Most existing upscaling methods attempt to evaluate effective permeabilities of coarse-scale gridblocks, so that the upscaled model locally reproduces the behavior of the fine-scale grid, under a set of boundary conditions. When applied to fractured reservoirs, this approach shows several drawbacks. First, it assumes the existence of a representative elementary volume (REV), which size is constrained by the practical needs for an efficient simulation. Yet, no REV exists for fractured systems which are characterized by a wide variety of fracture sizes. Second, the dynamic behavior of the model is unknown far from the applied boundary conditions. Third, this approach tends to underestimate the impact of steep pressure gradients that may occur between fracture and matrix media.

The presented method overcomes all three limitations by upscaling transmissibilities, so that the coarse-scale model preserves the same pressure response as the detailed geological model at a set of arbitrarily chosen observation points. A discrete fracture network and a corner-point grid are first jointly discretized using a dual approach (pipe network). Nodes of the pipe network represent either discrete fractures or matrix blocks. Pipes stand for matrix-to-matrix, fracture-to-fracture and matrix-to-fracture connections. Then, upgridding and upscaling are simultaneously performed, without imposing any boundary conditions: nodes are iteratively removed by applying electric simplifications (series, parallel, star-mesh transformations) until only the selected observation points remain. This process introduces new connections that may link nodes that were initially not connected, thus better modeling features such as super-K or large-scale fractures. This tends to convert a large sparse system into a smaller but fuller one; therefore parts of the network need to be lopped off before informing a flow simulator. Pipes holding the lowest transmissibilities are decimated and the remaining transmissibilities are updated accordingly in an optimization procedure. Flow simulation results obtained for several data sets on upscaled models are in good accordance with those obtained before upscaling, and show appreciable improvements compared to conventional structured local approaches.

You can access this article if you purchase or spend a download.