# A New Algorithm Model Based on Extended Kalman Filter for Predicting Inter-Well Connectivity
## 4 Production Performance of Single Well Pair
### Sensitivity Analysis of Inter-Well Connectivity
#### 4.3.1 Permeability of Permeable Channels  
The high-permeability channel is oriented along the diagonal connecting the injector and producer and has an initial width of 14.1 m (the grid side is 5 m long). The permeability of the matrix is 5 mD, and the permeability of the permeable channel is chosen to be four separate values with identical intervals (30 mD, 60 mD, 90 mD, and 120 mD). Figure 7 shows a significant positive correlation between the channel permeability and inter-well connectivity coefficient. The reason is that high permeability improves the ability of the fluid to migrate within the reservoir, making the production well more sensitive to the response of the applied pressure impulses. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Scenario**} & **Injection** & **Pressure Change** & **Producer** & \multirow{2}{*}{**Channel Width**} & **Channel** \\  & **Pressure** & **Duration** & & **BHP** & **(m)** & **Permeability** \\  & **(Bar)** & **(Month)** & **(Bar)** & & **(mD)** \\ \hline
1 & 780, 800, 760 & 6 & 600 & 7.1 & 30, 60, 90, 120 \\
2 & 780, 800, 760 & 6 & 600 & 7.1, 14.1, 21.1, 28.3 & 30 \\
3 & 780, 800, 760 & 2, 6, 12 & 600 & 7.1 & 30 \\
4 & 780, 800, 760 & 6 & 600 & 7.1 & 30 \\ \hline \end{tabular}
\end{table} 
Table 3: Basic parameters for sensitivity analysis of inter-well connectivity. Interestingly, the inter-well connectivity during the pressure stimulation stages is significantly higher than that of the non-pressure stimulation stages. When the channel permeability reaches 90 mD and 120 mD, the effect of increasing permeability on the inter-well connectivity becomes insignificant. In the later stage of production, roughly corresponding to 1 June 2027, the connectivity coefficients under different permeability channels tend to be stabilized within a certain range (0.65-0.75) since the water occupies the pore space under high water content and the mobility of water in all permeable channels is transferred from two-phase oil-water flow to single-phase water flow. Therefore, the connectivity differences caused by varied permeability channels may be weakened. Figure 8 shows the dynamic change in the dimensionless time-lag coefficient \(\tau\), a key indicator of the time required for fluid to flow from the injector to the producer. According to the calculation results, it is observed that the relationship between the \(\tau\) value of the four producers is \(\tau_{30}>\tau_{60}>\tau_{90}>\tau_{120}\) that is, the \(\tau\) value is inversely proportional to the permeability. This indicates that fluid migration rates are accelerated within a higher permeability channel, resulting in a faster fluid flow to the producer. This finding is consistent with observations at the time of the water breakthrough. Since the fluid flow rate is directly related to the formation permeability, fluid mobility is enhanced in the advantage channel with high permeability, giving it a lower time-lag coefficient. As can be seen from Figure 9, there is an obvious negative correlation between permeability and water breakthrough time. A producer connected to the center injector at a permeability of 30 mD has a water breakthrough time of 24 months. For producers with 60 mD permeability channels, the water is encountered after 12 months of production. However, the water breakthrough times for producers with 90 mD and 120 mD permeability are 6 months and 5 months, respectively. Figure 7: Dynamic changes in inter-well connectivity coefficients over time for permeable channels. This indicates that injected fluid can move more rapidly through the higher permeability channels, resulting in an earlier appearance of injected water in the producer. This phenomenon is twofold: higher water injection efficiency is its advantage, but it is also accompanied by the risk of water-driven fingering (increasing the cost of water plugging), lowering the water sweep efficiency, and jeopardizing the life cycle of the oil wells. Figure 8: Dynamic changes in time-lag coefficients with time under different permeable channels.