Transient gas diffusivity evaluation and modeling for methane and helium in coal

Abstract

Gas diffusion in coal in known to be a transient process. A conceptualized cylindrical pore network was proposed in this study to quantify the transient mass transfer in coal at various pressures. Experimental measurements were carried out to measure the time-dependent mass transfer through the volumetric method. Based on the geometrical model, a new analytical model was proposed to describe and quantify the dynamic contributions of bulk diffusion, Knudsen diffusion and surface diffusion to the total gas mass transfer. In the model, the nanoscale pore deformation and dynamics were implicitly considered and modeled through the pore volume compressibility and the matrix shrinkage and swelling variations. This allows to model the gas transient process with pore structure modification. The analytical model is being solved through a numerical approach. The numerical model also combines the interactions between gas adsorption and desorption by recalling the converse source terms in the governing equations. The transient gas transport process can be divided into two stages, namely, the fast bulk and Knudsen diffusion controlled free pressure equilibrium and the slow sorption-controlled mass transfer due to the gradient of free gas pressure (pf) and adsorption equivalent pressure (pa). The numerical model was calibrated and validated against with the laboratory measurements. Comparing the cases that helium and methane injections at similar pressure (~315.98 psi for helium and ~319.90 psi for methane), the equilibrium time for helium is ~ 4.5% shorter than that of methane does attributed to the relative slow sorption kinetics. Also, the pore radius with methane injection will never recover to the initial pore radius, a 3.3% irreversible strain on pore radius induced by sorption effects was observed. A 3.6% difference between the relative probability of the molecular-wall collisions for helium (~97.7%) and the relative probability of molecular-wall collisions between methane molecules (~ 94.1%) was believed to be induced by the sorption effects. These results can ultimately provide the approach and data for analyzing the dynamic sorbing gas transport behaviors in sorptive coal.