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基于二维自适应hp有限元的自然电位高精度计算
王正楷,张贵宾
0
(中国地质大学地球物理与信息技术学院,北京 100083;中国石油大学地球科学与技术学院,山东青岛 266580)
摘要:
将自适应hp有限元方法引进到自然电位的计算中。采用基于参考解投影型插值后验误差估计的自适应hp策略引导网格hp细化。利用该方法求解二维轴对称条件下的自然电位的矢量势方程,分析三层模型下的井径、钻井液、目的层电阻率、目的层厚度、侵入带半径和侵入带电阻率等因素对自然电位的影响规律。同时,计算五层介质和两层旋度源等复杂条件下自然电位。结果表明,该方法用较少的自由度获得较高精度的数值解,在计算精度和效率方面明显优于其他数值方法。
关键词:  自然电位  矢量势  自适应hp有限元  数值模拟  偶极层
DOI:10.3969/j.issn.1673-5005.2013.06.007
投稿时间:2013-03-01
基金项目:中国国家专项项目(SinoProbe-02);中国地质调查局地质调查项目(科[2012]01-046-012);国家科技重大专项(2011ZX05009-003)
High accuracy computations of spontaneous potential based on 2-D hp-adaptive finite element method
WANG Zheng-kai,ZHANG Gui-bin
(School of Geophysics and Information Technology in China University of Geosciences, Beijing 100083, China;School of Geosciences in China University of Petroleum, Qingdao 266580, China)
Abstract:
An hp-adaptive finite element method was introduced to the computation of spontaneous potential. The hp-adaptive strategy was based on projection-based interpolation of the reference solution which approached the true solution, and was used to solve for the vector potential equation in the two-dimensional axisymmetric media. The influences of the radius of the borehole, the mud-filtrate, the resistivity in goal formation, the thickness of the goal formation, the diameter of the invasion zone, as well as the resistivity of the invasion zone on the spontaneous potential in three-layer model were analyzed. The spontaneous potential was calculated in a complicated environment in which five-layer formation and two-layer sources were present. Numerical results show that the hp-adaptive finite element method can achieve higher accuracy level with less number of degrees of freedom, and provide better computation accuracy and efficiency than any other numerical method.
Key words:  spontaneous potential  vector potential  hp-adaptive finite element  numerical modeling  dipole layers
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