Determining fractal dimensions of coal pores by FHH model: Problems and effects

The Frenkel-Halsey-Hill (FHH) model is one of the important methods of obtaining the specific surface fractal dimension (DS) of complex fractal porous media. Specific surface fractal dimension provides useful information about pore structure that could help better understand the gas flow behavior. Thus it could be a useful method for coalbed methane evaluation. Based on the FHH model, the fractal characteristics of 58 coals from 14 mining areas in the eastern margin of the Ordos Basin, China are analyzed. The difficulties associated with the FHH model in obtaining the DS are solved by the classification of ln V vs. ln(ln(P0/P)) plots (types P1, P2, P3, and P4). It is suggested that the fractal dimension should be obtained from the linear segment of the plots when capillary condensation controls the adsorption process. The results show that the DS ranges from 2.22 to 2.77 for the 58 coals, except for six samples with plots Type P4, for which correct DS could not be obtained. In general, the DS has a positive correlation with specific surface area and a negative correlation with the median pore diameter. In addition, the DS is affected by coal rank and maceral content and decreases with increasing carbon and hydrogen contents and decreasing ash yield ratio. Furthermore, when the coal rank increases from low to relatively high, the DS tends to be higher for drained swamp coal facies that are rich in minerals and inertinite, and tends to be lower for moisture swamp coal facies that are rich in vitrinite.