水平井中感应测井、电磁波测井测量响应研究
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摘要
由于水平井中物理模型失去了轴对称性,使得测井响应曲线形状发生了很大的变化,传统上成功应用的响应关系、各种校正图版均不适用,从测井曲线上无法提取相关地层信息,地层评价难于得到正确结论。本文的目的就是研究水平井中感应测井、电磁波测井的测量响应。由于几何模型失去了轴对称性,且介质非均匀,解析方法无法求解。另外,在考虑了仪器线圈尺寸、井眼和侵入带等的影响后,使几何和物理模型变得更为复杂,文中采用矢量有限元方法进行数值模拟和分析。通过与二维轴对称、均质地层情况对比,验证了方法的正确性。对应钻井的倾斜井段,计算了斜井中不同地层倾角下感应测井、电磁波测井的测量响应。同时对有侵入带的情况也进行了考察,与无侵入情况相比,界面上的畸变明显减小。在水平井中,首先考察了穿越模型,即测井仪器平行经过地层界面的情况,结果表明电磁波测井相位差视电阻率在界面上表现出较为明显的畸变。其次在水平井三层对称模型中,分别考虑了距离层边界、侵入带、层厚等因素的影响,进行了数值考察,制作了相应的校正图版。利用感应测井中相应的图版校正了水平井中现场数据资料,大大提高了测井解释符合率,体现了本文的实用价值。
In the oil and natural gas exploration and development of underground resources, the nature of the resistivity of the reservoir are the base for evaluation whether the formation are oil-bearing strata, including gas, oil or water-bearing layer, and it is the important parameters of evaluating oil and gas saturation. In horizontal and deviated wells, curve of logging has changed because borehole dot not cross through vertically the formation. The successful application of the traditional relationship and the response of various calibration plate do not be applied, the staff did not know to explain logging curve and can not extract information related to stratigraphy, formation evaluation conclusions is difficult to get right. Actual production need is urgent to the response characteristics of induction logging and electromagnetic wave logging in horizontal wells. This article has been made because evaluation of horizontal wells is needed in oil and gas exploration and development. It can help explained staff of well logging to correctly understand curve shape and calibration plate, enhance formation evaluation of horizontal well in line with the rate of horizontal wells at the same time can reduce the overall oil and gas exploration and development costs and risks, improve economic efficiency, the practical value of this article is self-evident.
The problem of induction logging and electromagnetic wave logging in horizontal wells, because azimuthal symmetry of the geometric model is broken and medium is non-uniform, the analytical method can not solve it, three methods is use of finite difference, finite element method, integral equations and numerical mode-matching, etc. Because it is three-dimensional problem in horizontal wells, and the electric and magnetic fields are vectors, vector finite element method for tetrahedral elements is used. Compared to the finite difference and numerical mode-matching, the most significant advantages of the finite element method are able to adapt to the complex geometry. In previous work, whether analytic or numerical algorithm algorithms have to simplify the physical model greatly, the actual process of logging equipment often eccentric, eccentric or eccentric invasive, whereas the finite element method is particularly adapted to the geometric situation of induction logging and electromagnetic wave logging at the horizontal wells.
Finite element method is a sophisticated method to calculate the electromagnetic field in the complex medium. There are many successful works to calculate tool response of induction and electromagnetic wave logging in two-dimensional axisymmetric formation. Because of the complexity of the formation, the three-dimensional finite element method must be to adopt. According to the characteristics of formation structure in horizontal wells, measurement methods and equipment structure of induction and electromagnetic wave logging tool, the mathematical and physical model simulating measurements response dual-induction and electromagnetic well logging are built in the horizontal wells. Vector element of tetrahedral used to overcome the shortcomings of node-based finite elements, such as the pseudo-solution problem, SSOR-BICG used for solving equations procedures also improve speed and stability.
The basic principles of induction logging can be using the role of double coil to illustrate: transmitter was passed alternating current, the receiver receive the induction electromotive force in the process of logging, which are effected by the formation. Coil placed in inhomogeneous media and the conductivity isσ, when the frequency of transmitter CT isωand the current is I, the transmitter produce an alternating electromagnetic field in the surrounding medium, known as first field, it excitated alternating current namely eddy current in conductivity medium. Eddy current line is concentric circles as the central axis of coil. Eddy current give rise to alternating electromagnetic field, called the secondary field, it produce induced electromotive force in the receiving coil, measurements of induction log is the induced electromotive force generated by the secondary field in the receiving coil. Dual-induction logging instruments are composed of three transmitter coils and eight receiving coils, it measure two curves that are deep-induction resistivity and medium-induction resistivity, which share three transmitter coils. Three receiving coils of deep induction and five receiving coils of medium induction are connected in series, Transmitter excitated AC current 20kHz, Alternating current generated in the formation alternating electromagnetic field which generated induced current in the conductive medium. The induced current in formation produce induced electromotive force in the receiving coil, the size of induced electromotive force is rate of conductivity in the formation medium. Adjust the coil spacing, number of turns and series direction, to offset the direct coupling signal to obtain purpose of the desired characteristics of the measurement. Electronic devices receive induced electromotive force measurement on coil and calibrate apparent resistivity. Analysis of the geometric factor showed that induction logging measurements have distinct characteristics, measured value of tool anywhere is co-contribution of upper and down formation. Contribution measured of deep and medium induction at the measuring point is 50 percent from up and down one meter thickness formation, Ninety five percent of the contribution for medium induction and deep induction at the measuring point are form 5-meter thickness formation and 10 meter thick formation respectively. When frequency of excitation current is 20 KHz, measuring instrument has good detection depth, depth of deep induction is 1.5-1.8 meters and medium induction is 0.5-0.7 meters for measuring electrical conductivity, at the same time the contribution of formation have the linear superposition. the detection characteristics of equipment decide that the interface layer was not clear for apparent resistivity at the thin layer, the response of amplitude is low at thin reservoir. When dip angle is zero, two-dimensional axisymmetric results are compared to verify the correctness of the method. The apparent resistivity is evaluated as the tool ascends the borehole. Seven different dip (150, 300, 450, 500, 550, 600 and 750) angles are considered. The results showed that with the increase in the angle of apparent resistivity the curves changes widely, the apparent resistivity is abrupt change in dipping bed boundaries. When it is the same dip angle, the apparent resistivity of deep induction is less than medium induction. When there is with the impact of invasive (low invasive), apparent resistivity of deep induction and medium induction have been decreased by the influence of the invasion, and abruption has been vanished. In models of horizontal well, first of all equipment passing through the two bed layers model is calculated, because apparent resistivity of medium induction is close to resistivity of formation equipment surround, when the apparatus pass through the interface layer, two curves of deep and medium induction apparent resistivity are cross, and the intersection is at high resistance layer. After multi-layer interface, the interface reaction layer can be in sight, but the interface was not clear, the response rate is low in thin layers. At the three-layer model, the apparatus separately from the layer boundaries, with a radius of invasion, thickness, etc. were studied, and finally produced invasive plate calibration. In distance from the layer boundary example, when the resistance in middle bed layer was lower than the surrounding rock’s, the apparent resistivity of deep and medium induction are almost not affected greatly in middle bed layer. With the increasing of resistivity middle layer, it is impacted significantly by wall rock. Although the physical model is axisal non-symmetry, but the formation model is symmetry so that two curves of apparent resistivity is also about the symmetry about the boundary layer. In the horizontal wells low invaded has been considered mainly, with the increase in radius of the invaded zone, apparent resistivity decrease rapidly, when the radius arrive at a value, the apparent resistivity is same as resistivity of invasion zone. From the impact of the thickness it is shown that apparent resistivity reduces gradually with thickness of layer increasing. In contrast, when resistivity of middle layer is greater than wall rock, along with the increasing of thickness, apparent resistivity gradually increase near the resistivity of middle layer. Through the study of distance from the border and thickness, the resistivity measured in horizontal well can be corrected; the real information of formation can get it.
Method of electromagnetic wave logging is different form the induction logging, electromagnetic wave logging measure mainly the phase shift and attenuation when spread in the media, in the non-magnetic medium, when the frequency is million hertz, the phase difference and amplitude attenuation depends primarily on the size of medium resistivity. The use of phase difference and attenuation measured can calculate apparent resistivity. Transmitter of Electromagnetic wave logging tool is passed alternating current, the phase difference and amplitude attenuation received by the two receivers are concerned with the resistivity nearby borehole. In uniform layer the phase difference and amplitude ratio of the corresponding relationship to the conductivity calibration, can be converted to apparent resistivity the corresponding formation. Transmitter excitated electromagnetic wave that spread in the formation, changes of the phase difference and amplitude ratio can determine characteristics of formation. This article elaborated on the principle of electromagnetic logging measurements, and derived the scale method. Analysis of phase difference, amplitude attenuation and apparent resistivity of the calibration chart we can see that resistivity of decay corresponding to formation is smaller dynamic range, and phase changes is more sensitive to formation resistivity, so this paper make use of phase difference to calculate apparent resistivity. To validate the computational efficiency and accuracy, the model was tested in a uniform medium with a resistivity and the dip angle of beds is 150. The relative error is less than 2%. The apparent resistivity is calculated as the tool ascends the borehole. Seven different dip (150, 300, 450, 500, 550, 600 and 750) angles are considered. The results showed that with the increase of the angle, apparent resistivity are impacted by the boundary of formation, when the frequency is 2MHz and angle is 750, the apparent resisitivity in boundaries is even larger than resisitivity of the middle bed. It’s shown that the invasion reduces the apparent resistivity in the center bed. Abrupt changes of apparent resistivity in dipping bed boundaries are reduced. In another situation, the response of electromagnetic wave tool crossing five layers formation, in the shoulder beds, the apparent resistivities are almost equal to the true resistivities. The apparent resistivities of middle three beds are less than the true resistivities. Although there are five layers in this example, the present method gives a reasonable result. Through analysis horizontal well model we can see through model, the frequency of electromagnetic wave logging is higher than induction logging and it have high-resolution, especially 2MHz electromagnetic is sensitive to layer interface, but also, it is that this characteristic can be used by LWD and Geosteering. Through the study of distance from the border and thickness, the resistivity measured in horizontal well can be corrected; the real information of formation can help to correct calibration plate.
A lot of works in this dissertation need improve constantly. The physical model should be much closer to actual physical model of logging, for example the size of drill collar and the groove of the situation in logging while drilling should be considered. Furthermore the stability and speed of the finite element method also need improve further.
In the oil and natural gas exploration and development of underground resources, the nature of the resistivity of the reservoir are the base for evaluation whether the formation are oil-bearing strata, including gas, oil or water-bearing layer, and it is the important parameters of evaluating oil and gas saturation. In horizontal and deviated wells, curve of logging has changed because borehole dot not cross through vertically the formation. The successful application of the traditional relationship and the response of various calibration plate do not be applied, the staff did not know to explain logging curve and can not extract information related to stratigraphy, formation evaluation conclusions is difficult to get right. Actual production need is urgent to the response characteristics of induction logging and electromagnetic wave logging in horizontal wells. This article has been made because evaluation of horizontal wells is needed in oil and gas exploration and development. It can help explained staff of well logging to correctly understand curve shape and calibration plate, enhance formation evaluation of horizontal well in line with the rate of horizontal wells at the same time can reduce the overall oil and gas exploration and development costs and risks, improve economic efficiency, the practical value of this article is self-evident.
The problem of induction logging and electromagnetic wave logging in horizontal wells, because azimuthal symmetry of the geometric model is broken and medium is non-uniform, the analytical method can not solve it, three methods is use of finite difference, finite element method, integral equations and numerical mode-matching, etc. Because it is three-dimensional problem in horizontal wells, and the electric and magnetic fields are vectors, vector finite element method for tetrahedral elements is used. Compared to the finite difference and numerical mode-matching, the most significant advantages of the finite element method are able to adapt to the complex geometry. In previous work, whether analytic or numerical algorithm algorithms have to simplify the physical model greatly, the actual process of logging equipment often eccentric, eccentric or eccentric invasive, whereas the finite element method is particularly adapted to the geometric situation of induction logging and electromagnetic wave logging at the horizontal wells.
Finite element method is a sophisticated method to calculate the electromagnetic field in the complex medium. There are many successful works to calculate tool response of induction and electromagnetic wave logging in two-dimensional axisymmetric formation. Because of the complexity of the formation, the three-dimensional finite element method must be to adopt. According to the characteristics of formation structure in horizontal wells, measurement methods and equipment structure of induction and electromagnetic wave logging tool, the mathematical and physical model simulating measurements response dual-induction and electromagnetic well logging are built in the horizontal wells. Vector element of tetrahedral used to overcome the shortcomings of node-based finite elements, such as the pseudo-solution problem, SSOR-BICG used for solving equations procedures also improve speed and stability.
The basic principles of induction logging can be using the role of double coil to illustrate: transmitter was passed alternating current, the receiver receive the induction electromotive force in the process of logging, which are effected by the formation. Coil placed in inhomogeneous media and the conductivity isσ, when the frequency of transmitter CT isωand the current is I, the transmitter produce an alternating electromagnetic field in the surrounding medium, known as first field, it excitated alternating current namely eddy current in conductivity medium. Eddy current line is concentric circles as the central axis of coil. Eddy current give rise to alternating electromagnetic field, called the secondary field, it produce induced electromotive force in the receiving coil, measurements of induction log is the induced electromotive force generated by the secondary field in the receiving coil. Dual-induction logging instruments are composed of three transmitter coils and eight receiving coils, it measure two curves that are deep-induction resistivity and medium-induction resistivity, which share three transmitter coils. Three receiving coils of deep induction and five receiving coils of medium induction are connected in series, Transmitter excitated AC current 20kHz, Alternating current generated in the formation alternating electromagnetic field which generated induced current in the conductive medium. The induced current in formation produce induced electromotive force in the receiving coil, the size of induced electromotive force is rate of conductivity in the formation medium. Adjust the coil spacing, number of turns and series direction, to offset the direct coupling signal to obtain purpose of the desired characteristics of the measurement. Electronic devices receive induced electromotive force measurement on coil and calibrate apparent resistivity. Analysis of the geometric factor showed that induction logging measurements have distinct characteristics, measured value of tool anywhere is co-contribution of upper and down formation. Contribution measured of deep and medium induction at the measuring point is 50 percent from up and down one meter thickness formation, Ninety five percent of the contribution for medium induction and deep induction at the measuring point are form 5-meter thickness formation and 10 meter thick formation respectively. When frequency of excitation current is 20 KHz, measuring instrument has good detection depth, depth of deep induction is 1.5-1.8 meters and medium induction is 0.5-0.7 meters for measuring electrical conductivity, at the same time the contribution of formation have the linear superposition. the detection characteristics of equipment decide that the interface layer was not clear for apparent resistivity at the thin layer, the response of amplitude is low at thin reservoir. When dip angle is zero, two-dimensional axisymmetric results are compared to verify the correctness of the method. The apparent resistivity is evaluated as the tool ascends the borehole. Seven different dip (150, 300, 450, 500, 550, 600 and 750) angles are considered. The results showed that with the increase in the angle of apparent resistivity the curves changes widely, the apparent resistivity is abrupt change in dipping bed boundaries. When it is the same dip angle, the apparent resistivity of deep induction is less than medium induction. When there is with the impact of invasive (low invasive), apparent resistivity of deep induction and medium induction have been decreased by the influence of the invasion, and abruption has been vanished. In models of horizontal well, first of all equipment passing through the two bed layers model is calculated, because apparent resistivity of medium induction is close to resistivity of formation equipment surround, when the apparatus pass through the interface layer, two curves of deep and medium induction apparent resistivity are cross, and the intersection is at high resistance layer. After multi-layer interface, the interface reaction layer can be in sight, but the interface was not clear, the response rate is low in thin layers. At the three-layer model, the apparatus separately from the layer boundaries, with a radius of invasion, thickness, etc. were studied, and finally produced invasive plate calibration. In distance from the layer boundary example, when the resistance in middle bed layer was lower than the surrounding rock’s, the apparent resistivity of deep and medium induction are almost not affected greatly in middle bed layer. With the increasing of resistivity middle layer, it is impacted significantly by wall rock. Although the physical model is axisal non-symmetry, but the formation model is symmetry so that two curves of apparent resistivity is also about the symmetry about the boundary layer. In the horizontal wells low invaded has been considered mainly, with the increase in radius of the invaded zone, apparent resistivity decrease rapidly, when the radius arrive at a value, the apparent resistivity is same as resistivity of invasion zone. From the impact of the thickness it is shown that apparent resistivity reduces gradually with thickness of layer increasing. In contrast, when resistivity of middle layer is greater than wall rock, along with the increasing of thickness, apparent resistivity gradually increase near the resistivity of middle layer. Through the study of distance from the border and thickness, the resistivity measured in horizontal well can be corrected; the real information of formation can get it.
Method of electromagnetic wave logging is different form the induction logging, electromagnetic wave logging measure mainly the phase shift and attenuation when spread in the media, in the non-magnetic medium, when the frequency is million hertz, the phase difference and amplitude attenuation depends primarily on the size of medium resistivity. The use of phase difference and attenuation measured can calculate apparent resistivity. Transmitter of Electromagnetic wave logging tool is passed alternating current, the phase difference and amplitude attenuation received by the two receivers are concerned with the resistivity nearby borehole. In uniform layer the phase difference and amplitude ratio of the corresponding relationship to the conductivity calibration, can be converted to apparent resistivity the corresponding formation. Transmitter excitated electromagnetic wave that spread in the formation, changes of the phase difference and amplitude ratio can determine characteristics of formation. This article elaborated on the principle of electromagnetic logging measurements, and derived the scale method. Analysis of phase difference, amplitude attenuation and apparent resistivity of the calibration chart we can see that resistivity of decay corresponding to formation is smaller dynamic range, and phase changes is more sensitive to formation resistivity, so this paper make use of phase difference to calculate apparent resistivity. To validate the computational efficiency and accuracy, the model was tested in a uniform medium with a resistivity and the dip angle of beds is 150. The relative error is less than 2%. The apparent resistivity is calculated as the tool ascends the borehole. Seven different dip (150, 300, 450, 500, 550, 600 and 750) angles are considered. The results showed that with the increase of the angle, apparent resistivity are impacted by the boundary of formation, when the frequency is 2MHz and angle is 750, the apparent resisitivity in boundaries is even larger than resisitivity of the middle bed. It’s shown that the invasion reduces the apparent resistivity in the center bed. Abrupt changes of apparent resistivity in dipping bed boundaries are reduced. In another situation, the response of electromagnetic wave tool crossing five layers formation, in the shoulder beds, the apparent resistivities are almost equal to the true resistivities. The apparent resistivities of middle three beds are less than the true resistivities. Although there are five layers in this example, the present method gives a reasonable result. Through analysis horizontal well model we can see through model, the frequency of electromagnetic wave logging is higher than induction logging and it have high-resolution, especially 2MHz electromagnetic is sensitive to layer interface, but also, it is that this characteristic can be used by LWD and Geosteering. Through the study of distance from the border and thickness, the resistivity measured in horizontal well can be corrected; the real information of formation can help to correct calibration plate.
A lot of works in this dissertation need improve constantly. The physical model should be much closer to actual physical model of logging, for example the size of drill collar and the groove of the situation in logging while drilling should be considered. Furthermore the stability and speed of the finite element method also need improve further.
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57.沈金松,用交错网格有限差分法计算三维频率域电磁响应,地球物理学报,2003,46(2):281-288
58.沈金松,用垂直数值模式匹配方法计算多频电磁测井响应,测井技术,2002,26(5):253-259
59.沈金松,用有限差分法计算各向异性介质中多分量感应测井的响应,地球物理学进展,2004,19(1):101-107
60. So?a Davydycheva, Vladimir Druskinz and Tarek Habashyz, An ef?cient ?nite-difference scheme for electromagnetic logging in 3D anisotropic inhomogeneous media, GEOPHYSICS, 2003, 68(5): 1525–1536.
61. Stan Gianzero and Shey-Min Su, The response of an induction dipmeter and standard induction tools to dipping beds, GEOPHYSICS, 1990, 55(9): 1128-1140
62.史晓锋,水平井中随钻电阻率测量仪定位和预测地层界面的方法,测井技术,2006,30(2):119-121
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41.江国明,邓少贵,范宜仁,毛广洲,大斜度井中的感应测井响应计算方法综述,勘探地球物理进展,2005,28(2):97-101
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45.康俊佐,杨善德,电磁波电阻率测井的二维全参数反演,测井技术,2007,31(4):314-320
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49. Louise Pellerin and Gerald W. Hohmann, Transient electromagnetic inversion: A remedy for magnetotelluric static shifts, 1990, GEOPHYSICS. 55(9): 1242-1250.
50.刘岩松等,水平井地质导向方法,石油钻采工艺,2007,29(supp):4-6
51.刘四新,佟文琪,电磁波测井的现状和发展趋势,地球物理学进展,2004,19(2):235-237
52. M.I. Epov, E.P. Shurina, O.V. Nechaev, 3D forward modeling of vector field for induction logging problems, Russian Geology and Geophysics, 2007, 48: 770–774
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56.其木苏荣,汪宏年,倾斜井眼中感应测井正演模拟与响应特征,计算物理,2003,20(2):161-168
57.沈金松,用交错网格有限差分法计算三维频率域电磁响应,地球物理学报,2003,46(2):281-288
58.沈金松,用垂直数值模式匹配方法计算多频电磁测井响应,测井技术,2002,26(5):253-259
59.沈金松,用有限差分法计算各向异性介质中多分量感应测井的响应,地球物理学进展,2004,19(1):101-107
60. So?a Davydycheva, Vladimir Druskinz and Tarek Habashyz, An ef?cient ?nite-difference scheme for electromagnetic logging in 3D anisotropic inhomogeneous media, GEOPHYSICS, 2003, 68(5): 1525–1536.
61. Stan Gianzero and Shey-Min Su, The response of an induction dipmeter and standard induction tools to dipping beds, GEOPHYSICS, 1990, 55(9): 1128-1140
62.史晓锋,水平井中随钻电阻率测量仪定位和预测地层界面的方法,测井技术,2006,30(2):119-121
63.孙向阳,聂在平,赵延文,李爱勇,罗曦,用矢量有限元方法模拟随钻测井仪在倾斜各向
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49. Louise Pellerin and Gerald W. Hohmann, Transient electromagnetic inversion: A remedy for magnetotelluric static shifts, 1990, GEOPHYSICS. 55(9): 1242-1250.
50.刘岩松等,水平井地质导向方法,石油钻采工艺,2007,29(supp):4-6
51.刘四新,佟文琪,电磁波测井的现状和发展趋势,地球物理学进展,2004,19(2):235-237
52. M.I. Epov, E.P. Shurina, O.V. Nechaev, 3D forward modeling of vector field for induction logging problems, Russian Geology and Geophysics, 2007, 48: 770–774
53.聂在平,周永祖,柳清伙.电磁波对轴对称二维层状介质的散射.地球物理学报,1992, 35:479-488.
54.聂在平,电法测井数值模拟研究进展,1995,24(supp):58-61.
55. Perry A. Eaton and Gerald W. Hohmann, The influence of a conductive host on two-dimensional borehole transient electromagnetic responses, GEOPHYSICS, 1984, 49(7): 861-869.
56.其木苏荣,汪宏年,倾斜井眼中感应测井正演模拟与响应特征,计算物理,2003,20(2):161-168
57.沈金松,用交错网格有限差分法计算三维频率域电磁响应,地球物理学报,2003,46(2):281-288
58.沈金松,用垂直数值模式匹配方法计算多频电磁测井响应,测井技术,2002,26(5):253-259
59.沈金松,用有限差分法计算各向异性介质中多分量感应测井的响应,地球物理学进展,2004,19(1):101-107
60. So?a Davydycheva, Vladimir Druskinz and Tarek Habashyz, An ef?cient ?nite-difference scheme for electromagnetic logging in 3D anisotropic inhomogeneous media, GEOPHYSICS, 2003, 68(5): 1525–1536.
61. Stan Gianzero and Shey-Min Su, The response of an induction dipmeter and standard induction tools to dipping beds, GEOPHYSICS, 1990, 55(9): 1128-1140
62.史晓锋,水平井中随钻电阻率测量仪定位和预测地层界面的方法,测井技术,2006,30(2):119-121
63.孙向阳,聂在平,赵延文,李爱勇,罗曦,用矢量有限元方法模拟随钻测井仪在倾斜各向REMOTE SENSING, 2007, 45(2):383-388
41.江国明,邓少贵,范宜仁,毛广洲,大斜度井中的感应测井响应计算方法综述,勘探地球物理进展,2005,28(2):97-101
42. Jin J. M.., The finite element method in electromagnetics [M]. New York: Wiley., 1993.
43.郊斌等,基于MWD和LWD信息估算钻头在地层中的位置,国外测井技术,2007,22(6):19-24.
44. Junsheng Hou1, Robert K. Mallan1 and Carlos Torres-Verdín1, Finite-difference simulation of borehole EM measurements in 3D anisotropic media using coupled scalar-vector potentials, GEOPHYSICS, 2006, 71(5): G225–G233
45.康俊佐,杨善德,电磁波电阻率测井的二维全参数反演,测井技术,2007,31(4):314-320
46. Laung Tsang. et al. Solution of The Fundamental Problem in Resistivity Logging With a Hybrid Method. Geophysics. 1984. 49(24):1596-1604
47. Liu Qing-Huo, Electromagnetic field generated by an off-axis source in a cylindrically layered medium with an arbitrary number of horizontal discontinuities, GEOPHYSICS, 1993, 58(5): 616-625
48. Liu Sixin and Motoyuki Sato, Transient radiation from an unloaded, ?nite dipole antenna in a borehole: Experimental and numerical results, GEOPHYSICS, 2005, 70(6): K43–K51.
49. Louise Pellerin and Gerald W. Hohmann, Transient electromagnetic inversion: A remedy for magnetotelluric static shifts, 1990, GEOPHYSICS. 55(9): 1242-1250.
50.刘岩松等,水平井地质导向方法,石油钻采工艺,2007,29(supp):4-6
51.刘四新,佟文琪,电磁波测井的现状和发展趋势,地球物理学进展,2004,19(2):235-237
52. M.I. Epov, E.P. Shurina, O.V. Nechaev, 3D forward modeling of vector field for induction logging problems, Russian Geology and Geophysics, 2007, 48: 770–774
53.聂在平,周永祖,柳清伙.电磁波对轴对称二维层状介质的散射.地球物理学报,1992, 35:479-488.
54.聂在平,电法测井数值模拟研究进展,1995,24(supp):58-61.
55. Perry A. Eaton and Gerald W. Hohmann, The influence of a conductive host on two-dimensional borehole transient electromagnetic responses, GEOPHYSICS, 1984, 49(7): 861-869.
56.其木苏荣,汪宏年,倾斜井眼中感应测井正演模拟与响应特征,计算物理,2003,20(2):161-168
57.沈金松,用交错网格有限差分法计算三维频率域电磁响应,地球物理学报,2003,46(2):281-288
58.沈金松,用垂直数值模式匹配方法计算多频电磁测井响应,测井技术,2002,26(5):253-259
59.沈金松,用有限差分法计算各向异性介质中多分量感应测井的响应,地球物理学进展,2004,19(1):101-107
60. So?a Davydycheva, Vladimir Druskinz and Tarek Habashyz, An ef?cient ?nite-difference scheme for electromagnetic logging in 3D anisotropic inhomogeneous media, GEOPHYSICS, 2003, 68(5): 1525–1536.
61. Stan Gianzero and Shey-Min Su, The response of an induction dipmeter and standard induction tools to dipping beds, GEOPHYSICS, 1990, 55(9): 1128-1140
62.史晓锋,水平井中随钻电阻率测量仪定位和预测地层界面的方法,测井技术,2006,30(2):119-121
63.孙向阳,聂在平,赵延文,李爱勇,罗曦,用矢量有限元方法模拟随钻测井仪在倾斜各向
84. Yik-Kiong Hue and Fernando L. Teixeira, FDTD Simulation of MWD Electromagnetic Tools in Large-Contrast Geophysical Formations, IEEE TRANSACTIONS ON MAGNETICS, 2004, 40(2): 1456
85. Yik-Kiong Hue, Fernando L. Teixeira, Luis San Martin, and Michael S. Bittar, Three-Dimensional Simulation of Eccentric LWD Tool Response in Boreholes Through Dipping Formations, IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, 2005, 43(2): 257
86. Y.-K. Hue, F. L. Teixeira, L. E. San Martin, and M. Bittar, Modeling of EM Logging Tools in Arbitrary 3-D Borehole Geometries Using PML-FDTD, IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 2005, 2(1): 78
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