Summary
Multipoint-flux-approximation (MPFA) methods were introduced to solve
control-volume formulations on general simulation grids for porous-media flow.
While these methods are general in the sense that they may be applied to any
matching grid, their convergence properties vary.
An important property for multiphase flow is the monotonicity of the
numerical elliptic operator. In a recent paper (Nordbotten et al. 2007),
conditions for monotonicity on quadrilateral grids have been developed. These
conditions indicate that MPFA formulations that lead to smaller flux stencils
are desirable for grids with high aspect ratios or severe skewness and for
media with strong anisotropy or strong heterogeneity. The ideas were pursued
recently in Aavatsmark et al. (2008), where the L-method was introduced for
general media in 2D. For homogeneous media and uniform grids, this method has
four-point flux stencils and seven-point cell stencils in two dimensions. The
reduced stencils appear as a consequence of adapting the method to the closest
neighboring cells.
Here, we extend the ideas for discretization on 3D grids, and ideas and
results are shown for both conforming and nonconforming grids. The ideas are
particularly desirable for simulation grids that contain faults and local grid
refinement.
We present numerical results herein that include convergence results for
single-phase flow on challenging grids in 2D and 3D and for some simple
two-phase results. Also, we compare the L-method with the O-method.
© 2010. Society of Petroleum Engineers
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History
- Original manuscript received:
5 December 2006
- Meeting paper published:
27 February 2007
- Revised manuscript received:
1 April 2009
- Manuscript approved:
3 October 2009
- Published online:
22 March 2010
- Version of record:
22 September 2010
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