| Massive multi-stage hydraulic fracturing is an effective way to develop unconventional reservoir.The intersection of Hydraulic fractures and natural fractures forms a highly complex fracture network,which is capable of increasing the contact area between matrix and fracture,reducing flow resistance of oil and gas,and so increasing the productivity of unconventional reservoir.However,on the other hand,due to the difference in the form of fracture network complexity and conductivity,it is hard to study fluid flow in fractured reservoir with complex fracture network easily and accurately,and even the fluid-structure interaction problem in the case of dynamically propagating fractures.Previous researches on fluid flow in fractured reservoir have several shortcomings.For example,dual permeability media theory assumes a uniform orthogonal distribution of fracture network,which is quite different from the actual situation;numerical methods such as discrete fracture network models are able to portray the irregular distribution of fractures,but these methods require that the fractures should be consistent with the grid edge,which can greatly increase the difficulty of meshing,is not effective to solve the coupling problems of fluid-structure interaction in the case of fracture dynamically propagation.In addition,the natural fractures of fractured reservoir are often cemented by a variety of secondary minerals.Such mineral-cemented fractures can be divided into thress classes,including the completely cemented fractures,the partly cemented fractures and uncemented fractures.The completely cemented fractures are generally non-permeable.Previous analysis on fluid flow in fractured reservoir,usually took into account only the high conductivity fractures,while ignored the lowly permeable fractures and impermeable fractures in fractured reservoir.In fact,many faults can also be viewed as a non-permeable barrier.Therefore,we need a new method,which can not only flexibly and conveniently consider the complexity of the fracture network(different fracture pattern,scale,conductivity,distribution,etc.),but also reflect the weak discontinuity feature of flow field and the strong discontinuity feature of stress-deformation field at the same time,and in addition the new method should be of low cost and easily applicated.Extended Finite Element Method(XFEM)is an important numerical method which has been developing gradually for several years.The core of the XFEM is partition of unit theory(PU).Based on the PU theory,some special functions which reflect the features of strong or weak discontinuous field can be directly introduced into the classical finite element approximation,so that the fractures can be independent of the grid and arbitrarily distributed.What's more,the fractures can propagate at arbitrary direction based on the XFEM.Therefore,it is of great significance to apply the extended finite element method to research the problems involving complex fractured network and dynamically propagating fractures.In this thesis,I completed the following several aspects of studies:(1)A variety of XFEM enrichment functions were analyzed;first adopted Polygonal Boolean Operation Method to creat a sub-mesh inside the element directly intersected by complex fracture network,and such a method is more convenient and applicable than the level set method;(2)An extended finite element model of stress-deformation field in the fractured reservoir was established,considering the effective stress principle.The coupling method of the stress-deformation field,pore pressure and the pressure inside the fracture were discussed.Three numerical examples,respectively involving the stress intensity factor,fracture width and the stress field before re-fracturing,were calculated to verify the validity of the extended finite element method in solving the strong discontinuity problems related to the stress-deformation field in the fractured reservoir;(3)An extended finite element model of single-phase liquid flow in fractured reservoir was established.In this paper,the previous assumption that the flow pressure inside the fracture cross-section keeps constant is improved,in order to analyze fluid flow in the direction normal to the fracture line and the resulting strong discontinuity problem;(4)Through numerical studies,the validity of utilizing the extended finite element method to address the strong/weak discontinuity problems due to highly permeable,lowly permeable and non-permeable fractures.For anisotropic-permeability fractures of which the vertical permeability is much smaller than the tangential permeability,the boundary layer assumption was proposed,as well as the improved matrix-fracture transfer equations.Numerical studies showed that boundary layer assumption can significantly improve the modeling accuracy;(5)According to the extended finite element theory,the morphology and distribution of the complex fracture network can no longer depend on the mesh,but the enrichment scheme of every element can be different due to the different fracture pattern inside the cell.For the characteristics of the complex fracture network,several different fracture patterns were proposed.Three fracture network examples from simple to complex were established to analyze the influence of fracture network on fluid flow;(6)An XFEM model of gas flow in multi-stage hydraulic fractured shale gas reservoir was established.The whole fractured shale gas reservoir was divided into three domains,including the matrix domain,the stimulated domain and the domain with macro length-scale fractures.Matrix domain has only one medium(namely the matrix);the stimulated domain is composed of not only the matrix,but also the fracture network caused by the numerous intersected micro-mecro length-scale fractures;the macro-scale fracture domain is composed merely by some macro length-scale fractures,which may also form a fracture network.Factors like Langmuir gas volume,the shape factor of matrix-fracture transfer and the permeability of the micro-mecro length-scale fracture network were analyzed,which had great influences on the shale-gas productivity performance;(7)An extended finite element model of gas flow in fractured reservoirs in the form of gas pseudo-pressure was established,and the weak discontinuity enrichment scheme was used to solve the model.Gas pseudo-pressure,which is obtained by integrating gas pressure,viscosity,compression factor and other factors,is usually used to substitute gas pressure,in order to simplify the expression of the gas flow equation,and thereby reduce the complexity of the equations and their non-linearity effectively.For tight gas reservoir,factors like matrix permeability,instantaneous productivity,the complexity of the fracture network were analyzed,which had great influences on wellbore pressure performance;(8)Considering oil-water two phase flow,this paper established an XFEM model to research hydraulic re-fracturing and the effect of fracturing fluid filter cake was considered. |
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