Efficient multi-scale image reconstruction of heterogeneous rocks with unresolved porosity using octree structures

Abstract Identifying rock properties at the pore scale plays a crucial role in understanding larger-scale properties. For this purpose, the digital rock physics technique is used to model rock images at the pore scale. Achieving high-resolution (HR) images with a large field of view (FoV) is essential for pore-scale modeling of heterogeneous rock samples, which presents significant challenges due to their complex structures. However, because of the trade-off between resolution and FoV, it is not possible to acquire large HR images. Multi-scale image reconstruction methods enable modeling images at different resolutions and FoVs. Despite various approaches being introduced, a common limitation is the high computational cost. In this study, a novel approach based on Octree structures is introduced to minimize computational cost while maintaining accuracy. A Berea sandstone (BS) and an Edward Brown Carbonate (EBC) sample were scanned at both HR and low resolution (LR) using X-ray microtomography. Our method involves splitting the unresolved porosity in rock images into smaller sections of unresolved templates using the watershed algorithm and considering the optimized parameters. We then applied a cross-correlation based simulation technique to find the best match of each unresolved template. The novelty of our approach lies in the use of an Octree structure to perform calculations on LR images, significantly reducing computation time and memory consumption due to the fewer number of pixels in Octree LR structures. The accuracy of the images thus reconstructed using our approach was compared with those from previous methods by evaluating geometric properties and single- and two-phase flow properties. The results were promising, demonstrating that our approach achieved a permeability close to the real value, while the previous method had an error of approximately 4% for both BS and EBC rocks. More importantly, our approach was approximately three times faster and reduced memory usage by 20 to 130 times. The findings of this study facilitate dual- or multi-scale modeling and evaluate heterogeneous rock images at a significantly lower computational cost. In particular, for heterogeneous rocks, where multi-scale image reconstruction demands substantial memory and runtime, the use of the Octree technique enables accurate reconstruction with lower computational cost.