TY - JOUR
AU - Shen,, Yongjin
AB - Abstract The monopole probe commonly used in acoustic logging can generate vibrations in its natural frequency under the excitation of the pulse signal, and excite transient electromagnetic (TEM) signals of the same frequency. The acoustic probe receives both acoustic and TEM field signals. The TEM field propagates and attenuates in conductive well fluid and formations, carrying formation resistivity information that could be used for formation evaluation. Based on the axisymmetry of the TEM field in an open-hole, theoretical calculation of the TEM field components in an open-hole model was performed. The results revealed that TEM response signals decay rapidly with time, and electric field intensity along the well axis Ez is approximately linear with formation resistivity. On this basis, we proposed a new method for measuring formation resistivity in an open-hole, which could supplement conventional logging methods. Also, it does not affect signal processing of acoustic logging and only applies the TEM signal to determine formation resistivity. The new method could accomplish a more comprehensive petroleum formation evaluation, which is of great significance to the integrated design of the well logging instrument. TEM field, monopole probe, resistivity, acoustic logging 1. Introduction Acoustic logging measurement (developed well before 1965) was originally designed for determining the compressional velocity of rocks surrounding a wellbore. Today, it plays an important role in a wide variety of geological, geophysical and engineering applications (Cheng et al. 1992; Ellis & Singer 2007; Zhao et al. 2016; Yao et al. 2019). During acoustic logging, a pulse of pressure must be applied to the formation surrounding the wellbore, which is based on the magnetostrictive behavior or piezoelectric effect of certain materials (Serra & Serra 2004; Serra 2008). Meanwhile, there are two kinds of transducer used in acoustic logging. The first type is the magnetostrictive transducer, which responds to changes in the magnetic field by a volume change of ferromagnetic material; while the second type is the piezoelectric transducer, which corresponds to an applied electric field by a volume change of ceramic materials. When the frequency of the applied magnetic field or electric field is identical to the natural frequency of the transducer, the transducer will vibrate according to its natural frequency, leading to the largest vibration amplitude. At the same time, sound waves with a similar frequency will be emitted at both ends of the transducer (Chu 1987; Zhang et al. 2009). Depending on the excitation mode, several types of acoustic source exist. Among them, monopole source acts as an omnidirectional pressure source and is widely used in acoustic logging. It creates a compressional wave pulse in the borehole fluid, which propagates out into the formation, exciting both compressional and shear waves in the formation (Haldorsen et al. 2006). Despite the advances in tool engineering and characterisation, transmitter technology and better understanding about the acoustic logging signals benefiting from computer modelling jointly promote the emergence of new technologies and transmitters (such as shear wave slowness measurements, dipole sources and sonic scanner tool), the monopole receivers and transmitters still deserve our attention (Close et al. 2009). In this paper, we consider the monopole transducer, which is usually a piezoelectric tube, as the source of acoustic signal. Under the excitation of the pulse excitation signal, the piezoelectric tube will vibrate and emit acoustic signals. At the same time, a sudden change in the voltage between the inner and outer surfaces of the piezoelectric tube will excite the TEM field in the surrounding medium (Nabighian 1987), which is widely used in the fields of mineral, coal, groundwater exploration, open-hole and cased-hole logging (Xue et al. 2012, 2015, 2018; Commer et al. 2015; Xi et al. 2016; Chen et al.2017; Khan et al. 2018; Rasmussen et al. 2018; Xue et al. 2018; Sheng et al. 2019). The TEM field propagates in the well (Song 2012), and the corresponding TEM response (shown in figure 1) is received by the acoustic receiving probes. This TEM signal, which arrives before the acoustic logging signal in the response waveform, is usually eliminated because it is an interference signal in acoustic logging (Rader 1982). In terms of signal composition, the TEM response received is mainly induced by the displacement current and conduction current. Since the influence of the dielectric constant on the electromagnetic response is relatively small within the working frequency band of acoustic logging, the TEM response in an open-hole is primarily affected by formation resistivity, i.e. the TEM response carries information about formation resistivity. Figure 1. Open in new tabDownload slide Waveforms measured using the array acoustic logging tools. Note that the longitudinal coordinate represents source-receiver spacing. Figure 1. Open in new tabDownload slide Waveforms measured using the array acoustic logging tools. Note that the longitudinal coordinate represents source-receiver spacing. In the process of open-hole logging, suppose that formation resistivity can be extracted from TEM responses (obtained by the acoustic logging tool); it would enrich the means of formation resistivity measurement in open-hole wells and significantly affect the integration of the instrument. By combining it with important information about the formation gathered from acoustic signals (such as slowness and porosity), it is possible to gain a more comprehensive understanding regarding the target formation. In this paper, we examine the feasibility of this idea experimentally and theoretically. The paper is organised as follows. In Section 2, we use the on-site acoustic logging data to present the source and characteristics of TEM induction signals in acoustic logging. In Section 3, we calculate the TEM field components excited by piezoelectric tube in the open-hole. In Section 4, by changing source-receiver spacing and formation resistivity, the characteristics of the responses are studied and the relationship between response signal and formation resistivity is also explored. Detailed analysis and discussion are performed in Section 5. Our findings are concluded in Section 6. 2. Electrical signals before the acoustic logging signals In this section, the characteristics of the raw single-receiver variable density plot in acoustic logging are studied. In addition, the initial reasons for our research on this subject are given. Briefly, the electrical signals (which arrive before the acoustic signal in the response waveform) are the TEM response signals excited by the piezoelectric tube. Figure 2 illustrates the processing result of the open-hole logging data obtained using the digital acoustic logging tool. Figure 2a presents the slowness-time-coherence (STC) plot obtained using the phase method; figure 2b shows the slowness curve; and figure 2c displays a raw single-receiver variable density plot. Apparently, figure 2 reflects that the physical parameters of the formation at different depths are different. Correspondingly, the amplitude of the TEM signal varies with depth (refer to figure 2c). Hence, we deduce that the TEM signal recorded by the acoustic logging tool is related to formation information. Since the frequency of acoustic logging is within a frequency range of about 20 kHz, the effect of the dielectric constant can be neglected. Thus, the induction signal should be related to the resistivity of the formation (Zhang 1984; Kaufman & Dashevsky 2003). As such, we perform the study of extracting formation resistivity information from TEM signals recorded in acoustic logging in current research. Figure 2. Open in new tabDownload slide Processing result of open-hole logging data obtained by a digital acoustic logging tool. (a) Slowness-time-coherence (STC) plot, (b) slowness and (c) raw single-receiver variable density plot. Figure 2. Open in new tabDownload slide Processing result of open-hole logging data obtained by a digital acoustic logging tool. (a) Slowness-time-coherence (STC) plot, (b) slowness and (c) raw single-receiver variable density plot. 3. Theoretical calculation of TEM field components: |${{{H}}_{\rm{\theta }}}$|⁠, |${{{E}}_{{r}}}$| and |${{{E}}_{{z}}}$| In this section, the TEM field components excited by piezoelectric tube in an open-hole are calculated using the open-hole model (figure 3). The cylindrical coordinate system |$( {r,{\rm{\ }}\theta ,{\rm{\ }}z} )$| is adopted in our calculation. Specifically, medium 1 represents the piezoelectric tube; medium 2 represents the well liquid and medium 3 represents the formation. The electromagnetic field excited by the piezoelectric tube is axisymmetric; while the electric field and magnetic field along the circumference are identical. When the excitation occurs, a high-voltage pulse signal of a certain frequency is applied on the inner and outer surfaces of the piezoelectric tube. The potential changes between the inner and outer surfaces, causing the acoustic vibration of the piezoelectric tube. Since the potentials of all points on the outer surface of the piezoelectric tube are identical, an infinite number of cylindrical equipotential surfaces are formed in the well fluid. There is a potential difference between any two equipotential surfaces, thus forming the electric field strength pointing to in r- and z-directions. The magnetic field induced by the changing electric field is along the circumference direction, perpendicular to the electric field direction. Figure 3. Open in new tabDownload slide Schematic diagram of the open-hole model. Figure 3. Open in new tabDownload slide Schematic diagram of the open-hole model. The current merely flows between the inner and outer walls of the piezoelectric tube and does not flow into the well fluid. The TEM field in the well fluid is generated by the variable magnetic field. This leads to the conductive current propagating along the radial r-direction and axial z-direction, thus we have |$\nabla \cdot \overset{{\rightharpoonup}}{{{E}}} = 0$|⁠. Following the basic principle of field theory (Pollack & Stump 2005), we write |${ \overset{{\rightharpoonup}}{E}}$| as: $$\begin{equation} \overset{{\rightharpoonup}}{{{E}}} = \nabla \times \overset{{\rightharpoonup}}{{{A}}},\end{equation}$$ (1) where |${{\overset{{\rightharpoonup}}{A}}}$| is the vector potential. It describes the TEM field excited by the piezoelectric tube. According to Maxwell's equation, |$\nabla {\rm{\ }} \times {{\ \overset{{\rightharpoonup}}{H}}} = {{\ \sigma \overset{{\rightharpoonup}}{E}}} + {\rm{\varepsilon }}\frac{{\partial \overset{{\rightharpoonup}}{E}}}{{\partial t}}$|⁠. For a sinusoidal time dependence |${e^{i\omega t}}$| $$\begin{eqnarray}\nabla {\rm{\ }} \times {{\ \overset{{\rightharpoonup}}{H}}} = \left( {{\rm{\sigma }} + {{i\varepsilon \omega }}} \right) {{\overset{{\rightharpoonup}}{E}}} &&= \left( {{\rm{\sigma }} + {{i\varepsilon \omega }}} \right){\rm{\ }}\nabla {\rm{\ }} \times {{\ }}\overset{{\rightharpoonup}}{A}\nonumber\\ &&= {\rm{\ }}\nabla {\rm{\ }} \times \left[ {\left( {{\rm{\sigma }} + {{i\varepsilon \omega }}} \right)\overset{{\rightharpoonup}}{A}} \right].\end{eqnarray}$$ (2) From equation (2), we have: $$\begin{equation}{{\overset{{\rightharpoonup}}{H}}} = \left( {{\rm{\sigma }} + {{i\varepsilon \omega }}} \right) {{\overset{{\rightharpoonup}}{A}}}.\end{equation}$$ (3) Due to the axisymmetry of the electromagnetic field, we define |$\overset{{\rightharpoonup}}{A}$| as having only a single component in the |$\theta $|-direction, i.e. |$\overset{{\rightharpoonup}}{A} = {A_\theta }\ {\overset{{\rightharpoonup}}{u}_\theta }$|⁠, to describe the TEM field, where |${\overset{{\rightharpoonup}}{u}_\theta }$| is the unit vector in the |$\theta $|-direction. Thus, the magnetic field caused by the conduction current has only one component in the |$\theta $|-direction, i.e. $$\begin{equation}{{{H}}_\theta } = \left( {{\rm{\sigma }} + {{i\varepsilon \omega }}} \right)\ {{{A}}_\theta }.\end{equation}$$ (4) By substituting |$\overset{{\rightharpoonup}}{A} = {A_\theta }\ {\overset{{\rightharpoonup}}{u}_\theta }$| into equation (1), we obtain: $$\begin{equation}{{\overset{{\rightharpoonup}}{E}}} = {\rm{\ }}\nabla {\rm{\ }} \times {{\ \overset{{\rightharpoonup}}{A}}} = {\rm{\ }} - \frac{{\partial {A_\theta }}}{{\partial z}}\overset{{\rightharpoonup}}{{{e_r}}} + \left( {\frac{{\partial {A_\theta }}}{{\partial r}} + \frac{{{A_\theta }}}{r}} \right)\overset{{\rightharpoonup}}{{{e_z}}}.\end{equation}$$ (5) Then $$\begin{equation}{E_r} = - \frac{{\partial {A_\theta }}}{{\partial z}},\end{equation}$$ (6) $$\begin{equation}{E_z} = \frac{{\partial {A_\theta }}}{{\partial r}}{\rm{\ }} + \frac{{{A_\theta }}}{r}.\end{equation}$$ (7) Following previous studies (Song 2012; Wu et al. 2017), the electric potential of the well liquid can be expressed as: $$\begin{eqnarray}{{{\Phi }}_\theta }\ ( {r,z}) &=& { \mathop \int \nolimits_{ - \infty }^\infty \mathop \int \nolimits_{ - \infty }^\infty [ {V ( \omega )}][ {B( {{k_z},\omega }){K_1}( {{l_2}r})}}\nonumber\\ &&\quad{ + C( {{k_z},\omega }){I_1}( {{l_2}r})}]{e^{i( {{k_z}z - \omega t})}}d{k_z}d\omega,\end{eqnarray}$$ (8) where |${l}_{2}^{2} = {{{k}}_{z}}\!\!^{2}{\rm{\ }} - {\gamma _2}\!\!^{2}$|⁠, |${\gamma _2} = {\rm{\ }}i\omega \mu ( {{\sigma _2} + i{\varepsilon _2}\omega } )$|⁠, |${\sigma _2}$| and |${\varepsilon _2}$| are the conductivity and dielectric constant of the well liquid, respectively. |$V( \omega )$| is the spectrum of the excitation source, |$B( {{k_z}\,,{\rm{\ }}\omega } )$| and |$C( {{k_z}\,,{\rm{\ }}\omega } )$| are generalised reflection coefficients related to resistivity and permeability of the formation surrounding the wellbore. The first term of the integrand in |${{{\Phi }}_\theta }( {r,{\rm{\ }}z} )$| represents the outward propagating directive waves excited by the piezoelectric tube; its second term represents all the reflected waves, which is also referred to as a generalised reflection wave due to the interfaces of the media. The electric vector potential of the formation outside the open-hole can be expressed as (Song 2012; Wu et al. 2017): $$\begin{eqnarray}{{{\Psi }}_\theta }\ ( {r,z}) = \scriptsize \mathop \int \nolimits_{ - \infty }^\infty \scriptsize \mathop \int \nolimits_{ - \infty }^\infty [ {V( \omega)}][ {D( {{k_z},\omega }){K_1}( {{l_3}r})}]{e^{i( {{k_z}z - \omega t})}}d{k_z}d\omega,\quad\quad \end{eqnarray}$$ (9) where |${l_3}\!\!^2 = {{\rm{k}}_z}\!\!^2{\rm{\ }} - {\gamma _3}\!\!^2$|⁠, |${\gamma _3} = {\rm{\ }}i\omega {\mu _3}( {{\sigma _3} + i{\varepsilon _3}\omega } )$| and |${\sigma _3}$| and |${\varepsilon _3}$| are the conductivity and dielectric constant of the formation, respectively. Under the tangentially continuous boundary conditions (⁠|${E_{{{ z}}2}} = {E_{{{ z}}3}}\ $|⁠, |${H_{\theta 2}} = {H_{\theta 3}}$|⁠) and the normal continuous boundary condition (⁠|${\varepsilon _1} {E_{{{r}}1}} = {\varepsilon _2}{E_{{{r}}2}} $|⁠), the coefficients |$B( {{k_z},{\rm{\ }}\omega } )$|⁠, |$C( {{k_z},{\rm{\ }}\omega } )$| and |$D( {{k_z},{\rm{\ }}\omega } )$| can be obtained by solving the equations. Thus, the integral solutions of TEM field components inside and outside the wellbore can be obtained. By solving the double integration in equations (8) and (9) using the real-axis integration method (Sheng et al. 2019), the TEM field components at different times and source-receiver spacings are acquired. In our calculation, the corresponding excitation waveform spectrum |$V( \omega )$| is the Gauss function |${e^{ - \frac{{{{( {f - {f_0}} )}^2}}}{{{p^2}}}}}$|⁠, whose main frequency is 25 kHz (see figure 4). The Gauss coefficient is |$p\ $|= 5. Figure 4. Open in new tabDownload slide Spectrum of excitation signal used in theoretical research. Figure 4. Open in new tabDownload slide Spectrum of excitation signal used in theoretical research. 4. Theoretical calculation results Based on the theoretical calculation method mentioned Section 3, the TEM field components excited by the piezoelectric tube in open-hole are calculated (with given calculation parameters) and their characteristics are studied. The relationship between TEM field signal and formation resistivity is explored by changing source-receiver spacing and formation resistivity. 4.1. TEM field components |${{\boldsymbol {H}}_{\rm{\boldsymbol \theta }}}$|⁠, |${{{\boldsymbol E}}_{{\boldsymbol r}}}$| and |${{{\boldsymbol E}}_{{\boldsymbol z}}}$| excited by piezoelectric tube in open-hole Figure 5a displays the calculated TEM field components (⁠|${H_\theta }$|⁠, |${E_r}$| and |${{{E}}_{{z}}}$|⁠) in the open-hole at 1.2 m source-receiver spacing. The calculation parameters are: |${\sigma _2}$| = 1 S m−1, |${\varepsilon _2}$| = 1, |${\mu _2}$| = 1; |${{\rm{\sigma }}_3}$| = 5 S m−1, |${\varepsilon _3}$| = 1 and |${\mu _3}$| = 1. Despite the similar parameters, our results reveal that the amplitudes and shapes of |${E_z}$|⁠, |${E_r}$| and |${H_\theta }$| waveforms are obviously different. Figure 5 parts b, c and d are the waveforms of |${H_\theta }$|⁠, |${E_r}$| and |${E_z}$| at different source-receiver spacings. It can be seen that with an increase of source-receiver spacing, the amplitudes of |${H_\theta }$|⁠, |${E_r}$| and |${{{E}}_{{z}}}$| gradually decrease, in which the shapes of |${{{H}}_{\rm{\theta }}}$| and |${E_z}$| remain unchanged, while the shape of |${E_r}$| changes considerably. Notably, the waveforms shift upward successively to a certain offset with the increase of source-receiver spacing for the convenience of observation (see figure 5b, c and c). Figure 5. Open in new tabDownload slide The waveforms of TEM field components (⁠|${H_\theta }$|⁠, |${E_r}$| and |${E_z}$|⁠) at different source-receiver spacings. Figure 5. Open in new tabDownload slide The waveforms of TEM field components (⁠|${H_\theta }$|⁠, |${E_r}$| and |${E_z}$|⁠) at different source-receiver spacings. 4.2. Relationship between TEM field components (⁠|${{{\boldsymbol H}}_{\rm{\boldsymbol \theta }}}$|⁠, |${{{\boldsymbol E}}_{{\boldsymbol r}}}$| and |${{{\boldsymbol E}}_{{\boldsymbol z}}}$|⁠) and formation resistivity To study the relationship between the TEM field components and formation resistivity, we calculate the TEM field components using different formation resistivity values. The waveforms of |${{{H}}_{\rm{\theta }}}$|⁠, |${E_r}$| and |${{{E}}_z}$| calculated using different formation resistivity values at a 1.2 m source-receiver spacing are shown in figure 6a, b and c, respectively; while the waveforms of |${E_z}$| at a 2.0 m source-receiver spacing are presented in figure 6d. In figure 6, the corresponding resistivity values in descending order are 15, 14, 13, 12, … , 2, 1, 1/2, 1/3, 1/4, … , and 1/25 Ω m−1, respectively. From figure 6a and b, it is obvious that the waveforms of |${H_\theta }$| and |${{{E}}_{{r}}}$| barely change with the formation resistivity. From figure 6c and d, the waveform of |${{{E}}_{{z}}}$| changes obviously with formation resistivity. The larger the formation resistivity value, the larger the amplitude. Therefore, the relationship between |${E_z}$| and formation resistivity is further explored to investigate the feasibility of extracting formation resistivity information from |${E_z}$|⁠. Figure 6. Open in new tabDownload slide Variation of waveforms of TEM field components at different formation resistivity values: (a) |${H_\theta }$| at 1.2 m source-receiver spacing, (b) |${E_r}$| at 1.2 m source-receiver spacing, (c) |${E_z}$| at 1.2 m source-receiver spacing and (d) |${E_z}$| at 2.0 m source-receiver spacing (from bottom to top, the corresponding resistivity values are 15, 14, 13, 12, … , 2, 1, 1/2, 1/3, … , and 1/25 Ω m−1, respectively.). Figure 6. Open in new tabDownload slide Variation of waveforms of TEM field components at different formation resistivity values: (a) |${H_\theta }$| at 1.2 m source-receiver spacing, (b) |${E_r}$| at 1.2 m source-receiver spacing, (c) |${E_z}$| at 1.2 m source-receiver spacing and (d) |${E_z}$| at 2.0 m source-receiver spacing (from bottom to top, the corresponding resistivity values are 15, 14, 13, 12, … , 2, 1, 1/2, 1/3, … , and 1/25 Ω m−1, respectively.). Figure 7 illustrates the relationship between formation resistivity and the maximum value of |${E_z}$|⁠. In figure 7a, the source-receiver spacing is 1.2 m where an obvious linear relationship is demonstrated; in figure 7b, the source-receiver spacing is 2.0 m where an approximately linear relationship is demonstrated. Figure 7. Open in new tabDownload slide Relationship between the formation resistivity and the maximum value of |${E_z}$| for: (a) 1.2 m source-receiver spacing and (b) 2.0 m source-receiver spacing. Figure 7. Open in new tabDownload slide Relationship between the formation resistivity and the maximum value of |${E_z}$| for: (a) 1.2 m source-receiver spacing and (b) 2.0 m source-receiver spacing. 5. Analysis and discussion The monopole acoustic probe commonly used in acoustic logging can generate acoustic vibration and excite the TEM field in the surrounding space when the pulse signal is excited. The TEM signal received by the acoustic receiving probe is the transient electric field signal, which is excited by the magnetic field coupling in the borehole. It is different from the direct current response where the current flows directly into the fluid and formation. There are two propagation modes of the TEM field in an open-hole, which are caused by the displacement current and conduction current, respectively. These two modes can be described using the Helmholtz equation of electric field |$\overset{{\rightharpoonup}}{E}$| and magnetic field |$\overset{{\rightharpoonup}}{H}$| expressed in equations (10) and (11): $$\begin{equation}{\nabla ^2}\overset{{\rightharpoonup}}{E} + ( {\mu \varepsilon {\omega ^2} - i\mu \sigma \omega })\ \overset{{\rightharpoonup}}{E} = {\rm{\ }}0,\end{equation}$$ (10) and $$\begin{equation}{\nabla ^2}\overset{{\rightharpoonup}}{H} + ( {\mu \varepsilon {\omega ^2} - i\mu \sigma \omega })\ \overset{{\rightharpoonup}}{H} = {\rm{\ }}0.\end{equation}$$ (11) The propagation velocity of the first mode, which is caused by displacement current, is |$1/\sqrt {\varepsilon \mu } $|⁠. It is the propagation velocity of the electromagnetic wave in the medium. The velocity of the second mode, which is caused by the conduction current, is |$2\sqrt {\frac{{f\pi }}{{\sigma \mu }}} $|⁠. If the conductivity of the media is 1 S m−1, the propagation velocity is |$2{\rm{\ }}\sqrt {\frac{{f\pi }}{{\sigma \mu }}} = {\rm{\ }}2{\rm{\ }}\sqrt {\frac{{\pi 25{\rm{\ }} \times {{10}^3}}}{{1{\rm{\ }} \times {\rm{\ }}4\pi \times {{10}^{ - 7}}}}} = {\rm{\ }}5{\rm{\ }} \times {10^5}$| m s−1. The superposition of these two propagation modes forms the TEM signals received in the open-hole acoustic logging data. Since the velocities of these two modes are far beyond the acoustic velocity in the well liquid (about 1.5 × 103 m S−1), the TEM signal appears at the front part of the received waveform, completely separated from the acoustic signals. The results of TEM field components show that the amplitude of |${E_z}$| is sensitive to the change of formation resistivity, while |${{{H}}_{\rm{\theta }}}$| and |${E_r}$| are insensitive. This phenomenon could be explained by using the boundary conditions of electromagnetic fields at dielectric surfaces. Since the operating frequency in acoustic logging is within the frequency range of about 20 kHz, the TEM field components calculated here are mainly caused by the conduction current. In the well liquid, the electric field intensity |${{\overset{{\rightharpoonup}}{E}}}$| can be decomposed into tangential component |${{{E}}_{{z}}}$| and normal component |${{{E}}_{{r}}}$|⁠, where |${E_r}$| plays the dominant role. Following |${\rm{\overset{{\rightharpoonup}}{j}}} = {{\ \sigma \ \overset{{\rightharpoonup}}{E}}} = {\rm{\ \sigma }}( {{E_z}{{\overset{{\rightharpoonup}}{u}}_z} + {{{E}}_r}{{\overset{{\rightharpoonup}}{u}}_r}} )$|⁠, the conduction current mainly concentrates in the r-direction and is incident to the formation obliquely at the wellbore. The resistivities of the formation and well fluid are different, so the direction of the current is changed when it enters the formation. If |${\sigma _2} < {\sigma _3}$|⁠, the amplitude of |${E_r}$| decreases, while |${E_z}$| remains unchanged, the |${{\overset{{\rightharpoonup}}{ E}}}$| in the formation will be more inclined to the z-axis. Thus, the current flowing along the z-axis in the formation is larger than that in the well fluid. If |${{\rm{\sigma }}_2} > {\sigma _3}$|⁠, the amplitude of |${E_r}$| increases, |${E_z}$| remains unchanged, the |${{\overset{{\rightharpoonup}}{E}}}$| in the formation will be more inclined to the r-axis. In both cases, the tangential components of the |${{\overset{{\rightharpoonup}}{E}}}$| on both sides of the wellbore are continuous (i.e. |${E_{z2}} = {E_{z3}}\ $|⁠). If the formation remains unchanged on the z-axis, the induced electromotive force (EMF) obtained, which is the integration of |${E_{z2}}$| along the z-direction, remains unchanged at short source-receiver spacing. Nonetheless, if the formation changes, for the simplest case, the current flowing along the z-direction from medium 3 to medium 4 (as illustrated in figure 8), things will be different. On the interface between media 3 and 4, the current density is continuous in the normal direction (i.e. |${{{J}}_{z3}} = {{{J}}_{z4}} $|⁠, we have |${\sigma _3}\ {E_{z3}} = {\sigma _4}{E_{z4}} $|⁠, |${E_{z3}}/{{\rm{\rho }}_3} = {E_{z4}}/{{\rm{\rho }}_4}$|⁠, |${E_{z4}} = {\rm{\ }}( {{E_{z3}}/{\rho _3}} ){\rho _4}$|⁠, |${E_{z2}} = {E_{z4}}\ $|⁠), indicating that the electric field intensity |${E_{z2}}$| in the well fluid is proportional to the resistivity of medium 4. The induced EMF obtained along the z-direction is directly affected by the resistivity of the medium 4 when it is at the short source-receiver spacing, causing the amplitude change of the TEM signal (shown in figure 2c). However, with an increase of source-receiver spacing, the linear relationship between |${{{E}}_{{z}}}$| and formation resistivity weakens due to other influence factors. Figure 8. Open in new tabDownload slide Schematic diagram of horizontal formation with the parameters {|${{\rm{\sigma }}_4}$|⁠, |${{\rm{\varepsilon }}_4}$|⁠, |${\mu _4}$|}. Figure 8. Open in new tabDownload slide Schematic diagram of horizontal formation with the parameters {|${{\rm{\sigma }}_4}$|⁠, |${{\rm{\varepsilon }}_4}$|⁠, |${\mu _4}$|}. As the acoustic receiving probes are arranged along the z-direction in the open-hole, the received EMF is directly related to |${{{E}}_{{z}}}$| and the formation resistivity. Therefore, when the formation resistivity changes, the amplitude of the electromagnetic induction signals arrive before the acoustic signal will change significantly. It should be noted that the results shown in figure 2 are measured using a digital acoustic logging tool, whose mechanical parts and the shell are all metal. The signals are transmitted through a shielded line and the logging tool is grounded at multiple locations. Hence, the electromagnetic signal has been attenuated severely. Nevertheless, we can see that the electromagnetic induction signal obviously changes with the formation. It can be inferred that the actual electromagnetic induction signal is relatively large. While the frequency band of the electromagnetic field excited by the acoustic probe is similar to that of induction logging, the electromagnetic field excited by the acoustic probe is perpendicular to that excited by the transmitter coil used in induction logging (because of their different excitation modes). Our method measures the formation resistivity along the z-direction, and induction logging measures formation resistivity along the circumferential direction. The EMF of induction logging is a circular closed eddy current, while in our method, the measured EMF is along the z-direction. 6. Conclusion By analysing the acoustic logging data, we found that: (i) in acoustic logging, a monopole probe can generate a relatively strong TEM field under the excitation of a periodic pulse signal; (ii) in the response waveform of acoustic logging, the TEM response signals, which arrive before the acoustic response signal can be clearly observed and (iii) if the formation changes, the amplitude of TEM response signal will change accordingly. Based on these findings, this paper calculated the TEM field components (⁠|${H_\theta }$|⁠, |${E_r}$| and |${E_z}$|⁠) in the open-hole and studied the relationship between the TEM field components and formation resistivity. The results revealed that |${E_z}$| is most closely related to formation resistivity and its amplitude is approximately proportional to formation resistivity at short source-receiver spacings. In this sense, the formation resistivity can be obtained by measuring the EMF received along the z-direction. On this basis, we proposed a new method for measuring formation resistivity in the open-hole, which is different from induction logging and lateral logging. The formation resistivity measured by this method is along the z-direction. It is a new method of formation resistivity measurement, which is different from the conventional logging methods (e.g. induction logging methods and resistivity logging methods). Furthermore, it can measure important information about the formation obtained from acoustic signals and formation resistivity simultaneously using one instrument. In this way, it should benefit the comprehensive detection of formation characteristics, and have a great significance in improving instrument integration. Acknowledgement This research was supported by the National Key Research and Development Program of China (no. 2016YFC0802008). Conflict of interest statement. None declared. References Chen W. , Xue G. , Muhammad Y.K. , Gelius L. , Zhou N. , Li H. , Zhong H. , 2015 . Application of Short-Offset TEM (SOTEM) technique in mapping water-enriched zones of coal stratum, an example from East China , Pure and Applied Geophysics , 172 , 1643 – 1651 . Google Scholar Crossref Search ADS WorldCat Chen W.Y. , Xue G.Q. , Olatayo A.L. , Chen K. , Khan M.Y. , Chen W.C. , Zhang L.B. , Chen W. , 2017 . A comparison of loop time-domain electromagnetic and short-offset transient electromagnetic methods for mapping water-enriched zones—A case history in Shaanxi, China , Geophysics , 82 , 201 – 208 . Google Scholar Crossref Search ADS WorldCat Cheng C.H. , Pennington W.D. , Paillet F.L. , 1992 . Acoustic waveform logging – advances in theory and application , The Log Analyst , 33 , 239 – 258 . WorldCat Chu Z.H. , 1987 . Principle of Acoustic Logging (in Chinese) , Petroleum Industry Press , Beijing . Google Preview WorldCat COPAC Close D. , Cho D. , Horn F. , Edmundson H. , 2009 . The sound of sonic: a historical perspective and introduction to acoustic logging , CSEG Recorder , 34 , 34 – 43 . WorldCat Commer M. , Hoversten G.M. , Um E.S. , 2015 . Transient-electromagnetic finite-difference time-domain earth modeling over steel infrastructure , Geophysics , 80 , 147 – 162 . Google Scholar Crossref Search ADS WorldCat Ellis D.V. , Singer J.M. , 2007 . Well Logging for Earth Scientists , Springer , Dordrecht, The Netherlands . Google Scholar Crossref Search ADS Google Preview WorldCat COPAC Haldorsen J.B. , Johnson D.L. , Plona T. , Sinha B. , Valero H.P. , Winkler K. , 2006 . Borehole acoustic waves , Oilfield Review , 18 , 34 – 43 . WorldCat Kaufman A.A. , Dashevsky Y.A. , 2003 . Principles of Induction Logging , Elsevier , Amsterdam . Google Preview WorldCat COPAC Khan M.Y. , Xue G.Q. , Chen W.Y. , Zhong H.S. , 2018 . Analysis of long-offset transient electromagnetic (LOTEM) data in time, frequency, and pseudo-seismic domain , Journal of Environmental and Engineering Geophysics , 23 , 15 – 32 . WorldCat Nabighian M.N. , 1987 . Electromagnetic Methods in Applied Geophysics: Volume 1, Theory, Society of Exploration Geophysicists , Tulsa, Oklahoma . Google Preview WorldCat COPAC Pollack G.L. , Stump D.R. , 2005 . Electromagnetism , Addison Wesley , San Francisco . Google Preview WorldCat COPAC Rader D. , 1982 . Acoustic logging: the complete waveform and its interpretation , in Developments in Geophysical Exploration Methods – 4 , Springer Netherlands , Dordrecht , 151 – 193 . Google Scholar Crossref Search ADS Google Preview WorldCat COPAC Rasmussen S. , Nyboe N.S. , Larsen J.J. , 2018 . Extraction and use of noise models from production-mode transient electromagnetic data , Geophysics , 83 , 37 – 46 . Google Scholar Crossref Search ADS WorldCat Serra O. , 2008 . Well Logging Handbook , Editions Technip , Paris . Google Preview WorldCat COPAC Serra O. , Serra L , 2004 . Well Logging: Data Acquisition and Applications, Méry Corbon , Serralog , France . Google Preview WorldCat COPAC Sheng X. , Shen J. , Shen Y. , Zhu L. , Zang D. , 2019 . Measurement of formation conductivity through-casing using a TEM method , Journal of Geophysics and Engineering , 2 , 439 – 450 . Google Scholar Crossref Search ADS WorldCat Song X.J. , 2012 . Theory and method of transient electromagnetic detection in production well (in Chinese), PhD thesis , Xidian University , Xi'an, China . Google Preview WorldCat COPAC Wu Y. , Guo B. , Zhang J. , 2017 . Analysis and simulation of metal casing effect on induction logging , Optik – International Journal for Light Electron Optics , 138 , 302 – 313 . Google Scholar Crossref Search ADS WorldCat Xi Z. et al. . , 2016 . Opposing-coils transient electromagnetic method focused near-surface resolution , Geophysics , 81 , 279 – 285 . Google Scholar Crossref Search ADS WorldCat Xue G.Q. , Chen W.Y. , Yan S. , 2018 . Research study on the short offset time-domain electromagnetic method for deep exploration , Journal of Applied Geophysics , 155 , 131 – 137 . Google Scholar Crossref Search ADS WorldCat Xue G. , Bai C. , Yan S. , Greenhalgh S. , Li M. , Zhou N. , 2012 . Deep sounding TEM investigation method based on a modified fixed central-loop system , Journal of Applied Geophysics , 76 , 23 – 32 . Google Scholar Crossref Search ADS WorldCat Xue G.Q. , Li X. , Yu S.B. , Chen W.Y. , Ji Y.J. , 2018 . The application of ground-airborne TEM systems for underground cavity detection in China , Journal of Environmental and Engineering Geophysics , 23 , 103 – 113 . WorldCat Yao Y.C. , Tan B.H. , Zhang K. , 2019 . A general experimental system for the development of acoustic logging tools , Review of Scientific Instruments , 90 , 045109 . Google Scholar Crossref Search ADS PubMed WorldCat Zhang G.C. , Jiang W.Z. , Pan H.P. , 2009 . Principle and Application of Acoustic Logging (in Chinese) , Petroleum Industry Press , Beijing . Google Preview WorldCat COPAC Zhang G.J. , 1984 . Electrical Logging (in Chinese) , Petroleum Industry Press , Beijing . Google Preview WorldCat COPAC Zhao Y. , Song X. , Dykstra J. , 2016 . Acoustic transmitter active vibration control for sonic logging , Offshore Technology Conference Asia, Kuala Lumpur, Malaysia . Google Preview WorldCat COPAC © The Author(s) 2019. Published by Oxford University Press on behalf of the Sinopec Geophysical Research Institute. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
TI - Formation resistivity measurement based on a transient electromagnetic field excited by an acoustic probe in an open-hole
JF - Journal of Geophysics and Engineering
DO - 10.1093/jge/gxz100
DA - 2020-04-01
UR - https://www.deepdyve.com/lp/oxford-university-press/formation-resistivity-measurement-based-on-a-transient-electromagnetic-ZYjc2Z8Mjl
SP - 1
VL - Advance Article
IS - 
DP - DeepDyve
ER -