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5. Pore-Network Modeling of Two-Phase Flow
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5.4.2.2 Relative permeability for a carbonate rock
In this section, we are applying the new formulation to a network which is based
on the statistical properties of a carbonate rock. Al-Kharusi and Blunt [2008]
applied a methodology to extract networks from pore space images of carbonate
rock samples, in order to make predictions of multiphase transport properties.
They started with a 2D thin-section image; then, converted it statistically
to a 3D representation of the pore space. Using concept of maximal ball [Al-
Kharusi and Blunt, 2008, 2007], they constructed a 3D pore-network model and
simulated primary drainage, waterflooding, and secondary drainage processes
[Valvatne and Blunt, 2004]. In that model, the resistance to flow was assigned
to pore throats only. The simulated results were compared to the laboratorymeasured
values obtained though centrifuge experiments. The good agreement
for capillary pressure-saturation and intrinsic permeability implied that they
had estimated pore and throat sizes correctly (Figure 5.13). However, the predicted
wetting-phase relative permeability was overestimated compared to the
experimental results, as shown in Figure (5.14). They mentioned the large coordination
number (which was derived using imaging technics) as a potential
reason for discrepancy between relative permeabilities. As another potential
source of discrepancy, they mentioned the fact that the pore-network model
did not capture all local heterogeneities of the sample due to the size of the
network. All of these arguments could potentially explain the overestimation
of the relative permeability. However, we believe that this discrepancy could
have been minimized by taking into account the resistance to the flow within
(partially-) drained pore bodies. To verify this explanation, we generated a
network with similar properties to those used by Al-Kharusi and Blunt [2008].
The capillary pressure-saturation curves obtained from our network and the
network model of Al-Kharusi and Blunt [2008] are shown in Figure (5.13), together
with the P c −S w curve measured in the centrifuge experiments. There is
good agreement between the two pore-network modeling results and measured
values. There is also a good agreement between calculated values of absolute
permeability using our network and that of Al-Kharusi and Blunt [2008] (Table
5.2). The relative permeability results of both pore-network models are shown
in Figure (5.14) together with values obtained from the centrifuge experiments.
It is clear that including the resistance to the flow within pore bodies improves
the agreement between simulated and measured values of relative permeability.
An important observation from Figure (5.14) is that the maximum discrepancy
between results from Al-Kharusi and Blunt [2008] and experiments occurs at
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