Using multiple linear models for permeability estimation and modeling in a well of sandstone reservoir

Abstract

In this paper, we present the multiple linear model to estimate the formation permeability at non-cored intervals as function of well logs and core measurements for a well in sandstone formation in West Africa. In Linear model, the least-squared function is used to generate the relationship between core permeability and the explanatory variables such as caliper (CCL), deep induction, gamma rays, neutron porosity, core porosity, deep resistivity, spontaneous potential (SP), corrected density, and rock facies. The resulted permeability equation has different intercept for each rock types. The linear model has been done three different ways to ensure the normal distribution for the response factor (permeability) and achieving the statistical tests. The first one is the full model that has all the independent variables with the original data. In the second one, a stepwise elimination has been used to delete the variables that don't have a significant effect on the model. A log transformation was applied in the third model to get an approximate normal transformation. To validate the linear model, t-test and ANOVA table have been considered to choose the optimal model that performs null hypothesis rejection for all the variables and the confidence interval to be greater than 95%.