Modelling the petrophysical properties such as permeability given multiple well logs and core data measurements is a crucial process in reservoir characterization because precisely permeability estimation in non-cored intervals leads to adequate overall reservoir characterization and perform an accurate reservoir model. However, this procedure is hard to be done with the conventional statistical approaches because of the lack and sparseness data in addition to the high degree of uncertainty in most cases. Consequently, the advance statistical learning algorithms would be efficiently suitable with these sensitive cases in order to perform accurate prediction. The lasso and generalized additive model have been considered in this paper as an efficient tools to model and predict the formation permeability given other well logs data for a well in sandstone reservoir in South Rumaila oil field, located in Iraq.
Prior fitting the statistical model, least absolute shrinkage and selection operator (Lasso) has been applied to refine the model and seek the optimal k-variables subset. Lasso is an extremely efficient procedures for fitting different regression models such as logistic and multinomial regression models. After choosing the best factors subset, the Generalized Additive Model (GAM) has been adopted to build the statistical modelling and generate the relationship between core permeability given the explanatory variables of neutron porosity, shale volume, and water saturation as function of depth.
The Generalized Additive Regression 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 penalized iteratively reweighted least squares.
The modelling has been done by lasso and GAM algorithms. The selected variables by lasso has been considered for subset selection in GAM. The non-influential variables have been treated through penalized terms. Variance and RMSE have been considered for model validation and comparisons. Additionally, t-test table has been considered to show whether the parameters perform null hypothesis rejection and the confidence interval to be greater than 95% or not.
The predicted permeability from each algorithm in each case have been outlined, depicted, and discussed for its compatible with the measured values.
