Volume 9, Issue 3
Treatment of Tensorial Relative Permeabilities with Multipoint Flux Approximation

M. Wolff, B. Flemisch, R. Helmig & I. Aavatsmark

Int. J. Numer. Anal. Mod., 9 (2012), pp. 725-744

Published online: 2012-09

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  • Abstract
Multi-phase flow in porous media is most commonly modeled by adding a saturationdependent, scalar relative permeability into the Darcy equation. However, in the general case anisotropically structured heterogeneities result in anisotropy of upscaled parameters, which not only depends on the solid structure but also on fluid-fluid or fluid-fluid-solid interaction. We present a method for modeling of incompressible, isothermal, immiscible two-phase flow, which accounts for anisotropic absolute as well as relative permeabilities. It combines multipoint flux approximation (MPFA) with an appropriate upwinding strategy in the framework of a sequential solution algorithm. Different tests demonstrate the capabilities of the method and motivate the relevance of anisotropic relative permeabilities. Therefore, a porous medium is chosen, which is heterogeneous but isotropic on a fine scale and for which averaged homogeneous but anisotropic parameters are known. Comparison shows that the anisotropy in the large-scale parameters is well accounted for by the method and agrees with the anisotropic distribution behavior of the fine-scale solution. This is demonstrated for both the advection dominated as well as the diffusion dominated case. Further, it is shown that off-diagonal entries in the relative permeability tensor can have a significant influence on the fluid distribution.
  • Keywords

porous media two-phase flow anisotropic medium anisotropy tensorial relative permeability MPFA upwinding capillary pressure gravity

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@Article{IJNAM-9-725, author = {M. Wolff, B. Flemisch, R. Helmig and I. Aavatsmark}, title = {Treatment of Tensorial Relative Permeabilities with Multipoint Flux Approximation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {3}, pages = {725--744}, abstract = {Multi-phase flow in porous media is most commonly modeled by adding a saturationdependent, scalar relative permeability into the Darcy equation. However, in the general case anisotropically structured heterogeneities result in anisotropy of upscaled parameters, which not only depends on the solid structure but also on fluid-fluid or fluid-fluid-solid interaction. We present a method for modeling of incompressible, isothermal, immiscible two-phase flow, which accounts for anisotropic absolute as well as relative permeabilities. It combines multipoint flux approximation (MPFA) with an appropriate upwinding strategy in the framework of a sequential solution algorithm. Different tests demonstrate the capabilities of the method and motivate the relevance of anisotropic relative permeabilities. Therefore, a porous medium is chosen, which is heterogeneous but isotropic on a fine scale and for which averaged homogeneous but anisotropic parameters are known. Comparison shows that the anisotropy in the large-scale parameters is well accounted for by the method and agrees with the anisotropic distribution behavior of the fine-scale solution. This is demonstrated for both the advection dominated as well as the diffusion dominated case. Further, it is shown that off-diagonal entries in the relative permeability tensor can have a significant influence on the fluid distribution.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/656.html} }
TY - JOUR T1 - Treatment of Tensorial Relative Permeabilities with Multipoint Flux Approximation AU - M. Wolff, B. Flemisch, R. Helmig & I. Aavatsmark JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 725 EP - 744 PY - 2012 DA - 2012/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/656.html KW - porous media KW - two-phase flow KW - anisotropic medium KW - anisotropy KW - tensorial relative permeability KW - MPFA KW - upwinding KW - capillary pressure KW - gravity AB - Multi-phase flow in porous media is most commonly modeled by adding a saturationdependent, scalar relative permeability into the Darcy equation. However, in the general case anisotropically structured heterogeneities result in anisotropy of upscaled parameters, which not only depends on the solid structure but also on fluid-fluid or fluid-fluid-solid interaction. We present a method for modeling of incompressible, isothermal, immiscible two-phase flow, which accounts for anisotropic absolute as well as relative permeabilities. It combines multipoint flux approximation (MPFA) with an appropriate upwinding strategy in the framework of a sequential solution algorithm. Different tests demonstrate the capabilities of the method and motivate the relevance of anisotropic relative permeabilities. Therefore, a porous medium is chosen, which is heterogeneous but isotropic on a fine scale and for which averaged homogeneous but anisotropic parameters are known. Comparison shows that the anisotropy in the large-scale parameters is well accounted for by the method and agrees with the anisotropic distribution behavior of the fine-scale solution. This is demonstrated for both the advection dominated as well as the diffusion dominated case. Further, it is shown that off-diagonal entries in the relative permeability tensor can have a significant influence on the fluid distribution.
M. Wolff, B. Flemisch, R. Helmig & I. Aavatsmark. (1970). Treatment of Tensorial Relative Permeabilities with Multipoint Flux Approximation. International Journal of Numerical Analysis and Modeling. 9 (3). 725-744. doi:
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