运移聚集角点网格三维数值模拟

发布时间：2019-05-18 14:34

【摘要】：油和水在盆地中的运移和聚集过程,是盆地模拟中最困难也是最关键的部分,我们又称之为二次运移,它的数学模型是一组非线性偏微分方程初边值问题,目前的数值方法均采用正交网格进行剖分.但是正交网格的局限性决定了其不能很好的逼近模拟复杂地形,如断层、尖灭区或者是不规则边界等.角点网格作为一种更加灵活、复杂的网格技术,目前已经在地质建模软件中广泛使用,这也对运移聚集的数值模拟提出了新的要求.针对这一要求,本文引入角点网格技术,设计算法计算角点网格的各项物理性质参数和传导率.构造以角点网格为基础的有限体积数值计算格式,建立新的三维运移聚集数学模型进行模拟和分析.我们将达西定律和状态方程代入连续性方程后,得到数学模型,即流动方程(0.1(a))—(0.1(b))：然后将流动方程差分离散化得到有限体积格式(0.2(a))—(0.2(b))：这个模型是一个非线性、大区域、动边界以及需要超长时间模拟的三维数学问题,我们采用交替方向隐式迭代格式,在每个方向上将差分方程归结为二阶块三角方程组(0.3(a))—(0.3(b)),然后通过一系列计算形成系数矩阵,最后求解方程组得到结果.基于交替方向隐式迭代格式,开发完整的FORTRAN程序,并针对多种概念模型和实际矿场数据进行测试,模拟结果很好地符合油水的运移聚集规律,表明我们的模型是正确有效的.本文主要分为三部分：一、建立角点网格三维模型并计算其各项参数.二、建立三维运移聚集数学模型并构造有限体积数值计算格式.三、开发程序进行数值模拟并分析结果.
[Abstract]:The migration and accumulation of oil and water in the basin is the most difficult and critical part of basin simulation. We also call it secondary migration. Its mathematical model is a set of nonlinear partial differential equation initial boundary value problems. At present, orthogonal grid is used to divide the current numerical methods. However, the limitation of orthogonal grid determines that it can not approach and simulate complex terrain well, such as fault, apocalypse area or irregular boundary and so on. Corner grid, as a more flexible and complex grid technology, has been widely used in geological modeling software, which also puts forward new requirements for numerical simulation of migration and accumulation. In order to meet this requirement, this paper introduces corner grid technology, and designs an algorithm to calculate the physical property parameters and conductivity of corner grid. A finite volume numerical calculation scheme based on corner grid is constructed, and a new three-dimensional migration and accumulation mathematical model is established for simulation and analysis. After we replace Darcy's law and equation of state with the continuity equation, we get the mathematical model. That is, the flow equation is 0.1 (a)-(0.1 (b):) and then the flow equation difference is separated and dispersed to obtain the finite volume scheme (0.2 (a)-(0.2 (b):) is a nonlinear, large region. Moving boundary and three-dimensional mathematical problems that need to be simulated for too long time, we use alternating direction implicit iterative scheme to reduce the difference equation to second-order block triangular equations (0.3 (a)-(0.3 (b),) in each direction. Then the coefficient matrix is formed by a series of calculations, and the results are obtained by solving the equations. Based on the alternating direction implicit iterative scheme, a complete FORTRAN program is developed, and a variety of conceptual models and actual field data are tested. The simulation results are in good agreement with the law of oil and water migration and accumulation, which shows that our model is correct and effective. This paper is divided into three parts: first, the three-dimensional model of corner grid is established and its parameters are calculated. Secondly, the mathematical model of three-dimensional migration and accumulation is established and the finite volume numerical calculation scheme is constructed. Third, develop the program to carry on the numerical simulation and analyze the result.
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P618.13;P628.3

【共引文献】