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A real-time borehole correction of electromagnetic wave resistivity logging while drilling
PETROLEUM EXPLORATION AND DEVELOPMENT Volume 40, Issue 5, October 2013 Online English edition of the Chinese language journal Cite this article as: PETROL. EXPLOR. DEVELOP., 2013, 40(5): 671–675.
RESEARCH PAPER
A real-time borehole correction of electromagnetic wave resistivity logging while drilling YANG Zhen1,*, YANG Jinzhou2, HAN Laiju2 1. Post Doctor Working Station of Shengli Oilfield, Sinopec, Dongying 257017, China; 2. Drilling Technology Research Institute, Shengli Petroleum Administration Bureau, Sinopec, Dongying 257017, China
Abstract: The response of electromagnetic wave logging while drilling is influenced greatly by borehole and drilling fluid resistivity when the size of borehole is relatively large and drilling fluid resistivity is low. Borehole radius and drilling fluid resistivity were introduced to obtain more accurate transformed resistivity on the basis of the commonly used resistivity transformation model. The influence of borehole was considered in the newly established three dimensional transformation model, and a new borehole correction method was proposed. The resistivity transformation database can be established by calculation according to a certain instrument, and the true resistivity is obtained by three dimensional interpolation search technology of real-time correction in practical use. The results of numerical simulation and modeling verification show that the transformed resistivity by real-time correction coincides with the resistivity corrected by charts. The method can eliminate the borehole influence, reduce calculation dimension, and improve the inversion efficiency of highly deviated and horizontal wells logging data. Key words: electromagnetic wave logging while drilling; resistivity; borehole influence correction; resistivity transformation model
Introduction The technology of logging while drilling is applied more and more widely, offshore logging abroad is almost all logging while drilling [1−2]. Electromagnetic wave propagation resistivity logging while drilling plays an important role in the formation boundaries determination and distance prediction of geosteering. In the process of resistivity transformation, the homogenous formation model is used in general, in which the borehole influence is ignored. However, the influence of borehole and drilling fluid can’t be ignored, especially when the diameter of borehole is big and the resistivity contrast of drilling fluid and virgin formation is large. High salinity drilling fluid can make the measurement under the frequency of 2 MHz over range, causing difficulty of logging data application [3]. Correction charts or inversion method are used in conventional borehole correction [4−8]. But it is well known from the Maxwell equation that the influences of various factors are nonlinear in electric logging response. Many other influences may be considered as the influence of borehole when the correction charts or inversion method are used. Moreover, the three-dimensional forward and inversion algorithms which consider all influence factors can’t be used in real time data process because of its inefficiency [9−11]. Con-
sequently, to obtain more accurate transformed resistivity, a kind of real time borehole correction method is proposed in the paper, which takes the influence of borehole and drilling fluid into consideration.
1 Conventional resistivity transformation method and borehole influence analysis Electrical properties of rocks are obtained by the transformation of amplitude ratio and phase shift of voltages on the two receivers of electromagnetic wave propagation resistivity tool [12−13]. The relationships of the amplitude ratio, the phase shift and the induction voltage of two receivers are expressed as follows: V Aamp = 20 lg R1 (1) VR2
Ppha = arg (VR1 ) − arg (VR2 )
(2)
The electromagnetic wave propagation resistivity transformation model assumes the formation is infinite and homogenous. Radially, the diameter of the tool is considered and the influence of the borehole is ignored. The transformation model is one-dimensional if the dielectric model is certain. The transformed resistivity is only related to the amplitude ratio or phase shift.
Received date: 04 Jan. 2013; Revised date: 12 Jul. 2013. * Corresponding author. E-mail: [email protected] Foundation item: Supported by the National Science and Technology Major Project (2011ZX05022-003). Copyright © 2013, Research Institute of Petroleum Exploration and Development, PetroChina. Published by Elsevier BV. All rights reserved.
YANG Zhen et al. / Petroleum Exploration and Development, 2013, 40(5): 671–675
Fig. 1
Schematic configuration of MPR
Fig. 3 Borehole influence correction chart of amplitude ratio resistivity (Rm=0.05 Ω·m)
Fig. 2 ence
Transformation Curves of MPR ignoring borehole influ-
Ramp = f ( Aamp )
(3)
Rpha = f ( Ppha )
(4)
Take for example the Baker Huge short spacing MPR tool (Fig. 1 [14]) with a diameter of 171.45 mm (6.75 in). The transformation charts calculated from one-dimensional model are shown in Fig. 2. The electric field can be written as the sum of incident wave, back wave and transmitted wave. The amplitude ratio resistivity and phase shift resistivity borehole correction charts are obtained by equation (5). f μ Ir ∞ Eφ2 = − 2 x ∫ cos ( kz ) ⎡⎣ J1 ( λ2 rmin ) H1( 2) ( λ2 rmax ) + 0 2 (5) A2 H1( 2) ( λ2 rz ) + B2 H1(1) ( λ2 rz ) ⎤⎦ dk where
λ2 =
σ ⎞ ⎛ f 2 μ 2 ⎜ εˆ2 − j m ⎟ − k 2 ω ⎠ ⎝
Fig. 4 Borehole influence correction chart of phase shift resistivity (Rm=0.05 Ω·m)
2
Improved resistivity transformation model
Because the electromagnetic wave propagation resistivity transformation model is based on well-established electromagnetic principles, it is not necessary to calibrate each tool in a simulated formation, which provides the base of the improved transformation model. By introducing the borehole size and drilling fluid resistivity into the conventional one-dimensional transformation model, the improved model can eliminate the borehole influence in real time. The improved model can be expressed as: Ramp = f ( Aamp , rb , Rm )
(6)
rmin = min ( rz , rx )
Rpha = f ( Ppha , rb , Rm )
(7)
rmax = max ( rz , rx )
The phase shift resistivity and amplitude ratio resistivity transformation charts of short spacing MPR tool by threedimensional model are shown in Fig. 5 and Fig. 6. The transformation database can be obtained by calculation for different instruments, borehole size and drilling fluid resistivity. The database can be saved in the downhole tool or monitor computer, then the corrected amplitude ratio resistivity and phase shift resistivity can be got by three-dimensional interpolation search in real time logging [15].
It can be seen from Fig. 3 and Fig. 4 that the transformed resistivity is affected significantly when the borehole is big or the resistivity contrast between the drilling fluid and virgin formation is large. The change trend of amplitude ratio resistivity and phase shift resistivity are different under the influence of borehole. High salinity drilling fluid can make the measurement under the frequency of 2 MHz over range. Since the borehole effect on amplitude ratio resistivity and phase shift resistivity are different. Other influence may be considered as borehole influence by correction charts or inversion method, and the calculation is inefficient. It is necessary to improve the commonly used resistivity transformation model.
3 Measurement methods of real-time well diameter Radius of borehole and drilling fluid resistivity are needed in real time by the borehole correction method proposed in the
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measured by a single detector is a function of formation density (obtained by compensated dual measurement), drilling fluid density and thickness. The drilling fluid thickness is the distance between the tool and borehole sidewall. This method can make an accurate measurement of drilling fluid thickness in 0.076 m (3 in) in some ideal cases. Besides the depth of investigation, the PE and density of drilling fluid will influence the accuracy of the density caliper too. The azimuthal diameter can only be obtained in rotary mode by the method. Fig. 5 Phase shift resistivity transformation chart for different drilling fluid resistivity (rb=0.152 m)
3.3
The phase signal has a shorter depth of investigation, and is more sensitive to borehole, so the propagation resistivity caliper mainly uses phase signals. The sum phase of voltage on the two receivers can reflect the borehole size [17]. The method is fit for water based drilling fluid, and a big resistivity contrast between the drilling fluid and virgin formation. There is a good linear relationship between the borehole diameter and sum phase in such cases. 3.4
Fig. 6 Amplitude ratio resistivity transformation chart for different drilling fluid resistivity (rb=0.152 m)
paper. Four methods are commonly used for well diameter measurement in logging while drilling. If there are no proper conditions for using these methods, the diameter of the drill bit can be regarded as the diameter of the borehole. 3.1
Ultrasonic caliber
Ultrasonic caliper measuring borehole size during drilling is a kind of commonly used method. The principle of measurement is to measure the travel time of ultrasonic wave as they travel from probe mounted on the tool collar to the borehole wall and return. The travel time is used to calculate the standoff of the tool [16]. If there are two sonic probes on the opposite directions of the tool, the diameter of the borehole can be converted in rotary mode and slide mode. If there is only one sonic probe, the diameter of the borehole can be converted only in rotary mode. The azimuthal diameters measured in rotary mode can be used for borehole imaging. The accuracy of the ultrasonic caliper is affected by the properties of drilling fluid significantly. High density drilling fluid will reduce the amplitude of the sonic, so the signal will suffer severe loss in high density drilling fluid and soft formation environment. The lower the density of drilling fluid, the larger the depth can be measured. The accuracy of this logging tool is also influenced by eccentricity, debris, borehole smoothness and gas content. 3.2
LWD density caliper
The density of rock and neutron porosity can be measured by neutron density tool while drilling. Apparent density
Propagation resistivity caliper
Neutron caliper
The neutron caliper algorithm uses the difference between the apparent near and far detector porosity and ratio-derived true porosity to derive the borehole size through an inversion method [18]. A main advantage of the neutron caliper is that it is available in the rotary and slide models. This is because the neutron caliper measure total borehole volume rather than tool standoff. The method is inaccurate above a borehole size of 0.254 m (10 in) for wells drilled with a 0.216 m (8.5 in) bit size and 0.203 m (8 in) for wells drilled with 0.165 m (6.5 in) bit size.
4 Verification of Real-time borehole influence Correction method Oklahoma formation model is a kind of classic homogenous model and is always used to validate the electric logging data process methods [19]. The model used in the paper with the resistivity from 0.4 Ω⋅m to 150 Ω⋅m, and the thickness of layers from 0.6m to 5.2 m, can fully reflect the complexity of real formation and the instrument response characteristics. The Oklahoma formation model was used to simulate MPR short spacing 2 MHz response in order to validate the effectiveness of the borehole correction method proposed in the paper (Fig. 7 and Fig. 8). The results show that the response is influenced by the thickness of layer and the borehole, the phase resistivity response in thick-layer can reflect the true resistivity, the amplitude ratio resistivity is affected more significantly than phase shift resistivity, and there is a big difference between the true resistivity and the phase shift resistivity or amplitude ratio resistivity when the layer is thin. The apparent resistivity of thick-layer is mainly affected by borehole when the borehole radius is 0.152 m and the resistivity of the drilling fluid is 0.05 Ω·m. In that borehole condition, the phase resistivity is larger than true resistivity and amplitude ratio resistivity is smaller when the conventional one-dimen-
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YANG Zhen et al. / Petroleum Exploration and Development, 2013, 40(5): 671–675
Fig. 9 Fig. 7 Simulated phase shift resistivity response with Oklahoma formation model
Fig. 8 Simulated amplitude ratio resistivity response with Oklahoma formation model
sion transformation model is used. The phase shift resistivity measured is over range in some cases, which is identical with the results shown in Fig. 3 and Fig. 4. The transformed resistivity is nearly completely identical with the results ignored the borehole influence when the three-dimensional transform model is used. The results show that the real-time borehole correction method proposed in the paper has better effect. Electromagnetic wave propagation resistivity logging while drilling is often used in highly deviated or horizontal wells, in that case the resistivity response is affected by deviation angles and layer thickness besides borehole. An ideal formation model was built in order to validate the effectiveness of the method in highly deviated wells, in which the deviation angle of well is 60°, radius of borehole is 0.152 m and the resistivity of drilling fluid is 0.1 Ω·m in the model. Three-dimensional finite difference method was used to simulate the MPR short spacing 2 MHz response (Fig. 9). The results show that the low resistivity of drilling fluid reduced the amplitude ratio resistivity and phase shift resistivity in the resistivity range of the model, especially when the resistivity contrast is large between the virgin formation and drilling fluid (well depth of 2–5 m, 7–9 m and 11–12 m). The three-dimensional transformed phase shift resistivity response can reflect the true resistivity, because it is small in investigation depth and little affected by deviation and layer thickness at the depth of 2–5
Transformed resistivity and inversion results
m and 7–9 m intervals. The one-dimensional transformed resistivity was lower because of the low resistivity of drilling fluid. The one-dimensional transformed resistivity was affected by deviation angle，layer thickness and borehole size, while the three-dimensional transformed resistivity was affected less by borehole at the layer depth of 11–12 m. If the influence of the borehole, deviated angles and layer thickness are considered at the same time in the forward and inverse modeling of highly deviated or horizontal wells logging data, the three-dimensional algorithm is needed. It cannot be used in the practical logging data process because of its huge computation, one-dimensional forward and inverse modeling is always used in the actual application. Using one-dimensional inversion algorithm to invert the resistivity transformed by the two models, the results are shown in Fig. 9. The figure shows that there are big errors between the one-dimensional transformed resistivity inversion results and the true resistivity, while the three-dimensional transformed resistivity inversion results are generally consistent with the true resistivity.
5
Conclusions
The transformed propagation resistivity from commonly used one-dimensional model is affected largely by high salinity drilling fluid, and the change trend of amplitude ratio resistivity and phase shift resistivity is sometimes different. High salinity drilling fluid and large resistivity contrast between the virgin formation and drilling fluid may make the measurement over range. The improved transformation model takes the borehole radius and drilling fluid resistivity into account, so as to correct the borehole influence in real time. The borehole size can be obtained by ultrasonic, neutron, nuclear density tool, the amplitude ratio resistivity and phase shift resistivity transformation charts were calculated and saved as transformation database. Oklahoma formation model was used to validate the effectiveness of the real time borehole correction method, and an ideal formation model was also built to validate the usability of the method in highly deviated wells. The results show that the method proposed in the paper can reduce the borehole influence, decrease the calculation dimension and improve the inversion efficiency of highly deviated and horizontal well logging data.
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YANG Zhen et al. / Petroleum Exploration and Development, 2013, 40(5): 671–675
Nomenclature Aamp—Amplitude ratio, dB; Ppha—Phase shift, (°); VR1, VR2—induction voltage on two receivers, V; Ramp—Amplitude ratio resistivity, Ω·m； Rpha—Phase shift resistivity, Ω·m; R—Transformed resistivity ignoring borehole influence, Ω·m; Eφ2—Electric field intensity on receiver, V/m; f—Working frequency, Hz; ω—Angular frequency, rad/s; μ2—drilling fluid magnetic permeability, H/m； I—Amplitude of electric current of the source, A; rx—Radius of the coil, m; k—Wave number; z—Coils spacing, m; J1(·)—The first order Bessel functions; H1(1)(·)—One order Hankel function of the first kind; H1(2)(·)—One order Hankel function of the second kind; A2, B2—constants, determined by the boundary conditions; rz—radius of collar, m; εˆ2 —Complex dielectric constant of drilling fluid, F/m; σm—Conductivity of drilling fluid, S/m; j—Imaginary unit; Ra—Apparent resistivity, Ω·m; Rc—Resistivity after borehole correction, Ω·m; Rm—drilling fluid resistivity, Ω·m; rb—Radius of borehole, m; σt—Formation conductivity, S/m; Rt—True resistivity, Ω·m; Ra1—Resistivity response of Oklahoma formation model ignoring borehole influence, Ω·m; Ra2—Transformed resistivity of Oklahoma formation model using one dimension transform model when the borehole radius is 0.152m and drilling fluid resistivity is 0.05 Ω·m, Ω·m; Ra3—Transformed resistivity of Oklahoma formation model using three-dimensional transform model when the borehole radius is 0.152m and drilling fluid resistivity is 0.05 Ω·m, Ω·m; h—Well depth, m; Rpha1, Ramp1—Transformed resistivity using three-dimensional transform model in highly deviated wells, Ω·m; Rpha2, Ramp2—Transformed resistivity using one-dimensional transformation model in highly deviated wells, Ω·m; Rinv1—One-dimensional inversion result of resistivity transformed by three-dimensional transformation model, Ω·m; Rinv2—One-dimensional inversion result of resistivity transformed by one-dimensional transformation model, Ω·m.
[4]
References
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Zhang Xinyun, Wang Jingnong, Guo Yanjun. Advances and trends in logging while drilling technology. Well Logging Technology, 2006, 30(1): 10–15. Su Yi, Qi Xin, Liu Yang, et al. Electromagnetic measurement while drilling technology based on the carrier communication principle. Petroleum Exploration and Development, 2013, 40(2): 226–231. Yang Zhen, Liu Qingcheng, Yue Bujiang, et al. Numerical simulation on influence factors of electromagnetic wave resis-
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RESEARCH PAPER
A real-time borehole correction of electromagnetic wave resistivity logging while drilling YANG Zhen1,*, YANG Jinzhou2, HAN Laiju2 1. Post Doctor Working Station of Shengli Oilfield, Sinopec, Dongying 257017, China; 2. Drilling Technology Research Institute, Shengli Petroleum Administration Bureau, Sinopec, Dongying 257017, China
Abstract: The response of electromagnetic wave logging while drilling is influenced greatly by borehole and drilling fluid resistivity when the size of borehole is relatively large and drilling fluid resistivity is low. Borehole radius and drilling fluid resistivity were introduced to obtain more accurate transformed resistivity on the basis of the commonly used resistivity transformation model. The influence of borehole was considered in the newly established three dimensional transformation model, and a new borehole correction method was proposed. The resistivity transformation database can be established by calculation according to a certain instrument, and the true resistivity is obtained by three dimensional interpolation search technology of real-time correction in practical use. The results of numerical simulation and modeling verification show that the transformed resistivity by real-time correction coincides with the resistivity corrected by charts. The method can eliminate the borehole influence, reduce calculation dimension, and improve the inversion efficiency of highly deviated and horizontal wells logging data. Key words: electromagnetic wave logging while drilling; resistivity; borehole influence correction; resistivity transformation model
Introduction The technology of logging while drilling is applied more and more widely, offshore logging abroad is almost all logging while drilling [1−2]. Electromagnetic wave propagation resistivity logging while drilling plays an important role in the formation boundaries determination and distance prediction of geosteering. In the process of resistivity transformation, the homogenous formation model is used in general, in which the borehole influence is ignored. However, the influence of borehole and drilling fluid can’t be ignored, especially when the diameter of borehole is big and the resistivity contrast of drilling fluid and virgin formation is large. High salinity drilling fluid can make the measurement under the frequency of 2 MHz over range, causing difficulty of logging data application [3]. Correction charts or inversion method are used in conventional borehole correction [4−8]. But it is well known from the Maxwell equation that the influences of various factors are nonlinear in electric logging response. Many other influences may be considered as the influence of borehole when the correction charts or inversion method are used. Moreover, the three-dimensional forward and inversion algorithms which consider all influence factors can’t be used in real time data process because of its inefficiency [9−11]. Con-
sequently, to obtain more accurate transformed resistivity, a kind of real time borehole correction method is proposed in the paper, which takes the influence of borehole and drilling fluid into consideration.
1 Conventional resistivity transformation method and borehole influence analysis Electrical properties of rocks are obtained by the transformation of amplitude ratio and phase shift of voltages on the two receivers of electromagnetic wave propagation resistivity tool [12−13]. The relationships of the amplitude ratio, the phase shift and the induction voltage of two receivers are expressed as follows: V Aamp = 20 lg R1 (1) VR2
Ppha = arg (VR1 ) − arg (VR2 )
(2)
The electromagnetic wave propagation resistivity transformation model assumes the formation is infinite and homogenous. Radially, the diameter of the tool is considered and the influence of the borehole is ignored. The transformation model is one-dimensional if the dielectric model is certain. The transformed resistivity is only related to the amplitude ratio or phase shift.
Received date: 04 Jan. 2013; Revised date: 12 Jul. 2013. * Corresponding author. E-mail: [email protected] Foundation item: Supported by the National Science and Technology Major Project (2011ZX05022-003). Copyright © 2013, Research Institute of Petroleum Exploration and Development, PetroChina. Published by Elsevier BV. All rights reserved.
YANG Zhen et al. / Petroleum Exploration and Development, 2013, 40(5): 671–675
Fig. 1
Schematic configuration of MPR
Fig. 3 Borehole influence correction chart of amplitude ratio resistivity (Rm=0.05 Ω·m)
Fig. 2 ence
Transformation Curves of MPR ignoring borehole influ-
Ramp = f ( Aamp )
(3)
Rpha = f ( Ppha )
(4)
Take for example the Baker Huge short spacing MPR tool (Fig. 1 [14]) with a diameter of 171.45 mm (6.75 in). The transformation charts calculated from one-dimensional model are shown in Fig. 2. The electric field can be written as the sum of incident wave, back wave and transmitted wave. The amplitude ratio resistivity and phase shift resistivity borehole correction charts are obtained by equation (5). f μ Ir ∞ Eφ2 = − 2 x ∫ cos ( kz ) ⎡⎣ J1 ( λ2 rmin ) H1( 2) ( λ2 rmax ) + 0 2 (5) A2 H1( 2) ( λ2 rz ) + B2 H1(1) ( λ2 rz ) ⎤⎦ dk where
λ2 =
σ ⎞ ⎛ f 2 μ 2 ⎜ εˆ2 − j m ⎟ − k 2 ω ⎠ ⎝
Fig. 4 Borehole influence correction chart of phase shift resistivity (Rm=0.05 Ω·m)
2
Improved resistivity transformation model
Because the electromagnetic wave propagation resistivity transformation model is based on well-established electromagnetic principles, it is not necessary to calibrate each tool in a simulated formation, which provides the base of the improved transformation model. By introducing the borehole size and drilling fluid resistivity into the conventional one-dimensional transformation model, the improved model can eliminate the borehole influence in real time. The improved model can be expressed as: Ramp = f ( Aamp , rb , Rm )
(6)
rmin = min ( rz , rx )
Rpha = f ( Ppha , rb , Rm )
(7)
rmax = max ( rz , rx )
The phase shift resistivity and amplitude ratio resistivity transformation charts of short spacing MPR tool by threedimensional model are shown in Fig. 5 and Fig. 6. The transformation database can be obtained by calculation for different instruments, borehole size and drilling fluid resistivity. The database can be saved in the downhole tool or monitor computer, then the corrected amplitude ratio resistivity and phase shift resistivity can be got by three-dimensional interpolation search in real time logging [15].
It can be seen from Fig. 3 and Fig. 4 that the transformed resistivity is affected significantly when the borehole is big or the resistivity contrast between the drilling fluid and virgin formation is large. The change trend of amplitude ratio resistivity and phase shift resistivity are different under the influence of borehole. High salinity drilling fluid can make the measurement under the frequency of 2 MHz over range. Since the borehole effect on amplitude ratio resistivity and phase shift resistivity are different. Other influence may be considered as borehole influence by correction charts or inversion method, and the calculation is inefficient. It is necessary to improve the commonly used resistivity transformation model.
3 Measurement methods of real-time well diameter Radius of borehole and drilling fluid resistivity are needed in real time by the borehole correction method proposed in the
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YANG Zhen et al. / Petroleum Exploration and Development, 2013, 40(5): 671–675
measured by a single detector is a function of formation density (obtained by compensated dual measurement), drilling fluid density and thickness. The drilling fluid thickness is the distance between the tool and borehole sidewall. This method can make an accurate measurement of drilling fluid thickness in 0.076 m (3 in) in some ideal cases. Besides the depth of investigation, the PE and density of drilling fluid will influence the accuracy of the density caliper too. The azimuthal diameter can only be obtained in rotary mode by the method. Fig. 5 Phase shift resistivity transformation chart for different drilling fluid resistivity (rb=0.152 m)
3.3
The phase signal has a shorter depth of investigation, and is more sensitive to borehole, so the propagation resistivity caliper mainly uses phase signals. The sum phase of voltage on the two receivers can reflect the borehole size [17]. The method is fit for water based drilling fluid, and a big resistivity contrast between the drilling fluid and virgin formation. There is a good linear relationship between the borehole diameter and sum phase in such cases. 3.4
Fig. 6 Amplitude ratio resistivity transformation chart for different drilling fluid resistivity (rb=0.152 m)
paper. Four methods are commonly used for well diameter measurement in logging while drilling. If there are no proper conditions for using these methods, the diameter of the drill bit can be regarded as the diameter of the borehole. 3.1
Ultrasonic caliber
Ultrasonic caliper measuring borehole size during drilling is a kind of commonly used method. The principle of measurement is to measure the travel time of ultrasonic wave as they travel from probe mounted on the tool collar to the borehole wall and return. The travel time is used to calculate the standoff of the tool [16]. If there are two sonic probes on the opposite directions of the tool, the diameter of the borehole can be converted in rotary mode and slide mode. If there is only one sonic probe, the diameter of the borehole can be converted only in rotary mode. The azimuthal diameters measured in rotary mode can be used for borehole imaging. The accuracy of the ultrasonic caliper is affected by the properties of drilling fluid significantly. High density drilling fluid will reduce the amplitude of the sonic, so the signal will suffer severe loss in high density drilling fluid and soft formation environment. The lower the density of drilling fluid, the larger the depth can be measured. The accuracy of this logging tool is also influenced by eccentricity, debris, borehole smoothness and gas content. 3.2
LWD density caliper
The density of rock and neutron porosity can be measured by neutron density tool while drilling. Apparent density
Propagation resistivity caliper
Neutron caliper
The neutron caliper algorithm uses the difference between the apparent near and far detector porosity and ratio-derived true porosity to derive the borehole size through an inversion method [18]. A main advantage of the neutron caliper is that it is available in the rotary and slide models. This is because the neutron caliper measure total borehole volume rather than tool standoff. The method is inaccurate above a borehole size of 0.254 m (10 in) for wells drilled with a 0.216 m (8.5 in) bit size and 0.203 m (8 in) for wells drilled with 0.165 m (6.5 in) bit size.
4 Verification of Real-time borehole influence Correction method Oklahoma formation model is a kind of classic homogenous model and is always used to validate the electric logging data process methods [19]. The model used in the paper with the resistivity from 0.4 Ω⋅m to 150 Ω⋅m, and the thickness of layers from 0.6m to 5.2 m, can fully reflect the complexity of real formation and the instrument response characteristics. The Oklahoma formation model was used to simulate MPR short spacing 2 MHz response in order to validate the effectiveness of the borehole correction method proposed in the paper (Fig. 7 and Fig. 8). The results show that the response is influenced by the thickness of layer and the borehole, the phase resistivity response in thick-layer can reflect the true resistivity, the amplitude ratio resistivity is affected more significantly than phase shift resistivity, and there is a big difference between the true resistivity and the phase shift resistivity or amplitude ratio resistivity when the layer is thin. The apparent resistivity of thick-layer is mainly affected by borehole when the borehole radius is 0.152 m and the resistivity of the drilling fluid is 0.05 Ω·m. In that borehole condition, the phase resistivity is larger than true resistivity and amplitude ratio resistivity is smaller when the conventional one-dimen-
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YANG Zhen et al. / Petroleum Exploration and Development, 2013, 40(5): 671–675
Fig. 9 Fig. 7 Simulated phase shift resistivity response with Oklahoma formation model
Fig. 8 Simulated amplitude ratio resistivity response with Oklahoma formation model
sion transformation model is used. The phase shift resistivity measured is over range in some cases, which is identical with the results shown in Fig. 3 and Fig. 4. The transformed resistivity is nearly completely identical with the results ignored the borehole influence when the three-dimensional transform model is used. The results show that the real-time borehole correction method proposed in the paper has better effect. Electromagnetic wave propagation resistivity logging while drilling is often used in highly deviated or horizontal wells, in that case the resistivity response is affected by deviation angles and layer thickness besides borehole. An ideal formation model was built in order to validate the effectiveness of the method in highly deviated wells, in which the deviation angle of well is 60°, radius of borehole is 0.152 m and the resistivity of drilling fluid is 0.1 Ω·m in the model. Three-dimensional finite difference method was used to simulate the MPR short spacing 2 MHz response (Fig. 9). The results show that the low resistivity of drilling fluid reduced the amplitude ratio resistivity and phase shift resistivity in the resistivity range of the model, especially when the resistivity contrast is large between the virgin formation and drilling fluid (well depth of 2–5 m, 7–9 m and 11–12 m). The three-dimensional transformed phase shift resistivity response can reflect the true resistivity, because it is small in investigation depth and little affected by deviation and layer thickness at the depth of 2–5
Transformed resistivity and inversion results
m and 7–9 m intervals. The one-dimensional transformed resistivity was lower because of the low resistivity of drilling fluid. The one-dimensional transformed resistivity was affected by deviation angle，layer thickness and borehole size, while the three-dimensional transformed resistivity was affected less by borehole at the layer depth of 11–12 m. If the influence of the borehole, deviated angles and layer thickness are considered at the same time in the forward and inverse modeling of highly deviated or horizontal wells logging data, the three-dimensional algorithm is needed. It cannot be used in the practical logging data process because of its huge computation, one-dimensional forward and inverse modeling is always used in the actual application. Using one-dimensional inversion algorithm to invert the resistivity transformed by the two models, the results are shown in Fig. 9. The figure shows that there are big errors between the one-dimensional transformed resistivity inversion results and the true resistivity, while the three-dimensional transformed resistivity inversion results are generally consistent with the true resistivity.
5
Conclusions
The transformed propagation resistivity from commonly used one-dimensional model is affected largely by high salinity drilling fluid, and the change trend of amplitude ratio resistivity and phase shift resistivity is sometimes different. High salinity drilling fluid and large resistivity contrast between the virgin formation and drilling fluid may make the measurement over range. The improved transformation model takes the borehole radius and drilling fluid resistivity into account, so as to correct the borehole influence in real time. The borehole size can be obtained by ultrasonic, neutron, nuclear density tool, the amplitude ratio resistivity and phase shift resistivity transformation charts were calculated and saved as transformation database. Oklahoma formation model was used to validate the effectiveness of the real time borehole correction method, and an ideal formation model was also built to validate the usability of the method in highly deviated wells. The results show that the method proposed in the paper can reduce the borehole influence, decrease the calculation dimension and improve the inversion efficiency of highly deviated and horizontal well logging data.
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YANG Zhen et al. / Petroleum Exploration and Development, 2013, 40(5): 671–675
Nomenclature Aamp—Amplitude ratio, dB; Ppha—Phase shift, (°); VR1, VR2—induction voltage on two receivers, V; Ramp—Amplitude ratio resistivity, Ω·m； Rpha—Phase shift resistivity, Ω·m; R—Transformed resistivity ignoring borehole influence, Ω·m; Eφ2—Electric field intensity on receiver, V/m; f—Working frequency, Hz; ω—Angular frequency, rad/s; μ2—drilling fluid magnetic permeability, H/m； I—Amplitude of electric current of the source, A; rx—Radius of the coil, m; k—Wave number; z—Coils spacing, m; J1(·)—The first order Bessel functions; H1(1)(·)—One order Hankel function of the first kind; H1(2)(·)—One order Hankel function of the second kind; A2, B2—constants, determined by the boundary conditions; rz—radius of collar, m; εˆ2 —Complex dielectric constant of drilling fluid, F/m; σm—Conductivity of drilling fluid, S/m; j—Imaginary unit; Ra—Apparent resistivity, Ω·m; Rc—Resistivity after borehole correction, Ω·m; Rm—drilling fluid resistivity, Ω·m; rb—Radius of borehole, m; σt—Formation conductivity, S/m; Rt—True resistivity, Ω·m; Ra1—Resistivity response of Oklahoma formation model ignoring borehole influence, Ω·m; Ra2—Transformed resistivity of Oklahoma formation model using one dimension transform model when the borehole radius is 0.152m and drilling fluid resistivity is 0.05 Ω·m, Ω·m; Ra3—Transformed resistivity of Oklahoma formation model using three-dimensional transform model when the borehole radius is 0.152m and drilling fluid resistivity is 0.05 Ω·m, Ω·m; h—Well depth, m; Rpha1, Ramp1—Transformed resistivity using three-dimensional transform model in highly deviated wells, Ω·m; Rpha2, Ramp2—Transformed resistivity using one-dimensional transformation model in highly deviated wells, Ω·m; Rinv1—One-dimensional inversion result of resistivity transformed by three-dimensional transformation model, Ω·m; Rinv2—One-dimensional inversion result of resistivity transformed by one-dimensional transformation model, Ω·m.
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