Digital images analysis and quantitative structure-permeability relationships

Abstract

In this work multiple linear regression was used to obtain mathematical models with which it is possible to predict the permeability of isotropic porous media. With this aim, a database containing the binary files of the digital images of a wide variety of structures was built. These files allowed to: 1) extract statistical and morphological descriptors of the solid and void phases that were used as independent variables and 2) calculate permeability (dependent variable) by computational fluid dynamics and the lattice Boltzmann method. The selection of the descriptors that constitute the models was carried out according to the stepwise method with backward elimination. In order to fulfill the linearity assumption, it was necessary to transform some of the descriptors by taking their natural logarithm. After removing the influential values, the regressions were analyzed by using different statistics and hypotheses testing. One of the models were able to explain the 93.3% of the variability of permeability as a function of the porous structure.