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5. Pore-Network Modeling of Two-Phase Flow
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Relativ ve Permeability
1.0
0.8
0.6
0.4
0.2
0.0
Including pore body resistances
Correction term using pore body conductances
Correction term uisng saturations
Centrifuge experiment
0.0 0.2 0.4 0.6 0.8 1.0
Saturation
Figure 5.17: Relative permeability curves obtained from our approach, i.e.,
including conductance of both pore bodies and pore throats (solid line), together
with calculation of k r using effective conductance approaches, Equations (5.20)
and (5.21) (dashed lines). Circles show measured values during primary drainage
experiment by Al-Kharusi and Blunt [2008].
5.5 Conclusion
In this study, we have presented a new formulation for pore-network modeling
of two-phase flow which enables us to calculate more accurate relative
permeability-saturation (k r − S w ) relationships. This goal was achieved by
including the resistance to the flow within pore bodies of a MDPN model.
Through quantitative analysis, we have calculated the influence of pore body
resistance under primary drainage conditions. Since pore bodies vary considerably
in size in porous media, including their effect will influence the relative
permeability curve. Using several pore-network models with different coordination
number distributions, we have shown that including the resistance to the
flow within the pore bodies significantly affects simulated k r − S relationship
and can improve the accuracy of results of pore-network models.
The approach presented helps to reduce sensitivity of pore-network modeling
to pore space discretization, based on direct imaging of porous media samples.
As mentioned earlier, based on images, the pore space is commonly partitioned
into pore bodies and pore throats. This nontrivial partitioning has a major effect
on results of flow calculations in current pore-network models [Sholokhova
et al., 2009], because the pore bodies do not contribute to the resistant to the
flow. But, because we account for the flow resistance within pore bodies as
well as pore throats, the results are less sensitive to the division of pore space
into pore bodies and pore throats.
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