Waves In Borehole Research Articles

Numerical Simulation Study on the Influence of Fracture on Borehole Wave Modes: Insights from Fracture Width, Filling Condition, and Acoustic Frequency.

Unconventional reservoirs, such as shale and tight formations, have become increasingly vital contributors to oil and gas production. In these reservoirs, fractures serve as crucial spaces for fluid migration and storage, making their precise assessment essential. Array acoustic logging stands out as a pivotal method for evaluating fractures. To investigate the impact of fracture width, fracture-filling conditions, and acoustic frequency on compressional and shear waves, a three-dimensional variable mesh finite difference program was employed for acoustic logging numerical simulation. Firstly, numerical models representing fractured formations with varying fracture widths and distinct fluid-filling conditions were established, and array acoustic logging numerical simulations were conducted at different frequencies. Subsequently, the waveform data were processed to extract acoustic characteristic parameters, such as velocities and amplitude attenuations of compressional and shear waves. Finally, a quantitative analysis was conducted to examine the variation patterns of characteristic parameters of refracted compressional and shear waves in relation to fracture properties. The research results indicate that amplitude attenuation information derived from borehole wave modes is particularly sensitive to the changes in fracture properties. As fracture width increased, we observed a significant amplitude attenuation in both compressional and shear waves, proportional to the logarithm of the attenuation coefficients. Furthermore, when the fracture width was constant, gas-filled fractures exhibited more prominent amplitude attenuation than water-filled fractures, with shear wave attenuation being more sensitive to the filling material. Moreover, from a quantitative perspective, the analysis revealed that the attenuation coefficients of refracted compressional and shear waves exhibited an exponential variation with gas saturation. Notably, once fracture width and filling conditions were established, the amplitudes of compressional and shear waves at the dominant frequency of 40 kHz were significantly reduced compared to those at 8 kHz, accompanied by increased attenuation. Subsequent quantitative analysis revealed that, when the product of fracture width and dominant frequency remains constant, the corresponding attenuation coefficient ratios approach 1. This indicates that the attenuation process of acoustic propagation in fractured media follows the principle of acoustic similarity. The findings of this study provide reference for further research on fracture property evaluation methods based on array acoustic logging data.

Inversion of shear wave slowness and attenuation from dipole acoustic logging data based on an equivalent tool theory

The presence of a sonic logging tool affects the propagation characteristics of dipole-flexural waves in a fluid-filled borehole. As a result, the tool effect should be considered during the processing and inversion of the dipole-flexural waves for the acoustic properties of a shear wave (S wave). We show that the presence of the tool not only changes the slowness dispersion of the flexural wave but also results in a shift of its frequency-dependent attenuation toward lower frequencies. The equivalent tool theory (ETT) can realistically model the effect of an acoustic tool on guided wave propagation. With the ETT framework, we develop a unified workflow for estimating the S-wave slowness and attenuation from dipole array acoustic waveforms. The workflow is an extension of the model-based dispersive processing of dipole logging data. Our workflow involves two inversion procedures. By matching the actual dispersion data with the theoretical dispersion predicted by the ETT, we can invert the S-wave slowness and tool parameters. With the estimated S-wave slowness and other borehole parameters, we further calculate the partition coefficients of flexural waves using the ETT. Based on the concept of energy partitioning, we formulate a linear optimization problem and invert for the S-wave attenuation from the frequency-dependent dipole attenuation. We use synthetic and field data to demonstrate the effectiveness and applicability of the developed method. The results show that it is important to incorporate the tool effect when processing dipole acoustic logging data for S-wave slowness and attenuation, especially in a fast formation.

Quantitative inversion of the elastic parameters outside the borehole based on exact Zoeppritz equations

The acoustic remote detecting method in the borehole has developed rapidly in the past few decades. It uses the reflected waves recorded by array receivers based on monopole or dipole sources in the fluid filled borehole to image geological structures outside the well. The result can provide guidance on the exploration and evaluation of oil and gas reservoirs and mineral resources. However, the present structure imaging results lack of the elastic information, which limit the quantitative evaluation of the resources. The AVO (amplitude variation with offset) inversion theory is introduced into the analysis of borehole waves. The interested interfaces (fractures or minor faults) with a generally larger wave impedance difference makes the widely used approximate equation in the surface exploration no longer applicable. Therefore, the exact Zoeppritz equations are used as the forward equations in the inversion. To reduce the nonlinearity of inversion, the initial model combining structure tensor and mode wave velocity analysis is constructed. The simultaneous inversion of the wave velocity and density of the reflector provides a theoretical basis for quantitatively evaluating the elastic parameters of the reservoir outside the borehole. [Work supported by the National Natural Science Foundation of China (42004117 and 42127807).]

Dispersion curves of acoustoelastic borehole waves: the perturbation method with the correct formulation of the stresses around the borehole

SUMMARY The acoustoelastic model has been widely used to investigate the influence of formation stresses on the dispersion curves of borehole waves. The analytical perturbation method (PM), the finite-difference time-domain (FDTD) and the semi-analytical finite element (SAFE) are three common-used methods to calculate the dispersion curves. However, due to different interpretations of the PM and plane strain assumptions, the obtained dispersion curves are incompatible among existing PMs, which may misguide the interpretation of formation stresses. It is therefore necessary to untangle the applicability and limitations of PM. Considering that the conventional PMs are usually inaccurate at the low frequency or inconsistent with Hamilton’s principle, we develop a revised PM to obtain the dispersion curves of borehole waves propagating along a borehole surrounded by the triaxially stressed formation assumed as a monoclinic medium. The revised PM is more accurate, reasonable and logical than existing PMs. When the formation is subjected to low stresses, our finding is of great benefit for quickly computing dispersion curves, since the revised PM is much more efficient than the FDTD method; and there are small discrepancies between the flexural dispersions obtained by the revised PM and those obtained by the FDTD method. Nevertheless, the revised PM has two limitations. The first limitation is that the revised PM cannot be used to compute the Stoneley dispersion curves, which have been validated by comparison with SAFE and FDTD methods. The second limitation is that flexural dispersion curves show significant discrepancies in the high-frequency domain when the low-stress assumption does not hold, as compared to those obtained by the FDTD method.

Component wave calculation and analysis of the acoustic field in a borehole within a three-phase porous medium

The knowledge of acoustic wave propagation in a borehole embedded in gas hydrate-bearing sediments is of great significance for the exploitation of gas hydrate. A gas hydrate-bearing sediment is a typical three-phase porous medium containing two solids and one fluid. However, until now, the borehole acoustic wavefield and its component waves within such a porous medium have never been calculated. In this work, a real-axis integration method is proposed to calculate the borehole acoustic field embedded in a three-phase porous medium based on the Biot-type three-phase theory. Meanwhile, a component wave approach, combined with the branch-cut integral method and the residue theorem, including residues at leaky poles is proposed to study the borehole wave propagation of a three-phase porous medium. The branch points and poles of the potential acoustic wave function are obtained, which correspond to the normal and leaky modes on various Riemann sheets. On this basis, the excitation intensity and waveforms of each component are obtained. The result shows that the waveform summed up from all individual waves agrees well with the full waveform calculated by real-axis integration, which provides a theoretical basis for the subsequent inversion of reservoir parameters by using the information of various mode waves.

Influencing Factors of Shear Wave Radiation of a Dipole Source in a Fluid-Filled Borehole

In shear wave far detection logging, dipole-source radiation is the main factor influencing the amplitude of the reflected shear waves. In this paper, a method is derived with the far-field asymptotic solution to calculate the dipole-source radiation of shear waves in a fluid-filled borehole. Then the dipole-source radiation of the shear waves is simulated under both low and high frequencies. In addition, the influences of formation elastic parameters on the dipole-source radiation of the shear waves are analyzed and the variations of the radiation characteristics of the shear wave with source main frequency and borehole radius are compared. Results show that the density and compressional wave velocity of the formation have little effect on the dipole-source radiation of the shear waves. However, the shear wave velocity not only affects the shear wave amplitude radiated to the formation by the dipole source (radiation performance), but also affects the energy distribution of the shear wave at different locations in space (radiation direction). The dipole source has better radiation performance and radiation coverage at low frequency and the optimal excitation frequency in different formations is very close, which is good for the application of this technology under different circumstances. At low frequency, the borehole has little influence on the dipole-source radiation, no matter how large the borehole radius is. However, at high frequency, the borehole modulation of the dipole-source radiation cannot be ignored, especially at large borehole radius.

Constraints on hydraulic properties from free pressure oscillations recorded during pumping operations in boreholes

SUMMARY Free pressure oscillations during pumping operations in boreholes may potentially constrain hydraulic characteristics of the surrounding material. These damped oscillations occur when flow rate is suddenly changed, and their period and decay rate depend on the hydraulic properties of the entire hydraulic system: the porous medium, a section of the borehole, and/or the injection line, depending on test set-up. There have been previous attempts to estimate transmissivity values from free pressure oscillations that occurred during slug tests in open boreholes. The analysis used did not account for viscous losses due to the fluid interacting with the borehole wall. In contrast, dispersion relations of flow waves in a tight borehole (i.e. a cylindrical hole in an impermeable medium) account for wall friction. We extend a previous analytical treatment of flow waves by changing the boundary condition of the fluid velocity at the borehole wall to include fluid exchange between borehole and porous medium. In addition, we performed numerical modelling of waves propagating in boreholes with impermeable and permeable walls to assess the effect of the assumptions behind the analytical solution. We established how to distinguish cases in which the flow into the porous medium affects the oscillation characteristics (suitable for a hydraulic analysis) from those in which the equipment properties dominate the observations. Applying our methods to a range of field observations yielded plausible hydraulic property values of the rock volume surrounding the borehole.

Pressure attenuation due to radiative exchange in fluid-filled boreholes

The paper deals with the propagation of low-frequency waves in fluid-filled boreholes surrounded by an infinite solid media. Its purpose is to give a better understanding of the pressure attenuation of the acoustic wave due to radiative exchange with the solid in the low frequency range applied to the study of hydraulic facilities prone to earthquakes and sizing of hydromechanical components. We consider the case of low frequency pressure waves generated in a reservoir lake under seismic loading in the frequency range [0–20 Hz] and propagating through the duct mouth in a borehole. At theses frequencies, the radiative exchanges between soil and fluid contained into the bore are very weak, thus modelling and quantifying them constitute a challenge. A semi-analytical model based on the derivation of the equations of motion in solid and of wave propagation in fluid is developed and its results are compared with a FEM modelling. Both methods are applied to the case of a semi-infinite cylindrical buried bore and lead to close results: the strong relationship between soil properties and pressure attenuation and the influence of the Stoneley boundary wave on the acoustic pressure wave celerity. Finally, a study implementing the FEM model highlights the influence of heterogeneous solid medium and non-axisymmetric boreholes sections on the radiative exchange.

Modeling of acoustoelastic borehole waves subjected to tectonic stress with formation anisotropy and borehole deviation

Sonic logging is a useful technique to estimate tectonic stress around a borehole. The key to successful evaluation of tectonic stress is having a thorough understanding of a forward model that generates responses of borehole waves to tectonic stress. We have developed a generic model to simulate responses of borehole waves to tectonic stress based on the semianalytical finite-element method and acoustoelasticity. This model can compute the distribution of tectonic stress around an inclined borehole with an arbitrary anisotropic formation and simulate the acoustoelasticities of borehole waves under this complicated stress. To avoid tedious and time-consuming code development, we also provide easy access to the model by reformulating and implementing the governing equations in a commercial software package. We validate the model by using three case studies in which analytical/numerical solutions are available, showing a good agreement between the results from our model and the solutions in the literature. We then apply the model to some important applications in boreholes, demonstrating that this model can provide a powerful tool for understanding the responses of borehole waves to tectonic stress.

Characteristics of the interface acoustoelectric conversion waveform in fluid-filled boreholes

When acoustic waves meet the side wall media in a fluid-filled borehole, the electromagnetic field at the borehole interface between the formation and borehole fluid called the interface acoustoelectric conversion wave signal is converted. The propagation of the refracted P wave, refracted S wave, Stoneley wave, and other borehole-mode waves in the fluid-filled borehole generates accompanying electromagnetic wave signals corresponding to various borehole-mode waves, called accompanying acoustoelectric conversion wave signals. In this study, we examined the interface acoustoelectric conversion wave. First, we numerically simulated the acoustoelectric wave fields in fluid-filled boreholes using a method of real axis integration and analyzed the effects of the borehole radius, porosity, and pore fluid salinity on the interface acoustoelectric conversion waves. The arrival time of the interface acoustoelectric conversion wave increased as the borehole radius increased, and the amplitude of the interface acoustoelectric conversion wave increased as the porosity increased and decreased as the pore fluid salinity increased. Using the self-developed acoustoelectric effect logging tool, we conducted an actual downhole test in a sand shale well in northern China and observed the interface and accompanying acoustoelectric conversion waves. The observations followed the acoustoelectric effect logging theory. Further, to characterize the interface acoustoelectric conversion wave, we calculated its arrival time using a method of long-short time window energy ratio and calculated its energy by taking the summation of squares of the waveform amplitude in a window, respectively. The arrival time approximated to the time in which the acoustic wave propagated from the radiating surface of the acoustic radiator to the side wall interface, and the energy was consistent with the energy ratio of the accompanying conversion Stoneley wave to the acoustic Stoneley wave. The energy curve of the interface acoustoelectric conversion wave and conventional logging curves were highly correlated. The interface acoustoelectric conversion wave in acoustoelectric logging signals can provide a new reference for evaluating the formation parameters associated with open-hole wells.

Spatial non-linearity of methane release dynamics in underground boreholes for sustainable mining

The paper is devoted to the problem of increasing energy efficiency of coalmine methane utilization to provide sustainable development of geotechnologies in the context of transition to a clean resource-saving energy production. Its relevance results from the fact that the anthropogenic effect of coalmine methane emissions on the global climate change processes is 21 times higher than the impact of carbon dioxide. Suites of gassy coal seams and surrounding rocks should be classified as technogenic coal-gas deposits, while gas extracted from them should be treated as an alternative energy source. Existing practices and methods of controlling coalmine methane need to be improved, as the current “mine – longwall” concept does not fully take into account spatial and temporal specifics of production face advancement. Therefore, related issues are relevant for many areas of expertise, and especially so for green coal mining. The goal of this paper is to identify patterns that describe non-linear nature of methane release dynamics in the underground boreholes to provide sustainable development of geotechnologies due to quality improvement of the withdrawn methane-air mixture. For the first time in spatial-temporal studies (in the plane of CH4-S) of methane concentration dynamics, according to the designed approach, the parameter of distance from the longwall (L) is introduced, which allows to create function space for the analyzed process (CH4 of S-L). Results of coalmine measurements are interpreted using the method of local polynomial regression (LOESS). The study is based on using non-linear variations of methane concentration in the underground boreholes and specific features of their implementation to perform vacuum pumping in the most productive areas of the undermined rock mass in order to maintain safe aerogas conditions of the extraction block during intensive mining of deep-lying gassy seams. Identification of patterns in the influence of situational geomechanical conditions of coal mining on the initiation of metastable gas-coal solution transformation and genesis of wave processes in the coal-rock mass allows to improve reliability of predicting methane release dynamics, as well as workflow manageability of mining operations. Presented results demonstrate that development of high-methane Donbass seams is associated with insufficient reliability of gas drainage system operation at distances over 40 m behind the longwall face. Obtained results confirm a working hypothesis about the presence of spatial migration of methane concentration waves in the underground gas drainage boreholes. It is necessary to continue research in the area of estimating deviation angles of “advance fracturing” zone boundaries from the face line direction. Practical significance of research results lies in the possibility to use them in the development of scientific foundation for 3D gas drainage of a man-made coal-methane reservoir, taking into account spatial and temporal advancement of the production face.

Gaussian beam imaging of fractures near the wellbore using sonic logging tools after removing dispersive borehole waves

The ability to image near-wellbore fractures is critical for wellbore integrity monitoring as well as for energy production and waste disposal. Single-well imaging uses a sonic logging instrument consisting of a source and a receiver array to image geologic structures around a wellbore. We use cross-dipole sources because they can excite waves that can be used to image structures farther away from the wellbore than traditional monopole sources. However, the cross-dipole source also will excite large-amplitude, slowly propagating dispersive waves along the surface of the borehole. These waves will interfere with the formation reflection events. We have adopted a new fracture imaging procedure using sonic data. We first remove the strong amplitude borehole waves using a new nonlinear signal comparison method. We then apply Gaussian beam migration to obtain high-resolution images of the fractures. To verify our method, we first test our method on synthetic data sets modeled using a finite-difference approach. We then validate our method on a field data set collected from a fractured natural gas production well. We are able to obtain high-quality images of the fractures using Gaussian beam migration compared with Kirchhoff migration for the synthetic and field data sets. We also found that a low-frequency source (around 1 kHz) is needed to obtain a sharp image of the fracture because high-frequency wavefields can interact strongly with the fluid-filled borehole.

A borehole multifrequency acoustic wave system for karst detection near piles

Karst cavities at or near pile locations pose a substantial danger to underground construction projects. To locate karst cavities at pile locations, advance drilling boreholes are commonly used, but a cavity can be missed due to its limited size. In this paper, we present a new borehole-based technology employing multifrequency acoustic wave (MFAW) detection of karst cavities near drilling boreholes. First, we developed an MFAW detector and signal processing software. The high- and low-frequency transmitters operate in the frequency range of 0.05 kHz to 10 kHz and the range of 1 kHz to 50 kHz, respectively. Next, we evaluated the performance of the prototype in a controlled borehole model. Lastly, the MFAW detection system was tested at a field site. A nearby borehole core was used to verify the MFAW detection results. The testing of the prototype detection system revealed the following findings. (1) The integrity of the rock surrounding the borehole can be assessed by the energy of the high-frequency zero-offset data. The zero-offset section has a high correlation with the energy of the high-frequency detection signal. The rock is intact when the high-frequency detection signal is strong. The rock is fragmented when the test signal exhibits amplitude variance over a short-range away from the borehole. The test signal becomes weak when the borehole meets a karst cavity filled with sand, clay or water. A color bar showing the signal amplitude can represent the integrity of the borehole wall more accurately than a core sample. (2) A karst cavity near the borehole can be detected by low-frequency waves. The low-frequency acoustic detection wave field includes a reflected guided wave from the interface that the borehole meets, the wave in the borehole, and the effective reflected body wave from the karst cavity. The integrity of the rock around the borehole wall obtained by high-frequency acoustic detection can help identify the reflected guided wave. Median filtering suppresses the strong amplitude borehole wave and helps reveal the weaker reflected waves. The reflected wave from the karst cavity near the borehole can be extracted after filtering. (3) The azimuth of the cavity is identified by the different detection recordings of the azimuthal receivers. Reflected wave amplitudes obtained by the azimuthal receivers facing the karst cavity are greater than those obtained by the receivers facing away from the karst cavity. The azimuthal angle can be obtained by the three-dimensional electric compass in the downhole tool. The MFAW detection system is shown to be an effective tool for investigating the geological environments at pile locations in detailed geo-investigation periods.

Determining fracture properties from acoustic borehole waves: theory and experimental results

A borehole in the subsurface may penetrate rocks which are porous, permeable and fractured. Pressure transients in the borehole will therefore cause viscous fluid to flow into and out of the wall of the borehole. This forced flow consumes some energy and affects the phase velocity and amplitude of the waves traveling in the borehole fluid column. These effects can be evaluated to extract information about the rocks adjacent to the borehole, which is of paramount importance for the oil and gas industry. This work discusses laboratory wave experiments in a 7.5 m long vertical shock tube. Rock samples having a vertical borehole and horizontal fractures are installed in the shock tube and filled with water. The shock tube generates broadband pressure transients in the borehole. These are measured in the borehole at variable depth by means of a sliding pressure probe. Repetitive experiments are combined into borehole microseismograms. In this way borehole wave reflection and transmission coefficients over the fractures are determined. The results show good agreement with low-frequency theory, where it is assumed that the wavelengths are much larger than the tube diameter. Inversely, it is shown that the aperture and the length of the fracture can directly be inferred from acoustic borehole experiments.

Quality Evaluation and Applicability Analysis of TRD Method in Sand Stratum of Subway Station

Trench re-mixing and cutting deep method (TRD) construction is a rising method for building waterproof curtains in deep foundation pits, providing the advantages of large construction depth, widespread applicability to soil layers, and high quality of the cement-soil wall. Against the background of the Miaotou subway station foundation pit project through the quaternary system watery sand layer containing cohesive soil in Qingdao, the applicability of cement-soil wall constructed by the TRD method in Qingdao’s soft soil was researched. A comprehensive testing method which can evaluate the quality of the cement-soil wall was proposed. A series of field detection and laboratory tests that include borehole water pressure tests, borehole television imaging, electromagnetic wave borehole radar, and unconfined compressive strength test of the drilling core was completed. The test results show that the cement-soil wall had good integrity and continuity without weak tectonic zones. The average strength of the cement-soil wall ranged from 0.94 to 1.21 MPa, and the strength of the cement-soil wall at different depths existed large discreteness. However, it still met the design requirements of no less than 0.8 MPa. Test results showed that the permeability of the clay layer decreased from 10−5 to 10−7 cm/s and the permeability of the sand layer decreased from 10−2 to 10−7 cm/s. Both strength and permeability of the wall satisfied the design requirements for a watertight screen. The research results may provide reference for pit waterproof curtain engineering in similar sand stratum.

3D-RVSP experimental study above a carbonate outcrop for coal resource exploration

In the areas where carbonate rocks expose to the near surface, there are several intractable issues in conventional surface seismic, including (1) weak reflection energy, (2) complex wave field and (3) serious static correction. Therefore, the seismic imaging result suffers significantly. However, RVSP is able to achieve reflected data with high quality since it generates seismic waves in borehole and receives seismic waves at the surface. In order to verify the applicability of RVSP technique in complex areas, this study carried out a 3D-RVSP seismic experiment in Wulunshan coal field, southwest China. Compared with the surface seismic data, RVSP data show higher signal-to-noise ratio, wider frequency band and weaker surface wave interference. In addition, two imaging methods (conventional CDP transform stack and novel equivalent-surface conversion) were implemented for RVSP data imaging. The imaging results show that the smaller and deeper structures can be revealed better by equivalent-surface conversion method than by CDP transform stack method. Hence, this study demonstrates that RVSP is an efficient method applied in the area with complex surface condition.

Surface waves in a cylindrical borehole through partially-saturated porous solid

Propagation of surface waves is discussed in a cylindrical borehole through a liquid-saturated porous solid of infinite extent. The porous medium is assumed to be a continuum consisting of a solid skeletal with connected void space occupied by a mixture of two immiscible inviscid fluids. This model also represents the partial saturation when liquid fills only a part of the pore space and gas bubbles span the remaining void space. In this isotropic medium, potential functions identify the existence of three dilatational waves coupled with a shear wave. For propagation of plane harmonic waves along the axially-symmetric borehole, these potentials decay into the porous medium. Boundary conditions are chosen to disallow the discharge of liquid into the borehole through its impervious porous walls. A dispersion equation is derived for the propagation of surface waves along the curved walls of no-liquid (all gas) borehole. A numerical example is studied to explore the existence of cylindrical waves in a particular model of the porous sandstone. True surface waves do not propagate along the walls of borehole when the supporting medium is partially saturated. Such waves propagate only beyond a certain frequency when the medium is fully-saturated porous or an elastic one. Dispersion in the velocity of pseudo surface waves is analysed through the changes in consolidation, saturation degree, capillary pressure or porosity.

Seismoelectric wave propagation modeling in a borehole in water-saturated porous medium having an electrochemical interface**Project supported by the National Natural Science Foundation of China (Grant Nos. 40974067, 41474098, and 11134011) and the State Key Laboratory of Acoustics, China (Grant No. SKLA201608).

Water-saturated porous media often exhibit a seismoelectric effect due to the existence of an electrical double layer and a relative flow of pore fluid. Here we consider the seismoelectric waves in an open borehole surrounded by water-saturated porous formation which exhibits discontinuity of electrochemical properties at a cylindrical interface. We carefully analyze the seismoelectric interface response since these signals show sensitivity to contrasts in electrochemical properties across an interface. Both coupled and approximate methods are used to compute borehole seismoelectric fields. The simulation results show that the radiated electromagnetic wave from the electrochemical interface is generated due to the change of salinity in pore fluid in the porous formation. However, the elastic properties of the formation remain unchanged across such an electrochemical interface. As a result it is difficult to recognize such a change in electrochemical properties using only elastic waves. Therefore, the seismoelectric interface response is potentially used to detect the changes of the electrochemical properties in the formation.

Local and global fluid effects on sonic wave modes

Most subsurface formations of value to exploration contain a heterogeneous fluid-filled pore space, where local fluid-pressure effects can significantly change the velocities of passing seismic waves. To better understand the effect of these local pressure gradients on borehole wave propagation, we combined Chapman’s squirt-flow model with Biot’s poroelastic theory. We applied the unified theory to a slow and fast formation with permeable borehole walls containing different quantities of compliant pores. These results are compared with those for a formation with no soft pores. The discrete wavenumber summation method with a monopole point source generates the wavefields consisting of the P-, S-, leaky-P, Stoneley, and pseudo-Rayleigh waves. The resulting synthetic wave modes are processed using a weighted spectral semblance (WSS) algorithm. We found that the resulting WSS dispersion curves closely matched the analytical expressions for the formation compressional velocity and solutions to the period equation for dispersion for the P-wave, Stoneley-wave, and pseudo-Rayleigh wave phase velocities in the slow and fast formations. The WSS applied to the S-wave part of the waveforms, however, did not correlate as well with its respective analytical expression for formation S-wave velocity, most likely due to interference of the pseudo-Rayleigh wave. To separate changes in formation P- and S-wave velocities versus fluid-flow effects on the Stoneley-wave mode, we computed the slow-P wave dispersion for the same formations. We found that fluid-saturated soft pores significantly affected the P- and S-wave effective formation velocities, whereas the slow-P wave velocity was rather insensitive to the compliant pores. Thus, the large phase-velocity effect on the Stoneley wave mode was mainly due to changes in effective formation P- and S-wave velocities and not to additional fluid mobility.

Broadband acoustic wave experiments in borehole configurations

A borehole in the ground may penetrate rocks which are porous, permeable, and fractured. Pressure transients in the borehole will therefore cause viscous fluid to flow into and out of the wall of the borehole. This forced flow consumes some energy and affects the phase velocity of the waves traveling along the fluid column. These two effects can be evaluated to extract information about the rocks adjacent to the borehole, which is of paramount importance for the oil and gas industry. This work discusses laboratory wave experiments in a 7.5 m long vertical shock tube. Rock samples containing a vertical borehole and pre-fabricated fracture configurations are installed in the test section and filled with water. The shock tube generates broadband pressure transients in the borehole. These are measured in the borehole at variable depth by means of a sliding pressure probe. In this way borehole microseismograms are constructed from repetitive wave experiments. Borehole wave modes are identified using coherence analysis. It is found that the presence of fractures significantly influences the transmission and reflection of borehole waves over the fracture zone. Moreover, there is a strong correlation between fracture aperture and borehole acoustic properties.