Numerical Simulation of Three-dimensional Complex Fracture Geometries Using an Unstructured Voronoi Mesh

To date, most numerical simulators developed to simulate production from unconventional gas reservoirs focus on two-dimensional (2d) representations of geological properties. Fracture geometry is, however, highly uncertain and three-dimensional models would enable more robust representations while considering gravity effects. In this paper, a Discrete Fracture Model (DFM) of 3d complex fracture geometries is developed where unstructured PEBI grids are used to discretize flow equations. The mesh generation algorithm, implemented in 3d space, is based on the equilibrium state of forces in a truss system. Each fracture is modeled as a 2d plane with an arbitrary orientation and shape. Nodes along the fracture plane are populated uniformly while the proposed dynamic force-based model is applied in the matrix region. A distance function is developed to assist node population in the matrix region. Fractures are regarded as bounded plane-constraints and the distance function is expressed in terms of geometrical information from nodes in the matrix and fracture planes in 3d space. Assuming isotropic media, the generated mesh guarantees local orthogonality, and two-point flux approximations (TPFA) are used in the numerical discretization scheme. Hydraulic and induced fractures and their intersections are accounted for explicitly without invoking transformations. A sensitivity study is performed to investigate the effect of grid size in regards to embedded fractures and optimal node density to balance accuracy and efficiency. The fully 3d model is validated against results from a commercial simulator using a synthetic case. Inclusion of gravity is shown to have a significant impact on gas and water production rates. In summary, the proposed approach enables modeling complex fractures in fully 3d space using an unstructured Voronoi mesh with gravity effects and provides a better understanding of two-phase systems representing recovery from fractured unconventional gas reservoirs.