针对石油勘探电法测井的三维电流场快速算法研究

项目名称： 针对石油勘探电法测井的三维电流场快速算法研究

项目编号： No.51307090

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 电工技术

项目作者： 顿月芹

作者单位： 济南大学

项目金额： 24万元

中文摘要： 大地钻井后放入测量仪器是常用的石油勘探方法，一种仪器是由多个向大地注入准直流的柱状电极构成，靠电流分布反映大地电气参数。若仪器偏心或地层不对称，则形成三维电流场，求解该电流场为正问题，其快速计算是确定地层参数逆问题的基础。目前多采用三维有限元求此类问题，速度较慢，本项目将研究三维电流场的快速算法。针对直井/水平井，研究半数值半解析的数值模式匹配法（NMM）与区域映射有限元结合的方法。提出一种递推NMM解析解的新方法，可提高计算精度与稳定性，实现各层解析式的统一化。用有限元与无限元结合的方法求开域场的数值解，研究网格分布及刚度阵性质与本征值的关系，优化本征值的分布，可降低矩阵维数，提高计算效率。针对NMM不适用于斜井的缺陷，研究将斜井变为"直井"的仿射变换，确定变换关系，对"直井"实施快速的NMM。目标是形成适用于直井/水平井和斜井模型的三维电流场的快速计算方法，为快速计算逆问题奠定基础。

中文关键词： 数值模式匹配法；本征方程；形状函数；无限元；仿射变换

英文摘要： A common method of oil exploration is putting a measuring instrument after drilling well in the earth. A kind of instrument consists of a few cylindrical electrodes leaking quasi-DC into the earth, and the electrical parameters of the earth can be reflected by the current distribution. If the instrument deviates from the axial of the borehole or the formation is asymmetry, then 3-D current field will be formed. Solving the 3-D current field is a forward problem, and fast calculation of the forward problem is the basis of the inverse problem to determine the formation parameters. Now 3-D finite element method was always used to solve this problem, and its speed is slow. This program will study the fast algorithm of the 3-D current field. The algorithm of combining the half numerical and half analytical numerical mode-matching method (NMM) with regional mapping finite element method will be studied for the vertical/horizontal well. A new method to solve the analytic expressions of NMM is presented, the calculation precision and stability will be improved, and the analytic expression of each layer will be unified. The numerical solution of the open boundary problem will be solved by combining the finite element method and the infinite element method, the relationship between grid distribution, stiffness matrix pro

英文关键词： Numerical mode matching method；eigen equation；shape function；infinite element；affine transformation