Methane adsorption characteristics on coal surface above critical temperature through Dubinin–Astakhov model and Langmuir model

To acquire the required information of the adsorption system under supercritical conditions, four different rank coals were selected as studied samples. The textures of the coals were characterized through N2 adsorption at 77 K. Their surface morphologies were analyzed by scanning electron microscopy (SEM). The high pressure adsorption data of methane on the coals were obtained at supercritical temperatures. The data were analyzed using the Dubinin–Astakhov (D–A) and Langmuir models. The methods for estimating pseudo-saturation vapor pressure were investigated. And the influence of the characteristic curve form on the D–A equation prediction was investigated. The results show that the constants derived by matching the experimental data to the Langmuir model might lack physical significance, though the Langmuir model was of the correct qualitative form to represent the isotherms of methane on coals. The method for estimating pseudo-saturation vapor pressures proposed by Schwarz failed to render the experimental data to fall onto one characteristic curve. A modified procedure of determining the value of parameter k in Schwarzʹs equation, i.e. ps = pc(T/Tc)k was proposed. It was found that the modified approach gave the most suitable temperature-independent characteristic curves with determination coefficient R2 > 0.9943. The form of the characteristic curve could influence the D–A model prediction. Using cubic polynomial as characteristic curve form would result in an abnormal prediction i.e. the adsorption amount would increase with the pressure dropping when the pressure is less than approximately 0.9 MPa for Xingq-1–5# and Xujd-1#, 0.8 MPa for Qingh-2–3#, and 0.5 MPa for Leiy-1#. A new form of the characteristic curve deduced from D–A equation was proposed. The prediction uncertainty of D–A equation by using this new characteristic curve form is less than 2.43%.