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-dimensionalMCaS nwk 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.