Validation of the multiscale mixed finite-element method

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 due 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 sub-grid 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.