Grid Optimization to Improve Orthogonality of Two-point Flux Approximation for Unstructured 3D Fractured Reservoirs

Today's geological models are increasingly complex. The use of unstructured grids is an efficient way to account for this complexity especially when dealing with large network of fractures and faults. Flux based approximations are commonly used in reservoir simulation community to discretize the flow equations. The two-point flux approximation (TPFA) is the simplest and the most robust discretization technique. Application of TPFA requires an orthogonal grid. When applied to an unstructured model, Perpendicular Bisector (PEBI) grids are usually used as they are orthogonal by construction. But the construction of PEBI grids can become challenging for fully 3D models containing a large number of fractures and faults. In this work we propose to use an unstructured grid which matches exactly all discrete features (fractures and faults) but may not be orthogonal. The objective is to relax the orthogonality criteria to simplify the grid generation step and to deal with the orthogonality at the flux approximation step. Typical discretization techniques for nonorthogonal grids are based on multiple-point flux approximation (MPFA) where more than two pressure points are used to evaluate the flux. Although substantial progress has been made in improving MPFA, they remain more complex and less robust than TPFA. In this work we present a simple methodology to apply a TPFA to unstructured nonorthogonal grids. The idea is to determine the location of the pressure node inside each control-volume to make the connections with the surrounding cells as orthogonal as possible. Although it is not always possible to make all connections perfectly orthogonal, this optimization procedure improves systematically the grid quality. In addition, this purely geometrical optimization is done at the preprocessing level and does not require any flow information and can be used with any connectivity based flow solver.