Darcy-scale digital core models for rock properties upscaling and computational domain reduction

The rapid development of Digital Rock Physics (DRP) requires the elaboration of robust techniques for closing the gaps between different scales of rock studies (upscaling). The upscaling workflows are especially needed to support the applicability of DRP for heterogeneous rocks. Basically, DRP involves two primary stages: model construction and simulation of physical processes on the models created. For heterogeneous rocks, there is an inherent trade-off between the spatial resolution of the data and the representativeness of the model size. The primary objective of this study was to implement and test a technique for upscaling digital core models from microscale to macroscale, enabling the computation of rock properties while accounting for heterogeneity of various scales. The upscaling is based on establishing correlations between tomography data of different resolutions and transforming low-resolution tomography into a multi-class model according to the defined correlation. The convolutional neural network for high-resolution tomography data was considered as the optimal algorithm for transforming low-resolution tomography into a multi-class model. The output of the neural network was an upscaled model of lower resolution than the original tomography image. Each cell in the upscaled model belonged to one of several types of formation, whose generalized characteristics were determined on the basis of the analysis of high-resolution tomography data. To validate the upscaling technique, we constructed a digital model of a complex carbonate reservoir based on data from multi-scale microtomography ($\mu$CT). A Darcy-scale model has been used and validated as a multi-class model, enabling the computation of flows in pore samples of various scales. By incorporating diverse pore space structures as different classes in the Darcy-scale model, it is possible to preserve the substantial physical size of the model while enhancing its level of complexity.