Semianalytical Representation of Wells and Near-Well Flow Convergence in Numerical Reservoir Simulation

Abstract

This paper presents a new approach to compute wellbore pressures and near-well flow convergence in numerical reservoir simulation. In this semi-analytical approach, the solution of the flow problem in porous media is related to the boundaryelement formulations. To account for reservoir heterogeneity, solution domain is subdivided into internally homogeneous reservoir blocks, which may include wells, and the solutions are coupled with the requirement of flux and pressure continuity at the block boundaries. Knowing the boundary values of the solution domain, this formulation solves for the flux at the block boundaries and flux and pressure on wells. Knowing the flux boundary condition, this formulation also enables the solution of pressure at any point within the reservoir blocks. This feature of the solution serves the purposes of multiscale simulation of flow and transport in porous media. Although the solution can be applied on field scale, this paper focuses on the applications to near-well flow convergence region. When the solution is used for the near-well flow-convergence region, the required boundary values of the solution domain can be obtained from any standard solution techniques, including finitedifference simulation, by accounting for wells as source terms.