Theoretical Analysis And Numerical Simulation Of Permeability For Single- And Two-phase Fluid Flow In Fractured-vuggy Porous Medium Based On Homogenization Method

Fractured-vuggy carbonate reservoir is well known as extremely anisotropy, heterogeneity and multiscale property, where pore structure is very complex. Therefore the rule of fluid flow in fractured-vuggy carbonate reservoir is different from that in the regular reservoir. Study on permeability in fractured-vuggy porous medium has important signification to oil recovery in such reservoirs. In this thesis, the permeability of fractured-vuggy porous medium is researched from theoretical analysis and numerical simulation. In the microscopic scale, a 2D vuggy porous medium with many small cavities throughout its extent on the microscale is modeled using stokes equation within the vugular inclusion, Darcy's law within the matrix, and a Beavers-Joseph-Saffman condition on the interface between the two regions. After that, Darcy-Stokes equation in fractured-vuggy porous medium is obtained. According to the homogenization method and assuming the medium is period, the homogenized model of Darcy-Stokes equation is derived, then the formula of permeability is given.First, according to the homogenization method, the macroscale model of Darcy-Stokes equation of single- and two-phase fluid flow in fractured-vuggy porous medium is derived respectively using mathematical-homogenization, and the expression of macroscale permeability is also derived. The research of theoretical analysis indicate that the homogenized result of Darcy-Stokes equation of steady single-phase and two-phase satisfy the Darcy's law of single-phase and two-phase in the form, respectively.Then, based on the foundation of theoretical research, The finite element method on the Darcy-Stokes equation, which the variation form of Darcy-Stokes equation is also derived, is studied and the FEM space of Darcy-Stokes equation is also given. The study of FEM about Darcy-Stokes equation demonstrate that Stokes unit can be used to solve the Darcy-Stokes equation, but when it is on the interface of Darcy and Stokes region, it should be modified properly to satisfy the boundary condition.The last, based on the foundation of theoretical research and FEM research, the x-permeability and y-permeability of fractured medium, vuggy medium and fractured-vuggy medium are computed, According to the analytical solution of fractured medium, the feasibility and validity of homogenization for getting macroscopic permeability of fractured-vuggy porous medium is verified. The relationships between x-permeability, y-permeability and slip coefficient, matrix permeability, fracture aperture and vuggy area are also discussed, which indicate that the fracture aperture is the main factor of affecting the macro permeability.The research results offer a new effective method for calculation of permeability in Fractured-vuggy carbonate reservoir.