Modeling of Gas Transport Driven by Density Gradients of Free Gas within a Coal Matrix: Perspective of Isothermal Adsorption

Abstract

Gas transport in a coal matrix is critical for the evaluation of coalbed methane storage and gas extraction. This transport behavior is generally considered to be in accordance with Fick's law but may lead to some prediction errors because of the misconception that the adsorbed gas is also involved in the flow. In this work, a density gradient-driven model of gas adsorption within the coal matrix was developed under confined-space adsorption conditions, and a new parameter named the microchannel diffusion coefficient was proposed to characterize the transport capability of gas. This new model was compared with some common models, in which their simulated adsorption curves were matched with isothermal adsorption data to distinguish the optimal model. The results show that (i) compared to Fick's model, the simulated curves of the density gradient model are in better agreement with the experimental data throughout the adsorption process; (ii) the permeability of Darcy's model is heavily influenced by adsorption pressures, while the microchannel diffusion coefficients are more realistic and independent of time and pressure. Therefore, the density gradient model is better suited to describe the transport behavior of gas in microchannels, which helps to understand the essence of gas transport in coal matrices.

Comparative Analysis of Gas Adsorption and Diffusion Characteristics of the Coal Matrix under Constant Pressure and Constant Volume Conditions

“…Based on the summary of experimental data on gas adsorption from coal samples at different pressures, the following new empirical formula for adsorption was proposed. 35 It is shown as follows:…”

“…To determine the gas permeability coefficient of coal particles, our research group proposed an inverse method in previous studies. ,, The simulated and experimental data points are put into the same plot for comparison, and finally, the K m value corresponding to the simulated curve when it matches well with the experimental data is made to be the accurate microchannel diffusion coefficient of the inverse performance. The simulated cumulative adsorption curves for coal samples were plotted separately to compare with the corresponding experimental data, as shown in Figure .…”

“…The nature of gas in coal particles, no matter what state it is in, can be understood as mass transfer. In view of this, our research group proposed that the flow of gas in the coal body follows the density gradient theory. − For both constant pressure and constant volume adsorption–diffusion models, the adsorption kinetics are morphologically similar to each other, but the boundary conditions are different. In engineering applications, different diffusion models should be selected due to the different distances of the coal body from the coal wall or the wall of the extraction borehole, i.e., from the constant air pressure or extraction pressure boundary.…”

Study on the Characteristics and Model Optimization of Coal Particle Gas Emission Law

“…The results show that the diffusion coefficient can characterize the speed of diffusion. Liu et al 22 deduced the gas transport model driven by free gas density gradient in coal matrix based on the perspective of temperature adsorption. Nie et al 23 established a gas diffusion model under the third kind of boundary conditions including the first kind of boundary conditions, which improved the applicability of the model.…”

“…Wang et al 19 established the complex coupling relationship between gas adsorption/desorption, gas seepage field, mechanical deformation field, and thermal field in the process of gas diffusion and discussed the contribution of each diffusion mechanism to the total gas diffusion under variable pressure and pore radius. Li et al 20 22 deduced the gas transport model driven by free gas density gradient in coal matrix based on the perspective of temperature adsorption. Nie et al 23 established a gas diffusion model under the third kind of boundary conditions including the first kind of boundary conditions, which improved the applicability of the model.…”