture model is implemented using a Galerkin finite-element method. The robustness and the accuracy of the approach are shown through several examples. First, we consider a single fracture in a rock matrix and compare the results of the discrete-fracture model with a single-porosity model. Then, we use the discrete-fracture model in more complex configurations. Numerical simulations are carried out in water-wet media as well as in mixed-wet media to study the effect of matrix and fracture capillary pressures.