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A Multi-Scale Fractal Approach for Coal Permeability Estimation via MIP and NMR Methods

Permeability in porous media has an important role in many engineering applications, which depends mainly on the pore size, distribution, and connectivity of porous media. As the pore structure distribution of coal has a multi-scale fractal dimension characteristic, this study aimed to propose a multi-scale fractal dimension characteristics units model (MFU) to describe the pore structure distribution by analyzing the multi-scale fractal dimension characteristics of coal pore media. Then, a multi-scale fractal permeability model was established based on MFU. The pore structure distribution was obtained by mercury injection porosimetry (MIP) and nuclear magnetic resonance (NMR) experiments. Based on MIP and NMR experimental data, the permeability contribution of different pore diameters were calculated. The results show that the permeability contribution of the micropore was minimal and can be ignored. The permeability contribution of mesopores was about 1–5%, and the permeability contribution of macropores was about 95–99%, which plays a decisive role in the seepage process. The calculated results, based on multi-scale fractal permeability model and the experimental permeability data, are in the same order of magnitude. The permeability prediction based on proposed model is better than classical single fractal permeability model.