Summary
A first attempt has been made to predict three-phase relative permeability
experimental data of a water-wet Berea sandstone obtained by Oak (1990) using
the three-phase flow network model for arbitrary wettability developed by van
Dijke and Sorbie (2002a). First, the network model is anchored to the
corresponding two-phase relative permeability and capillary pressure data using
an idealized representation of the pore geometry and a simple parameter-fitting
procedure. Then, predictions of three-phase properties are made, which are
compared with experimental data as well as previous predictions from different
network models. The present study has confirmed that the relatively simple
network model, anchored to experimental data, is able to predict three-phase
relative permeabilities with reasonable accuracy, comparable to the accuracy of
more-complex models. On the basis of these preliminary results, a limited
sensitivity study is carried out with respect to different wettability states
and two combinations of interfacial tensions (IFTs). This study reveals some
new results with respect to the invariance of relative permeability to
interfacial-tension combinations and the trend of water relative permeability
as a function of the fraction of oil-wet pores in systems of nonuniform
wettability.
Introduction
Relative permeabilities in a three-phase system depend not only on phase
saturations, but also on the saturation history and may be further complicated
by wettability effects. Careful measurement of three-phase relative
permeabilities is a very difficult task, which is probably the reason why so
few data sets have been reported (Oak 1990, 1991; Egermann et al. 2000; Element
et al. 2003; Skauge and Larsen 1994). Empirical correlations, which were
designed to predict three-phase relative permeabilities from more readily
available two-phase data (as demonstrated in Stone 1970, 1973), are not capable
of reproducing this complex behavior. Alternatively, network models predict the
three-phase relative permeabilities by simulating the flow processes on the
basis of details of pore-space representation, fluids, and pore-scale flow
mechanisms. Existing network-model formulations vary from simple bond models
with idealized pore geometries to complex models with a detailed geometrical
representation of the reconstructed 3D pore space. Theoretically, a more
detailed representation of the porous medium and the flow processes should
provide a better approximation of the macroscopic flow behavior and better
predictive capabilities. However, measuring all the detailed pore-scale
parameters, as well as modeling these features, is clearly impossible.
Therefore, measurement of three-phase relative permeabilities remains
essential, if only for validation of the network models.
Many studies report predictions of two-phase relative permeabilities (for
examples, see Øren et al. 1998, and McDougall et al. 2002), but relatively few
attempts have so far been made to predict three-phase properties. Two
network-model studies have been published (Lerdahl et al. 2000, Piri and Blunt
2002) predicting three-phase experimental data of Oak (1990), (see also Piri
and Blunt 2005a, 2005b). Both studies are based on the stochastically
reconstructed 3D microstructure of Berea sandstone. To reduce the computational
cost of solving the transport equations, the detailed microstructure was
converted into a pore network with a simplified pore and throat geometry, which
was supposed to preserve all relevant features of the reconstructed pore space.
Additionally, both networks incorporate a detailed explicit description of
intrapore fluid configurations. Because the above models have been conditioned
to a particular rock, no further adjustment of network parameters is needed.
Both networks additionally incorporate a detailed, explicit description of the
intrapore-fluid configurations and distinguish between receding and advancing
contact angles. For a simulation of the water/oil imbibition, the latter were
randomly distributed between 10 and 30° (Lerdahl et al. 2000) and between 30and
80o (Piri and Blunt 2005a). Predicted two- and three-phase relative
permeabilities of both studies are in reasonable agreement with experimental
data.
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
4 June 2004
- Meeting paper published:
26 September 2004
- Revised manuscript received:
30 March 2007
- Manuscript approved:
10 April 2007
- Version of record:
20 October 2007
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