# 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
#### 4.3.3 Duration of Pressure Impulses  
Figure 12 shows the variation in inter-well connectivity coefficient for different pressure impulse durations, which are 3 months, 6 months, 9 months, and 12 months, respectively. It is found that after the first pressure impulse is applied, there is a significant increase in the connectivity coefficient. It is most likely that the applied pressure impulses stimulate fluid migration, facilitating a dominant water flow channel. Notably, the second pressure impulse with the highest amplitude (+20 bar) corresponded to a more significant rise in the connectivity coefficient.  
Figure 11: Variations in time-lag coefficients under different widths of permeable channels.  
Figure 12: Inter-well connectivity coefficients for different pressure impulse durations.  
With the increase in the duration of pressure impulses, the inter-well connectivity coefficient increases, which may be because the longer pressure differential provides more possibilities for oil and water migration and exchange, which is conducive to enhance the inter-well connectivity.  
However, once the applied injection pressure differential is over, the connectivity coefficients for each pressure differential are consistent, indicating a similar flow pattern and equilibrium state. From a long-term perspective, inter-well connectivity eventually shows a consistent trend regardless of how long the injection pressure differential lasts.  
The time-lag coefficient decreases steadily under different durations of pressure impulses, indicating an improved fluid transfer efficiency in the reservoir, and the impact of water injection can be felt more quickly in the producers. At the same time, it is observed in Figure 13 that the time when the time-lag coefficient begins to decline is related to the time when the injection pressure differential plays a role. For the pressure differential duration of 3 months, the decline of the time-lag coefficient starts earlier, but at 12 months, the decline of the time-lag coefficient commences later. This shows a swift self-adaptation and recovery of the fluid transfer system when the reservoir experiences a short-term pressure impulse. In contrast, long-term pressure differential causes the fluid flow system to respond steadily after adjustment. This trend may be related to reservoir fluid dynamics and the establishment of ineffective circulation channels. Short-term pressure differential may cause rapid fluid movement and redistribution in the reservoir, while long-term pressure differential may cause far-reaching adjustments in the fluid flow path. Once the change in injection pressure differential ends, the time-lag coefficients of each period eventually converge, indicating that the reservoir has reached a new dynamic equilibrium state. On the whole, the change in time-lag coefficients under different pressure differential durations reflects the adaptability and recovery of the reservoir to operation schedule changes. This insight is valuable for developing and adjusting oil field development strategies, especially when designing water injection schemes and predicting long-term field performance.