A method for measuring surface diffusion coefficient of coal-adsorbed gas using a differential pressure permeation method

The surface diffusion behavior of coal-adsorbed gas is difficult to measure and quantitatively characterize, which has always been a problem or difficulty in the study of the migration law of coalbed methane (coal mine gas). The paper adopts the adsorption kinetics method, based on the Maxwell-Stefan diffusion theory, utilizes the consistency of the chemical potential change between the bulk phase and the adsorbed phase at each adsorption equilibrium to deduce the surface diffusion flux equation dependent on coverage and expressed in the form of Fick’s law; Combined with the mass conservation equation, a unified model for two-phase gas transport in coal under differential pressure is established, the principle and the experimental method for measuring the surface diffusion coefficient of coal-adsorbed gas using a differential pressure penetration method are proposed, and the surface diffusion coefficient and the contribution of two-phase gas transport are measured by the differential pressure penetration method. The results show that: The surface diffusion coefficient of the surface diffusion flux equation dependent on coverage conforms to the HIO model relationship with that of the Maxwell-Stefan diffusion theory. It is an extension of the Maxwell-Stefan diffusion theory, can be expressed in the form of the Arrhenius equation, and can be used to characterize the surface diffusion behavior of coal-adsorbed gas. The theoretical derivation result is correct. The unified model of two-phase gas transport in coal under differential pressure describes the unified process of adsorbed gas and free gas transport in coal under differential pressure. This model is constructed in combination with the physical model of coal multiscale pore structure in series, taking into account the influence of surface coverage of coal-adsorbed gas, and serves as the basis for the principle of differential pressure penetration method. Based on the model, the differential pressure-time relationship equation is constructed, the surface diffusion coefficient is inverted by using the sensitive parameter of surface diffusion (differential pressure-time curve), and the principle of the differential pressure penetration method is proposed. Based on the principle, the experiment of differential pressure penetration method is designed, and the experimental device of differential pressure penetration method is set up, and the differential pressure-time curve is measured. The fitting degree R² of the differential pressure-time relationship equation and the differential pressure-time curve reached 0.977 6, verifying the principle of the differential pressure penetration method and indicating that the surface diffusion coefficient can be extracted from the total gas transport process (differential pressure-time curve). The surface diffusion coefficient measured by differential pressure penetration method can be described by the characteristic equation of surface diffusion coefficient of coal-adsorbed gas in the principle. The fitting degree R² reaches 0.997 9, and the fitting parameters D⁰_s∞ and α are within the value range of theoretical analysis, which indicates that the experimental results are correct and can be applied to the surface diffusion coefficient determination of single component gas in coal with a coverage of 0 to 1. Under the experimental conditions of temperature 303 K, adsorption equilibrium pressure 0.1～3 MPa, changing the same differential pressure dp/dx, the contribution of the surface diffusion of coal-adsorbed gas (methane-Jiulishan coal sample) is 95.70%～29.08%, and the contribution of the migration of free gas is 4.30%～70.92%. As the pressure decreases, the gas migration process in coal gradually transitions from being dominated by the migration of free gas to being dominated by the surface diffusion of adsorbed gas. The experimental results show that there is not only the surface diffusion behavior of adsorbed gas in coal, but also the migration process of coalbed methane (coal mine gas) will be dominated by the surface diffusion of adsorbed gas (contribution is more than 50%) under the low pressure condition (˂1.5 MPa), and the surface diffusion behavior of coal-adsorbed gas can not be ignored. To evaluate the transport capacity of adsorbed gas in coal and reliably predict the long-term impact of adsorbed gas on the extraction efficiency of coalbed methane (coal mine gas), the experimental measurement of the surface diffusion coefficient of coal-adsorbed gas is essential.