A dynamic fractal permeability model for heterogeneous coalbed reservoir considering multiphysics and flow regimes

Heterogeneous pore structure is critically important for unconventional gas recovery. In this paper, a dynamic fractal permeability model is proposed to investigate the interplay between heterogeneous pore structures and gas transport for coal seam gas reservoir. In this model, pore diameter and fractal dimension of pore size distribution are dynamically changing as a result of the variation of effective stress. Besides, based on fractal approach, a new Klinkenberg coefficient that dynamically changes with pore pressure is employed to incorporate the non-Darcy effect. This dynamic permeability model is applied to couple Multiphysics in coal seam gas recovery process. The impacts of these fractal parameters on permeability evolution are explored through a benchmark reservoir simulation. The numerical results exhibit good agreements with experimental data. The simulation results indicate that: (1) the dynamic permeability model matches better with experimental data than other homogeneous models, especially in low-pressure stage; (2) reservoir with larger initial fractal dimension is more sensitive to pressure depletion; (3) fractal dimension would change more dramatically when initial porosity is relatively smaller; (4) Klinkenberg coefficient increases with the decreasing of reservoir pore pressure during gas depletion. In summary, the dynamic permeability model predicts permeability evolution well in gas production process and provide some fundamental insights into the implications of reservoir heterogeneity on gas transport in reservoir simulation.