# Wettability of Carbonate Reservoir Rocks:
## 4 Results and Discussion  
Figure 2 shows the measured forced displacement capillary pressure curves. In this figure, the positive curves correspond to secondary drainage process where the negative ones represent primary imbibition displacement. The area below each curve was determined to calculate the USBM and USBM* indices using Equations (4) and (5), respectively. The Amott index of oil, Equation (1), and water, Equation (2) as well as the Amott-Harvey index Equation (3) were also calculated using the variations in saturation corresponding to the spontaneous and forced displacements. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Test** & **Property** & **Water Density** & **Oil Density** & **Interfacial Tension** & **Water Viscosity** & **Oil Viscosity** \\  & **(gr-/cc)** & **(gr-/cc)** & **(dyne/cm)** & **(cp)** & **(cp)** \\ \hline Primary drainage capillary & & & & & \\ pressure at 50 \({}^{\circ}\)C & 1.125 & 0.857 & 26.79 & - & 3.29 \\ \hline Imbibition/secondary drainage & & & & & \\ capillary pressure at 25 \({}^{\circ}\)C & 1.145 & 0.731 & - & 1.36 & 2.44 \\ \hline Relative permeability at 25 \({}^{\circ}\)C & 1.145 & 0.731 & - & 1.36 & 2.44 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fluid characteristics used in the primary drainage and imbibition/secondary drainage experiments. Figure 2: The measured forced displacement capillary pressure curves for 16 samples studied here. Table 3 summarizes the calculated values of the Amott, Amott-Harvey, USBM, and USBM* indices. As indicated in Table 3, for three samples (8, 16, and 18) the capillary pressure curves were not available, for which \(I_{w}\), \(I_{o}\), \(I_{AH}\), \(I_{USBM}\) and \(I_{USBM^{*}}\) were not reported. For the remaining 16 samples, we found general agreement among these five indices. Results showed oil-wet conditions for 14 samples and intermediate-wet conditions for samples 7 and 10. Figure 3 shows the oil and water relative permeability curves measured on the 19 core samples. Although the oil relative permeability curves are similar in terms of shape (upward curvature), the water relative permeability curves are diverse representing a wide range of behaviors. Figure 4 shows the normalized water fractional flow data, Equation (7), against the normalized water saturation, Equation (8). As can be seen, most data points are above the 1:1 line, which indicates oil-wetness of the samples. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Plug No. **} & **Amott Water** & **Amott Oil** & **Amott–Harvey** & **USBM Index** & \begin{tabular}{c} **USBM* \\ **Index** \\ **I\({}_{w}\)** \\ \end{tabular}  \\ \hline \(1\) & \(0.09\) & \(0.55\) & \(-0.46\) & \(-0.87\) & \(-0.76\) \\ \hline \(2\) & \(0.07\) & \(0.47\) & \(-0. The relative permeability measurements were used to evaluate [PERSON]'s rules of thumb and the modified [PERSON]'s second rule, plot the normalized water fractional flow curves, and calculate the values of Lak and modified Lak indices (Table 4). As Table 4 indicates, the results of [PERSON]'s second rule and those of the modified [PERSON]'s second rule are in agreement for all samples except samples 7 and 10. For these two samples other indicators show water-wet conditions. While [PERSON]'s second rule characterizes these samples as oil-wet, the modified [PERSON]'s second rule labels them as water-wet. Furthermore, [PERSON]'s third rule also provided results inconsistent with the others. Although [PERSON]'s third rule predicted water-wet conditions, other indices recommend oil-wet. Such inconsistencies have been previously reported by [PERSON] [15]. Since the results of [PERSON]'s second and third rules are inconsistent with those of other approaches, we excluded them from further analyses. Figure 4: Normalized water fractional flow, Equation (7), against normalized water saturation, Equation (8), for all the 19 samples studied here. The solid black line indicates the 1:1 line. Figure 3: The oil and water relative permeability curves measured on 19 carbonate rock samples studied here.