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

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 X-rays, thermal neutrons, and synchrotron radiation. Utilizing X-rays from tubes, we mapped two 2.5and 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 is 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 100to 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 of 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. FLOW AND TRANSPORT PROCESSES in soils or other porous media depend on their structure, that is, on the spatial arrangement of the soil constituents. Structure controls the storage of water, the availability of dissolved essential elements, aeration, and the transport time of hazardous substances. To understand flow of water and air, or to predict the transport of dissolved pollutants and nutrients, the interaction between soil structure and transport processes must be investigated. To do this, we face a scale dilemma. Ultimately, we are interested in processes on scales ranging from meters to kilometers, such as the transport of liquid manure constituents from the soil surface to groundwater, the dynamics of heavy metals or pesticides in the topsoil, or the amount of available water for crops within an agriculturally used area, but these processes are dominated by the geometry of microscopic structures, in particular the shape and size of the pores. Pores form a network with openings ranging from less than one to a few thousand micrometers. Air, water, and dissolved substances move through this network of fine pores. Their mobility depends on the width and connectivity of the pore space. Connectivity is probably the most pertinent property in this sense and, at the same time, the most difficult to quantify. Pore size has various effects on transport processes: the mean velocity of water and dissolved solutes in a pore increases with pore radius to the power of two and the local flow velocity in pores grows in proportion to the square of the distance from the solid wall (Hagen-Poiseuille Law). The residence time of reactive substances is determined by the ratio of the sorbing surfaces to the volume of soil solution, a ratio that hyperbolically decreases with increasing pore size. The same functional dependence exists between pore size andwater retention, so the energy needed to drain water from soil increases with decreasing size of the pores (i.e., Young– Laplace equation). To understand transport processes in porous media, we need to determine the pore structure with a voxel size of a few micrometers. To assess the size of the pores and the pore-size distribution, indirect methods are often used: the solid phase is complementary to the pore space, and some soil properties can be estimated using the measured particle-size distribution (Arya and Paris, 1981; Arya et al., 1999). However, the structure of the porous medium does not depend on the size of the particles alone. Structure is the result of soil formation processes. A living organism, for example, may form a burrow or may produce organic substances that act as cementing P. Lehmann, A. Kaestner, A. Gygi, and H. Flühler, Institute of Terrestrial Ecology, Swiss Federal Institute of Technology, ETH Zurich, Switzerland; P. Wyss and A. Flisch, Centre for Non-destructive Testing, Swiss Federal Laboratories for Materials Testing and Research, EMPA, Switzerland; E. Lehmann and P. Vontobel, Spallation Neutron Source Division, Paul Scherrer Institute, PSI, Switzerland; M. Krafczyk, Institut für Computeranwendungen im Bauingenieurwesen, TU Braunschweig, Germany; F. Beckmann, GKSS-Research Centre, Geesthacht, Germany. Received 10 Dec. 2004. *Corresponding author ([email protected]). Published in Vadose Zone Journal 5:80–97 (2006).