A model of fully coupled two-phase flow and coal deformation under dynamic diffusion for coalbed methane extraction

To further explore the mechanism of fluid migration during long-term CBM recovery, a fully coupled model of two-phase flow and coal deformation is developed in this investigation based on gas dynamic diffusion. Although the coal mass is considered to be a dual-porosity single-permeability (DPSP) geological model, multiscale fractal characteristics of multistage pores are considered to illustrate the decrease in the gas diffusion coefficient over time. In addition, the model also considers water saturation, relative permeability, Klinkenberg effects and the changes in permeability caused by the fracture pressure (including the water pressure and gas pressure), matrix pressure (only the gas pressure), and desorption-induced shrinkage. Considering the combined impact of the abovementioned parameters, we established four governing equations and two supplementary equations and solved these problems with COMSOL multiphysics software. Subsequently, the model is validated via field test data, and then, through a comparison between our model and two typical coupled models for CBM extraction, we observed that the model that simplified CBM extraction as a single-phase flow process could overestimate gas production at the early stage, while the model that disregarded the impacts of the dynamic diffusion coefficient could overestimate gas production at the later stage. Finally, the coupled model was used to model long-term CBM and water production. The numerical results show that the gas pressure in the fracture and matrix and the water saturation decrease with time. And matrix gas pressure obtains a higher value than the fracture gas pressure in the later stage of extraction. In the area far from the wellbore, the permeability is lower than its initial value, while in the near-wellbore region, the permeability shows the opposite behavior. A sensitivity analysis of the current model illustrates that increases in the Langmuir strain constant, Young's modulus, initial permeability diffusion coefficient could promote the rate of gas production. Overall, our modified model for CBM extraction can enhance the gas and water migration rules and provide more accurate predictions for gas production.