【作者】 周志军；

【导师】 刘永建；

【作者基本信息】 大庆石油学院 ， 油气田开发工程， 2003， 博士

【摘要】 近年来，随着石油工业的发展以及解决复杂石油工程问题的需要，流固耦合研究在石油钻井、开采、开发领域显得越来越重要，并已受到人们的高度重视。为了正确预测油气田开采过程，准确模拟油藏中的流体流动过程，揭示流体的分布规律，必须考虑由于注水和开采所引起的多相流体的渗流、应力状态的变化和储层变形之间的耦合作用。 本文在前人大量的实验和理论研究成果的基础上，在低渗透储层流固耦合理论方面完成了以下研究工作： 1、根据流固耦合渗流理论的基本思想，建立流固耦合渗流运动方程。在此基础上，将地质力学、渗流力学、岩土力学相结合，根据质量守恒原理，考虑低渗透油藏渗流时启动压力梯度和渗流特征，建立可变形低渗透多孔介质中流固耦合多相多组份渗流的数学模型，它包括流固耦合渗流的基本微分方程及其求解所需要的辅助方程。对流固耦合多相多组分渗流数学模型进行简化，即可得到低渗透储层流固耦合黑油模型和油水两相渗流的数学模型。 2、在油藏岩土应力和应变分析基础上，结合有效应力原理和岩石骨架本构关系，建立了低渗透储层岩层骨架的数学模型，包括孔隙度方程、平衡方程、几何方程、岩石骨架本构关系等。固相平衡方程和流体黑油模型组成了多相(油、气、水)液体渗流的流固耦合模型，它们之间互含耦合项，互不独立，是一组完全耦合的偏微分方程，必须进行耦合求解。 3、针对低渗透储层在变应力下的弹塑性变形特征，建立了弹性储层和弹塑性储层的本构模型，并给出了相应的矩阵描述和矩阵表达式。 4、结合低渗透油藏的具体特征，给出了毛管压力和相对渗透率的计算模型。总结物性参数动态模型已有的研究成果，研究了低渗透储层渗流场和应力场之间的耦合关系，给出低渗透油藏流固耦合数值模拟求解所需的孔隙度、渗透率等物性参数动态变化的理论计算模型。并给出了计算启动压力梯度的动态模型。 5、系统的研究了低渗透储层流固耦合数学模型的迭代耦合、解耦耦合和全耦合数值求解技术。 迭代耦合的数值求解方法是：采用显式交替求解方式，即岩土变形数学模型滞后于渗流数学模型一个时间步。流体渗流数学模型采用块中心有限差分方法求解，其中油水两相流体渗流方程采用IMPES方法处理，即隐式求解油藏压力显式求解流体饱和度，油气水三相渗流方程采用SEQ顺序求解方法处理，并对流体和井参数处理进行了分析，采用正交极小化方法求解方程组；而岩土变形数学模型则采用有限元法求解，根据有限元基本原理，在建立位移函数的基础上，结合有效应力原理、虚位移原理和虚功等效原理，建立了单元平衡方程。并给出单元刚度矩阵以及自重载荷、孔隙流体压力载荷、面力载荷和初应力载荷的等效结点力的计算方法，在此基础上，建立总体平衡方程，采用增量初应力法求解单元平衡方程。由物性参数动态模型进行渗流场和变形场之间参数的相互修正。 根据GALERKIN有限元法基本原理，建立了岩层骨架控制方程、压力方程、饱和度方程的GALERKIN有限元空间离散方程，利用全隐式格式对上述方程进行时间域的差分离散，建立了解耦耦合的数值求解模型。采用顺序求解方法，即先由固相方程求得固体变形，然后由压力方程求得压力分布，再顺次求得饱和度分布。 以孔隙流体压力和岩石的结点位移作为基本未知量，推导出了可变形低渗透储层多相流体渗流和岩石变形之间耦合的有限元数值模型，利用GALERKIN有限元法得到了三相流体渗流的控制方程在摘要几何域上的离散方程，利用差分法得到了时间域上的离散方程，建立了全藕合数值求解模型。 6、将有限差分法和有限元法结合起来，根据迭代祸合数值求解方法，进行了计算机程序设计。 7、利用所编制的程序，对低渗透储层流固祸合渗流理论进行了应用示例模拟研究。 本文建立的流固祸合模型、理论研究方法以及开发的数值模拟软件，可用于分析低渗透油藏地应力、岩石应变、孔隙度、渗透率、油藏压力等随时间和空间的变化规律，以及对油藏的渗流和开采动态的影响，对于真实模拟低渗透油藏的开发，指导低渗透油藏生产具有重要的意义。更多还原

【Abstract】 With the recent development of oil industry and the need of solving complicated petroleum engineering problems, fluid-solid coupling study which is highly valued is becoming more and more important in oil drilling ^ oil production and oil development. In order to accurately predict production process on the oil-gas field > simulate fluid flowing process and reveal fluid distribution regularity, multiphase seepage flow derived from water injection and production process, change of stress state and coupling effect amongst reservoir distribution must be taken into consideration.On the basis of a great number of experiments and theoretical studies performed by former researchers, the work finished in this paper concerning fluid-solid coupling theory in low permeability reservoir focuses on several aspects of the following:1. According to the basic conception of fluid-solid coupling seepage flow theory, an equation of motion should be founded. Moreover, depending on mass conservation law, combing geomechanics seepage mechanics and rock mechanics, considering start-up pressure gradient and seepage flow characteristics while seeping in low permeability reservoir, then fluid-solid coupling multiphase and polycomponent seepage mathematical model in changeable low permeable and porous media is established, which includes basic differential equation of fluid-solid coupling seepage and its subsidiary equation needed when extracting an answer. Fluid-solid coupling black oil model and oil-water two-phase seepage mathematic model are captured by simplifying fluid-solid multiphase and polycomponent seepage mathematical model.2. Based on the analysis of rock stress and strain, combining effective stress principle and rock matrix constitutive relation, establishing mathematical model of rock matrix in low permeability reservoir including porosity equations, balance equations, geometrical equations and rock matrix constitutive relations, etc. Fluid-solid coupling model of multiphase (oil, gas, water) seepage are composed of solid phase balance equations and fluid black oil model. They contains coupling factors each other and also depends on each other, which are a group of partial differential equations solved by coupling.3. As to the elastic plastic distortion characteristics under the condition of changeable stress in low permeability reservoir, elastic reservoir and elastic plastic reservoir constitutive model are established and corresponding matrix description and matrix expressions are given, either.4. Calculation model of capillary pressure and relative permeability is given by combining specific characteristics in low permeability reservoir. Theoretical calculation model of dynamic variation on porosity, permeability and the like physical parameters needed when solving fluid-solid numerical simulation in low permeability reservoir is given through summarizing former results of physical parameters dynamic model, meanwhile, a dynamic model of computing start-up pressure gradient is given.5. Systematically studying fluid-solid coupling mathematical model of iterative coupling decoupled coupling and fully coupled numerical solution technique in low permeability reservoir.Numerical solution method of iterative coupling is: adopt explicit alternating solution method, that is, rockdistortion mathematical model lag behind seepage mathematical model just one-step time. Fluid seepage mathematical model is solved by using block center finite difference method, oil-water two-phase fluid seepage equation belonging to the model adopts IMPES method, that is, adopting implicit method to solve reservoir pressure and explicit method to solve fluid saturation, oil-gas-water triphase seepage equations are solved by using SEQ sequence, and also analyzes fluid and well parameters, equation group is solved by using orthomin method, whereas rock distortion mathematical model is solved by using finite element method. According to the basic principle of finite element method, on the basis of establishing d更多还原