A Semi-Analytical Model of an Off-Center Multi-Wing Fractured Well in a Low-Permeability Gas Reservoir


 Since there are several hydraulic fractures around a wellbore after a large-scale hydraulic fracturing and the well is not in the center of the reservoir, no corresponding semianalytical model for wellbore pressure analysis has been proposed. To bridge this gap, this paper aims to present a semianalytical model of the off-center multiwing fractured well. With consideration of permeability stress sensitivity, the reservoir model and hydraulic fracture model are established, respectively. The coupling approach of the reservoir model and hydraulic fracture model is used to obtain the wellbore pressure solution. Meanwhile, the off-center multiwing fractured well is verified with a numerical solution. The seven flow regimes can be distinguished according to the characteristics of the pressure derivative curve. Furthermore, the effect of different fracture distributions on wellbore pressure and the derivative curve is discussed and analyzed. Assuming that the fracture wing number is equal to the average length of all fracture wings, the wellbore pressure is lowest before the radial flow regime when the fracture wing has a uniform distribution around the angle and all fracture wings are equal in length. Besides, the influence of other important parameters (fracture wing number, off-center distance, etc.) is discussed. According to the analysis, we conclude that fracture wing number has a significant influence on the pressure and derivative curves before the radial flow regime. The off-center distance has no influence on the pressure and derivative curve before the radial flow regime, but it has an obvious influence on arc boundary reaction time. Finally, the advantages of the semianalytical solution are fast calculation speed and high calculation accuracy (especially in the early flow regime).