An adsorption model for cylindrical pore and its method to calculate pore size distribution of coal by combining NMR

Coalbed methane (CBM) adsorption is closely related to pore size distribution in coal, the study of its adsorption state and pore characteristics of coal are of great significance to its exploitation and storage. In this paper, an extended simplified local density adsorption (SLD) model is proposed, which can be applied to cylindrical pores. Combining with the nuclear magnetic resonance (NMR) tests, the extended SLD model can predict the adsorption amount and pore size distribution of the whole sample without destroying its original pore structure. Three coal samples collected from different areas are selected for NMR test to measure T2 distribution and Magnetic Resonance Imaging (MRI) image. Then, the adsorption amount of the samples are obtained under constant temperature and different pressures. The fitting coefficients of the extend SLD model and experimental data of the three samples are all greater than 0.99, indicating that the proposed model matches the experimental results well. The two parameters obtained by fitting, transverse surface relaxivity (K) and the total number of pore (N), combined with T2, can get the radius and number of each pore in the sample. The inversion results show that the number summation of micropores and mesopores of the three samples are all exceeds 99%. However, due to the small pore size of micropores and mesopores, the pore volume summation of the three coal samples occupied by fractures and macropores are all over 27%. Further observation of cylindrical pore size and fluid molecular position shows that the distance between fluid-solid molecules is the main factor affecting the adsorption. The results of this paper are beneficial to predict and calculate the adsorption amount and pore size distribution of coal.