Model and Experiment of Multiscale Dynamic Permeability in Series for Coalbed Gas Flowing through Micro-Nanopores

Coal is a porous medium with pores that vary in size from nanometer to millimeter, which entails multiscale characteristics in space and time that influence coal permeability. The current steady-state method used to measure coal permeability cannot reflect these multiscale characteristics and often results in an insufficient understanding of the ultralow coal permeability. To reveal the multiscale flow mechanism of methane in coal, a cylindrical coal sample is used to conduct the unsteady diffusion-seepage experiment using CH4/He under triaxial stress condition and a dynamic attenuation of the apparent diffusion coefficient is experimentally observed. Based on the characteristic of the coal pore structure, a mathematical model of the multiscale pores in series is proposed and then validated experimentally using mercury injection. The flow of methane in multiscale pores is revealed as a step-by-step mechanism of gas outflow from interior pores to surface pores. As the number of the connected pore series increases, the equivalent pore radius decreases and the equivalent permeability is determined by the minimum pore radius. Furthermore, a dynamic apparent diffusion model is proposed to describe the full-time unsteady flow of methane in the multiscale pores. Finally, a permeability model that accounts for multiscale pores in series is built to reflect the influence of flow regime, stress, and pore pressure. The research results show that the micro-nanopore radius and number of connected pore series are vital for determining coal permeability. A larger pore radius ratio indicates a greater permeability attenuation. As pore radius decreases, the gas flow regime gradually changes from continuous flow to slip flow, transition flow, and finally to Knudsen flow. This explains the ultralow coal permeability as well as the fast reduction of coalbed gas production and concentration.