Research On Numerical Simulation Method Of Multi-stage Fractured Horizontal Wells Based On VEM

With the development of domestically-developed reservoirs with good physical properties entering the middle and late stages,Oil and gas resources of low permeability and tight reservoirs with great development potential on land and at sea have become the focus.Fractured horizontal well is an effective means to develop low-permeability and tight reservoirs.Hydraulic fracturing technology is used to transform reservoir physical properties,reduce formation seepage resistance and improve economic benefits of low-permeability reservoirs.Due to the complex shape of the fractures in the reservoir,and the existence of natural fractures often lead to reservoir anisotropy,analytical methods and numerical simulation methods based on structural grids have been unable to meet the actual production requirements.Therefore,the development of numerical simulators for fractured reservoirs has far-reaching implications.Fractured horizontal well mesh partitioning system based on unstructured PEBI grid is established.The LGR method is used to describe the different types of fracture network in multi-stage fractured horizontal wells.Meshing of conventional fractured horizontal wells,volume fractured horizontal wells and different injection-production well patterns are completed.A single-phase flow and oil-water two-phase flow mathematical model considering reservoir anisotropy under two-dimensional conditions is established.The numerical simulation of the seepage equations is performed by the virtual element method(VEM),and the projection operator and the geometric parameters of the mesh element are used to solve local stiffness matrix and local mass matrix indirectly with shape functions.A numerical integration method based on unstructured PEBI grid is established by using grid quadratic partitioning and Gaussian integration method.The source and sink models are used to treat the boundary conditions of vertical and horizontal wells.Develop a multi-stage fracturing horizontal well numerical simulation program that can interface with PEBI mesh pre-processing software.The program implements grid geometry parameter calculation,local coefficient matrix construction,global coefficient matrix assembly and linear equations solution.The single-phase flow developed by the vertical well is simulated and the analytical solution is used to verify the correctness of the program.Simulation of the oil-water two-phase flow developed by the vertical well confirmed that the water will swell in the direction of maximum permeability.After that,the numerical simulation of single phase flow of fracturing horizontal wells was carried out,and the influence of basic parameters of fractures and different fracture network forms on the productivity of fractured horizontal wells was studied.Numerical simulation is carried out on the development of water injection in fractured horizontal wells,and the development effects of different injection wells are compared.It has certain guiding significance for the development of multi-stage fracturing horizontal wells in low permeability and tight reservoirs.