Hengshan Hu

Theoretical simulation of electroacoustic borehole logging in a fluid-saturated porous formation

Electroacoustic (E-A) logging describes the acoustic response to an electromagnetic (EM) source in a fluid-filled borehole surrounded by a porous medium. The E-A response is simulated by two different methods in this paper. In the coupled method, the EM field and the acoustic field are modeled using Prides model, which couples Maxwells equations and Biots equations. In the uncoupled method, the EM field is uninfluenced by the converted acoustic field, resulting in separate acoustic formulation with an electrokinetic source term derived from the primary EM field. The difference of the transient full waveforms between the above two methods is remarkably small for all examples, thus confirming the validity of using the computationally simpler uncoupled method. It is shown from the simulated waveforms that an EM-accompanying acoustic field is coupled to the EM field and appears with an apparent phase velocity of the EM wave in the formation. Acoustic waves with the conventional acoustic velocities are also seen in the converted full waveforms. For the sandstone models used in this paper, when permeability is less than 1 Darcy, the E-A Stoneley wave amplitude increases with porosity, which is different from that in conventional acoustic-to-acoustic logging.

Finite-difference modeling of the monopole acoustic logs in a horizontally stratified porous formation

Monopole acoustic logs in a homogeneous fluid-saturated porous formation can be simulated by the real-axis integration (RAI) method to analytically solve Biots equations [(1956a) J. Acoust. Soc. Am. 28, 168-178; (1956b) J. Acoust. Soc. Am. 28, 179-191; (1962) J. Appl. Phys. 33, 1482-1498], which govern the wave propagation in poro-elastic media. Such analytical solution generally is impossible for horizontally stratified formations which are common in reality. In this paper, a velocity-stress finite-difference time-domain (FDTD) algorithm is proposed to solve the problem. This algorithm considers both the low-frequency viscous force and the high-frequency inertial force in poro-elastic media, extending its application to a wider frequency range compared to existing algorithms which are only valid in the low-frequency limit. The perfectly matched layer (PML) is applied as an absorbing boundary condition to truncate the computational region. A PML technique without splitting the fields is extended to the poro-elastic wave problem. The FDTD algorithm is validated by comparisons against the RAI method in a variety of formations with different velocities and permeabilities. The acoustic logs in a horizontally stratified porous formation are simulated with the proposed FDTD algorithm.

Borehole flexural modes in transversely isotropic formations: Low-frequency asymptotic velocity

Dipoleacousticloggingiswidelyusedforinsitumeasurement of formation shear velocity. This technique is based on the theoretical result in isotropic formations that the velocity ofthedispersiveflexuralmodeapproachestheshearvelocity at the low-frequency limit. Transversely isotropic TI formations frequently are encountered in petroleum engineering, so it is necessary to determine if shear velocity along the borehole can be determined from the low-frequency flexural wave in TI cases. The flexural wave in a borehole parallel to thesymmetryaxisofaTIformationisinvestigated.Theborehole acoustic field is formulated in the frequency-wavenumber domain as the sum of a direct field from the source and a reflected field from the borehole wall. Poles and branch points of the reflection coefficient are analyzed, and component waves contributed by those singularities are calculated. ThedispersionfeatureoftheflexuralmodeinsomeTIformationsdiffersfromisotropiccases.Thelow-frequencylimitof flexural-mode velocity trends to a value lower than the shear velocity when parameters of the formation satisfy c44/2c33,where and areThomsenparametersandc33 and c44 are the elastic moduli. That asymptotic value corresponds to a newly found branch point of the reflection function. Numerical results show that the low-frequency flexural wave travels slower than the shear wave in the synthetic full waveforms in Mesaverde clayshale 5501. Extracting the shearvelocityfromtheflexuralarrivalleadstoinaccuracyon theorderof10%inthisformation.

Induced electromagnetic field by seismic waves in Earth’s magnetic field

Studied in this article are the properties of the electromagnetic (EM) fields generated by an earthquake due to the motional induction effect, which arises from the motion of the conducting crust across the Earths magnetic field. By solving the governing equations that couple the elastodynamic equations with Maxwell equations, we derive the seismoelectromagnetic wavefields excited by a single-point force and a double-couple source in a full space. Two types of EM disturbances can be generated, i.e., the coseismic EM field accompanying the seismic wave and the independently propagating EM wave which arrives much earlier than the seismic wave. Simulation of an Mw6.1 earthquake shows that at a receiving location where the seismic acceleration is on the order of 0.1 m/s2, the coseismic electric and magnetic fields are on the orders of 1 μV/m and 0.1 nT, respectively, agreeing with the EM data observed in 2008 Mw6.1 Qingchuan earthquake, China, and indicating that the motional induction effect is effective enough to generate observable EM signal. We also simulated the EM signals observed by Haines et al. (2007) which were called the Lorentz fields and cannot be explained by the electrokinetic effect. The result shows that the EM wave generated by a horizontal force can explain the data well, suggesting that the motional induction effect is responsible for the Lorentz fields. The motional induction effect is compared with the electrokinetic effect, showing the overall conclusion that the former dominates the mechanoelectric conversion under low-frequency and high-conductivity conditions while the latter dominates under high-frequency and low-conductivity conditions.

Comparison of full and quasi‐static seismoelectric analytically based modeling

Quasi-static electromagnetic (EM) approximation was frequently used in numerical modeling of the seismoelectric wavefields, but the computational error it brings is unclear. In this study, we investigate the error caused by the quasi-static EM approximation based on a horizontally layered model. With such an approximation we obtain a simplified set of Prides equations and present an analytically based algorithm to solve the seismoelectric responses to an explosive source. First, we solve the seismic wavefields by ignoring the influence of the converted EM fields on the propagation of the seismic waves. Second, we simplify Maxwell equations to a Poisson equation of the electric potential, from which the EM signals are solved. The solved EM signals are compared with the solutions solved from the full Prides equations to investigate the error caused by the quasi-static EM approximation. The result shows that the quasi-static EM approximation causes the loss of the electric field accompanying the S waves and yields errors in modeling the coseismic magnetic fields accompanying the S waves. The errors tend to become smaller when increasing the frequency and decreasing the salinity, implying that the quasi-static EM approximation seems to be more suitable for simulating the coseismic EM signals under high-frequency and low-salinity conditions. The quasi-static EM approximation also affects the simulation of the interfacial EM waves. Only under the condition that the wavelength of the EM wave is much larger than the source-receiver distance, the quasi-static method is valid in simulating the EM wave.

Seismoelectric responses to an explosive source in a fluid above a fluid‐saturated porous medium

We numerically compute seismoelectric wavefields generated at a fluid/porous medium interface by an explosive source in the fluid. Our numerical experiments show that electromagnetic (EM) signals accompanying the P, S and interface waves can be observed at receivers located in the fluid regions near the interface. Such accompanying EM signals are produced by the inhomogeneous EM waves that are generated by the seismic waves at the interface and their amplitudes decrease with the distance from interface. Under the excitation of an explosive source whose strength is within the capability of industry air-guns, electric and magnetic fields that accompany the Scholte wave are on the order of 1 μV/m and 0.01 nT, respectively. This means that the EM signals arising from the electrokinetic effect at an ocean bottom are detectable and suggests that it is possible to measure the EM signals during marine seismic explorations to study the properties of the seafloor material. EM signals that accompany the P, S and interface waves are also observed in the porous medium region near the interface. Component analysis shows that they contain contributions from multiple modes of waves, among which the slow compressional wave contributes significantly to the vertical electric field, leading to a much stronger vertical electric field than the horizontal electric field during the passage of a seismic wave along the interface.

The theoretical simulation of the seismoelectric logging while drilling based on an elastic formation model

In recent years, the acoustic LWD technology which is drilling and logging at the same time has been developing rapidly. However, the collar wave could cover or interfere with signals from the formation to affect the extraction of P and S wave velocities in the sonic logging. In order to solve this problem, this paper makes a research about the seismoelectric LWD response. In this study, we use the decoupling algorithm to calculate seismoelectric field in the borehole. We can obtain the elastic sound field by solving the wave equation firstly, and then calculate the electromagnetic field excited by the sound field by using the Pride control equations. Although using the elastic model in the calculation, we simulate the attenuation effect of pore formation by introducing quality factor and gain the pressure of the fluid within the pore by introducing the Skempton factor. Finally this paper shows the full waveforms of the electromagnetic and acoustic fields excited by multipole source. We find that the coll...

The simulation of the seismoelectric logging while drilling based on elastic model

In recent years, the acoustic LWD technology which is drilling and logging at the same time has been developing rapidly. However, the collar wave could cover or interfere with signals from the formation to affect the extraction of P and S wave velocities in the sonic logging. In order to solve this problem, this paper makes a research about the seismoelectric LWD response. In this study, we use the decoupling algorithm to calculate seismoelectric field in the borehole. We can obtain the elastic sound field by solving the wave equation first, and then calculate the electromagnetic field excited by the sound field by using the Pride control equations. Although using the elastic model in the calculation, we simulate the attenuation effect of pore formation by introducing quality factor and gain the pressure of the fluid within the pore by introducing the Skempton factor. Finally, this paper shows the full waveforms of the electromagnetic and acoustic fields excited by multipole source. We find that the colla...

The low-frequency asymptotic velocity of pseudo-Rayleigh, flexural, and screw modes in anisotropic formations

Summary The flexural wave as well as other guided waves in a borehole has been used to measure the axial shear velocity. Dipole shear logging is supported by the theoretical conclusion that the flexural mode velocity equals the formation shear velocity at the low-frequency limit. This conclusion is derived in isotropic formations and seems undoubtedly correct for anisotropic cases. But our analysis reveals that the flexural mode in certain transversely isotropic formations propagates at a velocity, which is lower than the shear velocity, at the low-frequency limit; similarly, the velocities of both pseudo-Rayleigh and screw modes do not approach the shear velocity in such a kind of formations. The dispersion curves of these guided waves are shown for several transversely isotropic formations. In this case, the measurement result for the shear velocity is incorrect by extracting the arrival times of low-frequency flexural waves.