Multifractal Analysis and Neural Network Prediction of Pore Structures in Coal Reservoirs Based on NMR T2 Spectra

Low-field nuclear magnetic resonance (NMR) is widely used for accurate characterization of coal pore structure. The NMR T2 spectrum represents the pore size distribution. Also, the T2 cutoff (T2c) value is a key parameter, reflecting the free/bound fluid proportion of coal. To characterize the pore structure of coal more comprehensively, the NMR T2 spectra of coals with different pore structures were characterized by multifractal, and then, the T2c values were predicted by a BP neural network model. The main conclusions are as follows: the T2 spectra of three ranks of coals (anthracite, bituminous coal, and lignite) showed typical unimodal, bimodal, and trimodal distributions, respectively. The porosity had a weak negative correlation with T2c, whereas the proportion of free fluid had a strong negative correlation with T2c. The quality indices τ(q) of the three coals changed monotonously, which conformed to the multifractal characteristics. The generalized fractal dimension spectra decreased in an inverse S-shape, decreasing while the multifractal singular spectra were hook-shaped. Dmin, ΔD, αmax, α0, and Δα showed strong positive correlations with T2c, which indicated that with an increase in T2c, the proportion of large-size pores decreased and the local pore size distribution became more concentrated and inhomogeneous. The predicted T2c values of the training, verification, and test sets of the BP neural network model fitted the measured T2c values well, and the mean square error was only 0.17%. The trained BP neural network model was reliable and can be used for the T2c prediction of more similar coal samples.