Abstract
This work consists of two parts. In the first part, we present new methods for generating unstructured polyhedral grids that align to prescribed geometric objects. Control-point alignment of cell centroids is introduced to accurately represent horizontal and multilateral wells, but can also be used to create volumetric representations of fracture networks. Boundary alignment of cell faces is introduced to accurately preserve geological features such as layers, fractures, faults, and/or pinchouts. Prescribed geometric objects will often intersect each other. To handle such cases, we propose a conflict-point handling scheme that creates conforming cells even at intersections. We also discuss how to generalize this method to 3D. Here, our method honors control-point alignment of cell centroids and boundary alignment of cell faces away from object intersections.
The predominant discretization method for multiphase flow in reservoir simulation is the two-point flux-approximation (TPFA) method. This finite-volume method is mass conservative, but only conditionally consistent and hence susceptible to grid-orientation effects. In the second part of the paper, we review a series of consistent methods and compare and contrast these methods both with respect to accuracy and monotonicity. Our comparisons include a multipoint flux-approximation (MPFA-O) method, the nonlinear TPFA method, mimetic methods, and the more recent virtual element methods. To limit the discussion, we focus on incompressible flow, for which we study the effects of deformed cell geometries, anisotropic permeability, and robustness with respect to various approaches to grid near wells and adapt it to lower-dimensional objects like faults and fractures.
