Discrete fracture model with multi-field coupling transport for shale gas reservoirs

In order to characterize the influence of fractures, multiple fields, and the differences between organic matter and inorganic matter on the transport of shale gas, a weighted coefficient is used to couple the transition diffusion model and Knudsen diffusion model to establish a permeability model of gas diffusion that is suitable for any Knudsen number. A gas flow model is established for organic matter considering diffusion, matrix shrinkage, stress sensitivity, and adsorption layer thickness; likewise, a gas flow model is established for inorganic matter considering diffusion and stress sensitivity. On this basis, the matrix grid in the discrete fracture model is further sub-divided into an organic matter grid and an inorganic matter grid, and the Galerkin finite element method is used to solve the discrete fracture model. The reliability of the established discrete fracture model is verified by comparing the proposed model to the BACA discrete fracture model. For validation, a shale gas well in the Yanan field in the Ordos basin is simulated using the proposed model. The results show that the effect of diffusion and matrix shrinkage on production can be ignored, but stress sensitivity and adsorption layer thickness have a moderate influence on production. Furthermore, neglecting the differences between organic matter and inorganic matter leads to errors. The errors are larger when there is less organic content or when the porosity ratio or pore diameter ratio are smaller. If hydraulic fracturing generates a larger number of fractures in the shale with relatively shorter half-lengths and bigger apertures, the production stabilization effects and the ultimate recovery rate will improve. For the shale gas well in the case study, the fitting error is approximately 74% if the dual-porosity model is used, but the fitting error decreases to less than 2% if the proposed discrete fracture model is used.