Theoretical Study Of The Equivalent Continuum Model For Simulating Oil-Water Two-Phase Flow In Fractured-Vuggy Porous Media

Fractured-vuggy media (FVM) occurs extensively in the field of fluid mechanics, materials sciences, biomedical science and chemistry, the study objects of many scientific problems are characteristic of FVM, such as carbonate formation of fractured-vuggy oil-gas reservoirs, underground Karst aquifers and biological tissues. Modeling and numerical simulation of fluid flow in FVM is a challenging issue due to the co-existence of multi-scale void spaces filled with different fluids and the complexity of the topology configuration, which results in the conventional continuum theory is not suitable for modeling fluid flow in this kind of media, accordingly it is necessary to develop a new methodology for modeling fluid flow in FVM more accurately. Equivalent continuum model (ECM) is proposed for estimating the equivalent permeability tensor (EPT), an equivalent intrinsic property of the FVM, and modeling two-phase fluid flow considering full tensorial permeability, integrating complexity of the flow calculation offered by continuum model with the realism of fracture and vug systems as captured by discrete model, this thesis presented the methodology of the equivalent continuum model for modeling fluid flow in FVM. First, methods of the determination of the equivalent permeability tensor (EPT) of fracture-vug-media block depending on the equivalent principle of ECM and basic calculation theory of EPT we presented are developed. A coupled Darcy-Stokes model is developed to describe the flow in single- fractured porous media. General cubic law and equivalent permeability considering the matrix permeability is proposed by applying classical continuous boundary conditions, Beavers–Joseph slipping velocity boundary conditions and Beavers–Joseph-Saffman slipping velocity boundary conditions respectively. Based on the research of permeability properties of single-fractured porous media, pretreatment of fractured media is developed to replace each fracture and surrounding porous media with continuous media characterized by equivalent permeability calculated by the theoretical formula we proposed for simplicity and efficiency of the problem; The equivalent-flow mathematical model considering the pretreatment of fractured media is established for calculating EPT of fractured media with the boundary element method; The methodology for efficiency decision of ECM is presented to predict the representative element volume (REV) of fractured reservoirs by calculating EPT; According to the structure of FVM and the flow characteristic in variable-scale space, FVM is divided into porous flow regions and free flow regions(containing fractures and vugs) governed by Darcy and Stokes equations with the Beavers–Joseph–Saffman boundary condition on the interface. The operation of two-step mirror imaging is implemented to any original block with asymmetric boundaries, so as to form new grid block with symmetric boundaries subject to periodic boundary conditions, finite-element method coupled with mixed finite-element method is used to solve the model to get the EPT of FVM block. Second, the mathematical models considering full tensorial permeability for single phase flow or two phase flow are presented and solved via finite element method and mixed finite element method respectively. Last, several numerical examples of modeling fluid flow in FVM were presented to demonstrate the validity and efficiency of our method. This research enhances the application scope of ECM. The research result provides a theoretical evidence to determine the parameters when analyzing the flow in FVM, which offer a feasible approach for modeling oil-water two-phase flow in FVM technically.