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 M –Ca –k 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 M –Ca –k nw correlation
diagram. We chose the 20% S nw condition because
it is realistic under all M –Ca 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).