裂缝性油藏离散裂缝网络模型数值模拟研究
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摘要
基于双重连续介质理论的裂缝性油藏数值模拟方法,当裂缝系统发育较差时其连续性与实际相差较大,因而这类方法的适应性受到限制。实际上,裂缝系统是一个分隔基质岩块系统的网络系统,可视为离散的裂缝网络系统,更能准确描述裂缝性油藏的非均质性。论文以离散裂缝网络模型为基础,利用有限元方法,突破了只能求解不可压缩流体的限定,成功解决了二维离散裂缝网络模型的微可压缩油水两相流动的数值模拟问题。首先,在对裂缝发育特征分析的基础上研究了天然裂缝、人工裂缝及其开启、半开启、充填、闭合(潜在)裂缝的识别特征,提出了裂缝参数的表征方法,基于体积法和Parsons的平板流动理论形成了裂缝的孔隙度和渗透率的计算方法,为裂缝性油藏的数值模拟奠定了基础;第二,考虑地质上所描述的裂缝发育分布情况以及裂缝的形态、充填性、渗流特性等因素建立了离散裂缝网络物理模型和微可压缩油水两相流动的数学模型;第三,提出了离散裂缝网络数学模型的有限元求解方法,分别对基岩和裂缝系统采用三角形单元和线单元进行离散并推导出了其有限元插值函数,通过采用加权余量法得到了离散裂缝网络数值模拟的压力和饱和度方程的等效积分“弱”形式,形成了离散裂缝网络数值模拟的单元特性矩阵和列阵,建立了离散裂缝网络的有限元数值模型;第四,通过梯度法、共轭梯度法和预条件共轭梯度法的对比分析,依据收敛速度、需求存储空间等特点优选了预条件共轭梯度法,并形成了离散裂缝网络模型的有限元数值模型的预条件共轭梯度求解方法;最后,基于Windows XP操作系统和多物理场耦合分析软件(COMSOL Multiphysics)编制了裂缝性油藏离散裂缝网络数值模拟器,并对各种典型的裂缝性油藏概念模型进行了数值模拟研究,表明离散裂缝网络模型数值模拟方法能够准确描述裂缝属性对流动的影响,其油藏动态更加符合真实情况,具有较强的实用性和广阔的应用前景。
When fracture development is poor, its continuity has a very great difference compared with the reality. The numerical simulation method of fractured reservoir based on double porosity medium theory is limited when applying. In fact, fracture system is a network system separating matrix block and it can be regarded as discrete fracture network (DFN) system, which describe the heterogeneity of fractured reservoir accurately. On the basis of DFN model, the thesis overcomes the limit of only solving incompressible fluid and solves numerical simulation problems of slightly compressible oil-water two-phase flow with finite element method (FEM) successfully. Firstly, the fracture identification characteristics of natural fracture, artificial fracture, unlocked and half-unlocked fracture, fracture filling and fracture closure was studied based on the analysis of field data, such as FMI imaging logging etc. The characterization method of fracture parameters is proposed. And the calculation method of porosity and permeability is formed respectively using Volume Method and Parsons Plate Flow Theory, which provides basis for fractured reservoir numerical simulation. Secondly, according to fracture development and distribution in geological description mathematical model, fracture morphology, fracture filling, fracture seepage characteristics and other factors, the thesis has built DFN physical model and slightly compressible oil-water two-phase flow mathematical model. Thirdly, the solving method of mathematical model on DFN was proposed with FEM. Matrix is discretized using linear triangular elements; fractures are discretized by linear line elements. And finite element shape function is derived. The equivalent integral weak form of pressure and saturation equation of DFN numerical simulation is established using weighted residual method. Element characteristic matrix and array of DFN numerical simulation is formed, and finite element numerical model of DFN is built. Fourthly, according to convergence rate, demanding storage space and so on, preconditioned conjugate gradient method (PCG) is the optimal method after the comparison and analysis with gradient method and conjugate gradient method. And then PCG solving method of DFN finite element numerical model is formed. Finally, DFN numerical simulator of carbonate fractured reservoir was drawn up by COMSOL Multiphysics software at the circumstance of Windows XP. Then the numerical simulation on different typical conceptual models of fractured reservoir is studied. The results show that effects of fracture attribute for the fluid flow is accurately accounted by DFN numerical simulation method, and its reservoir performance is more close to realities. This method has strong practicability and wide application prospect.
When fracture development is poor, its continuity has a very great difference compared with the reality. The numerical simulation method of fractured reservoir based on double porosity medium theory is limited when applying. In fact, fracture system is a network system separating matrix block and it can be regarded as discrete fracture network (DFN) system, which describe the heterogeneity of fractured reservoir accurately. On the basis of DFN model, the thesis overcomes the limit of only solving incompressible fluid and solves numerical simulation problems of slightly compressible oil-water two-phase flow with finite element method (FEM) successfully. Firstly, the fracture identification characteristics of natural fracture, artificial fracture, unlocked and half-unlocked fracture, fracture filling and fracture closure was studied based on the analysis of field data, such as FMI imaging logging etc. The characterization method of fracture parameters is proposed. And the calculation method of porosity and permeability is formed respectively using Volume Method and Parsons Plate Flow Theory, which provides basis for fractured reservoir numerical simulation. Secondly, according to fracture development and distribution in geological description mathematical model, fracture morphology, fracture filling, fracture seepage characteristics and other factors, the thesis has built DFN physical model and slightly compressible oil-water two-phase flow mathematical model. Thirdly, the solving method of mathematical model on DFN was proposed with FEM. Matrix is discretized using linear triangular elements; fractures are discretized by linear line elements. And finite element shape function is derived. The equivalent integral weak form of pressure and saturation equation of DFN numerical simulation is established using weighted residual method. Element characteristic matrix and array of DFN numerical simulation is formed, and finite element numerical model of DFN is built. Fourthly, according to convergence rate, demanding storage space and so on, preconditioned conjugate gradient method (PCG) is the optimal method after the comparison and analysis with gradient method and conjugate gradient method. And then PCG solving method of DFN finite element numerical model is formed. Finally, DFN numerical simulator of carbonate fractured reservoir was drawn up by COMSOL Multiphysics software at the circumstance of Windows XP. Then the numerical simulation on different typical conceptual models of fractured reservoir is studied. The results show that effects of fracture attribute for the fluid flow is accurately accounted by DFN numerical simulation method, and its reservoir performance is more close to realities. This method has strong practicability and wide application prospect.
引文
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[12] M. Karimi-Fard, L. J. Durlofsky, K. Aziz. An efficient discrete-fracture model applicable for general-purpose reservoir simulators. the 2003 SPE Reservoir Simulation Symposium[C]. Houston: SPE 88812, 2003.
[13] Hugo Araujo, Pablo Lacentre, Tomas Zapata. Dynamic behavoir of discrete fracture network models. the 2004 SPE International Petroleum Conference[C]. Puebla, Mexico: SPE 91940, 2004.
[14] J. E. P. Monteagudo, A. Firoozabadi. Numerical simulation of water injection in disconnected and connected fractured media using jacobian-free fully implicit control volume method. the 2004 SPE/DOE 14th Symposium on Improved Oil Recovery[C]. Tulsa, Oklahoma, U.S.A.: SPE 89449, 2004.
[15]王洪涛,王恩志,金宜英.裂隙岩体渗流耦合数值分析方法及其工程应用[J].南京水利科学研究院水利水运科学研究,1998,(4):320-328.
[16]王洪涛,王恩志.岩体主干裂隙系统三维非稳定渗流分析模型[J].水动力学研究与进展,1998,13(2):206-213.
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