Pressure-dependent characteristics of the diffusion coefficient during the gas desorption process in coal cuttings: Numerical modelling and analysis

Determining the diffusion coefficient is crucial in coalbed methane development. Existing models have limitations, as they often apply only to spherical systems, cannot describe nonlinear adsorption, and do not quantify the impact of gas pressure on diffusion coefficients. Additionally, traditional trial methods struggle to accurately compute diffusion coefficients in numerical solutions. To address these challenges, our study builds two unipore diffusion models (EPDDM and PPDDM) by introducing exponential and power pressure-dependent diffusion coefficients, considering three-dimensional coordinates and Langmuir adsorption. And then proposes a diffusion coefficient determination method using a particle swarm optimization algorithm. Through desorption experiments, numerical modelling, and model comparisons, we analyze the evolution law of diffusion coefficient, gas pressure, and desorption volume during the desorption process. Our results show that the proposed models quantitatively depict the positive correlation between diffusion coefficient and gas pressure. Furthermore, they accurately reflect changes in desorption volume. During early-stage desorption, the diffusion coefficient of EPDDM is 1.63-1.85 times greater than that of PPDDM, while their desorption volumes are similar. This observation motivates the proposal of a more versatile Logistic pressure-dependent diffusivity model, aiming to unify the above two models. These achievements are anticipated to serve as a foundational framework for exploring the mechanisms governing gas diffusion.