Multifractal Characteristics of Low-Field Nuclear Magnetic Resonance of Different Rank Coals and Its Permeability Predicting Method

The permeability of methane in coal is a crucial factor in the production of coal-bed methane (CBM), which is dependent on the pore size distribution (PSD) of coal. The transverse relaxation time cutoff value (<i>T</i>_2C) is a crucial parameter in nuclear magnetic resonance (NMR) techniques for converting NMR data into an absolute PSD. To investigate an appropriate approach for predicting the <i>T</i>_2C and permeability of different rank coals, this study first revealed, through centrifuge experiments with a centrifugal force of 1.38 MPa, the <i>T</i>_2C values of five coal samples: anthracite coal (3 ms), lean coal (8 ms), coking coal (12 ms), fat coal (11 ms), and lignite coal (13 ms). These <i>T</i>_2C values were then employed to obtain the absolute PSD values of the coal samples. The results demonstrated that the pore structure characteristics of these coal samples are essentially identical, with micropores constituting the majority, varying between 63.47% and 93.74%. Subsequently, the multifractal analysis method was introduced to establish a new <i>T</i>_2C value calculation model. A comparison of the model-calculated <i>T</i>_2C values with those obtained from centrifugal experiments revealed an average deviation of only 5.26%. Finally, a new permeability model was developed by conducting multiple regressions on permeability and multifractal parameters. In comparison to classical models, such as the Timur-Coates (TC) model and the Schlumberger Dauer Research Center (SDR) model, the developed permeability model offers more accurate predictions. These results are applicable to pore structure characterization and methane permeability prediction in coal reservoirs of varying rank and other unconventional gas reservoirs.