Summary
Multidimensional transport for reservoir simulation is typically solved by
applying 1D numerical methods in each spatial-coordinate direction. This
approach is simple, but the disadvantage is that numerical errors become highly
correlated with the underlying computational grid. In many real-field
applications, this can result in strong sensitivity to grid design not only for
the computed saturation/composition fields but also for critical integrated
data such as breakthrough times. Therefore, to increase robustness of
simulators, especially for adverse-mobility-ratio flows that arise in a variety
of enhanced-oil-recovery (EOR) processes, it is of much interest to design
truly multidimensional schemes for transport that remove, or at least strongly
reduce, the sensitivity to grid design.
We present a new upstream-biased truly multidimensional family of schemes
for multiphase transport capable of handling countercurrent flow arising from
gravity. The proposed family of schemes has four attractive properties:
applicability within a variety of simulation formulations with varying levels
of implicitness, extensibility to general grid topologies, compatibility with
any finite-volume flow discretization, and provable stability (monotonicity)
for multiphase transport. The family is sufficiently expressive to include
several previously developed multidimensional schemes, such as the narrow
scheme, in a manner appropriate for general-purpose reservoir simulation.
A number of waterflooding problems in homogeneous and heterogeneous media
demonstrate the robustness of the method as well as reduced transverse
(cross-wind) diffusion and grid-orientation effects.
© 2010. Society of Petroleum Engineers
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History
- Original manuscript received:
3 November 2008
- Meeting paper published:
2 February 2009
- Revised manuscript received:
3 June 2010
- Manuscript approved:
16 June 2010
- Published online:
13 January 2011
- Version of record:
17 June 2011
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