3.1.2 Effect of Ca change on k nw andk w
The k nw and k w curves for four different values of log Ca at M = 1 (−0.25, −1.25, −2.25, and −2.95) are plotted in Fig. 7. The Ca value is altered by changing the IFT value. The k nw values remain relatively constant between log Ca = −0.25 and −1.25, i.e., for high Ca /low IFT values, and the relative permeability curve for the nonwetting fluid is an approximately straight line, in agreement with previous studies (Asar & Handy, 1989; Shen et al., 2010). However, as log Ca becomes lower than −1.25, k nwnotably decreases. This decrease occurs because the flow of the nonwetting fluid is more strongly inhibited by capillary force whenCa is low. Capillary force is controlled by IFT, the surface tension forces between the nonwetting and wetting fluids. As IFT increases, the nonwetting fluid becomes trapped by the larger capillary force in the small pore spaces, thus causing k nwto decrease. As Ca becomes lower, the influence of capillary force becomes more dominant. The result suggests thatk nw does not decrease linearly with changes in IFT/Ca .
For the wetting fluid, k w also decreases asCa decreases (Fig. 7), but at a much smaller rate compared tok nw, consistent with previous research (Harbert, 1983; Jiang et al., 2014; McDougall et al., 2007; Ramstad et al., 2010; Zhao et al., 2017). The reason is that as shown in Fig. 3, in our simulation, the wetting fluid only flows along the rock surface and the nonwetting fluid flows in the central part of the pores. Thus, the wetting fluid is mainly affected by interaction with the rock surface, and the change in capillary force has a negligible effect. We conclude that the variation in k w is dominated by the fluid saturation in the system and is little affected by changes in IFT or Ca .
3.2 MCak nw color diagram
After confirming the influence of M and Ca onk nw and k w in a two-phase flow system, we conducted simulations with various values of Mand Ca at a constant 20% S nw value to create an MCak nw correlation diagram. We chose the 20% S nw condition because it is realistic under all MCa conditions (Tsuji et al., 2016). We created the color diagram only for the nonwetting fluid because the relative permeability curves (Fig. 7) demonstrate thatk w does not respond markedly to changes inCa .
Color maps are useful to provide estimates of k nwunder a wide range of M and Ca conditions in a reservoir and to analyze the degree of influence on k nw byM and Ca . Two color maps are presented in Fig. 8. The first color map (Fig. 8a) depicts the parameter space of log M = −0.70 to 0.70 and log Ca = −3.00 to −0.50, which represents the broad range of conditions relevant to reservoirs. Values higher than this range are hard to achieve at the field scale, and lower values are outside the stable range of the simulation. The second color map (Fig. 8b), covering the lower left quadrant of the parameter range shown in Fig. 8a, was produced to increase the accuracy ofk nw estimates for a system with low M and low Ca , which is common in the CCS field (Zheng et al., 2017).