非均質(zhì)各向異性地層中方位隨鉆電磁測(cè)井響應(yīng)三維有限體積法數(shù)值模擬算法_圖文

1、 物 理 學(xué) 報(bào) Acta Phys. Sin. Vol. 65, No. 7 (2016 079101 為 (T = 0 , R = 0 , (T = 0 , R = 45 和 (T = 45 , R = 0 的三種線圈系組合形成的隨鉆 電磁測(cè)井儀器的響應(yīng)曲線變化均較為平緩, 在層界 面附近均沒有出現(xiàn)跳躍; 高阻層上的幅度比與相位 差相對(duì)較小, 而低阻層上則相對(duì)較大, 且在所有的 地層上均有較明顯的響應(yīng); (T = 0 , R = 45 和 (T = 45 , R = 0 這兩種線圈系組合的隨鉆電磁 測(cè)井儀器的響應(yīng)曲線完全重合在一起, 這是由于在 -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 直井中這兩種線圈系的組合是等價(jià)的. 而傾角為 (T = 45 , R = 45 的隨鉆方位電磁測(cè)井儀器的 響應(yīng)曲線與前三種情況存在較大差異: 幅度比與相 位差的值明顯變大; 在層界面附近出現(xiàn)犄角, 曲線 形態(tài)更復(fù)雜, 這主要是層界面上積累面電荷的影響 造成的. 此外, 特別需要指出的是, 相位差曲線在 0.5 m 的薄層上的響應(yīng)比幅度比曲線更加明顯, 說(shuō) 明前者具有更高的縱向分辨率. -

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 圖6 (網(wǎng)刊彩色 直井中四種不同傾角的方位隨鉆電磁測(cè)井響應(yīng)的對(duì)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 圖7 (網(wǎng)刊彩色 30 斜井 11 層模型中四種不同傾角的方位隨鉆電磁測(cè)井響應(yīng)的對(duì)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 學(xué) 報(bào) 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 圖8 (網(wǎng)刊彩色 60 斜井 11 層模型中四種不同傾角的方位隨鉆電磁測(cè)井響應(yīng)的對(duì)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. 圖 7 和 圖 8 分 別 是 30 和 60 斜 井 情 況 下 (如 圖 1 (b, 方位隨鉆電磁測(cè)井四種線圈系組合的 幅 度 比 與 相 位 差 曲 線 響 應(yīng). 可 以 看 出, 在 井 眼 傾 斜 情 況 下, (T = 0 , R = 0 的 線 圈 系 組 合 的 響 應(yīng) 曲 線 變 化 較 小, 但 (T =

8、 0 , R = 45 , (T = 45 , R = 0 以及 (T = 45 , R = 45 線 圈系組合的測(cè)井響應(yīng)曲線均出現(xiàn)了較大的變化, 這 時(shí)由于在傾斜井眼中地層電導(dǎo)率在儀器坐標(biāo)系中 已變成完全各向異性, 電導(dǎo)率的交叉分量不等于零 造成的, 也說(shuō)明完全各向異性地層上測(cè)井曲線的處 理和解釋會(huì)更加困難. 數(shù)值結(jié)果表明: 鉆鋌、 電導(dǎo)率各向異性、 層邊界 均對(duì)方位隨鉆電磁波測(cè)井響應(yīng)產(chǎn)生較大的影響; 在 電阻率較大的地層, 幅度比和相位差響應(yīng)越小; 發(fā) 射線圈和接收線圈同時(shí)傾斜時(shí), 幅度比和相位差響 應(yīng)受地層的影響更靈敏. 參考文獻(xiàn) 1 Li Q M, Omeragic D, Chou L

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12、mposium Tulsa, USA, 4 結(jié) 論 本文根據(jù)方位隨鉆電磁測(cè)井儀器的典型線圈 系結(jié)構(gòu)以及電磁場(chǎng)的疊加原理, 利用柱坐標(biāo)系下完 全各向異性非均質(zhì)地層中電流源電場(chǎng)并矢 Green 函數(shù)的混合勢(shì)方程的三維 FVFD 算法, 研究并建立 了一套方位隨鉆電磁波測(cè)井響應(yīng)的數(shù)值模擬算法. 在電流源電場(chǎng)并矢 Green 函數(shù)的混合勢(shì)方程的離 散化過(guò)程中, 引入了 Lebedev 網(wǎng)格、 非均質(zhì)單元上 等效電導(dǎo)率的標(biāo)準(zhǔn)化算法等技術(shù), 有效提高了方程 的離散精度以及數(shù)值結(jié)果的穩(wěn)定性. 并通過(guò)數(shù)值結(jié) 果研究考察了各向異性地層對(duì)感應(yīng)電場(chǎng)空間分布 的影響, 以及線圈和井眼傾斜角變化等對(duì)儀器響應(yīng) 的影響.

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21、bashy T, Lee P, Davydycheva S 1999 Siam. J. Numer. Anal. 36 442 079101-12 物 理 學(xué) 報(bào) 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