Numerical modeling of fluid flow through multiscale fractured-porous media by quadtrees

Abstract

A multiscale fractured-porous medium has several hierarchical levels of heterogeneity and consists of a connected network of fractures and a periodic system of low permeable blocks. Each of them also consists of smaller fractures and smaller blocks. Repeating this procedure n times, we obtain a fractured-porous medium with n scales. Numerical simulation of fluid flow in such a medium is impossible due to the need to use a very fine numerical grid. To reduce the number of numerical cells, we suggest using irregular grids based on quadtree technology. We simulated numerically an example of flow in a four-scale medium and compared it with the results obtained using regular grids, as well as with the averaged process model. We have introduced a quantitative criterion that enables us to identify which cells should be refined and which should not. This gave us the opportunity to formalize the procedure for building a quadtree and embed it in the Basilisk platform.