Pressure Transient Analysis Of Three-Dimensional Hydraulic Orthogonal Fractures

Hydraulic fracturing is one of the main treatments for unconventional oil and gas reservoir stimulation.In the process of hydraulic fracturing,especially volume fracturing and refracturing,the change of in-situ stress or the interface effect caused by the difference of lithology may cause the change of fracture extension direction and lead to three-dimensional orthogonal fracture systems,such as a system with a vertical fracture orthogonalized by either another vertical fracture or a horizontal fracture.The purpose of this paper is to establish a calculation method of pressure transient analysis of three-dimensional infinite conductivity orthogonal fracture systems,which could provide theoretical guidance for the pressure transient analysis of such complicated fracture systems.In this thesis,the one-dimensional point source function is derived by Laplace transform method and Fourier transform method.Combined with Newman product principle,in real time domain pressure solutions of vertical fractured well with uniform flux and rectangular horizontal fractured well with uniform flux are obtained.For vertical fractured wells with infinite conductivity,the bottomhole pressure function is presented by introducing equivalent pressure point,and then the bottomhole pressure of vertical fractured wells with finite conductivity is calculated by combining with a conductivity influence function,and applicable conditions of this function are emphatically analyzed.For the rectangular horizontal fractured wells with infinite conductivity,the equivalent pressure point is inferred by discretizing the horizontal fracture into multiple fracture elements and superposing the pressure drop of the elements.On this basis,physical models of orthogonal vertically-fractured wells and "+" shape fractured wells are established respectively.The pressure solutions of the two fracture systems are coupled through superposition principle and Duhamel's convolution theorem,and the corresponding calculation method of three-dimensional orthogonal fractured system with infinite conductivity is obtained.Calculation results in this thesis are compared with the results of numerical simulator Eclipse,the bottom hole pressure and its pressure derivative are basically the same on the log-log plot,which verifies the correctness of this method.The influence of the main parameters on the pressure performance and the contribution ratio of each fracture are discussed,and the results show that for the orthogonal vertically-fractured system,the penetration ratio of the vertical fracture mainly affects the elliptical flow stage,the vertical fracture length mainly affects the linear flow stage,and the formation thickness mainly affects the transition flow stage.For the "+" shape fractured system,the position of horizontal fracture mainly affects the elliptical flow stage,the shape factor of rectangular horizontal fracture and the penetration ratio of vertical fracture mainly affect the transition flow stage,and the formation thickness has a significant effect on each flow stage.Moreover,through the comparison of three-dimensional orthogonal fractured well and single vertical fractured well,it can be seen that orthogonal fractured well has obvious and intense fracture interference phenomenon in transition flow stage compared with single vertical fractured well,which is a significant sign to identify three-dimensional orthogonal fractured well.Finally,combined with the actual production data of the oilfield,the corresponding calculation and analysis are carried out,and the key parameters such as formation thickness,formation permeability and fracture half-length are obtained by use of the typical curve fitting method,which provides the corresponding reference for the application of the type-curves formed in this paper.