A new approach for gas-water flow simulation in multi-fractured horizontal wells of shale gas reservoirs

Shale gas reservoirs demonstrate low matrix porosity and permeability, and show obvious heterogeneity due to the existence of natural fractures. During the production process, fracturing fluid can easily invade the reservoir and result in a low fracturing flowback rate. The existing numerical methods are troublesome and have poor convergence. Therefore, it is necessary to develop a new approach to study the gas-water two-phase flow in shale gas reservoirs. In this paper, fractal theory is used to quantitatively characterize the heterogeneous fractures. A Mathematical model considering fractal induced-fracture distribution and gas-water two-phase flow in shale reservoirs is established. The meshless weighted least squares (MWLS) method is applied, for the first time, to the numerical simulation of gas-water two-phase flow in multi-fractured horizontal wells of shale gas reservoirs. Based on the moving least squares approximation, the variation principle is derived in detail. A numerical model of gas-water two-phase flow in the shale gas reservoir fracturing horizontal well based on the meshless method is obtained. The gas and water production of fractured horizontal shale gas wells are predicted by the model. The model simulation results are found to be in good consistent with the mathematical calculation results obtained through finite difference method. but the proposed new approach shows significant higher calculation efficiency. In addition, by applying this new approach, The influences of fracture distribution, initial water saturation, and reservoir reconstruction degree on the utilization range and production were also systematically compared and analyzed. The results showed that the smaller the fracture fractal index a in the reservoir reform area, the lower the pressure, the higher the daily gas production and the daily water production, indicating that the fracture network is densely distributed and the production effect is better. The larger the initial water saturation resulted in the greater flow resistance of the gas phase and the decrease of daily gas production. When the fracture spacing decreases in reservoir reconstruction, the daily gas production increases, but the increase range is gradually reduced and it has little effect on the daily water production.