Flexible grids for reservoir simulation

A flexible grid is made up of polygons, in two-dimensions, and polyhedra, in three-dimensions, whose shape and size vary from place to place in the reservoir. Existing finite-difference schemes for flexible grids lack the ability to model full, anisotropic and asymmetric permeability tensors. Such tensors may arise when fine-scale permeability distribution is upscaled to obtained gridblock-scale permeability distribution. Also, most of the existing schemes have to include regions of widely varying permeability in the same control-volume. It is shown in this work that such an approach may lead to significant numerical errors.; A control-volume based finite-difference scheme is proposed which uses control-volumes of uniform property with full, anisotropic and asymmetric permeability tensor. It uses triangles in two-dimensions and tetrahedra in three-dimensions to define the control volume boundaries. The transmissibility matrix is derived by satisfying potential continuity at specific points on control-volume boundaries and flux-continuity across these boundaries. The assumption of linear potential variation in the region associated with each node in each triangle/tetrahedron is used to obtain the transmissibility matrix.; There are various types of control-volumes with which this method can be used. Voronoi control volume (PEBI) and finite element control volume (CVFE) are two such examples. A modified finite element control volume called CVFE-BAG (boundary adapting grid) is defined in this work. CVFE-BAG grid is very flexible because it can perfectly align its control-volume boundaries with boundaries in the reservoir. Several grid construction procedures for two-dimensions and three-dimensions are presented in this work. It is shown that most of the finite-difference schemes can be put under a common framework of a connection-based approach which allows all these methods to be implemented in the same manner in any reservoir simulator.; Pressure distribution around a well is found to be more accurate with hexagonal Voronoi grids as compared with Cartesian grids, even for full and anisotropic tensors. Hexagonal Voronoi grids also show, in general, less grid orientation effects than Cartesian grids for highly adverse mobility ratio displacement processes. The flexibility of the proposed grid is expected to enhance the quality of reservoir simulation for nonconventional wells in geologically complex reservoirs.