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

1、 物 理 学 报 Acta Phys. Sin. Vol. 65, No. 7 (2016 079101 为 (T = 0 , R = 0 , (T = 0 , R = 45 和 (T = 45 , R = 0 的三种线圈系组合形成的随钻 电磁测井仪器的响应曲线变化均较为平缓, 在层界 面附近均没有出现跳跃; 高阻层上的幅度比与相位 差相对较小, 而低阻层上则相对较大, 且在所有的 地层上均有较明显的响应; (T = 0 , R = 45 和 (T = 45 , R = 0 这两种线圈系组合的随钻电磁 测井仪器的响应曲线完全重合在一起, 这是由于在 -4 -2 0 2 4 Depth/m 6

2、8 10 12 14 (a 16 1.8 2.0 2.2 2.4 2.6 Amplitude ratio 2.8 3.0 T=0O R=0O T=45O R=0O T=0O R=45O T=45O R=45O 直井中这两种线圈系的组合是等价的. 而倾角为 (T = 45 , R = 45 的随钻方位电磁测井仪器的 响应曲线与前三种情况存在较大差异: 幅度比与相 位差的值明显变大; 在层界面附近出现犄角, 曲线 形态更复杂, 这主要是层界面上积累面电荷的影响 造成的. 此外, 特别需要指出的是, 相位差曲线在 0.5 m 的薄层上的响应比幅度比曲线更加明显, 说 明前者具有更高的纵向分辨率. -

3、4 -2 0 2 4 Depth/m 6 8 10 12 14 (b 16 -5 0 5 10 15 20 25 30 Phase difference/(O 35 T=0O R=45O T=45O R=45O T=0O R=0O T=45O R=0O 图6 (网刊彩色 直井中四种不同倾角的方位随钻电磁测井响应的对比 (a 幅度比; (b 相位差 Fig. 6. (color online The logging response of logging while drilling (LWD with dierent angles coil tilted angles in vertical

4、borehole: (a Amplitude ratio; (b phase dierence. -4 -2 0 2 4 Depth/m 6 8 10 12 14 (a 16 1.8 2.0 2.2 2.4 2.6 2.8 T=0O R=0O T=45O R=0O T=0O R=45O T=45O R=45O -4 -2 0 2 4 6 8 10 12 14 (b 16 -5 0 T=0O R=0O T=45O R=0O Depth/m T=0O R=45O T=45O R=45O 5 10 15 20 25 30 35 40 45 Phase difference/(O Amplitude

5、ratio 图7 (网刊彩色 30 斜井 11 层模型中四种不同倾角的方位随钻电磁测井响应的对比 (a 幅度比; (b 相位差 Fig. 7. (color online The logging response of LWD with dierent angles coil tilted angles in 30 inclined borehole: (a Amplitude ratio; (b phase dierence. 079101-10 物 理 学 报 Acta Phys. Sin. -4 -2 0 2 4 Depth/m 6 8 10 12 14 (a 16 1.8 2.0 2.

6、2 2.4 2.6 Amplitude ratio 2.8 3.0 T=0O R=45O T=0O R=0O T=45O R=0O Vol. 65, No. 7 (2016 079101 -4 -2 0 2 4 Depth/m 6 8 10 12 14 16 T=0O R=0O T=45O R=0O T=0O R=45O T=45O R=45O T=45O R=45O (b 50 0 10 20 30 40 Phase difference/(O 图8 (网刊彩色 60 斜井 11 层模型中四种不同倾角的方位随钻电磁测井响应的对比 (a 幅度比; (b 相位差 Fig. 8. (color o

7、nline The logging response of LWD with dierent angles coil tilted angles in 60 inclined borehole: (a Amplitude ratio; (b phase dierence. 图 7 和 图 8 分 别 是 30 和 60 斜 井 情 况 下 (如 图 1 (b, 方位随钻电磁测井四种线圈系组合的 幅 度 比 与 相 位 差 曲 线 响 应. 可 以 看 出, 在 井 眼 倾 斜 情 况 下, (T = 0 , R = 0 的 线 圈 系 组 合 的 响 应 曲 线 变 化 较 小, 但 (T =

8、 0 , R = 45 , (T = 45 , R = 0 以及 (T = 45 , R = 45 线 圈系组合的测井响应曲线均出现了较大的变化, 这 时由于在倾斜井眼中地层电导率在仪器坐标系中 已变成完全各向异性, 电导率的交叉分量不等于零 造成的, 也说明完全各向异性地层上测井曲线的处 理和解释会更加困难. 数值结果表明: 钻铤、 电导率各向异性、 层边界 均对方位随钻电磁波测井响应产生较大的影响; 在 电阻率较大的地层, 幅度比和相位差响应越小; 发 射线圈和接收线圈同时倾斜时, 幅度比和相位差响 应受地层的影响更灵敏. 参考文献 1 Li Q M, Omeragic D, Chou L

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12、mposium Tulsa, USA, 4 结 论 本文根据方位随钻电磁测井仪器的典型线圈 系结构以及电磁场的叠加原理, 利用柱坐标系下完 全各向异性非均质地层中电流源电场并矢 Green 函数的混合势方程的三维 FVFD 算法, 研究并建立 了一套方位随钻电磁波测井响应的数值模拟算法. 在电流源电场并矢 Green 函数的混合势方程的离 散化过程中, 引入了 Lebedev 网格、 非均质单元上 等效电导率的标准化算法等技术, 有效提高了方程 的离散精度以及数值结果的稳定性. 并通过数值结 果研究考察了各向异性地层对感应电场空间分布 的影响, 以及线圈和井眼倾斜角变化等对仪器响应 的影响.

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21、bashy T, Lee P, Davydycheva S 1999 Siam. J. Numer. Anal. 36 442 079101-12 物 理 学 报 Acta Phys. Sin. Vol. 65, No. 7 (2016 079101 Three-dimensional nite volume simulation of the response of azimuth electromagnetic wave resistivity while drilling in inhomogeneous anisotropic formation Wang Hao-Sen1 Yang

22、Shou-Wen1 Bai Yan12 Chen Tao2 Wang Hong-Nian1 1 (College of Physics, Jilin University, Changchun 130012, China 2 (China Petroleum Logging Co., Ltd, Xian 710077, China ( Received 13 November 2015; revised manuscript received 17 January 2016 Abstract The azimuth electromagnetic wave resistivity while

23、drilling is a new type of well logging technique. It can realtime detect the formation boundary, realize geosteering and borehole imaging in order to keep the tool always drilling in the some meaning reservoir. For eectively optimizing tool parameters, proper explanation and evaluation of the data o

24、btained by azimuth electromagnetic wave resistivity while drilling, the ecient numerical simulation algorithm is required. In this paper, we use the nite volume algorithm in the cylindrical coordinate to establish the corresponding numerical method so that we can eectively simulate the response of t

25、he tool in various complex environments and investigate the inuences 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 rst introduce the electrica

26、l and magnetic dyadic Greens 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 eld intensity excited by tilted transmitter coils and the induction el

27、ectrical potential on tilted receiving coils both mounded on the drill collar. Then, we use the coupled electrical potentials of the dyadic Greens functions to overcome the low induction number problem during modeling the electrical elds in inhomogeneous anisotropic formation. Furthermore, we use Le

28、bedev grid in both 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 nite volume method, we discrete the equations about the coupled e

29、lectrical potentials in the cylindrical coordinates and obtain the large sparse algebraic equation sets about the coupled electrical potentials eld 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 dierent methods, study the eects of the drill collar, anisotropy, the tilted angles of both coil, and borehole on the instrument response in inhomogeneous anisotropic formation. The numerical re