Fractal Characterization of Fracture Structure of Coal Seam Water Injection Based on NMR Experiment

The complex fracture structure of coal bodies determines the seepage characteristics of water within them. Such characteristics are key for accurately guiding the coal seam water injection process. In this paper, nuclear magnetic resonance (NMR) and two characterization parameters (i.e., pore size distribution and porosity) were used to explore the change law of fracture structure in coal under different stress conditions. Based on the analytical geometry theory, the newly obtained NMR water injection displacement image was binarized, and the two-dimensional fractal dimension of the fracture structure (Ds\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{s}$$\end{document}) was obtained by applying the box dimension method. Through a linear fitting of the T2 spectrum data obtained by NMR, the fractal dimension of the fracture structure distribution (DV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{V}$$\end{document}) was obtained and compared with the three-dimensional fractal dimension of a theoretical fracture. Based on the NMR experimental results, we determined the maximum and minimum pore sizes of the coal fractures, the fractal dimension of coal fracture tortuosity (DT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{T}$$\end{document}), and the relationship between the fractal dimension and porosity. Overall, the results showed that the two fractal dimensions can describe the change law of coal fracture structure under different stress conditions; moreover, they can be used to quantitatively characterize the change law of coal fracture structure during coal seam water injection. This demonstrates the applicability of the above two fractal dimensions in real mechanical environments.