Predicting the Permeability Using Geometric Properties of Micro-Computed Tomography Images by Linear Regression Models

Challenges of rock absolute permeability prediction of tiny samples are remarkable when laboratory apparatus is not applicable and there is no pore network modeling. The prediction using the characterization of micro-computed tomography images has been studied in this paper. Twenty series of ۲D micro-computed tomography rock binary images have been collected, and each was considered a ۳D binary image. Their geometric measures in ۲D and ۳D for measuring image properties have been considered using Minkowski functionals and available functions, developing a regression model; absolute permeabilities have also been evaluated. Some ۲D and ۳D geometric properties are considered. The area, the perimeter, and the ۲D Euler number are ۲D binary image properties. The volume, surface area, mean breadth, integral of the mean curvature, and the ۳D Euler number are ۳D binary image properties. The porosity and number of objects have also been considered parameters of a regression model. Twenty-four parameters were evaluated, and some were chosen to perform linear regression. An equation was proposed based on the extensive study to predict rock permeability. This equation has two sets of parameter coefficients: one set predicts high-permeability rocks (above two Darcy), and the other used for low- and medium-permeability rocks (less than two Darcy) can be employed for carbonated rock. The average absolute relative error for conducted cases is ۰.۰۶.