Physico-Mathematical Model of the Surface Layer of Coals of Different Rank in the Karaganda Basin

Source abstract

The surface layer of coal influences its physicochemical, mechanical, and gas-storage properties, but its characteristic thickness has not been systematically determined for coals of different rank within a single basin. This study quantifies the surface-layer thickness of coals from the Karaganda Basin (Kazakhstan) using a physi-co-mathematical surface-layer model combined with previously obtained laboratory, geophysical, and production data. After substitution of the surface-energy relation-ship, the temperature cancels out, giving d ≈ 0.17 × υ (nm), where υ = M100/ρ is the mo-lar volume of the organic matter of coal. The calculated thickness decreases from 198.7 ± 19.1 nm (long-flame coals) to 151.5 ± 17.0 nm (anthracites), and the number of mon-olayers from ≈550 to ≈420; all values (146.0–214.2 nm) are consistent between adjacent ranks within ±10–11%, whereas the end members differ significantly. The theoretical shear strength of the surface layer, τt = 2σ/d, increases from 4.4 to 9.0 MPa, comparable to the strength of the basin coals estimated from the Protodyakonov coefficient. The calculated thickness covaries with gas content, permeability, and propensity for spon-taneous combustion; these relationships are mediated by depth and rank and are for-mulated as testable hypotheses. The results can serve as an additional structural indi-cator for ranking seams in degassing and hazard prediction, but not as a stand-alone hazard index. Future work will focus on experimental validation (nanoindentation, low-temperature N2/CO2 adsorption, surface-energy measurements) and model cali-bration.