# Causes of Multi-Mechanism Abnormal Formation Pressure in Offshore Oil and Gas Wells
## 4 Analysis of Abnormal Formation Pressure Mechanisms  
Utilizing well logging data, we extracted and calculated essential parameters, including effective well depth, sonic velocity, density, resistivity, and natural gamma radiation. A detailed analysis of the sonic velocity as a function of depth was conducted to identify the location of the normally compacted section, which is determined to be situated at depths exceeding 1300 m. The corresponding data for this normally compacted section are presented in Figure 7. Subsequently, this dataset was employed to establish the Gardner correction equation, facilitating the derivation of the normal trend line for the velocity-density relationship. This trend line serves as a critical reference point for identifying and analyzing abnormal pressures in the subsequent stages of the study. Using hierarchical clustering algorithms to cluster data, determining the number of clusters in the clustering algorithm before clustering is a crucial step, which directly affects the quality and application effect of the final clustering results. This paper combines the elbow method and silhouette method to determine the optimal number of clusters. Figure 8 is the elbow method graph, which plots the distortion values corresponding to each number of clusters. The number of clusters is on the X axis, and the distortion values are on the Y axis. By observing the shape of the elbow graph, the elbow point usually refers to the position where the curve changes sharply at an inflection point. The number of  
Figure 7: Normal compaction section logging data. clusters corresponding to the elbow point is generally considered to be the optimal number of clusters. According to the elbow method graph, the optimal number of clusters is \(n=6\). On the basis of the elbow method, clustering results under different numbers of clusters are compared. When \(n=6\), hierarchical clustering identifies clusters that conform to the pressure recognition mechanism, and the classification effect on the dataset is more obvious. Some clustering results under different numbers of clusters are shown in Figure 9.  
To accurately divide the clustering results of different abnormal pressure mechanisms, a normal compaction trend line is drawn using the Gardner correction equation established by the data from the normal compaction section. The Gardner empirical formula is a method that reveals the relationship between formation density and P wave velocity, and there is often a certain error when directly using the Gardner formula to research velocity-density relationships. Therefore, based on the Gardner formula, the Gardner correction equation is obtained by fitting the normal compaction section data from the #A well and #B well in Cameroon. The Gardner correction equation fitted based on the normal compaction section data is shown in Figure 10.  
Figure 8: Elbow method for determining cluster number. Figure 9: Clustering results with different numbers of clusters. In the Rio Del Rey Basin, by combining the geological data of the target area and the velocity-density cross-plot, it can be seen that various mechanisms such as under-compaction, fluid expansion, and shale diapirism are superimposed and jointly affect the formation of abnormal high pressure. The corrected Gardner curve is used as a loading curve on the velocity-density cross-plot to identify the abnormal pressure mechanism.