4 Discussion
We have demonstrated how M and Ca can markedly change the
relative permeabilities of the nonwetting and wetting fluids in a
reservoir; thus, our results can help identify the optimum properties of
the immiscible fluids to be used in a geologic reservoir. For example,
in a CCS project, the injectivity of the CO2 is highest
when the reservoir fluid has a lower viscosity and the IFT between the
two fluids is low. Thus, the relative permeability of injected
CO2 is higher in a saline aquifer than in an oil field.
For an EOR project, the relative permeability of oil is higher when a
fluid with low viscosity is injected.
The relative permeability map (Fig. 8) is useful to provide accurate
estimates of k nw in reservoir-scale simulations.
Currently, the relative permeabilities of the nonwetting and wetting
fluid are simulated on the basis of a uniform relative permeability
curve, without regard to the M and Ca conditions. However,
we have shown that the nonwetting fluid, at a typical saturation
(S nw) of 20%, can vary in relative permeability
by an order of magnitude, from 0.02 to 0.54, depending on M andCa conditions. The color map created in this study can provide
more accurate estimates of relative permeability (e.g., temporal
permeability variations in a 3D reservoir model) if Ca andM are derived from the reservoir simulation. In addition,
although the M generally remains constant in the two-phase flow,
the Ca value can greatly changes depending on the distance from
the injection well in a reservoir. For example, when evaluating the
reservoir area located near the injection well, the injection pressure
creates a high-pressure gradient which causes the injected fluid
velocity to be high. As the fluid flows away from the injection site,
the fluid velocity becomes slower, thus the k nwbecomes lower. This means that fluid relative permeability varies based
on location inside the reservoir, and the permeability variation can be
evaluated using the relative permeability map, thus providing a more
accurate relative permeability estimation.
In this study, we created a relative permeability map forS nw = 20%, which is a reasonable condition that
can be achieved in all or most systems. As S nwincreases, k nw also increases until it reaches
its maximum value (e.g., k nw at the irreducible
saturation). Therefore, it is advisable to create relative permeability
maps for several saturation conditions. One possible future direction
from this study would be to create a four-dimensionalM –Ca –S nw–k nwgraph to yield k nw estimates for all saturation
conditions. Nevertheless, the great consistency of variations ink caused by changes in M and Ca found in this study
suggests that maps for other saturation conditions will have similar
features to Fig. 8.
In this study, we produced a relative permeability diagram for a digital
specimen of Berea sandstone. In addition to M and Ca , the
influences upon relative permeability include the pore geometry of the
rock, such as pore size distribution, pore connectivity, and other
parameters. These parameters differ among rock formations, meaning that
the relative permeability maps of different types of reservoir rocks
will vary. Our methodology makes it possible to create accurate maps of
relative permeability for other reservoir rocks.
In geological CO2 storage, the maximum amount of
CO2 that can be stored and the injectivity of the
CO2 into the reservoir must both be considered (Tsuji et
al., 2016). Thus, the results of this study must be combined with
information on the effects of M and Ca on the maximum
saturation of the nonwetting fluid. In this study, we showed that, for
CO2 as the nonwetting fluid, the relative permeability
increases as M increases and decreases as Ca becomes very
small. In contrast, Tsuji et al. (2016) demonstrated that the maximumS nw increases as M increases and notably
increases at low Ca . Thus, although a high value of M is
desirable to increase both the CO2 capacity and
injectivity, a low Ca value can also increase the maximum
CO2 saturation but at the cost of reduced relative
permeability. Both factors must be taken into account when choosing
suitable conditions for CO2 storage.
An advantage of using M and Ca is that both parameters are
dimensionless, meaning that the results obtained in this pore-scale
study can potentially be upscaled to the reservoir scale. Ideally, the
pore-scale results are also valid at the reservoir scale as long as the
ratios of the parameters (viscosity and IFT) are maintained for both
fluids, because the fluid flow behavior at the reservoir scale is
controlled by the fluid dynamics at the pore scale. However, this ideal
is challenged by the inhomogeneity of the porous medium. The relative
permeability is likely to vary throughout the reservoir due to
differences in pore size, pore connectivity, and many other factors.
Nevertheless, the results of a pore-scale simulation are important to
verify relative permeability variations arising from selected factors
(in this study, M and Ca ) by eliminating other factors.
The results of a pore-scale study of relative permeability could then be
upscaled by considering the structural factors of the reservoir, e.g.,
its porosity and pore connectivity, using advanced techniques such as
machine learning.