Validation of the multiscale mixed finite‐element method
Mayur Pal, Sadok Lamine, Knut‐Andreas Lie, Stein Krogstad · International Journal for Numerical Methods in Fluids · 2014
SUMMARY Subsurface reservoirs generally have a complex description in terms of both geometry and geology. This poses a continuing challenge in modeling and simulation of petroleum reservoirs owing to variations of static and dynamic properties at different length scales. Multiscale methods constitute a promising approach that enables efficient simulation of geological models while retaining a level of detail in heterogeneity that would not be possible via conventional upscaling methods. Multiscale methods developed to solve coupled flow equations for reservoir simulation are based on a hierarchical strategy in which the pressure equation is solved on a coarsened grid and the transport equation is solved on the fine grid, and the two equations are treated as a decoupled system. In particular, the multiscale mixed finite‐element (MsMFE) method attempts to capture subgrid geological heterogeneity directly into the coarse‐scale equations via a set of numerically computed basis functions. These basis functions are able to capture the predominant multiscale information and are coupled through a global formulation to provide good approximation of the subsurface flow solution. In the literature, the general formulation of the MsMFE method for incompressible two‐phase and compressible three‐phase flow has mainly addressed problems with idealized flow physics. In this paper, we first outline a recent formulation that accounts for compressibility, gravity, and spatially dependent rock‐fluid parameters. Then, we validate the method by evaluating its computational efficiency and accuracy on a series of representative benchmark tests that have a high degree of realism with respect to flow physics, heterogeneity in the petrophysical models, and geometry/topology of the corner‐point grids. In particular, the MsMFE method is validated and compared against an industry‐standard fine‐scale solver. The fine‐scale flux, pressure, and saturation fields computed by the multiscale simulation show a noteworthy improvement in resolution and accuracy compared with coarse‐scale models. Copyright © 2014 John Wiley & Sons, Ltd.