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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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[4] Coope D, Shen L C, Huang F S 1984 The Log Analyst 25 35
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[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
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[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]
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[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
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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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[35] Moskow S, Druskin V, Habashy T, Lee P, Davydycheva S 1999 Siam. J. Numer. Anal. 36 442
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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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