Coal geomechanical properties are of importance in various applications, including drilling in coal seams, ensuring long-term borehole stability, and predicting the permeability evolution in coal seam gas reservoirs. However, coal is highly cleated and fragile. Obtaining standard drill cores for the laboratory test becomes exceptionally challenging. Also, the anisotropic characterizations of coal mechanical properties are often overlooked despite being essential in understanding directional drilling to increase gas production. In this study, nanoindentation tests were conducted to investigate the anisotropic nanomechanical properties of coal macerals and then the nano-scale data was used to predict the corresponding macroscopic mechanical properties. Overall, 900 indents were made on three types of coal polished surfaces perpendicular to the bedding plane, face, and butt cleats, respectively. The load-displacement curves obtained from the nanoindentation tests were used to calculate the elastic modulus and hardness. We then employed the dilute and Mori-Tanaka homogenization schemes to upscale the nano-scale results. To validate our findings, we compared our predicted values with the results obtained from direct laboratory measurements across different scales. According to the nanoindentation tests, the averaged elastic modulus is 5.89 GPa, 5.75 GPa, and 5.11 GPa, for the directions perpendicular to the bedding (Z), face cleats (Y), and butt cleats (X), respectively. Three coal macerals are identified. The elastic modulus of vitrinite is averaged as 4.55 GPa, 4.75 GPa, and 4.58 GPa for Z, Y, and X directions, respectively. For liptinite and inertinite, their elastic moduli are 4.35 GPa, 4.70 GPa, and 4.24 GPa, as well as 8.76 GPa, 7.80 GPa, and 6.51 GPa, respectively. It was observed that the elastic modulus of inertinite was anisotropic, with the measurement perpendicular to the bedding plane being greater than in the two directions parallel to the bedding plane. There was, however, no significant anisotropy identified for vitrinite and liptinite. This work provides direct measurements of the anisotropic mechanical properties of coal at the nano-scale, and establishes a correlation among the elastic modulus at different scales, especially at the nano-scale. By estimating the coal's mechanical properties from measurements on smaller samples, we provide an alternative approach to understanding the bulk anisotropic features of coals, which benefits various operations, especially directional drilling and permeability.

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