A quantitative study of 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 an X-ray computed micro tomography images. The complexity and randomness in the pore system are explained through the concept of fractal dimension (FD). In this article, a quantitative analysis of 2D and 3D fractal dimension of pores, grains, and interface has been done for the Indian Gondwana Shale, using the Box counting method. A pore network is formed by the connection of many sub-pore clusters, each with a different volume. Hence, an image segmentation algorithm has been applied to label different sub-clusters, and subsequently, analysis of FD is done on such sub-clusters 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 pore-grains interface, while the FD of pores was found to be the least. Consequently, we also observed how the FD of both pores and grains is majorly controlled by the largest sub-cluster, and during fluid intrusion, we see a significant decrease in FD of pores. Lastly, the pore network, with a larger B0 and larger difference of B1 can be proved best for the storage of hydrocarbon content and its fluid movement understanding due to more flow channels.