NUMERICAL SIMULATION OF MULTI-SCALE COUPLED FLOW IN AFTER-FRACTURING SHALE GAS RESERVOIRS

Under the national policy background of peak carbon dioxide emissions, shale gas becomes an important transition and energy fulcrum for the transition from traditional energy to green, clean and low-carbon energy. And the fluid flow mechanism of shale gas reservoirs after fracturing becomes a key mechanical problem for the efficient development of shale. In this paper, the small-scale low-conductivity natural fractures are equivalently upgraded to a continuous medium, and a triple organic-inorganic-natural fracture continuous medium model is established. The discrete fracture model is used to portray the large-scale high-conductivity fractures, which are embedded into the natural fracture continuous medium, and a multiple continuous/discrete fracture model (MC/DFM) is constructed. The non-equilibrium nonlinear desorption and surface diffusion of adsorbed gas, viscous flow, and Knudsen diffusion of free gas are integrated to give a nonlinear coupled flow mathematical model of shale gas in the multi-scale complex medium. The multi-scale extended finite element method (MXFEM) is proposed to solve the discrete fractures explicitly, and three types of enrichment functions are innovatively constructed to capture the local flow field characteristics of the discrete fractures, which solves the flow simulation problems of the massive fractures and multi-scale flow channels in the after-fracturing shale. The model and method proposed in this paper can not only accurately characterize the effect of high conductivity fractures on gas flow, but also overcome the problem of the dramatic increase in computational amount due to massive multi-scale discrete fractures. The pressure decay law of each continuous medium is demonstrated by a calculation example, and the pressure/concentration diffusion phenomena of free gas in fracture, free gas in organic medium, and adsorbed gas in the inorganic medium are found to lag in sequence. The analysis focuses on the effects of adsorbed gas surface diffusion coefficient, free gas Knudsen diffusion coefficient, natural fracture continuous medium permeability, and adsorbed gas desorption rate on shale gas production. This paper focuses on the characterization of multi-scale flow channels and modeling of complex coupled flow mechanisms in after-fracturing shale reservoirs and developing an efficient numerical simulation algorithm, which is meaningful for the production assessment of the shale formation after fracturing.