Advances in computation of local problems for a flow-based upscaling in fractured reservoirs

In this article we present some numerical techniques to increase efficiency and applicability of a flow-based upscaling procedure used to solve single and multi-phase flows in naturally fractured reservoirs. These geological formations may be characterized by hundreds up to hundreds of thousands of fractures, ranging from small to medium scales, spreading all over the reservoir. In these scenarios numerical simulations using an explicit discretization of all fractures become rapidly unfeasible. The problem may be overcome by upscaling procedures. In this work we assume that the flow in the reservoir is simulated by using a corner-point grid completely unrelated to the fracture network. The presence of the latter is accounted for by a numerical upscaled procedure that employs an embedded discrete fracture model (EDFM). To characterize the scaled up problem, we consider a flow-based upscaling procedure where multiple sub-regions are used to derive transmissibilities, mean depths and pore volumes related to the degrees of freedom associated with fractures and rock matrix. An important aspect of the work with respect to others presented in the literature is the enhancement of the upscaling process by splitting the degrees of freedom associated with unconnected portions of the rock matrix. Numerical examples confirm the effectiveness of the proposed approach. We also compare two ways of setting up the boundary conditions of the local problems, that is a well known open issue, used to compute the upscaled transmissibility between cells. Though the experiments lead to a similar result, at the best of our knowledge, it is the first time that such a comparison is made for fractured reservoir.