Experiment, Model, and Mechanism of Multiscale Dynamic Diffusion-Permeability in Coal under Different Fluids

The permeability of coal exhibits multiscale characteristics in space and time, which is caused by the presence of micro and nanopores in coal. Water, free gas, and adsorbed gas are common engineering fluids in coal seams during gas extraction. Thus, it is of significance to study the multiscale characteristics and mechanisms of seepage-diffusion of different fluids in coal for gas extraction engineering. Experiments of seepage-diffusion for He, CH₄, and water are carried out using ϕ50 × 100 mm cylindrical coal. It is found that the apparent diffusion coefficient for He, CH₄, and water are not a constant but a variable that decays dynamically with time. The phenomenon is independent of fluid properties and determined only by the multiscale characteristics of pores in coal, and then a novel model of multiscale dynamic apparent diffusion that can accurately describe the full-time process of flow in various fluids is proposed. The mechanism of dynamic seepage-diffusion for different fluids in coal is elucidated based on a new proposed geometrical model of multiscale pores. At the early stage of flow, fluids first flow in or out of the largest pores outside coal, and at the later stage of flow, fluids flow in the micro and nanopores inside the coal matrix. The pore sizes through which the fluid flows decrease with time, which leads to a dynamic attenuation of the apparent diffusion-permeability with time. The initial apparent permeability K ₀ for He/CH₄ shows a "U"-shaped pattern of decreasing and then increasing with the decrease of gas pressure. When the gas pressure is lower than the turning point, the slip effect dominates, making the initial apparent permeability K ₀ decrease with the increase of gas pressure. When the gas pressure is higher than the turning point, the effect of the pressure difference of the gas dominates, and K ₀ increases with the increase of gas pressure. When water flows in multiscale pores, it occupies the space of large pores, making the homogeneity of pores increase, and the decay coefficient of apparent permeability becomes smaller. The multiscale permeability can explain the reason for the rapid attenuation of coalbed methane production in the late stage. It is of great significance for coalbed methane productivity prediction.