Effective flux boundary conditions for upscaling porous media equations

We introduce a new algorithm for setting pressure boundary conditions in subgrid simulations of porous media flow. The algorithm approximates the flux in the boundary cell as the flux through a homogeneous inclusion in a homogeneous background, where the permeability of the inclusion is given by the...

Full description

Saved in:
Bibliographic Details
Published inTransport in porous media Vol. 46; no. 2-3; pp. 139 - 153
Main Authors WALLSTROM, T. C, CHRISTIE, M. A, DURLOFSKY, L. J, SHARP, D. H
Format Conference Proceeding Journal Article
LanguageEnglish
Published Dordrecht Springer 01.02.2002
Springer Nature B.V
Subjects
Algorithms
Axes (reference lines)
Boundary conditions
Computer simulation
Earth sciences
Earth, ocean, space
Exact sciences and technology
Flux
Hydrocarbons
Hydrogeology
Hydrology. Hydrogeology
Inclusions
Mathematical analysis
Permeability
Porous media
Sedimentary rocks
Tensors
Variations
reservoir rocks
saturation
algorithms
fluctuations
permeability
reservoirs
digital simulation
pressure
transport
boundary conditions
porous media
heterogeneity
Online AccessGet full text

Cover

More Information
Summary:We introduce a new algorithm for setting pressure boundary conditions in subgrid simulations of porous media flow. The algorithm approximates the flux in the boundary cell as the flux through a homogeneous inclusion in a homogeneous background, where the permeability of the inclusion is given by the cell permeability and the permeability of the background is given by the ambient effective permeability. With this approximation, the flux in the boundary cell scales with the cell permeability when that permeability is small, and saturates at a constant value when that permeability is large. The flux conditions provide Neumann boundary conditions for the subgrid pressure. We call these boundary conditions effective flux boundary conditions (EFBCs). We give solutions for the flux through ellipsoidal inclusions in two and three dimensions, assuming symmetric tensor permeabilities whose principal axes align with the axes of the ellipse. We then discuss the considerations involved in applying these equations to scale up problems in geological porous media. The key complications are heterogeneity, fluctuations at all length scales, and boundary conditions at finite scales.
ISSN:0169-3913
1573-1634
DOI:10.1023/A:1015075210265