A method to predict the production of fractured horizontal wells in low/ultra-low permeability reservoirs

In consideration of the matrix-crack-wellbore coupling flow and matrix-wellbore coupling flow in an open-hole fractured horizontal well in low/ultra-low permeability reservoirs, mathematical models were derived on the basis of the equivalent flowing resistance method and the superposition principle. For an open-hole fractured horizontal well, the flow field was divided into three regions according to the different flow mechanism:Darcy flow in artificial fractures, low-velocity non-Darcy elliptical flow in the matrix around artificial fractures, and low-velocity non-Darcy plane radial flow in the peripheral matrix. A non-Darcy analytical productivity equation for an open-hole fractured horizontal well was obtained considering mutual interference between multi-transverse fractures. The influences of hydraulic fracture parameters on oil production were analyzed, which reveals the variation in development of an open-hole fractured horizontal well. Numerical results show that the more the artificial fractures, the stronger the interference of artificial fractures, and consequently there exists an optimal quantity of artificial fractures. It is suggested that the artificial-fracture distribution should be dense at two ends of the wellbore and sparse in the middle of the wellbore; in addition, the length of artificial fractures at the two ends should be larger than that in the middle.