Modeling of diffusion in complex fractured porous media by using hierarchical material properties

The variable length scales of fractures and the heterogeneity of the surrounding porous rock impose high computational costs and excessive mesh refinement in fractured porous media modeling. To overcome these challenges, we utilize the hierarchical finite element method (Hi-FEM) that has been previously developed to model the electric potentials in complex geologic environments. By employing the hierarchical basis functions in the finite element analysis, the Hi-FEM enables to represent the material properties on each dimensional component of a 3D unstructured tetrahedral mesh and inherently allow the fracture-rock interactions. Here, the application of the Hi-FEM is extended for the physics of transient fluid flow and heat conduction. The diffusion equation is solved in the Laplace domain and the time-domain solutions are obtained by using the numerical inverse Laplace transform. We consider a set of benchmark models to test the Hi-FEMs accuracy and basin-scale rock mass models with embedded complex fracture networks to evaluate its robustness and computational performance. Results show that the Hi-FEM is computationally economical and numerically robust even for basin-scale simulations without the need of coupling or transfer mechanism. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.