A coupled matrix-fracture productivity calculation model considering low-velocity non-Darcy flow in shale reservoirs

The flow behavior of shale reservoirs is extremely complex. The mainly used development method of large-scale volume fracturing of horizontal wells is associated with a series of problems such as low productivity in general, fast decrease in productivity, and difficulty to increase productivity. Therefore, it is necessary to evaluate the productivity of shale oil wells and determine the key control factors. Considering low-velocity non-Darcy flow, this paper establishes an analytical solution model for productivity calculation of multi-fracture shale oil horizontal wells with coupled matrix-fracture flow. Calculating the oil production rate by considering low-velocity non-Darcy flow in shale oil reservoirs obtains values closer to the actual oil production rate on site. The average relative error of the oil production rate of the H8 shale oil well is 4.27%. The average relative error of the oil production rate of the TMS shale oil wells is 34.97%, which exceeds the rate of the semi-analytical model by 47.84%. Sensitivity analysis shows that the oil production rate of multi-fracture shale oil horizontal wells is most sensitive to fracture cluster spacing and flowing bottom hole pressure. With decreasing fracture cluster spacing and flowing bottom hole pressure, both the matrix pressure gradient and the apparent permeability of the matrix increase. These increases not only increase the oil production rate but also reduce the influence of the non-Darcy effect on the oil production rate caused by boundary effect. In addition, the limits of the impact of non-Darcy effects caused by boundary effect on oil production rate have been clarified. The results enable not only the prediction of the oil production rate, cumulative oil production, and recovery factor of multi-fracture horizontal shale oil wells, but also the finding of the shale oil sweet spot according to the influence of matrix permeability and crude oil viscosity on the oil production rate.