A Discretization-Independent Distributed Well Model

Abstract

Summary In this paper, we present a new well model for reservoir simulation. The proposed well model relates the volumetric flow rate and the bottomhole pressure (BHP) of the well to the reservoir pressure through a spatially distributed source term that is independent of the numerical method and the discrete mesh used to solve the flow problem. This is in contrast to the widely used Peaceman–type well models, which are inherently tied to a particular numerical discretization by the definition of an equivalent well radius. The proposed distributed well model does not require the calculation of an equivalent well radius. Hence, it can be readily applied to finite–difference, finite–volume (FV), or finite–element discretizations on arbitrarily unstructured meshes, which also makes it an attractive option for mesh–adaptation schemes. The new well model is demonstrated on a steady-state single-phase flow problem and an unsteady two-phase flow problem, using a conventional FV method and a high–order discontinuous Galerkin (DG) method. The distributed well model produces error–convergence behaviors that are very similar to the Peaceman well model on uniform structured meshes, but its applicability to high–order discretizations and mesh–adaptation schemes allows for higher convergence rates and more cost-efficient solutions, especially on adapted unstructured meshes.