Using Generalized Linear Regression Of Multiple Attributes For Modeling And Prediction The Formation Permeability In Sandstone Reservoir

Abstract

Abstract In this paper, we present an efficient flexible algorithm for modeling the formation permeability with respect to other well and core petrophysical properties for a well in sandstone formation in West Africa. In Generalized Linear Regression, the monotonic link function, glm, has been used to generate the relationship between the core permeability and the explanatory variables such as caliper log (CCL), deep induction log, medium induction log, gamma rays, neutron porosity, core porosity, deep resistivity, medium resistivity, spontaneous potential (SP), density & corrected density, in addition to rock facies. Meanwhile, the glm function has been adopted for attaining normal distribution for the continuous variables and multinomial distribution for the discrete (rock facies). The link function relates the expected value of the distribution to the predictor variables. Fitting of a GLM model was achieved through optimization of maximum likelihood estimates by an iteratively reweighted least-squares mechanism. The Root mean square errors (RMSE) is not a sufficient indicator of bias for an estimate because RMSE could be changed due to a change in variance, with no change in bias. Consequently, variance, analysis of deviance, and RMSE have been considered for model comparisons. In GLM results, a significant overall reduction in model deviance with less variance, residual deviance, and RMSE that reflects the reduction in both variance and bias and the validity of the fitted linear model.