Summary
In the coarse-scale simulation of heterogeneous reservoirs, effective or
upscaled flow functions (e.g., oil and water relative permeability and
capillary pressure) can be used to represent heterogeneities at subgrid scales.
The effective relative permeability is typically upscaled along with absolute
permeability from a geocellular model. However, if no subgeocellular-scale
information is included, the potentially important effects of smaller-scale
heterogeneities (on the centimeter to meter scale) in both capillarity and
absolute permeability will not be captured by this approach.
In this paper, we present a two-stage upscaling procedure for two-phase
flow. In the first stage, we upscale from the core (fine) scale to the
geocellular (intermediate) scale, while in the second stage we upscale from the
geocellular scale to the simulation (coarse) scale. The computational procedure
includes numerical solution of the finite-difference equations describing
steady-state flow over the local region to be upscaled, using either constant
pressure or periodic boundary conditions. In contrast to most of the earlier
investigations in this area, we first apply an iterative rate-dependent
upscaling (iteration ensures that the properties are computed at the
appropriate pressure gradient) rather than assume viscous or capillary
dominance and, second, assess the accuracy of the two-stage upscaling procedure
through comparison of flow results for the coarsened models against those of
the finest-scale model.
The two-stage method is applied to synthetic 2D reservoir models with strong
variation in capillarity on the fine scale. Accurate reproduction of the
fine-grid solutions (simulated on 500´500 grids) is achieved on coarse grids of
10´10 for different flow scenarios. It is shown that, although capillary forces
are important on the fine scale, the assumption of capillary dominance in the
first stage of upscaling is not always appropriate, and that the computation of
rate-dependent effective properties in the upscaling can significantly improve
the accuracy of the coarse-scale model. The assumption of viscous dominance in
the second upscaling stage is found to be appropriate in all of the cases
considered.
Introduction
Because of computational costs, field-simulation models may have very coarse
cells with sizes up to 100 to 200 m in horizontal directions. The cells are
typically populated with effective properties (porosity, absolute permeability,
relative permeabilities, and capillary pressure) upscaled from a geocellular
(or geostatistical) model. In this way, the effects of heterogeneity on the
geocellular scale will be included in the large-scale flow calculations. The
cell sizes in geocellular models may be on the order of 20 to 50 m in
horizontal directions. However, heterogeneities on much smaller scales (cm- to
m- scale) may have a significant influence on the reservoir flow (Coll et al.
2001; Honarpour et al. 1994), and this potential effect cannot be captured if
the upscaling starts at the geocellular scale.
© 2006. Society of Petroleum Engineers
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History
- Original manuscript received:
12 January 2004
- Revised manuscript received:
31 May 2005
- Manuscript approved:
27 January 2006
- Version of record:
20 September 2006
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