# Matching of Water Breakthroughs in a Low-Resistivity Oil Reservoir Using Permeability Anisotropy
## 4 Results and Discussion
### Water Saturation Calculation  
Water saturation was calculated using [PERSON]'s equation:  
\[\text{Sw}=[(\text{aRw}/\text{RtPhi}^{\text{m}})^{1/\text{n}} \tag{4}\]  
where m is the cementation exponent, n is the saturation exponent, aRw is the formation water resistivity (Rw) multiplied by tortuosity (a), Rt is the Formation resistivity, and Phi is porosity.  
A Pickett plot was used to derive [PERSON]'s parameters, as shown for two wells in Figure 4. The slope of the line across the water zone is 1/m, while the resistivity on the \(x\)-axis corresponding to the y-intercept at Phi = 1 indicates Rw = 0.025 Ohmm, with a = 1. The lines across oil zones are parallel to that of the water zone, implying similar m in both zones. Pickett plot can also be used to determine n-m for the oil zone. Red lines indicate n-m = 0.4, which implies that n = 2. The data more clearly follow the lines with slopes of 0.4 in the plot of Well E.  
Figure 4: Pickett plots for (**a**) Well G; (**b**) Well E. Rw—resistivity of formation water; m—cementation factor; n—saturation exponent.  
Figure 3: Permeability anisotropy (Kv/Kh) derived from core data from four wells in LHS.  
Two field water samples with total dissolved solids of 166 and 183 g/L collected in the year 2005 (although water injection started in 1997) were considered to determine the formation water salinity. At a reservoir temperature of 90 \({}^{\circ}\)C, such salinity results in the resistivity close to the Rw determined using the Pickett plot, which can indicate that the Rw reflects the actual formation water resistivity.  
The cementation exponent can vary laterally as well as vertically with the depth [23; 24]. The m decreases with a decrease in porosity and salinity [25]. Experiments using a porosity greater than 65% showed that an increase in m is universally correlated with the volume fraction of pore throats for all of the samples, regardless of their particle shapes, particle size range, and porosities [26]. On the other hand, m decreases with the increase in clay volume due to the large amount of interconnected clays combined with the formation water effect [24]. As a result, m = 1.3 can be obtained in unconsolidated sand, as well as in shaly sand [27; 28]. A cementation exponent of 1.5 represents the analytical solution for the case where the rock is composed of perfect spheres [25].  
Based on that, it can be concluded that the cementation exponent of the LHS reservoir, which is uniformly close to 1.6 in all wells, indicates a high degree of connectivity in the pore network and poor cementation if such a low value is not associated with the shaliness. The parameters m and n are often close in magnitude; however, n = 2 was used in the Sw calculations, since most of the data clearly followed two lines of n-m = 0.4 in Figure 4b.  
Thus, the obtained Archie's parameters are as follows: aRw = 0.025, m = 1.6, and n = 2. In the previous calculations, the parameters used were aRw = 0.035, m = 1.66, and n = 2 and aRw = 0.054, m = 1.8 or 1.95, and n = 2 [16]. It is important to highlight that small differences in [PERSON]'s parameters can cause big differences in the Sw. Therefore, the sensitivity of the Sw to [PERSON]'s parameters was studied using our values (revised) and previous datasets. The decrease in aRw by 0.1 decreased the Sw by about 5%, while a decrease in m by 0.06 decreased Sw by about 2%. In general, the Sw calculated using the revised parameters is about 7-8% lower than the previous dataset, thus increasing oil saturation to values higher than 60%. Regardless of the specific [PERSON]'s parameter set used, the calculated oil saturation remains above 50% in both cases, indicating a significant oil presence in the formation. In this regard, previous evaluations of Sw can be considered conservative, and, hence, high water production cannot be associated with underestimations of Sw.