# Wettability of Carbonate Reservoir Rocks:
## 4 Results and Discussion
Results of the relative permeability-based methods implied that the qualitative and quantitative indices consistently predicted oil-wet conditions for 14 samples (all samples excluding 7, 9, 10, 11, and 16). Such methods indicated almost water-wet conditions for samples 7 and 10. For samples 9, 11, and 16 there was no agreement among the different methods. For samples 9 and 16, while qualitative methods characterized oil-wet rocks, quantitative indices showed intermediate-wet conditions. For sample 11, while [PERSON]'s first rule indicated that the rock sample should be water-wet, the modified Craig's second rule and normalized water fractional flow curve recommended oil-wet. For this sample the Lak and modified Lak indices represented intermediate-wet rock. Comparing the results of the relative permeability-based methods with those of the Amott, Amott-Harvey, USBM, and USBM* techniques showed generally good agreements among these approaches, despite their difference in terms of concepts and methodologies. We also investigated possible correlations and trends among the wettability indices. Cross-plots of different wettability indices studied here are shown in Figure 5 in which the dashed line represents the 1:1 line and the solid red line denotes the linear equation fitted to the data. As mentioned earlier, while USBM is an unbounded index it is usually mistakenly assumed to vary over the range of \(-1\) to \(1\) and compared with other indices. Comparison between USBM and other indices may cause erroneous interpretations due to dissimilar ranges of variation (other indices vary in the range of \(-1\) to \(1\)). In this study, we therefore used USBM* as a replacement of the traditional USBM index [66] in the comparative analysis. USBM* varies over the range of \(-1\) to \(1\), similar to other indices. Although the trends are similar (as one index increases another one increases as well), the correlation coefficient R\({}^{2}\) varies from one plot to another. The highest correlation coefficient values belong to the USBM*-Amott-Harvey (see Figure 5a) and Lak-Modified Lak (see Figure 5b) plots. The high R\({}^{2}\) value between the Lak and modified Lak indices might  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multirow{2}{*}{\(k_{m}\) at \(S_{m^{*}}\)} & \multirow{2}{*}{**CS (\%)**} & \multirow{2}{*}{**S\({}_{m}\)(\%)**} & \multirow{2}{*}{**S\({}_{m}\)(\%)**} & & \multicolumn{4}{c}{**Qualitative Methods**} & \multicolumn{2}{c}{**Quantitative**} \\  & & & & & & & & & & & & & & & \\  & & & & & & & & & & & & & & \\  & & & & & & & & & & & & & & \\ \hline
1 & 0.70 & 38.9 & 29.1 & 40.9 & 44.1 & OW & OW & WW & O  
be because these two methods apply the same concepts based on relative permeability measurements. The relatively high correlation coefficient between Amott-Harvey and USBM* indices (R2 = 0.70), given that they are based on different concepts, might be due to lack of spatial heterogeneity in the database studied here. Recall that the carbonate rock samples were collected along a well from a single carbonate reservoir. Analyzing samples from different geologic formations might lead to higher level of heterogeneity and accordingly lower correlation coefficients. The modified Lak index, \(I_{ML}\), was correlated to the USBM* and Amott-Harvey indices with R2 = 0.44 (Figure 5c,f). However, the Lak index, \(I_{L}\), was slightly more correlated to \(I_{USBM^{*}}\) with R2 = 0.48 and I\({}_{\rm AH}\) with R2 = 0.52 (Figure 5d,e). In the literature, there exist various approaches for rock typing. For recent reviews see [74,75]. To explore the trends among wettability indices and rock quality indicators, we calculated \(RQI\) and \(FZI\) values based on Equations (13) and (14), respectively. The Winland \(R_{35}\)[76], as one of the widely used rock quality indicators, was also determined from the porosity and permeability measurements as follows  
\[\log(R_{35})=0.732+0.588\log k-0.864\log(100\phi) \tag{15}\]  
where \(R_{35}\) is in microns.