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方位随钻电磁测井是一种能够实时探测地层边界、实现地质导向与井眼成像的新型测井技术. 本文根据方位随钻电磁测井仪器的典型线圈系结构, 首先引入柱坐标系下非均质完全各向异性地层中电流源并矢Green函数, 并利用电磁场叠加原理给出倾斜发射线圈激发的电场以及倾斜接收线圈上感应电动势的计算公式; 然后应用电流源电场并矢Green函数的混合势克服非均质地层中电磁数值模拟的低感应数问题, 通过 和z方向上Lebedev网格设法降低网格节点个数, 并且利用标准化算法确定柱坐标系下非均质单元上的等效电导率. 在此基础上, 用三维有限体积法建立柱坐标系电场混合势的离散方法, 得到一个交错网格上电场矢势和标势大型代数方程, 并用不完全LU分解以及稳定双共轭梯度法确定数值解. 最后, 通过数据模拟结果对算法的有效性进行检验, 并考察钻铤、线圈倾斜角度以及地层各向异性等参数对仪器响应的影响. 数值结果表明: 在柱坐标系下用三维有限体积法的数值模拟算法处理非均质各向异性层中方位随钻电磁测井响应可以得到很好的结果. 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.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 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.
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Keywords:
- finite volume method /
- inhomogeneous anisotropic media /
- Lebedev grid /
- azimuth electromagnetic wave resistivity while drilling
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[2] Seydoux J, Legendre E, Mirto E, Dupuis C, Denichou J M, Bennett N, Kutiev G, Kuchenbecker M, Morriss C, Schlumberger L Y 2014 SPWLA 55th Annual Logging Symposium Abu Dhabi, UAE, May 18-22, 2014 SPWLA-2014-LLLL
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[7] Kennedy W D, Corley B D 2009 SPWLA 50th Annual Logging Symposium Houston, USA, June 21-24, 2009 SPWLA-2009-ZZ
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[28] Li H, Liu D J, Ma Z H, Gao X S 2012 Procedia Eng. 29 2122
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[33] Zhang Y, Wang H N, Tao H G, Yang S W 2012 Chin. J. Geophys. 55 2141 (in Chinese) [张烨, 汪宏年, 陶宏根, 杨守文 2012 地球 55 2141]
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[1] Li Q M, Omeragic D, Chou L, Yang L, Duong K, Smits J, Yang J 2005 SPWLA 46th Annual Logging Symposium New Orleans, USA, June 26-29, 2005 SPWLA-2005-UU
[2] Seydoux J, Legendre E, Mirto E, Dupuis C, Denichou J M, Bennett N, Kutiev G, Kuchenbecker M, Morriss C, Schlumberger L Y 2014 SPWLA 55th Annual Logging Symposium Abu Dhabi, UAE, May 18-22, 2014 SPWLA-2014-LLLL
[3] Neville T J, Weller G, Faivre O, Sun H 2007 SPE Reserv. Eval. Eng. 10 132
[4] Coope D, Shen L C, Huang F S 1984 The Log Analyst 25 35
[5] Zhou Q, Hilliker D J 1991 Geophysics 56 1738
[6] Gianzero S, Merchant G A, Haugland M 1994 SPWLA 35th Annual Logging Symposium Tulsa, USA, June 19-25, 1994 SPWLA-1994-MM
[7] Kennedy W D, Corley B D 2009 SPWLA 50th Annual Logging Symposium Houston, USA, June 21-24, 2009 SPWLA-2009-ZZ
[8] Everett M E 2012 Surv. Geophys. 33 29
[9] Wang H N, Tao H G, Yao J J, Chen G 2008 IEEE Trans. Geosci. Remote. 46 1525
[10] Wang H N 2011 IEEE Trans. Geosci. Remote. 49 4483
[11] Wang H N, Hu P, Tao H G, Yang S W 2012 Chin. J. Geophys. 55 717 (in Chinese) [汪宏年, 胡平, 陶宏根, 杨守文 2012 地球 55 717]
[12] Zhou J M, Wang H N, Yao J J, Yang S W, Ma Y Z 2012 Acta Phys. Sin. 61 089101 (in Chinese) [周建美, 汪宏年, 姚敬金, 杨守文, 马寅芝 2012 61 089101]
[13] Yang S W, Wang J X, Zhou J M, Zhu T Z, Wang H N 2014 IEEE Trans. Geosci. Remote. 52 6911
[14] Zhou J M, Wang J X, Shang Q L, Wang H N, Yin C C 2014 J. Geophys. Eng. 11 02500301
[15] Wang J X, Wang H N, Zhou J M, Yang S W, Liu X J, Yin C C 2013 Acta Phys. Sin. 62 224101 (in Chinese) [汪建勋, 汪宏年, 周建美, 杨守文, 刘晓军, 殷长春 2013 62 224101]
[16] Wang H N, So P M, Yang S, Hoefer W J R, Du H L 2008 IEEE Trans. Geosci. Remote. 46 1134
[17] Wang H N, Tao H G, Yao J J, Zhang Y 2012 IEEE Trans. Geosci. Remote. 50 3383
[18] Li F Y, Wen H, Fang Z Y 2013 Chin. Phys. B 22 120402
[19] Shen J S 2003 Chin. J. Geophys. 46 281 (in Chinese) [沈金松 2003 地球 46 281]
[20] Li J H 2014 Sci. China: Ser. D 44 928 (in Chinese) [李剑浩 2014 中国科学: 地球科学 44 928]
[21] Liu N Z, Wang Z, Liu C 2015 Chin. J. Geophys. 58 1767 (in Chinese) [刘乃震, 王忠,刘策 2015 地球 58 1767]
[22] Horstmann M, Sun K, Berger P, Olsen P A, Omeragic D, Crary S 2015 SPWLA 56th Annual Logging Symposium Long Beach, USA, July 18-22, 2015 SPWLA-2015-LLLL
[23] Wang H N, Yang S D, Wang Y 1999 Oil Geophys. Prospect. 34 649 (in Chinese) [汪宏年, 杨善德, 王艳 1999 石油地球物理勘探 34 649]
[24] Yao D H, Wang H N, Yang S W, Yang H L 2010 Chin. J. Geophys. 53 3026 (in Chinese) [姚东华, 汪宏年, 杨守文, 杨海亮 2010 地球 53 3026]
[25] Xu Z F, Wu X P 2010 Chin. J. Geophys. 53 1931 (in Chinese) [徐志锋, 吴小平 2010 地球 53 1931]
[26] Hue Y K, Teixeira F L 2006 IEEE Trans. Antenn. Propag. 54 1058
[27] Zhang L, Chen H, Wang X M 2012 Chin. J. Geophys. 55 3493 (in Chinese) [张雷, 陈浩, 王秀明 2012 地球 55 3493]
[28] Li H, Liu D J, Ma Z H, Gao X S 2012 Procedia Eng. 29 2122
[29] Liu G S, Teixeira F L, Zhang G J 2012 IEEE Trans. Antenn. Propag. 60 318
[30] Haber E, Asch U M 2001 Siam. J. Sci. Comput. 22 1943
[31] Novo M S, Silva L C, Teixeira F L 2010 IEEE Trans. Geosci. Remote. 48 1151
[32] Zhou J M, Zhang Y, Wang H N, Yang S W, Yin C C 2014 Acta Phys. Sin. 63 159101 (in Chinese) [周建美, 张烨, 汪宏年, 杨守文, 殷长春2014 63 159101]
[33] Zhang Y, Wang H N, Tao H G, Yang S W 2012 Chin. J. Geophys. 55 2141 (in Chinese) [张烨, 汪宏年, 陶宏根, 杨守文 2012 地球 55 2141]
[34] Davydycheva S, Druskin V, Habashy T 2003 Geophysics 68 1525
[35] Moskow S, Druskin V, Habashy T, Lee P, Davydycheva S 1999 Siam. J. Numer. Anal. 36 442
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