Summary
The two-point flux finite-volume method (2P-FVM) is the most widely used
method for solving the flow equation in reservoir simulations. For 2P-FVM to be
consistent, the simulation grid needs to be orthogonal (or k-orthogonal if the
permeability field is anisotropic). It is well known that corner-point grids
can introduce large errors in the flow solutions because of the lack of
orthogonality in general. Multipoint flux formulations that do not rely on grid
orthogonality have been proposed, but these methods add significant
computational cost to solving the flow equation.
Recently, 2.5D unstructured grids that combine 2D Voronoi areal grids with
vertical projections along deviated coordinate lines have become an attractive
alternative to corner-point gridding. The Voronoi grid helps maintain
orthogonality areally and can mitigate grid orientation effects. However,
experience with these grids is limited.
In this paper, we present an analytical and numerical study of these 2.5D
unstructured grids. We focus on the effect of grid deviation on flow solutions
in homogeneous, but anisotropic, permeability fields. In particular, we
consider the grid deviation that results from gridding to sloping faults. We
show that 2P-FVM does not converge to the correct solution as the grid refines.
We further quantify the errors for some simple flow scenarios using a technique
that combines numerical analysis and asymptotic expansions. Analytical error
estimates are obtained. We find that the errors are highly flow dependent and
that they can be global with no strong correlation with local nonorthogonality
measures. Numerical tests are presented to confirm the analytical findings and
to show the applicability of our conclusions to more-general flow
scenarios.
© 2009. Society of Petroleum Engineers
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History
- Original manuscript received:
8 December 2004
- Meeting paper published:
31 January 2005
- Revised manuscript received:
16 June 2008
- Manuscript approved:
21 June 2008
- Published online:
16 March 2009
- Version of record:
1 March 2009
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