Determination of shale macroscale modulus based on microscale measurement: A case study concerning multiscale mechanical characteristics

Shale mechanical properties are important for shale gas production, but the magnitudes are difficult to estimate, standard size cores are hard to sample, and secondary interstice generation is inevitable. This paper proposes a method for determining shale macroscale modulus, which is determined at a hierarchy of scales from the nano-to macro-scales. Microscale measurements are upscaled to estimate the corresponding magnitudes at the macroscale. A case study is conducted with Silurian shale samples, using the hierarchy scales, gridding nanoindentation, atomic force microscopy (AFM), mineral liberation analysis (MLA), X-ray diffraction (XRD), and uniaxial compression tests. The mineral compositions are analyzed using MLA and XRD, and the shale composition is described in terms of clay minerals, organic matter, and siliceous and carbonate contents. The variation in the Young's modulus is analyzed based on the recorded indentation depth curves and modulus distributions. The nanoindentation and AFM results are upscaled to the centimeter scale through the Mori–Tanaka method. The upscaled results exhibit satisfactory fitting with the conventional uniaxial compression results, although the fitting of the upscaled AFM results is better than nanoindentation. The proposed approach can be applied to promptly and comprehensively predict the shale mechanical parameters during shale gas exploration.