A Finite-Difference-Based Multiscale Approach for Electromagnetic Digital Rock Modeling

Conventional methods to extract the electrical properties from Micro-CT rock images require significant computational resources. This paper describes a novel multiscale method for such large-scale modeling, based on a hierarchy approach. Without losing any information from the original Micro-CT images, the method uses the mixing theory to extract equivalent rock electrical properties at multilevel and cascades all results at different level to achieve the overall rock properties. The method proposed in this paper effectively overcomes previous approximation that needs to decimate the original images and all the vital information will be retained. Real-world sandstone images were used as an example to demonstrate the accuracy and efficiency of this approach. Modeling and simulations are performed at multiscale with different choices of submodel sizes to understand the effect of partition on the overall accuracy. It shows that relative larger submodel size will generally lead to better solution but requires more computational resources. A preliminary investigation on the tradeoff between submodel size and the relative errors are presented. Numerical examples demonstrate the accuracy and efficiency of this approach.