Deriving coal fractal dimensions from low-pressure nitrogen adsorption isotherms applying an integrated method

Abstract

The internal surface roughness of coals determines, to an extent, the quantity of natural gas, specifically methane, that they can readily adsorb/store and the ease with which that gas can flow and be produced from coal formations. Coals’ fractal dimensions (D) provide a quantitative measure of the degree of roughness of their internal surfaces (pores and microfractures). Low pressure nitrogen adsorption isotherms are commonly used to derive D values for coal applying the Frenkel–Halsey–Hill (FHH) method. However, the isotherm data points for many coals do not conform to the theoretically expected FHH trends. In this study, two other fractal determination methods, those of Neimark (NMK) and Wang & Li (W&L), are evaluated, together with the FHH method for 26 published coal isotherms. The NMK method is considered unsuitable as it generates unreasonably high D values. For many coals W&L and FHH methods are observed to derive consistently close D values. Detailed graphical analysis of the isotherm data points and their trends can explain the discrepancies that exist in the D values derived from the whole isotherms of some coals. Discrepancies are also observed in the fractal dimensions derived by the different methods for the low (D1) and high (D2) relative pressure portions of the coal isotherms. More realistic D1 values are derived by the W&L method than the FHH method. A novel workflow integrating detailed graphical analysis with optimized curve fitting is proposed to better quantify and verify the derivation of coal fractal dimensions from nitrogen adsorption isotherms.