Calculation of Tilted Coil Voltage in Cylindrically Multilayered Medium for Well-Logging Applications
In cylindrical multilayered medium, we develop two tool models for electromagnetic (EM) well logging: a metal mandrel winding with a co-axial (tilted) transmitter coil and a tilted (coaxial) receiver coil. The voltages on receivers in those two models are proven to be the same and only zero-order ha...
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| Veröffentlicht in: | IEEE access 2020, Vol.8, p.30081-30091 |
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| creator | Bai, Yan Zhan, Qiwei Wang, Hongnian Chen, Tao He, Qiuli Hong, Decheng |
| description | In cylindrical multilayered medium, we develop two tool models for electromagnetic (EM) well logging: a metal mandrel winding with a co-axial (tilted) transmitter coil and a tilted (coaxial) receiver coil. The voltages on receivers in those two models are proven to be the same and only zero-order harmonic of EM field need to be considered for voltage calculation. To calculate the voltage, two pseudo-analytical formulae are presented by using the integral of electrical field in spatial and wavenumber domain, respectively. Those two alternative pseudo-analytical formulae can be used to verify calculation accuracy of each other in some scenarios when other numerical methods do not work well. Furthermore, the reflection coefficients of EM fields, consisting of the ratios of the cylindrical functions, are introduced to avoid overflow problems in the numerical integral. Numerical examples corroborate the correctness and stability of the proposed formulae. These formulae help advance the forward modeling and inversion of logging-while-drilling (LWD) azimuthal resistivity measurements and new extra-deep azimuthal resistivity tools (EDAR). |
| doi_str_mv | 10.1109/ACCESS.2020.2971535 |
| format | Article |
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The voltages on receivers in those two models are proven to be the same and only zero-order harmonic of EM field need to be considered for voltage calculation. To calculate the voltage, two pseudo-analytical formulae are presented by using the integral of electrical field in spatial and wavenumber domain, respectively. Those two alternative pseudo-analytical formulae can be used to verify calculation accuracy of each other in some scenarios when other numerical methods do not work well. Furthermore, the reflection coefficients of EM fields, consisting of the ratios of the cylindrical functions, are introduced to avoid overflow problems in the numerical integral. Numerical examples corroborate the correctness and stability of the proposed formulae. 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The voltages on receivers in those two models are proven to be the same and only zero-order harmonic of EM field need to be considered for voltage calculation. To calculate the voltage, two pseudo-analytical formulae are presented by using the integral of electrical field in spatial and wavenumber domain, respectively. Those two alternative pseudo-analytical formulae can be used to verify calculation accuracy of each other in some scenarios when other numerical methods do not work well. Furthermore, the reflection coefficients of EM fields, consisting of the ratios of the cylindrical functions, are introduced to avoid overflow problems in the numerical integral. Numerical examples corroborate the correctness and stability of the proposed formulae. These formulae help advance the forward modeling and inversion of logging-while-drilling (LWD) azimuthal resistivity measurements and new extra-deep azimuthal resistivity tools (EDAR).</description><subject>Antenna measurements</subject><subject>Coils (windings)</subject><subject>Conductivity</subject><subject>Directional antennas</subject><subject>Electric potential</subject><subject>Electrical resistivity</subject><subject>electromagnetic propagation in absorbing media</subject><subject>geophysical measurement techniques</subject><subject>Harmonic analysis</subject><subject>Integrals</subject><subject>Mathematical models</subject><subject>Numerical methods</subject><subject>Receiving antennas</subject><subject>Transmitters</subject><subject>Voltage</subject><subject>Wavelengths</subject><subject>well logging</subject><issn>2169-3536</issn><issn>2169-3536</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>ESBDL</sourceid><sourceid>RIE</sourceid><sourceid>DOA</sourceid><recordid>eNpNkctLxDAQxosoKOpf4CXguWseTZocl-ILVjz4OoZpHiVLbNa0Pex_b9eKOJcZhu_7zcBXFFcErwjB6mbdNLcvLyuKKV5RVRPO-FFxRolQJeNMHP-bT4vLYdjiueS84vVZ4RqIZoowhtSj5NFriKOzqEkhovcUR-gcCj1q9jH0NgcDMe7R0xTHEGHv8ix9cjZMn8injD5cjOUmdV3oO7Te7eKsP4CHi-LEQxzc5W8_L97ubl-bh3LzfP_YrDelqbAcS0UBfM09prSCihnvgUoP0LaKcpCKYrCCWQKYGwnACW6ZVa5lQgirasrOi8eFaxNs9S6HT8h7nSDon0XKnYY8BhOd5pXChHAMlJNK1jUI40VNCTPQYtvymXW9sHY5fU1uGPU2Tbmf39e04pVkBAsxq9iiMjkNQ3b-7yrB-hCPXuLRh3j0bzyz62pxBefcn0MqSRRX7Bt-aouK</recordid><startdate>2020</startdate><enddate>2020</enddate><creator>Bai, Yan</creator><creator>Zhan, Qiwei</creator><creator>Wang, Hongnian</creator><creator>Chen, Tao</creator><creator>He, Qiuli</creator><creator>Hong, Decheng</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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The voltages on receivers in those two models are proven to be the same and only zero-order harmonic of EM field need to be considered for voltage calculation. To calculate the voltage, two pseudo-analytical formulae are presented by using the integral of electrical field in spatial and wavenumber domain, respectively. Those two alternative pseudo-analytical formulae can be used to verify calculation accuracy of each other in some scenarios when other numerical methods do not work well. Furthermore, the reflection coefficients of EM fields, consisting of the ratios of the cylindrical functions, are introduced to avoid overflow problems in the numerical integral. Numerical examples corroborate the correctness and stability of the proposed formulae. 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| subjects | Antenna measurements Coils (windings) Conductivity Directional antennas Electric potential Electrical resistivity electromagnetic propagation in absorbing media geophysical measurement techniques Harmonic analysis Integrals Mathematical models Numerical methods Receiving antennas Transmitters Voltage Wavelengths well logging |
| title | Calculation of Tilted Coil Voltage in Cylindrically Multilayered Medium for Well-Logging Applications |
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