物理学报2016，Vol.65Issue(7)：079101-1-079101-13,13.DOI:10.7498/aps.65.079101
非均质各向异性地层中方位随钻电磁测井响应三维有限体积法数值模拟算法∗
Three-dimensional finite volume simulation of the resp onse of azimuth electromagnetic wave resistivity while drilling in inhomogeneous anisotropic formation
摘要
Abstract
The azimuth electromagnetic wave resistivity while drilling is a new type of well logging technique. It can real-time detect the formation boundary, realize geosteering and borehole imaging in order to keep the tool always drilling in the some meaning reservoir. For effectively optimizing tool parameters, proper explanation and evaluation of the data obtained by azimuth electromagnetic wave resistivity while drilling, the efficient numerical simulation algorithm is required. In this paper, we use the finite volume algorithm in the cylindrical coordinate to establish the corresponding numerical method so that we can effectively simulate the response of the tool in various complex environments and investigate the influences of the change in formation and tool parameters on the tool response. Therefore, according to the typical coil architecture of the instrument of azimuth electromagnetic wave resistivity while drilling, we first introduce the electrical and magnetic dyadic Green’s functions in inhomogeneous anisotropic formation by the electrical current source in the cylindrical coordinate. Through superposition principle, we derive the integral formula to compute the electric field intensity excited by tilted transmitter coils and the induction electrical potential on tilted receiving coils both mounded on the drill collar. Then, we use the coupled electrical potentials of the dyadic Green’s functions to overcome the low induction number problem during modeling the electrical fields in inhomogeneous anisotropic formation. Furthermore, we use Lebedev grid in both ρ and z directions to reduce the number of grid nodes, and the standard method to compute the equivalent conductivity in heterogeneous units for enhancing the discrete precision. On the basis, by the three-dimensional finite volume method, we discrete the equations about the coupled electrical potentials in the cylindrical coordinates and obtain the large sparse algebraic equation sets about the coupled electrical potentials field on the Lebedev grid. A combination of incomplete LU decomposition with the bi-conjugate gradient stabilization is used to solve the numerical solution. Finally, we validate the algorithm by comparing the numerical results obtained by two different methods, study the effects of the drill collar, anisotropy, the tilted angles of both coil, and borehole on the instrument response in inhomogeneous anisotropic formation. The numerical results show that the tool response obtained by the three-dimensional finite volume algorithm in the cylindrical coordinate system in anisotropic formation accord with that those obtained by other algorithms. The drill collar, inhomogeneous anisotropic n the formation will lead to both the smaller amplitude ratio and the smaller phase difference. In addition, when the coils of both transmitting and receiving coils are tilted, the amplitude ratio and phase difference of the tool are more sensitive to the change in formation parameter.关键词
有限体积法/各向异性地层/Lebedev网格/方位随钻电磁测井Key words
finite volume method/inhomogeneous anisotropic media/Lebedev grid/azimuth electromag-netic wave resistivity while drilling引用本文复制引用
王浩森,杨守文,白彦,陈涛,汪宏年..非均质各向异性地层中方位随钻电磁测井响应三维有限体积法数值模拟算法∗[J].物理学报,2016,65(7):079101-1-079101-13,13.基金项目
国家自然科学基金(批准号:41574110)和国家科技重大专项(批准号:2011ZX0520-001)资助的课题 （批准号:41574110）
