HR: 1340h
AN: H33H-1733    [Abstracts]
TI: A Variational Multiscale – High-Resolution Method for the Simulation of Unstable Multiphase Flow in Heterogeneous Formations
AU: Dub, F
EM: fxdub@mit.edu
AF: Massachusetts Institute of Technology, Civil and Environmental Engineering 77 Massachusetts Ave, Room 48-319, Cambridge, MA 02139, United States
AU: * Juanes, R
EM: juanes@mit.edu
AF: Massachusetts Institute of Technology, Civil and Environmental Engineering 77 Massachusetts Ave, Room 48-319, Cambridge, MA 02139, United States
AB: Multiscale phenomena are ubiquitous to flow and transport in porous media. They manifest themselves through at least the following three facets: (1) effective parameters in the governing equations are scale dependent; (2) some features of the flow (especially sharp fronts and boundary layers) cannot be resolved on practical computational grids; and (3) dominant physical processes may be different at different scales. Numerical methods should therefore reflect the multiscale character of the solution. In this paper, we concentrate on the development of simulation techniques that account for the heterogeneity present in realistic reservoirs, and have the ability to capture (on coarse grids) the detailed pattern of unstable flows due to viscous fingering and channeling. We express the governing equations of multiphase flow as a pressure equation and a saturation equation. Both are nonlinear but are only weakly coupled. The pressure equation is elliptic, while the saturation equation is quasi-hyperbolic. Traditionally, the large degree of heterogeneity in the coefficients of the pressure equation has been tackled by upscaling the fine-scale properties to coarse-scale effective coefficients. Here, we avoid upscaling and propose a variational multiscale (VMS) method that splits the original problem is (rigorously) into a coarse-scale problem and a subgrid-scale problem. The framework is very flexible with respect to how each of these problems is approximated. The proposed VMS method employs a low-order mixed finite element method at the coarse scale, and a finite volume method at the subgrid scale. The method is therefore locally conservative at both the coarse and fine scales. We pay special attention to the definition of the local boundary conditions for the subgrid problems. In particular, we develop a well model, which accounts for subgrid heterogeneity and radial flow regime in a consistent fashion, without compromising the local mass conservation property. The saturation equation is then solved on the fine scale by a high-resolution explicit finite difference method that captures fingering and channeling when a low-viscosity fluid displaces a more viscous one. We present the application of the method to two-dimensional, highly heterogeneous problems.
UR: http://web.mit.edu/juanes/www/
DE: 1829 Groundwater hydrology
DE: 1832 Groundwater transport
DE: 1847 Modeling
DE: 1849 Numerical approximations and analysis
DE: 1869 Stochastic hydrology
SC: Hydrology [H]
MN: 2007 Fall Meeting