Multisource and multiscale modelling 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 modelling formation core permeability given well logs and Lithofacies classification for a well in sandstone formation in South Rumaila Oil Field, located in Iraq. The core permeability was modelled give well logs interpretation: neutron porosity, shale volume, and water saturation as function of depth, in addition to the vertical Lithofacies sequences. The statistical learning algorithms that were adopted in this paper are Generalized Linear Models (GLM) & Smooth Generalized Additive Model (sGAM) for permeability and Probabilistic Neural Networks (PNN) for Lithofacies prediction.
Firstly, the Probabilistic Neural Networks was adopted for modelling and prediction the continuous and discrete Lithofacies distribution. The classified Lithofacies were considered as a discrete independent variable in core permeability modelling in order to provide different model fits given each Lithofacies type to capture the permeability variation. Then, GLM and sGAM models were applied to build the statistical modelling and create the relationship between core permeability and the explanatory variables of well logs and Lithofacies. GLM considers the maximum likelihood function to estimate the coefficients; however, sGAM considers a sum of nonparametric smoothing functions to identify nonlinear relationships depending on the degree of smoothing. The cubic spline function provides the closest fit as it minimizes a penalized negative log-likelihood function, which represents the smooth terms, by minimizing of an internal generalized cross validation function by iteratively reweighted least squares.
In sGAM results, Root Mean Square Prediction Error (RMSPE) and the R-squared have better values than GLM especially in the reduced models. The stepwise elimination was considered to find the best predictors subset in GLM; nevertheless, the non-influential predictors in sGAM were recognized and treated as splines smoothed term to ensure rejection for the null hypothesis and ensure the confidence interval to be greater than 95%. The sGAM model has led to overcome the multicollinearity that was available between one pair of the predictors by using the smoothed terms. All the multivariate statistics analyses of Lithofacies classification and permeability modelling with results visualizations were done through R, the most powerful open-source statistical computing languages.