# Matching of Water Breakthroughs in a Low-Resistivity Oil Reservoir Using Permeability Anisotropy
## 4 Results and Discussion
### Influence of Relative Permeability on Water Production  
Wettability can significantly influence oil recovery. The position of relative permeability curves on the plot of water saturation indicates wettability: lower Sw--oil-wet; higher Sw--water-wet. Reliable relative permeability data to be used in the simulation were not available for the LHS reservoir. For the simulations of OPR and WPR shown in Figures 9 and 10, a pair of relative permeability curves called Case 1 (Base case) were  
Figure 10: Observed and simulated oil production rate (OPR) and water production rate (WPR) designated as historical and simulated values using a Kv/Kh of 1 and 0.1: (**a**) Well E, (**b**) Well A. The Kv/Kh = 0.1 scenario better matches the WPR, indicating lateral water inflow. used with Kv/Kh = 0.1 (Figure 11). To test the sensitivity of the simulation results to the changes in relative permeabilities, six additional pairs of curves were generated. The curves were shifted relative to the curves of base Case 1, as follows: Case 2--shifting both curves to the right; Case 3--shifting both curves to the left; Case 4--shifting Krw only to the left; Case 5--shifting Krw only to the right; Case 6--shifting Kro only to the right; and Case 7--modifying the curvature by changing the curvature and reducing the Krw max (Figure 11). Shifting to the left indicates more water-wet and shifting to the right indicates more oil-wet contact between the rock and fluid. In the result, the following pairs of Kr with the specific crossing points were used to build the cases: Case 1 with Sw = 0.58 for (1, 2); Case 2 with Sw = 0.68 for (3, 4); Case 3 with Sw = 0.48 for (5, 6); Case 4 with Sw = 0.51 for (5, 2); Case 5 with Sw = 0.63 for (3, 2); Case 6 with Sw = 0.61 for (1, 4); and Case 7 with Sw = 0.6 for (7, 8). Crossing points and intervals of Sw are shown in Table 2. Thus, of all these cases, Case 3 indicates the most oil-wet and Case 2 indicates the most water-wet conditions, while Case 7 covers the widest Sw range. Changes in WPR due to variations in relative permeabilities were investigated using simulation, as shown in Figure 12 for two wells. In Well D, no increase in water production was predicted using any of the pairs, which corresponds to the observed small WPR in this well. The most oil-wet scenario, Case 3, with the lowest Sw intersection of 0.48, predicted the highest WPR in all wells, excluding Well C. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Case N** & **Kr Oil** & **Kr Water** & **Crossing** & **Sw Min** & **Sw Max** \\ \hline
1 & 2 & 1 & 0.58 & 0.3 & 0.8 \\
2 & 4 & 3 & 0.68 & 0.37 & 0.8 \\
3 & 6 & 5 & 0.48 & 0.2 & 0.7 \\
4 & 2 & 5 & 0.51 & 0.2 & 0.8 \\
5 & 2 & 3 & 0.63 & 0.37 & 0.8 \\
6 & 4 & 1 & 0.61 & 0.25 & 0.9 \\
7 & 8 & 7 & 0.6 & 0.2 & 0.9 \\ \hline \end{tabular}
\end{table} 
Table 2: Relative permeability curves and their parameters used for the simulation. The parameters are shown for Case 3 (green curves) in Figure 11 for example. Figure 11: Relative permeability curves (Kr) for water and oil used to build various simulation cases. Except for the modified Case 7, crossing Sw increased in the following order of cases: 3, 4, 1, 6, 5, and 2. However, WPR does not strictly follow the same order. In all wells, the highest WPR indeed decreased in the following order of cases: 3, 4, and 6. The lowest WPR was predicted by Cases 2, 5, and 7 distributed in random order from well to well. WPR predicted by Case 1 varies randomly in a broad range, predicting the maximum WPR in Well C and the minimum in Well B. With the decrease in Sw, the start of water breakthrough shifted to much earlier dates, which did not correspond to the start of water breakthrough in Wells G, B, and E.  
The simulated WPR matched the observed WPR in Wells G and C, although the prediction in WPR was substantially lower. In Wells B, E, and A, the prediction of WPR was higher in the first part of the considered period and lower in the second part, while it was the opposite for the observed WPR.