Integrating K-means clustering analysis and generalized additive model for efficient reservoir characterization

Abstract

We present new efficient algorithm for modeling the formation permeability given the well logs and core petrophysical properties in addition to vertical facies classification for a well in sandstone formation in West Africa. Firstly, the k-mean cluster analysis has been used to obtain the vertical rock types (Facies) sequences along the whole depth interval of the formation. K-means algorithm begins by choosing k observations to serve as centers for the clusters. Then, the distance from each of the other observations is calculated for each of the k clusters, and observations are put in the cluster to which they are the closest. This process is repeated until no observations switch clusters. Additionally, by using K-mean, the optimal number of clusters (Facies) have been specified. Then, Generalized Additive Model (GAM) was considered to build the relationship between core permeability and the explanatory variables. GAM considers a sum of nonparametric smoothing functions to identify nonlinear relationships depending on the degree of smoothing. In GAM results, Mean Square Prediction Error (MSPE) and Analysis of Variance (ANOVA) have been considered to select the optimal model that performs null hypothesis rejection for all parameters. Consequently, a significant overall reduction in model deviance leading to variance reduction