【作者】 刘振宇；

【导师】 翟云芳；

【作者基本信息】 大庆石油学院 ， 油气田开发工程， 2004， 博士

【摘要】 目前用于研究油藏渗流问题的数值解法主要是有限差分法，而有限元法作为一种有效的数值解法与有限差分法相比具有诸多的优点，但是，在油藏渗流问题方面的研究目前还不深入。本文对有限元法求解油藏渗流问题的一些基础性和关键性的问题进行了深入研究，为有限元法用于研究复杂的油藏渗流问题打下基础。具体开展了以下方面的研究： 1．在理论上系统地建立了油藏渗流问题的有限元方程，包括：单相液体渗流、油—水两相液体渗流、油—气—水三相流体渗流问题，有限单元类型包括3结点三角形、4结点任意四边形、8结点任意六面体，采用等参元对渗流方程在空间上离散，采用向后差分在时间上离散，线性方程组的求解采用变带宽高斯消去法，该方法充分利用刚度矩阵呈条带状和其对称性，将刚度矩阵中的非零元素用一维数组存储，大大减少了所需存储空间； 2．对单相液体的不稳定流问题，将有限元解与解析解进行了认真的对比分析，包括：平面单向流、平面径向流以及三维条件下的渗流，对比了地层中不同位置处的压力情况，对比采用有因次量和无因次量两种形式，结果表明：有限元法的解与解析解相比足够地精确，这一方面说明本文所建立的方法和计算程序是正确的，同时亦说明有限元法求解油藏渗流问题是准确、可靠的： 3．对有限元分析中的重要影响因素，如时间步长、网格尺寸及网格比例进行了深入的研究和分析，结果表明：在应用有限元法求解渗流问题时，它们是相互关联的，本文在对比分析的基础上得到了它们的关系式，为有效地进行有限元分析提供了理论依据； 4．对油井井底处的压力梯度进行了合理的计算，给出了井底压力梯度的校正公式，由此可以准确地计算油井的产量，这是油藏模拟计算中十分重要的一点： 5．对三个实际问题进行了模拟计算，第一，模拟计算了人工压裂井的生产动态，对人工裂缝进行了深入细致的刻划，用于描述人工裂缝的网格宽度最小达到0.5m，假设裂缝的几何形状为矩形或楔形，裂缝导流能力随距离和时间是变化的，或只随距离变化(分三种规律)，或只随时间变化(也分三种规律)，或同时随距离和时间变化(以上两种情况的迭加)，裂缝的方位可以任意变化，在以上条件下模拟计算了油井的生产动态，分析对比了不同假设条件对油井生产动态的影响，结果表明：对裂缝几何形状以及裂缝内部渗流规律作不同的假设，油井的生产动态有所不同，另外，还研究了裂缝长度、裂缝宽度以及地层各向异性对油井产量的影响，给出了综合以上因素对油井动态特性的影响情况，本文认为，对人工压裂井的动态模拟在以下假设条件下进行，条件更加接近实际，结果更为合理：①人工裂缝的几何形状为楔形；②裂缝导流能力同时随距离和时间变化；③地层为各向异性；④人工裂缝有一定方位角； 第二，研究了5点法井网中一个井组的生产动态，结果表明：本文的模拟计算方法不仅可以正确地模拟单井的动态情况，而且可以有效地模拟井组的动态情况，进一步可模拟区块的生产动态情况； 第三，研究了混合油藏边界渗流场的压力分布，结果表明：有限元法处理复杂的混合油藏边界问题是十分方便和有效的，这为研究复杂油藏的渗流问题提供了有力的手段； 6．利用Fortran 90编制了一个数值模拟器，该模拟器采用高度结构化和模块化的设计思想和方法，结构严谨，计算效率高，便于维护和扩充。更多还原

【Abstract】 In present, finite difference method is the main numerical method of studying the flow in reservoir, meanwhile, finite element method is a valid numerical method and has more superiority than finite difference method, but it is not deeply studied in solving reservoir problems. Some basic and critical problems that appear in the process of applying finite element method to reservoir simulation are studied in this thesis, it lays the foundation for the further research into complex reservoir problems. Topics included in the thesis are as follow:1. Equations of finite element method are established systematically in theory, including single phase flow, oil-water two phases flow, oil-water-gas three phases flow. The types of finite element employed in this thesis are 3-nodes triangle, 4-nodes quadrilateral, 8-nodes hexahedron. Those equations are dispersed in space by using iso-parameter element method and in time by using backward difference method. The linear equations are resolved by variable band Gauss Method, which makes full use of the symmetry and band of stiffness matrix and makes the non-zero element store in one dimension array to reduce occupation in the computer memories.2. To the unstable state flow of single phase fluid, the finite element method is compared with analytical solution, including: planar one-dimension flow, radial flow and three-dimensions flow. The pressure at different position are compared in dimension and dimensionless respectively. It is shown that the finite element solution is precise enough compared to analytical method, which proves that the method and program provided in the thesis are correct, and that it is precise and reliable to solve reservoir problems with the finite element method.3. Some significant factors in finite element analysis, such as time-step, the size of grid and the ratio of grid lengths, are studied and analyzed deeply. It is indicated that those factors are relative and the relative equation is proposed through analysis, which provide valid theoretical rules for finite element analysis.4. The mathmatic model of calculating bottom hole pressure gradient is developed to calculate the pressure gradient in bottom hole reasonably. It can be used to calculate the flow rate precisely , and this is very important in reservoir simulation.5. Simulations are demonstrated in three cases. The first, the production performances of hydrauliclly fractured well are simulatied, meanwhile, the fracture is described carefully and the minimum width of grid describing the fracture in 0.5m only. The geometry of fracture is assumed as rectangle or cuniform, and the transmissibility changes with only distance (having three models ), or changes with only time(having three models ), or changes with distance and time simultaneously(which is a composition about two situation described) , the orientation of fracture is variable. Under the assumption, the well performance is simulated, and different effect is analysed. It is shown that well performance is different when the geometry of fracture and the flow rule in fracture are different. In addition , the influences of fracture length and fracture width andanisotropy of formation to production are studied, the effects of all above factors on well performance are drawn. The assumptions, under which well performance can be simulated precisely , should be that: 1) the geometry of fracture is cuniform, 2) the transmissibility changes with distance and time simultaneously,3) the formation is anisotropy, 4) the fracture have certain orientation angle.The second, the performance of one well group in five-spot pattern is studied. It is shown that the simulation method proposed in this thesis can simulate not only single well performance ,but also well grop performance validly and block performance further.The third, the pressure distribution in mixed boundaries reservoir is studied. It is shown that the finite element method is easy and valid in solving problems with complex mixed boundaries,It provides更多还原