Abstract
Various production and injection processes with the attendant well controls represent the most important boundary conditions for a reservoir simulator. Therefore, it is of significant interest that the modeling of wells be done in an accurate and robust manner. Recent development of horizontal wells, maximum reservoir contact (MRC) wells, and smart wells further increase the demand for more comprehensive numerical treatment of wells. In mega-cell simulation, wells can be perforated in more than one hundred computational layers known as well cells whose layer productivity indices (LPI) can vary widely. Contributions of inflow from each of the well cells make up the total target well rates. Collectively, the well cells communicate through the wellbore pressure boundary condition. A converged time step means the material balance is satisfied for all grid cells plus all the well constraint equations active at that particular time step.
In this paper, the fully-implicit fully-coupled treatment of well constraint equations in the context of parallel mega cell reservoir simulation is described. In parallel computation utilizing several processors, grid cells are partitioned roughly evenly into these processing units. A single well can traverse several grid cells residing in multiple processors where information pertaining to well inflow must be gathered to construct the well constraint equations. These well equations are unstructured and are solved simultaneously with the multi-million grid cell material balance equations. The paper describes the well modeling equations and the numerical procedures for solving these equations in a fully-implicit fully-coupled manner. Furthermore, methods for treating fully implicit wells in several special simulation features such as local grid refinement, dual porosity dual permeability, and complex MRC wells with flow hydraulic calculation are also included. A number of examples on the advantages of applying the implicit well model as compared to the less rigorous well treatments are also discussed. In addition, for some mega-cell simulation cases, we compare the field-scale performance and parallel scalability of the methods.
