Applicability Analysis of Determination Models for Nanopores in Coal Using Low-Pressure CO₂ and N₂ Adsorption Methods

The development characteristics of nanopores (with pore sizes <200 nm) in coal are a key factor affecting the accumulation and migration of coalbed methane (CBM). Thus, an appropriate determination method and calculation model are essential for accurate nanopore representation. Based on the experiments of low-pressure CO₂ adsorption (LP-CO₂GA) at 273 K and low-pressure N₂ adsorption (LP-N₂GA) at 77 K on four coals with different ranks, the abilities of different models (e.g., Langmuir, Dubinin-Radushkevich (D-R), Dubinin-Astakhov (D-A), Brunauer-Emmett-Teller (BET) and nonlocal density functional theory (NLDFT)) to accurately predict the pore parameters were analyzed. The results showed that (1) for LP-N₂GA, the Langmuir model is only suitable for gas adsorptions at low relative pressure conditions (P/P₀ < 0.01), and its error value increased with the relative adsorption pressure. The fitting results of the D-R model showed good agreement with the D-A model under low relative pressure of LP-CO₂GA (P/P₀ < 0.01), and the D-A model had more accurate fitting results. The BET model is more accurate than the other models (φ = -1.2733%) only in the interval of LP-N₂GA with 0.05 < P/P₀ < 0.35. The data also showed that the NLDFT model can maintain a higher fitting accuracy for LPCO₂/N₂GA processes at relative adsorption pressures from 0.001-0.9996. (2) Using LP-CO₂GA with the Langmuir, D-R, D-A, and NLDFT models, the micropore specific surface area (SSA; 66.9570-248.6736 m²/g) and pore volume (0.0201- 0.0997 cm³/g) were obtained, while the values of meso-/macropore SSA (0.0007-2.3398 m²/g) and pore volume (0.0036-0.04 cm³/g) were calculated by LP-N₂GA with the BET and NLDFT models. The results showed that the fitting accuracy in descending order was the D-R, D-A, Langmuir and NLDFT models. (3) In combination with the applicable model range, LP-CO₂GA with the NLDFT model was recommended for micropore analysis of the coal pore sizes from 0.36-1.1 nm, while LP-N₂GA combined with the NLDFT model was recommended for nanopore analysis of pore sizes from 1.1-200 nm. (4) The characteristics of pore development in the Beiloutian coal were analyzed using LP-CO₂/N₂GA combined with the NLDFT model. It was found that a pore volume and SSA less than 1.0 nm accounted for 88.82% of the total pore volume and 98.05% of the total SSA, indicating that micropores in coal are the main space for CBM storage and are key physical factors for the occurrence and migration of coalbed methane. The conclusions of this article will provide a basis for the accurate calculation of nanopores in coal.