Tomographical Imaging and Mathematical Description of Porous Media Used for the Prediction of Fluid Distribution

Abstract

Flow and transport processes in porous media depend on the geometric properties of their pores, where the diameters typically range from micrometers to millimeters. In this study, we mapped the pore structure of glass bead and sand columns using tomography with rays, thermal neutrons, and synchrotron radiation. Utilizing X-rays from tubes, we mapped two 2.5- and 5.3-cm-diam. sand samples that contained particles with sizes ranging from 0.08 to 1.25 mm. The resulting voxels (i.e., the unit of a three-dimensional image, the smallest distinguishable box-shaped part of a three-dimensional image) were cubes of 60-mm length in the case of microfocus X-rays, and 70 mm in case of industrial X-rays. In the latter case, each voxel represented the material density of a rectangular parallelepiped with side lengths of 70 mm and a height of 210 mm. The material density of cubes of 70 mm was reconstructed by applying an optimized filter in Fourier space. Columns with diameters of 4.0 and 5.3 cm containing glass beads with diameters of 3.0 and 2.0 mm were scanned with thermal neutrons. The voxel size was 167 mm. Because this technique sensitive to the presence of water, it was possible to measure the water table in a partially water-filled sample. Two sand columns were scanned with synchrotron X-rays, and the resulting voxel sizes were 11.5 and 3.5 mm. In the first case, the sample with a diameter of 15 mm contained particles of sizes ranging from 300 to 900 mm. In the second case, a sample with a diameter of 5 mm was filled with 100- to 200-mm particles. In a numerical analysis of the sphere packings, we computed various geometric properties of the porous media as a function of the resolution. The pore-size distribution and the Minkowski functionals quantities that define the morphology of a structure) were used to describe changes in the imaged pore space as a function of voxel size. We found that the geometric properties of the mapped pore space converged to true values for a voxel size of 10 to 20% of the mean particle radius. Based on this analysis, we postulate that the resolution a tomographic measurement must be in the range of 10% of the mean particle radius for repacked media to reconstruct the characteristic features of the pore space. This condition was fulfilled for the tomography with synchrotron light. Using the images of the sand samples measured with synchrotron light, we predicted the amount of water and air for a drainage process. For the pore space mapped with tube X-rays, it was possible to make qualitative predictions of the hysteretic water and air distribution.