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Multiscale method for simulating two and three-phase flow in porous media


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 transport equation is solved on the fine grid as a decoupled system. The multiscale mixed finite-element (MsMFE) method attempts to capture sub-grid geological heterogeneity directly into the coarse-scale via mathematical basis functions. These basis functions are able to capture important 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 present a new formulation that accounts for
compressibility, gravity, and spatially-dependent capillary and relative-permeability effects.

We evaluate the computational efficiency and accuracy of the method by reporting the result of series of representative benchmark tests that have a high degree of realism with respect to flow physics, heterogeneity in petrophysical model, and
geometry/topology of the corner-point grids. In particular, the MsMFE method is validated and compared against Shell's in-house simulator MoReS. 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.


Academic chapter/article/Conference paper





  • Netherlands
  • SINTEF Digital / Mathematics and Cybernetics




Curran Associates, Inc.


SPE reservoir simulation symposium 2013 : The Woodlands, Texas, USA, 18-20 February 2013




1283 - 1296

View this publication at Cristin