Integrating Probabilistic Neural Networks and Generalized Boosted Regression Modeling for Lithofacies Classification and Formation Permeability Estimation
Authors: Al-Mudhafar Watheq J. , Jaber Ali K. , Al-Mudhafar Ali 
Published: April 2016

Abstract
Multisource and multiscale modeling of formation permeability is a crucial step in overall reservoir characterization. Thus, it is important to find out an efficient algorithm to accurately model permeability given well logs data. In this paper, an integrated procedure was adopted for accurate Lithofacies classification prediction to be incorporated with well log attributes into core permeability. Probabilistic Neural Networks and Generalized Boosted Regression Models were adopted for Efficient Lithofacies Classifications and Formation Permeability Estimation, respectively.
The Probabilistic Neural Networks (PNN) is an implementation of a statistical algorithm called kernel discriminant analysis in which the operations are organized into a multi-layered feedforward network with four layers: Input, Pattern, Summation, and Output layers. It was used to model Lithofacies sequences in order to predict discrete lithofacies distribution at missing intervals. Then, Generalized Boosted Regression Modeling (GBM) was used as a to build a nonlinear relationship between core and log data. GBM is a recent data mining technique that has shown considerable success in predictive accuracy as it maintains a monotonic relationship between the response and each predictor.
The well log interpretations that were considered for Lithofacies classification and permeability modeling are neutron porosity, shale volume, and water saturation as function of depth; however, the measured discrete lithofacies types are Sand, Shaly Sand, and Shale. Firstly, the Probabilistic Neural Networks was adopted for modeling and prediction the discrete Lithofacies distribution at missing intervals. The classified Lithofacies were considered as a discrete independent variable in core permeability modeling in order to provide different model fits given each Lithofacies type to capture the permeability variation. Then, GBM was applied to build the statistical modeling and create the relationship between core permeability and the explanatory variables of well logs and Lithofacies. In GBM results, Root Mean Square Prediction Error (RMSPE) and adjusted R-square have incredible positive values, as there was an excellent matching between the measured and predicted core permeability. The GBM model has led to overcome the multicollinearity that was available between one pair of the predictors. All the multivariate statistics analyses of Lithofacies classification and permeability modeling with results visualizations were done through R, the most powerful open-source statistical computing languages.
Based on the same dataset, the PNN Lithofacies algorithm is the best classification approach as the total percent correct of the predicted discrete Lithofacies has exceeded 97.5% in comparison with other methods such as Linear Discriminant Analysis and Support Vector Machine. In addition, the RMSPE and Adjusted R-square obtained by GBM are much better than linear regression methods and Generalized Additive Models that have been applied on the same data as well.