Well modeling in the multiscale finite volume method for subsurface flow simulation

A multiscale method for effective handling of wells (source/sink terms) in the simulation of multiphase flow and transport processes in heterogeneous porous media is developed. The approach extends the multiscale finite volume (MSFV) framework. Our multiscale well model allows for accurate reconstruction of the fine-scale pressure and velocity fields in the vicinity of wells. Accurate and computationally efficient modeling of complex wells is a prerequisite for field applications, and the ability to model wells within the MSFV framework makes it possible to solve large-scale heterogeneous problems of practical interest. Our approach consists of removal of the well singularity from the multiscale solution via a local change of variables and the computation of a smoothly varying background field instead. The well effects are computed using a separate basis function, which is superposed on the background solution to yield accurate representation of the flow field. The multiscale well treatment accounts for both types of well constraints: fixed pressure and fixed rate. The details of modeling wells with one or multiple completions ( perforations) are also presented. The accuracy of the method is assessed using a variety of examples including highly heterogeneous permeability fields.