Discontinuous boundary elements for steady-state fluid flow problems in discrete fracture networks

Modeling fluid flow in three-dimensional (3D) Discrete Fracture Networks (DFNs) is of relevance in many engineering applications, such as shale oil/gas production, geothermal energy extraction, nuclear waste disposal and CO2 sequestration. A new Boundary Element Method (BEM) technique with discontinuous quadratic elements, in conjunction with a parallel Domain Decomposition Method (DDM), is presented for the simulation of the steady-state fluid flow in DFNs, consisting of stochastically generated 3D planar fractures, arbitrarily oriented, and having differing hydraulic properties. Numerical examples characterized by DFNs of increasing complexity are proposed to show the accuracy and the efficiency of the presented technique, that provides good approximations of the fluid flow around domain interfaces, where the solution usually displays sharp gradients, like around intersections between traces (the segments originated by the intersection between two fractures), intersections between traces and fracture boundaries, or intersections between fractures and wellbores. The conjunction with a DDM approach is a promising strategy to speed up the computations, by also exploiting the advantages of parallel computing techniques. The technique is implemented in the code PyDFN3D, available at https://github.com/BinWang0213/PyDFN3D.