Permeability anisotropy is a common feature of hydrocarbon reservoirs. In practice, hydraulic fracturing has been an effective technique for enhancing the productivity of wells in low permeability reservoirs. However, most study about hydraulic fractures focuses on isotropic reservoirs and few literatures discussed the effect of permeability anisotropy and azimuth angle of fractures on the producer’s transient flow. Therefore, we attempt to develop an analytical model for a fracture with an arbitrary azimuth angle in an anisotropic reservoir. First, we derive an analytical solution by spatial integration of point-source along the direction of the fracture. Then, we do Cartesian-coordinate transformation to transform the original problem with anisotropic permeability into an equivalent problem with isotropic permeability. Finally, we obtain an analytical solution for the proposed model. Several general conclusions drawn from this model are as follows: 1) The solutions obtained by the conductivity influence function are validated with Chen and Raghavan’s results. Five flow regimes can be observed: bilinear flow, linear flow, early radial flow, compound linear flow, and pseudo-steady-state flow. 2) Horizontal permeability anisotropy has a strong effect on transient responses, which can be extended to pseudo-steady-state flow regime. Effect of the azimuth angle of a fracture mainly focuses on the bilinear and linear flow regimes. The more the fracture deviates from the direction of maximum horizontal permeability, the less the drawdown needed to maintain constant flow rate. Therefore, the optimum orientation for the hydraulic fracture is perpendicular to the direction of maximum horizontal permeability. 3) Outer boundary size dominates pseudo-steady-state flow and aspect ratio mainly affects the periods of radial flow and compound linear flow. The larger the outer boundary size, the longer the radial flow regime and the later pseudo-steady-state flow appears. The existence and duration of bilinear flow and linear flow are mainly determined by dimensionless fracture conductivity. This model provides a theoretical basis for well pattern deployment and fracture configuration in anisotropic reservoirs.
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