Robust Determination of the Pore Space Morphology in Sedimentary Rocks

Abstract

We present a new robust approach to study the morphology (shapes and connectivity) of the pore space of a sedimentary rock. Our approach is based on the longestablished, fundamental concepts of mathematical morphology. In particular, we propose an efficient and stable algorithm which distinguishes between the "pore bodies" and "pore throats," and establishes their respective volumes and connectivity. Our algorithm is extensively tested on the 3D digital images of computer-generated and natural sandstones. The algorithm tests on a pack of equal spheres, for which exact results can be verified visually, confirm its stability. Computer-generated pore space images are used to investigate the impact of image resolution on the algorithm output. Presently, the proposed algorithm produces a stick-andball diagram of the rock pore space. One of distinctive features of our approach is that no image thinning is applied. Instead, the information about the skeleton is stored through the maximal balls associated with each voxel. These maximal balls retain information about the entire pore space. Comparison with the results obtained by a thinning procedure preserving some topological properties of the pore space shows that our method produces more realistic estimates of the number and shapes of pore bodies and pore throats, and the pore coordination numbers. Based on the information about the maximal ball distribution, we simulate mercury injection and compute a dimensionless drainage capillary pressure curve. We demonstrate that the calculated capillary pressure curve is a robust descriptor of the pore space geometry and, in particular, can be used to determine the quality of computer-based rock reconstruction.

A New Method for Generating Pore-Network Models of Porous Media

“…They have utilized the concept of "maximal balls" (Silin et al 2003) to compute the locations and sizes of pores and throats and to create a topologically equivalent representation of 3D images.…”

A pore-scale model of two-phase flow in water-wet rock

“…Once a three-dimensional table of such maximal radii is generated, one can simulate various invasion scenarios using cluster search algorithms. A more detailed description of the method is in [38,41].…”

“…At the microscopic scale of a computer-tomography image, the compressibility of the fluid can be neglected as well, which yields a linear system of Stokes equations. To simulate two-phase flow at a pore scale, we combine a finite-differences discretization of the Stokes equations with the Maximal Inscribed Spheres (MIS) algorithm [42,38,37]. MIS-calculations are based on simple rules end employ efficient cluster search algorithms [39], so that the simulations do not require super-computer power.…”

A hydrologic view on Biot's theory of poroelasticity

“…Since the magnitude of the tortuosity in Biot's equations ranges, in general, between one to infinity [28], it is very important to know typical tortuosity factors for different types of rock. Microscopic flow modeling on pore networks [30] and morphological pore geometry analysis of tomographic images of the pore space [36] are very promising approaches from this point of view.…”