# A New Algorithm Model Based on Extended Kalman Filter for Predicting Inter-Well Connectivity
## 3 Construction of Numerical Model
### Model Construction  
SV-DC model analysis requires comprehensive and continuous data, which can be accessible by either numerical simulation or field monitoring. Compared with the field monitoring data that are often incomplete and susceptible to events such as well leakage, equipment failure, and shut-in maintenance, numerical simulation can ensure the integrity and continuity of data. When constructing the SV-DC model, the EKF algorithm requires the data to be continuous, complete, and uninterrupted. The numerical data meet all these strict requirements. With this in mind, this paper chose data based on numerical simulation rather than directly using field data to reveal the influence law of inter-well connectivity and perform the sensitivity analyses.  
This study chooses the widely used reservoir simulator tNavigator (Version 23.3) to simulate oilfield production [40]. The tNavigator is a new efficient reservoir numerical simulation system that combines static (geological) and dynamic (reservoir) models comprehensively. The tNavigator is the first industry-leading product that dynamically integrates a fully 3D interactive user interface with a record-breaking CPU+GPU co-parallel computing engine.  
Figure 2: Geological overview of the Nm13 sand body in southern Qinhuangdao 32-6 oilfield. The black lines in the larger image indicate potential faults detected, and the blue dot in the zoomed image represent the central one injector, and the four red dots represent the four producers peripherally.  
A 3D reservoir model with 305 m \(\times\) 305 m \(\times\) 5 m (length \(\times\) width \(\times\) height) was developed according to the geology data (Figure 3a). A single oil formation was considered with a thickness of 5 m according to the average oil layer thickness. A typical five-spot well pattern was adopted. According to the model symmetry, a one-quarter model was considered with the production well and injection well arranged at the corners of the rectangle model domain (Figure 3b). A high-permeable channel was simulated along the model diagonal with varied absolute permeabilities and channel widths.  
The production well BHP was set at 600 bar throughout the run (Table 1). Initially, the injection well had a BHP of 750 bar, which was subsequently adjusted to 780 bar, 800 bar, and 760 bar at different stages. These adjustments occurred as distinct rectangular impulse signals. The adjustments were scheduled for January 2024, January 2027, and January 2031, with each adjustment period lasting six months.  
The petrophysical parameters of the ideal reservoir model are listed in Table 2. The reservoir porosity and matrix permeability of the model were assigned as 2% and 10 mD, respectively. Water density was assumed to be 1000 kg/m\({}^{3}\), and the oil density was estimated to be the average oil density (867 kg/m\({}^{3}\)) of most oil fields in China.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Production** & **Reservoir** & **Injection Pressure** & **Each Pressure** & **Distance Between** \\
**Well BHP** & **Average** & **Regulation** & **Regulation** & **Injector and** \\
**(Bar)** & **Pressure (Bar)** & **(Bar)** & **Duration (Month)** & **Producer (m)** \\ \hline
600 & 750 & 780, 800, 760 & 6 & 424.3 \\ \hline \end{tabular}
\end{table}
Table 1: Model setup for injection and production wells.  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameters** & **Value** & **Unit** \\ \hline Depth & 6000 & m \\ Porosity & 2 & \% \\ Initial water saturation & 0.2 & / \\ Matrix permeability & 5 & mD \\ High-permeability channel permeability & 30/60/90/120 & mD \\ Oil density (at surface conditions) & 867 & kg/m\({}^{3}\) \\ Water density (at surface conditions) & 1000 & kg/m\({}^{3}\) \\ BHP of productor & 600 & bar \\ BHP of injector & 750 & bar \\ \hline \end{tabular}
\end{table}
Table 2: Petrophysical parameters used in the ideal model.  
Figure 3: Three-dimensional reservoir model (**a**) and high-permeability channel between injector and producer (**b**).