Incorporation of Bootstrapping and Cross-Validation for Efficient Multivariate Facies and Petrophysical Modeling

Abstract

Abstract An integrated multivariate statistics procedure was adopted for the accurate Lithofacies classification prediction to be incorporated with well log attributes into core permeability modeling. Logistic Boosting Regression and Generalized Linear Modeling were adopted for Lithofacies Classification and core permeability estimation, respectively. Logistic Boosting Regression (LogitBoost) was used to model the lithofacies sequences given well log and core data to predict the discrete lithofacies distribution at missing intervals. In this paper, the permeability modeling and estimation was validated through bootstrapping and cross-validation. The well log interpretations that were considered for lithofacies classification and permeability modelling are neutron porosity, shale volume, and water saturation as a function of depth. The measured discrete lithofacies types include three main lithology types: sand, shaly sand, and shale. LogitBoost was adopted for modelling and prediction the discrete Lithofacies distribution for the entire reservoir depth that was then incorporated into permeability modelling. Next, GLM was applied to create the relationship between core permeability and the explanatory variables of well log and Lithofacies. In GLM results, the accuracy of the entire permeability modelling was assessed by K-fold cross-validation that showed significant reduction in prediction variance. GLM has also led to overcome the multicollinearity that was available between shale volume and water saturation. Bootstrapping was then adopted, as an approval tool to ensure that there is no doubt about the validity and accuracy of the fitted GLM model. Bootstrapping simply re-samples the data into a specific number of times and recalculates the variable given each sample. The bootstrapping was implemented for Adjusted R-squared of the overall GLM approach.