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 long-established, 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-and-ball 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.