【摘要】 在三维非均匀介质中,提出一种新型的矢量有限元素法(FEM),用来模拟随钻(LWD)电阻率测井仪器的响应。在斜井和水平井中,成层的介质空间被离散成多个四面体单元,每个四面体有6个矢量棱边元。在三维地层模型中,未知数个数可以超过一百万个,采用代数多重网格结合多重前线解法,使用个人计算机即可求解这样大规模的线性方程。通过已发表的时域有限差分法(FDTD)的数值结果和实际测井数据,对仿真结果的有效性进行了双重验证。由此开发的算法已应用到模拟井眼、偏心、倾角、围岩校正和其他一些三维的测井响应中。所提方法也能为LWD电阻率测井仪器的设计提供理论支持。更多还原

【Abstract】 A novel vector finite element method(FEM) was proposed to simulate the response of logging-while-drilling(LWD) resistivity tool in 3D inhomogeneous medium.Layered medium combined with dipping borehole and invaded zones is partitioned into tetrahedrons.Each tetrahedron has six vector edge elements.The number of unknowns can be over 1 million for 3D LWD applications.In this case,an algebraic multigrid(AMG) method combined with multifrontal solver is developed to solve this very large scale problem with personal computers.The resulting program is validated through the published results derived from finite difference time-domain(FDTD) method and the borehole measurement data.The code can be used to compute the borehole correction charts,eccentric correction charts,side bed effects,and dipping angle effects for LWD tools.The proposed method can also provide theory support for LWD resistivity logging instrument design.更多还原