缝洞型介质等效连续模型油水两相流动模拟理论研究
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摘要
缝洞型介质存在广泛,在流体力学、材料科学、生物科学和化学科学中,许多问题的研究对象都具有缝洞型介质的特征,如缝洞型碳酸盐岩油气储层、地下喀斯特含水层、生物组织结构等。缝洞型介质由于含有基岩孔隙和丰富的缝洞结构,介质类型多,尺度差别大,流动规律复杂,流动模拟困难,传统的连续介质理论已不适用,有必要开展缝洞型介质的流动模拟研究。等效连续介质模型结合了离散介质模型能够准确描述缝洞型介质中的复杂流动的特点,并可沿用经典的连续介质渗流理论进行分析,在理论及求解方法上均具有雄厚的经验和基础,本论文对等效连续介质模型在缝洞型介质流动模拟中的应用展开研究。首先,建立了复杂多尺度介质等效渗透率张量求解的等效原则和计算原理,分别对裂缝型介质和缝洞型介质的等效渗透率张量确定方法进行了研究。建立了考虑基岩渗透性和不同交界面条件(包括连续边界条件、Beavers-Joseph滑移速度边界条件和Beavers-Joseph-Saffman滑移速度边界条件)的广义立方定律和单裂缝多孔介质的等效渗透率理论计算公式;基于单裂缝多孔介质渗透特性的研究结果,提出了较经典的立方定律更加准确和高效的裂缝预处理方法;将裂缝预处理方法运用到裂缝型介质等效渗透率张量求解的等效流动数学模型中,并采用边界元方法求解数学模型;在此基础上,根据所建立的裂缝型介质表征单元体积的确定方法,对等效连续模型的有效性判定进行了研究;针对缝洞型介质,建立了基于裂缝预处理方法和缝洞型介质网格块镜像反映处理方法的缝洞型介质等效流动数学模型,采用有限元-混合有限元耦合求解方法求解数学模型,从而得到缝洞型介质的等效渗透率张量;利用等效渗透率张量表征的连续介质体等效替换原缝洞型介质体,形成新的等效研究区域。其次,建立了全张量渗透率等效连续介质单相及两相流动模拟理论与方法,分别采用有限元方法和混合有限元方法求解单相和两相流动数学模型。最后,给出了缝洞型介质等效流动模拟数值实例的研究,验证论文所建立的缝洞型介质等效连续模型流动模拟理论的有效性和可靠性。本研究丰富了等效连续介质模型理论,拓宽其适用范围。研究结果为缝洞型介质流动分析的参数确定和规律研究提供了理论依据,是目前可以解决缝洞型介质油水两相流问题技术上可行的有效方法。
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.
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.
引文
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