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The porous media community extensively utilizes digital rock images for core analysis. High-resolution digital rock images that possess sufficient quality are essential but often challenging to acquire. Super-resolution (SR) approaches enhance the resolution of digital rock images and provide improved visualization of fine features and structures, aiding in the analysis and interpretation of rock properties, such as pore connectivity and mineral distribution. However, there is a current shortage of real paired microscopic images for super-resolution training. In this study, we used two types of Scanning Electron Microscopes (SEM) to obtain the images of shale samples in five regions, with 1X, 2X, 4X, 8X and 16X magnifications. We used these real scanned paired images as a reference to select the optimal method of image generation and validated it using Enhanced Deep Super Resolution (EDSR) and Very Deep Super Resolution (VDSR) methods. Our experiments show that the bilinear algorithm is more suitable than the commonly used bicubic method, for establishing low-resolution datasets in the SR approaches, which is partially attributed to the mechanism of Scanning Electron Microscopes (SEM).

In the hydraulic fracturing of natural rocks, understanding and predicting crack penetrations into the neighboring layers is crucial and relevant in terms of cost-efficiency in engineering and environmental protection. This study constitutes a phase field framework to examine hydraulic fracture propagation in naturally-layered porous media. Biot's poroelasticity theory is used to couple the displacement and flow field, while a phase field method helps characterize fracture growth behavior. Additional fracture criteria are not required and fracture propagation is governed by the equation of phase field evolution. Thus, penetration criteria are not required when hydraulic fractures reach the material interfaces. The phase field method is implemented within a staggered scheme that sequentially solves the displacement, phase field, and fluid pressure. We consider the soft-to-stiff and the stiff-to-soft configurations, where the layer interface exhibits different inclination angles $\theta$. Penetration, singly-deflected, and doubly-deflected fracture scenarios can be predicted by our simulations. In the soft-to-stiff configuration, $\theta=0^\circ$ exhibits penetration or symmetrical doubly-deflected scenarios, and $\theta=15^\circ$ exhibits singly-deflected or asymmetric doubly-deflected scenarios. Only the singly-deflected scenario is obtained for $\theta=30^\circ$. In the stiff-to-soft configuration, only the penetration scenario is obtained with widening fractures when hydraulic fractures penetrate into the soft layer.