The Study On Transient Flow Problems Of Multifractures In Anisotropic Reservoirs

In the process of fracturing in rectangular anisotropic reservoirs,due to the influence of permeability anisotropy and uneven distribution of in-situ stress,there is usually a certain angle between the hydraulic fractures and the orientation of the dominant permeability,which makes the seepage problems of the arbitrary angular fractured well and arbitrary angular fractured horizontal well complicated.Based on the theory of flowing through anisotropic media and point source function,considering the permeability anisotropy and the angle between the fractures and the orientation of dominant permeability,the mathematical model for a fracture with an arbitrary angle in a rectangular reservoir is established by use of Cartesian-coordinate transformation.Furthermore,the pseudo-steady productivity and transient pressure behaviors of the arbitrary angular fractured well and arbitrary angular fractured horizontal well are completely studied in this paper.This paper provides a theoretical basis for well pattern deployment and fracture configuration in anisotropic reservoirs.On the basis of the point-source solution,the arbitrary angular fractured well can be regarded as a uniform-flux line source with arbitrary angles.Thus,an analytical solution is derived by spatial integration of point-source along the direction of the fracture for a fracture with arbitrary angles in a rectangular reservoir.The influence of permeability anisotropy,the fracture angles and dimensionless fracture conductivity on dimensionless production index curve is analyzed.Calculative results show that the more the fracture deviates from the direction of maximum horizontal permeability,the higher the dimensionless productivity index is.A mathematical model of vertically fractured wells in a rectangular stress-sensitive gas reservoir is established.The governing equation can be linearized by use of the modified pseudo-functions approach.Thus,the solution to investigate the effect of stress sensitivity on pressure and flow rate in Laplace transform domain can be obtained.An analytical solution is derived by spatial integration of point-source along the direction of the fracture for a fracture with arbitrary angles in a rectangular reservoir.The solutions obtained in this paper are validated with the solution in the literature and a fully numerical model.Type curves are generated to investigate the influence of the main parameters on transient pressure behavior,including permeability anisotropy,fracture angles and so on.According to the superposition principle,the transient flow model of a fractured horizontal well with multiple vertical fractures in rectangular reservoirs is obtained.Thus,the solution of the finite-conductivity fractures in Laplace transform domain can be obtained by adding the impact functions of fracture conductivity and type curves are generated to investigate the influence of the main parameters on transient pressure behavior.Calculative results show that increasing the number of fractures?space between fractures?length of fractures and fracture conductivity will reduce the pressure and pressure derivative.Based on the model of a fracture with an arbitrary angle,the transient pressure distribution of an arbitrary angular fractured horizontal well is obtained using the principle of superposition in a rectangular anisotropic reservoir.Furthermore,the influence of the main parameters on transient pressure behavior,including permeability anisotropy,azimuth of the fracture,and fracture conductivity are investigated.