A surface diffusion block coefficient and model about coal-adsorbed gas

80%−90% of coalbed methane(CBM)/coal mine gas is stored in adsorbed state, and the diffusion of adsorbed gas is dominated by surface diffusion, which plays a decisive role in the transportation of CBM. The paper adopts kinetic and thermodynamic methods, based on CHEN and YANG’s surface diffusion gas molecules random hopping mechanism and the transition state theory on the diffusion of adsorbed gases, deduces the theoretical calculation method of the surface diffusion block coefficient(κ) by combining the surface diffusion kinetic parameter with the isosteric heat of adsorption, and establishes the surface diffusivity model of coal-adsorbed gas. The effects of temperature, pressure, isosteric heat of adsorption, and the block coefficient on the surface diffusivity are discussed using the model. Gain the following conclusion: ① A method for calculating the block coefficient using isosteric heat of adsorption was developed. Coal adsorption of gases process, 0 < κ < 1; adsorption equilibrium, where gas molecules bounce forward and backward with equal probability, κ=1; surface diffusion in an ideal state of infinite space with no blockage, κ=0. ② The surface diffusivity model of coal-adsorbed gas is established and validated. The surface diffusivity of coal-adsorbed gas is only a function of the isosteric heat of adsorption, coverage and temperature, and the parameters can be obtained by conventional adsorption isothermal experiments, which is applicable to the whole process from low pressure to high pressure, and the model is simple and practical. It is verified that the developed model fits the experimental data with R² = 0.7438−0.9834, indicating that the model is reliable. ③ The effects of temperature, pressure, isosteric heat of adsorption, and block coefficient on surface diffusion are discussed. The temperature is linearly and positively correlated with the surface diffusion coefficient, the pressure varies with the surface diffusivity in the form of the Langmuir equation, the isosteric heat of adsorption is exponentially correlated with the surface diffusivity, and the block coefficient is correlated with the surface diffusivity in the form of a power function. ④ CBM surface diffusion is an activation jump process of adsorbed gas molecules (activation caused by adsorption potential difference) at a micro level and is driven by concentration gradient at a macro level. The results enrich the knowledge of the surface diffusion behavior of CBM and provide a method to evaluate the surface diffusivity of CBM using thermodynamic parameters.