A quantitative study of the microstructure of Indian Gondwana shale: a fractal and algebraic topology approach

Abstract

This paper covers a novel micro-level application of image processing in understanding the topological and petrophysical properties of Indian Gondwana shale using X-ray computed microtomography images. The complexity and randomness in the pore system are explained through the concept of fractal dimension (FD). In this paper, a quantitative analysis of 2D and 3D fractal dimensions of pores, grains and interfaces was performed for Indian Gondwana shale, using the box-counting method. A pore network is formed by the connection of many subpore clusters, each with a different volume. Hence, an image segmentation algorithm was applied to label different subclusters, and subsequently an analysis of FD was carried out on such subclusters of pores and grains. We implemented a novel application of Betti numbers (B0, B1 and B2) and Euler characteristics on our sample and calculated the possible flow channels of the sample. The FD of grains was found to be greater than the FD of the pore–grain interfaces, while the FD of pores was found to have the smallest value. Consequently, we also observed how the FD of both pores and grains was majorly controlled by the largest subcluster, and during fluid intrusion we observed a significant decrease in the FD of pores. Finally, the pore network with a larger B0 and larger difference of B1 was proved to be best for the storage of hydrocarbons and for fluid movement along more flow channels.