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Petroleum Engineering Handbook

Larry W. Lake, Editor-in-Chief

Volume V – Reservoir Engineering and Petrophysics

Edward D. Holstein, Editor

Chapter 3C - Acoustic Logging

Doug Patterson, Baker Hughes and Stephen Prensky, SPE, Consultant

Pgs. 167-242

ISBN 978-1-55563-120-8
Get permission for reuse

Petroleum applications of acoustic-wave-propagation theory and physics include both surface- and borehole-geophysical methods. These data-acquisition methods cover a broad range of scales from millimeters to hundreds of meters (Fig. 3C.1). Acoustic logging is a subset of borehole-geophysical acoustic techniques. This chapter provides an overview of borehole acoustic-logging theory, modern tool design, data processing methods, and data applications. Table 3C.1 lists other common surface- and borehole-geophysical methods. The chapter on the Fundamentals of Geophysics, in this volume, and the chapter on Reservoir Geophysics, in the Emerging and Peripheral Technologies volume of this Handbook, also discuss these methods.

A virtual explosion in the volume of acoustic research conducted over the past 20 years has resulted in significant advances in the fundamental understanding of downhole acoustic measurements. These advances, in turn, have greatly influenced practical logging technology by allowing logging-tool designs to be optimized for specific applications.[2]

Borehole acoustic-logging measurements are used in a wide variety of geophysical, geological, and engineering applications and play an important role in evaluating reservoirs, reducing exploration and production risks, selecting well locations, designing completions, and increasing hydrocarbon recovery (Table 3C.2).

Modern logging tools include conventional borehole-compensated (BHC) monopole devices as well as the newer array devices—both monopole and multipole (monopole/dipole)—and logging-while-drilling (LWD) acoustic services. These logging tools provide acoustic measurements in all borehole mud types (but not in air- or foam-filled boreholes) in vertical, deviated, and horizontal wells, in both open and cased hole. They are combinable with other logging devices and are available in a variety of sizes to accommodate a range of borehole and casing diameters. Specialized tool designs are used for cement and casing evaluation and borehole imaging.

Historically, the primary and the most routine uses of acoustic logs in reservoir engineering have been porosity determination, identification of gas-bearing intervals, and cement evaluation. Continuing developments in tool hardware and in interpretation techniques have expanded the utility of these logs in formation evaluation and completion (fracture) design and evaluation. This chapter discusses the potential applications of these logs to allow the reader to evaluate the appropriate applications for a particular well or field. However, site-specific assessments are required to determine whether acoustic logs, with the proper planning, can provide the desired results in a cost-effective manner.

Acoustic Theory and Wave Propagation

The principles of borehole acoustic logging (and surface seismic methods) are based on the theory of wave propagation in an elastic medium, as detailed in several sources[3][4][5][6]. The oscillating motion generated by a sound source (transducer) in an elastic medium (rock formation) is called an elastic wave or acoustic wave (also called head or body waves). Wave theory predicts how an acoustic signal propagates through the borehole and formation. Snell’s law explains how the acoustic signal behaves at the velocity boundary separating the borehole and the formation, that is, how it is transmitted into the formation and back to the receivers. Elasticity is the property of matter that causes it to resist deformation in volume or shape. It is the elastic nature of rock formations that permits wave propagation. Acoustic waves have four measurable properties: velocity, amplitude, amplitude attenuation, and frequency. Acoustic logging tools are designed to measure one or more of these properties, with velocity (slowness) being the most common.

The waveform recorded at the logging tool’s receivers is a composite signal containing different energy modes, each with a different frequency, velocity, and amplitude. For borehole logging, the modes of primary interest are (in order of arrival) compressional, shear, and Stoneley (tube) waves (Fig. 3C.2). The waveform is recorded as acoustic amplitude as a function of time.

These waves are transmitted through the medium some distance from the origin of displacement. The particles of the medium do not travel with the wave, but only vibrate around their mean central position. Acoustic waves are classified according to the direction of particle displacement with respect to the direction of wave propagation as either longitudinal (i.e., particle displacement is parallel to the direction of propagation) or transverse (i.e., direction of particle displacement is perpendicular to the direction of propagation). In acoustic logging, the longitudinal wave is known as the compressional wave and the transverse wave is known as the shear wave. The presence of the borehole excites two additional acoustic energy modes, called guided waves: normal (pseudo-Rayleigh) and tube (Stoneley) waves.

Acoustic-wave velocity is controlled by a number of factors: lithology (mineralogy), cementation, clay content, texture, porosity, pore-fluid composition and saturation, overburden-and pore-fluid pressure (stress), and temperature. The rock’s mechanical properties, elastic dynamics, and density are a constant for a particular homogeneous and isotropic material. Acoustic-wave velocity can be related to rock elastic properties through three constants of proportionality, elastic moduli (e.g., Young’s, shear, and bulk), and Poisson’s ratio. This serves as the basis for mechanical-property evaluation by acoustic logs (see the additional discussion under Geomechanical Applications—Rock Mechanical Properties). In reality, most petroleum reservoirs contain varying pore sizes, pore fill (e.g., clays), fractures, etc. and consequently, are neither truly isotropic nor homogeneous. Furthermore, in fluid-saturated rocks, these acoustic properties also depend on the type and volume of fluids present.

Compressional Waves

Compressional (P, primary, or pressure) waves are longitudinal waves that are transmitted through an elastic formation by compression or pressure. Particle motion is parallel to the direction of wave propagation (Fig. 3C.3[7]). They can travel through solids, liquids, and gases and are the fastest wave type—they represent the acoustic first arrival. Of all acoustic wave types, they are least affected by faults, unconsolidated formations, and borehole fluids, and are, therefore, the most reliable. The wave is transmitted by both the rock matrix (i.e., the framework) and the fluid present in the pore throats. A compression, together with an adjacent rarefaction preceding or following it, constitutes a complete cycle. The distance between complete cycles is called the wave length and the number of cycles propagating through a point in the medium per unit time is the frequency. The velocity of elastic-wave propagation in an isotropic homogeneous medium can be derived from a combination of the theory of elasticity with Newton’s law of motion. Compressional-wave velocity (or travel time) is a function of the density and elasticity of the medium and is a constant for a given material.

Shear and Borehole Flexural Waves

Shear (S, secondary) waves are transverse waves that are transmitted by lateral displacement of particles in a rigid elastic formation. Particle motion is perpendicular to the direction of motion (Fig. 3C.3). Normally, shear waves are the second arrival in an acoustic wave train. In most reservoir rocks, shear waves generally have higher amplitudes than compressional waves but lower velocities, by as much 40 to 50%. There are two types of borehole shear waves—direct and indirect, also known as refracted or induced. Indirect shear waves are induced in a formation through a process known as mode conversion in which some of the compressional energy is transferred from the borehole fluid into the rock formation. Monopole transmitters generate these indirect shear waves while dipole transmitters generate direct shear waves by inducing a flexural (asymmetric mode) in the borehole. Shear-wave propagation requires a medium that has shear strength (rigidity). Consequently, shear waves can only travel in solids, not in liquids or gas. In liquids and gas, the shear head-wave generated within the formation is converted into a compressional wave and propagated back across the borehole fluid to the acoustic receivers as a later-arriving compressional wave.

Unconsolidated or poorly consolidated sandstones ("soft" or "slow" rocks) are less rigid and more compressible than well-consolidated ("hard" or "fast") rocks. When the formation shear-wave velocity is less than the acoustic velocity of the borehole fluid (Vs < Vf), a rock formation is called "slow." There is no refracted shear-wave from monopole devices in slow formations and low-frequency dipole transmission and reception is required to adequately detect low-frequency flexural arrivals for the shear-wave slowness determination. However, if a monopole-array tool is used in these conditions, a shear-wave slowness can be estimated from Stoneley-wave velocity dispersion.[8] In very slow formations, where Vc < Vf, special processing may be required to extract the formation compressional signal.[9]

Flexural-wave velocity varies with frequency—a phenomenon called dispersion. In contrast, the compressional and shear headwaves generated by monopole sources are generally not dispersive. At very low frequencies, the flexural wave travels at the formation shear velocity. This dispersion effect diminishes as the wavelength of the flexural-wave increases and is generally minimal when the wavelength is at least three times the borehole diameter. Fast formations exhibit a center frequency slightly greater than 3 kHz, while slow formations exhibit a center frequency of ≈ 1 kHz, or less. The received frequency spectrum of a dipole array is a function of transmitter frequency, rock properties, and borehole size. Modern dipole transmitters are broadband transmitters, i.e., they operate over a range of frequencies, to account for dispersion and to accommodate different formation types.

Stoneley Waves

Stoneley (tube) waves are high-amplitude guided waves that are generated by a radial (symmetric) flexing of the borehole as the acoustic energy passes from the borehole fluid into the rock formation. They propagate at low frequencies along the fluid-rock interface at the borehole wall; hence, they are sensitive to the rock properties adjacent to the borehole wall. They are the slowest acoustic mode. They can be measured in both open and cased boreholes, but in cased holes Stoneley-wave features are primarily controlled by the casing rigidity. Similarly to shear waves, Stoneley waves are also dispersive; i.e., wave velocity varies with frequency—the amount of dispersion is related to formation rock properties. However, Stoneley waves are notable for several special properties: there is no cut-off frequency; dispersion is very mild; for all frequencies, Stoneley-wave velocity is less than fluid velocity; and group velocity nearly equals phase velocity over the frequency range.

All acoustic waves undergo attenuation, a reduction in signal amplitude away from the source. For logging devices this means radially away from the borehole wall. Signal attenuation results from the geometric spread of energy through reflection, refraction, and scattering, and through absorption by the medium through which the acoustic energy travels. Attenuation, usually expressed in dB/ft, is characteristic of different materials and increases with frequency of the acoustic wave. Generally, attenuation is large in slow formations and very small to negligible in fast formations. Because of these features, Stoneley waves are used to identify acoustic leakage away from the borehole that may be caused by formation permeability or the presence of fractures.

Acoustic-Logging Tools

Acoustic-logging devices are comprised of transmitters (sources), receiver arrays, and accompanying electronics. They have been designed to measure one or more acoustic-wave properties. Acoustic sources (transmitters) generally consist of piezoelectric transducers that generate the acoustic signal by converting electrical signals into a sonic vibration that travels through the borehole and adjacent rock formations. Monopole (axisymmetric) transducers generate omnidirectional acoustic waves around the tool circumference, while dipole (nonaxisymmetric) transducers generate azimuthally oriented acoustic waves (Fig. 3C.3).

Modern receivers are piezoelectric crystals that transform the received (measured) acoustic signal back into electrical signals. Different logging tools use different piezoelectric materials and operate at different frequencies to measure different energy modes (wave types). The pressure variation produced by an acoustic wave displaces the piezoelectric material causing it to ring or oscillate. When the receiver oscillates, it develops a small voltage. This voltage is amplified and the raw data are processed downhole and sent to the surface-acquisition system in the form of a waveform signal (wireline) or acoustic slowness (wireline and LWD). Digital data are stored, either at the surface (wireline) or downhole (LWD), for wellsite log presentations and post-acquisition processing and playback.

The energy (amplitude) of acoustic waves is lost (attenuated or dispersed) primarily by travel through the borehole fluid and rock matrix. Additional attenuation may result from a number of other factors that include internal particle friction within the propagation medium, changes in acoustic impedance [the product of density (ρ) and acoustic velocity (V)] at interfaces (boundaries) between different mediums, borehole rugosity, and signal cancellation resulting from tool eccentering. In general, the largest signal possible occurs when the instrument is in the center of the hole; a dipole tool in an extremely large borehole may be exception to this rule. For high frequencies, the monopole signal is reduced by as much 50% of the centralized value by displacing the instrument only inches from the center of the hole. Consequently, whenever possible, centralizers should be used with acoustic-logging tools.

Critical Spacing

The acoustic wave travels through the formation much faster than it does through the borehole fluid and reaches the receiver by the longer formation route first. This is true as long as the critical spacing is less than actual spacing. Critical spacing is the transmitter-to-receiver spacing at which the fluid-signal and formation-signal arrive at the receiver at the same time. The critical-spacing value depends on the diameter of the logging sonde, the diameter of the borehole, the time of travel through the fluid, and the time of travel through the rock.

In soft formations, and under certain conditions, the critical spacing can exceed actual spacing and the fluid arrival, which exists for a noncentralized tool, can interfere with the acoustic signal. When this occurs, data-processing methods can exclude this fluid arrival, thereby reducing or possibly eliminating interference from the fluid arrival. Longer transmitter-receiver spacings are used to minimize this occurrence.

The transmitter-to-receiver spacing in modern monopole tools is set to enable separation of the compressional- and shear-energy packets to allow for accurate measurement of both in fast formations. When logging with an array-acoustic device, the receivers nearest the transmitter see stronger acoustic waves than the more distant receivers.

Monopole Excitation

The transmitter emits acoustic energy uniformly around the tool. In fast formations, this energy excites three waves that travel down the borehole wall: compressional, shear, and Stoneley. The compressional wave travels away from the transmitter with a velocity, Vf, in the mud. When these waves reach the borehole face, they are reflected, refracted, and converted according to Snell’s law (Fig. 3C.4).

For angles of incidence less than the compressional-wave critical angle (θc, Fig. 3C.4), part of the energy is transmitted into the formation in the form of compressional wave (Wave A, Fig. 3C.4), another part is converted as a (refracted) shear wave (Wave B, Fig. 3C.4), and the remainder is reflected back into the mud as a compressional wave (Wave C, Fig. 3C.4). The transmitted waves travel at velocity Vp and Vs in the formation, close and parallel to the borehole wall, while continuously radiating energy back into the mud as converted compressional-waves, at the same compressional-wave critical angle at which it entered. It is this radiated energy that is detected by the receivers.

If the formation shear-wave velocity is slower than borehole-fluid compressional velocity (Vs < Vf), shear waves cannot be refracted along the borehole wall, and no shear wave is measured. Beyond the shear-wave critical angle, all the incident energy is reflected back into the mud to form the guided waves. The Stoneley wave travels at approximately the velocity of compressional waves in the borehole fluid. Compressional and Stoneley arrivals are always present. In the absence of a refracted shear-wave arrival (i.e., in formations in which Vp < Vf), the Stoneley wave can be used to estimate formation shear-wave velocity when a formation bulk-density measurement is available, using certain assumptions. However, because of the uncertainty associated with these assumptions, dipole shear-wave measurements are recommended in slow formations. Stoneley-wave amplitude decreases (attenuates) significantly at high frequencies and modern tools use low-frequency transmitters (< 1 to 12 kHz) to ensure acquisition of the Stoneley arrival in slow formations.[10]

Dipole Excitation

The dipole transmitter exerts a differential pressure on one side of the transmitter element that creates a flexural wave in the borehole, much like the wave produced when a vertical rope is shaken from side to side. The flexural wave is dispersive, but at low frequencies this wave travels down the borehole at the formation shear velocity. Receivers, sensitive only to differential pressures, are used to detect this flexural wave. Because the receivers are not sensitive to axially symmetric pressure fields, both the compressional head wave and the Stoneley waves are suppressed. This is desirable because it simplifies data processing. The desired output is the velocity of the formation shear wave. If the wavelength of the flexural wave is at least three times the diameter of the borehole, the flexural wave travels at very nearly the formation bulk-shear velocity. However, because this is a dispersive mode, if the wavelength is shorter (because of higher frequency), this flexural mode will travel slower than the shear velocity and dispersion corrections are needed.

Logging Documentation

All types of well logs, both open- and cased-hole, should be accompanied by complete documentation to ensure good-quality logs and sound interpretation. It is important to remember that any acoustic analysis represents an interpretation of measured acoustic waves. The wellsite engineer or geologist must ensure that all data pertaining to a particular log run, including borehole information (bit and casing sizes and depths), tool configuration, borehole fluid, formation parameters, and tool centralization are recorded in the well-log header for future reference. Cased-hole logs should also contain information on cement composition, casing weight and thickness, if the log was run with pressure, and the amount of that pressure.

Evolution of Acoustic-Logging Tools

The most commonly used acoustic-wave property acquired in borehole logging is the compressional-wave velocity. Modern velocity-logging tools measure the time, Δt, required for a compressional or shear wave to travel through a fixed distance of formation; it is recorded as a function of depth. This parameter, Δt, referred to as the interval transit time, transit time, travel time, or slowness, is the reciprocal of the velocity of the compressional waves, Δt = 1/ Vp. For the formations typically encountered in acoustic logging, travel times range from 40 to 250 μsec/ft, corresponding to velocities ranging from 25,000 to 4,000 ft/sec (Table 3C.3).

The resolution of any acoustic method is a function of the signal wavelength; the lower limit is one-quarter of the propagating wavelength. Seismic-reflection exploration methods typically operate in the frequency range of 10 to 50 Hz. In typical petroleum reservoir rocks, the resolution of these methods is approximately 30 to 160 ft (10 to 50 m), depending on depth (signal strength). In contrast, conventional BHC logging tools operate within the frequency range of 10 to 40 kHz, while newer array devices operate at even lower frequencies, 1 to 12 kHz. Logging-tool resolution is also a function of both the array aperture and the methodology employed for the array processing. Consequently, acoustic-logging tools typically have resolutions on the order of 1.0 to 4.0 ft (0.3 to 1.2 m) (see the section on Resolution Enhancement in this chapter).

Velocity/Porosity Logging

Acoustic well logging developed out of the need for downhole velocity (time-depth) measurements to improve the accuracy (calibrate) of surface seismic measurements. Surface seismic maps out sub-surface structures referenced to time and borehole acoustic tools provide a bridge to understand how time is related to depth. Downhole geophones were introduced in the 1930s to provide acoustic travel times to the surface, and continuous-velocity-logging tools were introduced in the 1950s (Table 3C.4). Soon after the introduction of the continuous-velocity log, it was recognized that these data also provided an excellent means for stratigraphic correlation, lithologic identification, and for evaluation of formation porosity.

The first acoustic-logging tools used a single monopole transmitter and a single receiver. Tool designs rapidly evolved to improve the accuracy of the velocity measurement by minimizing or eliminating influences related to borehole effects, i.e., fluid, geometry, and tool position (tilt) within the borehole (see the next section of this chapter); and to measure additional acoustic-wave properties.

These simple devices were soon replaced by two receiver designs that had the advantage of eliminating the need to correct for travel time in the drilling mud (for more on the historical development of acoustic logging, consult the literature[11][12][13][14]). Modern borehole-compensated designs, introduced in the 1960s, use two transmitters and two receivers to compensate for variations in borehole diameter and tool position within the borehole (Fig. 3C.5). Two separate values of two receiver (R1 and R2) and two transmitters (T1 and T2) interval-transit times are provided, and an average of the two effectively compensates for any problems (Eq. 3C.1).


where t1 = travel time between T2 and R1; t2 = travel time between T2 and R2; t3 = travel time between T1 and R1; t4 = travel time between T1 and R2 ; and X12 = distance between R1 and R2. Fig. 3C.5 illustrates travel paths that show that the averages of AA′, BB′, and CC′ are essentially equal.

The BHC tools’ velocity measurements may be affected by a variety of factors including borehole diameter, signal noise, cycle skipping, Δt stretch, velocity inversion, gas effect, and dip angle, with respect to the borehole (Table 3C.5). Modern digital-circuitry and array-tool designs reduce or eliminate many of these problems, but they may still be present on older logs.

Conventional BHC monopole-acoustic logs, with their short transmitter-to-receiver spacing, have shallow depths of investigation and they largely measure mud filtrate that fills the pore space in the invaded (flushed) zone around the borehole. Long-spaced and array devices can acquire measurements beyond the filtrate and altered zone.

Long-Spaced Acoustic Tools

Typical BHC devices have a transmitter-to-receiver spacing (TR) of 3 to 5 ft. These work well in many circumstances; however, in cases which borehole enlargement prevents acquisition of reliable data, due to the increase of the critical spacing, or in which the drilling process damages or alters the shales surrounding the borehole, long-spacing tools (TR = 8 to 15 ft) may be necessary, or advised, to obtain accurate measurements. In contrast to conventional BHC devices, in which the transmitters and receivers are arranged symmetrically, long-spacing tools use an asymmetric arrangement with the receivers at varying distances from the monopole transmitter (Fig. 3C.6). Consequently, these devices have deeper depths of investigation that make them less susceptible to borehole conditions such as enlargement and shale alteration. These tools operate in both open and cased holes.

Because long-spaced and array tools use an asymmetric configuration of transmitters and receivers, borehole compensation is achieved through a process called depth-derived borehole compensation (DDBHC)[15] (Fig. 3C.6). The processing is accomplished downhole by either the tool’s electronics or in the surface recording system and uses a depth-based delay to create synthetic transmitter arrays from multiple tool positions. The compensated travel-time measurement, Δt, is determined through the following procedure. At position three (Fig. 3C.6), the transmitter (T) is at the depth where the far receiver (R2) will be when the tool is moved to position one. The interval-transit time (A) between the transmitter (T) and near receiver (R1), which includes mud and formation signals, is recorded and delayed (memorized). At position two (Fig. 3C.6), the transmitter (T) is at the same depth the near receiver (R1) will be when the tool moves to position one. The interval transit time or waveform (B) between T and R2 is recorded and delayed. When the tool reaches position one, the two interval transit times (A and B) are equal to the interval transit time that would result if a second transmitter were below the receivers. The correct compensated value of Δt is obtained by combining the two delayed values of transit time (recorded at positions two and three) with transit times C and D, recorded at position one. Compensated transit time (Δt) is then correctly represented by


where x = the distance between R1 and R2 .

Analog recording of full acoustic waveforms, called "amplitude" logging, was developed in the 1960s. However, it was not until digital technology, instrumentation, and signal-processing methods were introduced in the late 1970s that the recording of full-waveform data became routine. While these techniques enabled the extraction of shear-wave data from conventional BHC acoustic data, determination of shear arrivals using conventionally spaced BHC tools (TR = 3 to 5 ft) suffers from interference between late-arriving compressional waves and shear-wave arrivals. The use of long-spaced tools reduced this problem by allowing greater temporal separation between the different wave packets and provided accurate estimates of shear–wave slowness.[16][17][18][19]

Monopole Array Devices

Modern array tools are a natural outgrowth of the long-spaced tool design. Additional receivers (4 to 13) were added to provide the statistical redundancy needed to enhance extraction of wave arrival times; some designs also include multiple transmitters. The monopole transmitters in these tools use lower frequencies (e.g., 1 to 12 kHz vs. 20 to 40 kHz) and have broader frequency ranges than earlier tools to permit acquisition of high-quality acoustic waveforms. These devices are typically comprised of several sections or subs that house the tool components: electronics, receiver array, acoustic isolator, and transmitters. The acoustic isolator, placed between the transmitter and receiver sections, prevents or minimizes and delays direct sound transmission between transmitters and receivers. The electronics section provides timing and control for the transmitter and receiver sections, digitizes the received acoustic waves, analyzes the acquired waveforms, and transmits the data to the surface-data-acquisition system, all in real time.

Array tools can record full waveforms: compressional, shear, and Stoneley arrivals. These tools operate in either a single or a variety of combination-acquisition modes that include full waveform, compression Δt, and cement-bond logging. The number of modes that can be activated during a single log run is a function of the logging speed. Acquisition of full waveforms permits the use of waveform-correlation techniques for waveform amplitude, coherent slowness from the coherent-wave moveout, arrival-time processing, and most importantly, allows for detailed post-acquisition processing that improves the interpreted results. Because these techniques are insensitive to cycle skipping, they are particularly effective in gas-saturated, rugose, and washed-out boreholes.

Through-Casing Acoustic Measurements

The extended transmitter-to-receiver offset (6 to 19 ft) provided by array instruments allows them to quantify formation-compressional and shear-wave energy through casing. Successful cased-hole operation requires a good cement bond to provide the necessary acoustic coupling to the formation and to minimize or eliminate the casing arrival.[20][21][22] New processing techniques may allow valid acoustic evaluation even in cases of poor bonding.<html><parsererror style="display: block; white-space: pre; border: 2px solid #c77; padding: 0 1em 0 1em; margin: 1em; background-color: #fdd; color: black">

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Tools using dipole transmitters were conceived as early as the 1960s,[25] but were not actually developed until the 1980s.[26] In contrast to monopole logging tools, dipole acoustic devices can excite a low-frequency flexural wave in the borehole at shear velocity. Low-frequency (< 1 kHz) dipole sources allow for shear-velocity determination that is much closer to seismic shear waves and permits acquisition of direct-shear velocities in slow and fast formations. However, increased noise (i.e., a lower signal-to-noise ratio) is one limitation of low-frequency operation. Noise has been reduced through improved acquisition electronics, the use of semi-rigid tool designs, and by choosing the operational mode of the dipole source. A semi-rigid tool body not only reduces the influence of the tool body on the measurement but also permits operation in deviated wells.

At high frequencies, or when the borehole diameter is large, flexural-mode propagation is slower and a dispersion correction is needed to obtain the shear velocity from the measured flexural velocity. This dispersion correction is a function of mud compressional velocity, formation compressional and shear velocities, the ratio of formation and mud densities, and the product of borehole diameter and processing frequency. Few, if any corrections are required if the flexural wavelength (velocity/frequency) is at least three times the borehole diameter, which is why low frequencies (< 1 kHz) are used. Where a correction is necessary, it is typically only a few percent, but can be higher under certain conditions.

The latest commercial tool designs are multipole array devices that operate in open and cased hole. These tools typically integrate multiple transmitters (monopole and dipole) and one or more arrays of monopole and dipole receivers. Multiple monopole transmitters, or a single "programmable" transmitter,[20][27][28] provide the preferred frequency-range for optimal acquisition of conventional BHC and long-spaced compressional, shear, low-frequency Stoneley modes along with cement-bond logs. The dipole transmitter, more recently a variable-frequency (wide bandwidth) transmitter, provides the crossed-dipole mode.[28][29][30][31][32] The receivers are positioned axially along the length of the tool, for short- and long-spaced measurements, and may be interlaced or independent. At each axial position a group of receivers (e.g., 4 or 8) is positioned azimuthally around the circumference of the sonde. The receivers are oriented with the transmitter to allow for alignment of directional (multimode) source excitation and data acquisition. This allows radial imaging of acoustic parameters and measured properties.[33][34] The dipole receivers may be aligned inline with the dipole transmitters or orthogonal (crossed) to them for crossed-dipole analysis.

Multipole tools provide enhanced Stoneley-wave and crossed-dipole shear-wave data for analysis of formation permeability and anisotropy (e.g., stress and fractures) (see later discussion).

Logging While Drilling

Acoustic slowness measurements are a relatively recent addition to the suite of LWD measurements.[35][36] Similar to wireline devices, LWD tools consist of transmitter, isolator, and receiver-array sections contained in either a single or separate drill-collars and use monopole-type (axisymmetric) transmitters. However, unlike wireline devices, which are small relative to the borehole size, the rigid collar, structural design, and large diameter of acoustic LWD drill collars may actually interfere with the physics of acoustic-energy propagation, making it more difficult to decouple the transmitter-to-receiver signal traveling along the tool body and complicating generation of borehole guided modes, such as Stoneley and flexural.

Downhole processing provides acoustic slowness data in real time and also allows for storage of raw waveform data in downhole memory that can be downloaded during bit trips. The receiver array provides data redundancy and is coupled with a much narrower recording bandwidth to enhance the signal-to-noise ratio in the presence of the drilling-related noise. This results in more accurate measurements of acoustic slowness. As with all types of LWD tools, the primary advantage of LWD acoustic measurements is the acquisition of data before significant fluid invasion or alteration of the formation can occur, and providing the data in sufficient time to influence drilling decisions for improved safety, well placement, and well productivity.[37][38] Table 3C.6 summarizes the advantages and disadvantages of LWD acoustic measurements. LWD acoustic data recorded in casing during bit trips offers the potential for cased-hole evaluation, e.g. formation velocity and cement-evaluation, during bit trips.[39]

Multipole tools (monopole and pseudo-dipole or quadrupole) have recently been introduced and continue to be developed.[40][41][42][43] These devices use the monopole transmitter for compressional-slowness and shear-slowness in fast formations. Similar to wireline tools, these tools may include an azimuthal receiver array.[42][43] With these tools, the compressional-slowness measurement is obtained in fast and slow formations by summing the azimuthal measurements at each receiver level. Fig. 3C.7 illustrates the excellent agreement between LWD data and wireline data. Measurement of compressional and shear slowness in slow formations is especially impacted as the diameter of the LWD drill collar approaches the borehole diameter. Because the drilling environment precludes propagation of a true dipole flexural mode, different methodologies are being used to obtain a pseudo-shear measurement using other borehole-guided modes, either through tool design, data processing, or both.[41][44][45][46][47][48][49][50][51] Current solutions include multiple-frequency and higher-frequency dipole-type transmitters, and quadrupole transmitters. These measurements require corrections for frequency dispersion and eccentering.[52][53][54][55]

Acoustic LWD can provide a limited real-time seismic-while-drilling capability in combination with a surface source.[56][57][58] There is also great interest among drillers and geophysicists to develop a viable drilling-based system in which the drillbit acts as the acoustic source and the sensors (ruggized geophones) are located in the borehole, as part of an LWD bottomhole assembly. Both types of systems provide checkshot surveys for time-depth correlation with pre-drill surveys and look-ahead seismic capability.[59]

Ultrasonic Reflection (Pulse/Echo) Acoustic Devices

Reflection (pulse/echo) acoustic devices were introduced in 1967 with the borehole televiewer (BHTV).[60] In contrast to conventional acoustic-logging devices, which record the transmission of acoustic waves through the formation, pulse/echo devices record the travel time, amplitude, and azimuth of ultrasonic acoustic pulses (echoes) that are reflected off the formation wall in openhole or off the casing or cement in cased hole (Fig. 3C.8[61]). The difference between the acoustic impedance of the borehole fluid and formation determines the magnitude (amplitude) of the transmitted ultrasound pulse that is reflected off the formation and back to the transducer. A portion of the transmitted signal is not reflected and continues to travel into the formation (openhole) or casing (cased hole) (Fig. 3C.8).

Televiewer-type devices use a rotating transducer that acts as both transmitter and receiver, to acquire as many as 250 samples per revolution. Because the tool is moving uphole continuously, data are acquired as a helical scan along the borehole (Fig. 3C.9). Magnetometers provide azimuthal information for each scan. Acoustic devices operate in both conductive (water-based) and nonconductive (oil-based) muds. Televiewer-type tools cannot operate in air- or gas-filled boreholes.

The ultrasonic pressure pulses transmitted from the front face of the transducer form a beam pattern that defines the resolution and detection capabilities of the tool. While image resolution is directly proportional to signal frequency, the operating frequency (200 to 650 kHz) is a compromise between the desire for high image resolution and the need to operate in high-density muds in which signal attenuation is directly related to the frequency. In openhole, in which high-resolution, focused transducers are used, resolution may be as fine as 0.2 in. Image resolution in cased hole, in which unfocused transducers may be used, is generally lower.

The peak amplitude of the reflected signal is used to generate a 360° image of the borehole wall and the travel-time measurements are used as a caliper to provide a measurement of borehole geometry or casing corrosion. The primary factors that contribute to the measured pulse/echo amplitude are borehole-fluid ultrasonic attenuation, borehole-fluid/formation reflection coefficient, physical features of the formation, and transducer-beam angle of incidence on the formation. Loss in signal amplitude (image quality) results from conditions that either scatter, absorb, or spread the acoustic energy, such as tool eccentering, irregularities in the borehole shape and surface, high-density and some oil-based drilling muds, and contrasts in acoustic impedance between the borehole fluid and borehole wall or casing (Table 3C.7). A separate transducer, commonly in the "mud-sub," continually measures the borehole-fluid velocity for the caliper measurement.

In openhole, amplitude images of the borehole wall are used for fracture analysis, stress analysis (borehole breakouts), and formation evaluation. Cased-hole applications include cement evaluation (distribution and quality), casing evaluation (wear and damage), and perforation control.[62] Smooth casing or borehole walls produce high-amplitude reflections (light), whereas openings (e.g., fractures or vugs) or imperfections (e.g., rugosity or pitting) in the borehole wall or casing result in low-amplitude reflections (dark). These images are displayed in the typical open-cylinder image presentation (Fig. 3C.10).

Cement-Bond Logging

Proper cement placement between the well casing and the formation is essential to support the casing (shear bond), to prevent fluid from leaking to the surface, and for isolating producing zones from water-bearing zones (hydraulic bond). Acoustic logs provide the primary means for evaluating the mechanical integrity and quality of the cement bond.[63][64][65][66][67] Acoustic logs do not measure cement quality directly, rather, this value is inferred from the degree of acoustic coupling of the cement to the casing and to the formation. Properly run and interpreted, cement-bond logs (CBL) provide highly reliable estimates of well integrity and zone isolation. Just as filtrate invasion and formation alteration may produce changes in formation acoustic properties, and thus variation in acoustic logs over time,[68][69][70] so too, cement-bond logs may vary over time as the cement cures and its properties change.

Modern acoustic cement-evaluation (bond) devices are comprised of monopole (axisymmetric) transmitters (one or more) and receivers (two or more). They operate on the principle that acoustic amplitude is rapidly attenuated in good cement bond but not in partial bond or free pipe. These cased-hole wireline tools measure compressional-wave travel time (transit time), amplitude (first pipe arrival), and attenuation per unit distance. Conventional CBL tools provide omnidirectional measurements, while the newer radial cement-evaluation tools provide azimuthally sensitive measurements for channel evaluation.

When the acoustic wave generated by the transmitter reaches the casing, part is refracted down the casing (amplitude and travel-time measurement), part travels through the mud (fluid arrival), and other parts are refracted into the annulus and the formation and received back (formation arrival). Amplitude, measured directly or as an attenuation ratio, is the primary bond measurement and is used to provide quantitative estimations of cement compressive strength, bond index, and qualitative interpretation of the cement-to-formation interface. Tool response depends on the acoustic impedance of the cement, which, in turn is function of density and velocity. On the basis of empirical data, the log can be calibrated directly in terms of cement compressive strength. However, in foamed cements or when exotic additives are used, these calibrations can be inaccurate. In these situations, users are advised to consult with the logging service company regarding the appropriate calibrations.

A typical cement-log presentation includes a correlation curve (gamma ray), travel time (μsec), amplitude (mV), and attenuation (dB/ft) curves, and a full-waveform display (μsec). Presentation of the full acoustic waveform assists in resolving bond ambiguities arising from use of an amplitude measurement alone and provides qualitative information about the cement-to-formation bond. Waveform displays may be in variable density (VDL) or intensity (also called microseismograms) formats, oscilloscope waves (also known as x-y or "signature"), or both (Fig. 3C.11).

Variable density is a continuous-depth time display of full-waveform amplitude presented as shades of black and white. Positive waveform amplitudes are shown as dark bands and negative amplitudes as gray or white bands; contrast is proportional to amplitude. On a variable-density log, free pipe and fluid arrivals (if present) are easily identified as straight dark and light lines (indicating homogenous acoustic properties) at either side of the display (Fig. 3C.12). The zigzag, wavy, or chevron pattern between these two arrivals is the formation signal (indicating varying acoustic transit time). In cases of poor bonding, casing-collar signals may also be identified as "w" patterns (anomalies) (Fig. 3C.13).[71]

Conventional Cement-Bond Devices. Early CBL designs (1960s) used a single transmitter and single receiver for an amplitude measurement. In an evolution similar to that of openhole acoustic logs (Table 3C.4), new designs were subsequently introduced that measured signal amplitude at a near receiver and a full waveform from a far receiver. Eventually, borehole-compensated devices using dual transmitters and dual receivers were introduced in the 1980s, and today most commercial devices use multiple transmitters and receivers in a variety of arrangements to provide compensated measurements. These devices measure the attenuation between two transmitters and receivers as a way of eliminating, or at least minimizing, the effects of tool eccentering, fluid attenuation, receiver sensitivity, temperature drift, and calibration. In addition to specialized cement-bond devices, modern openhole array tools are designed to also provide conventional cement-evaluation measurements in cased hole. The cement-bond instrument sleeve is typically slotted to suppress and delay the tool signal that might otherwise be confused with the important casing signals.

TR spacing typically ranges from 3 to 5 ft. The shorter spacing (e.g., 3 ft) provides optimum signal level and resolution at high attenuation rates and is normally used for amplitude and travel-time (TT) measurements. A longer spacing, commonly ≥ 5 ft, is used for the full-waveform recording because longer TR spacing provides greater separation of the casing and formation-signal arrival times. This separation allows for easier analysis of the formation-signal strength and is used to monitor cement-to-formation bonding.

These tools typically operate at higher frequencies than conventional openhole tools—between 20 and 30 kHz. As with openhole tools, cement-bond tools require centralization to ensure accurate measurements. Centering in the cased hole is more critical because the higher-operating frequencies (i.e., shorter wavelengths) and the tool measurement are based on signal amplitude. Tool eccentering reduces signal amplitude and travel time (Fig. 3C.14).

Cement-bond logging tools use gated systems to measure the specific parts of the acoustic waveform needed for the primary bond-amplitude measurement. Gates are time periods during which measurements are made—they can be either fixed or sliding (floating). Fixed-gate systems are commonly used for amplitude measurements and floating gates for travel-time measurements. Fixed gates are set (generally at the wellsite) to open, remain open, and close at designated times; opening time for the gate is a function of the casing size and the borehole-fluid velocity. If the gate opening is too large, there may be interference between early and late-arriving signals. Floating gates remain open, but recording is only triggered by an amplitude value greater than a designated threshold value.

A casing cement job can result in one or more of the following situations: free pipe, good bond, bond to casing only, and partial bond. In the first scenario, free pipe, there is no cement bond between the casing and cement. Consequently, there is no acoustic coupling with the formation and most of the transmitted acoustic energy is confined to the casing and the borehole fluid. As a result, a free-pipe acoustic signal is long-lived, high-amplitude, and of uniform frequency.

In the second scenario, good bond, cement is properly bonded to casing and to the formation. This provides good acoustic coupling and most of the acoustic energy is transmitted to the formation, resulting in little (weak) to no casing signals and little amplitude until the arrival of the strong formation signal.

The third scenario, bond to casing only, is a common condition in which cement is bonded to the casing but not to the formation. This can occur because the mudcake dries and shrinks away from cement, or because the cement did not bond with mudcake in poorly consolidated formations. In this situation, energy traveling through the casing is attenuated drastically because of the highly attenuating cement sheath. At the same time, the annulus outside the cement sheath provides poor acoustic coupling. The result is that little energy is transferred to the annular fluid and virtually none is transferred to the formation. This condition is indicated by the lack of later-arriving formation energy. A similar response can be caused by the presence of formation gas in shallow, high-porosity zones.

In the last scenario, partial bond, a space exists within an otherwise well-bonded casing. This may occur with the presence of a microannulus or channels within the cement. The resulting waveform is comprised of a casing signal and a formation signal; the casing signal arrives first, followed by the formation signal.

When channeling occurs, it is generally localized and nonuniform; that is, it occurs over relatively short intervals and can frequently be identified by variations in the amplitude response. Channeling is significant because it prevents a hydraulic seal. In contrast, a microannulus (a small gap between the casing and cement sheath) may extend over long sections of casing but may not prevent a hydraulic seal. Microannulus may result from thermal expansion or contraction of the pipe during cementing or to the presence of contaminants, such as grease or mill varnish, on the casing’s exterior surface. A common practice is to run cement-bond logs with the casing under pressure to expand the casing against the cement, thereby decreasing any microannulus that might exist. If the initial log run was not under pressure and the log indicates poor bond, the presence of a microannulus can be evaluated by running a second bond log under pressure to see if there is a difference. Pressuring the casing improves the acoustic coupling to the formation and the casing signal will decrease and the formation signal will become more obvious (Fig. 3C.15). However, if only channeling exists, pressuring the casing will not significantly change the log. When conducting a cement evaluation, information on the type of cement used is essential. For example, foam cements, which intentionally create void spaces in the cured cement, can be misinterpreted as partial bond if normal cement is assumed. Fig. 3C.16 summarizes this discussion, and Table 3C.8 lists additional factors that may affect interpretation of bond quality from the amplitude response.

One caveat regarding the use of the amplitude curve for bond evaluation: pipe amplitude represents the quality of the bond of pipe to cement but provides no indication of the quality of the bond between the cement and the formation. Whenever possible, amplitude data should be used in conjunction with the other measurements presented on the log (e.g., travel time or full waveform) for a more-reliable bond evaluation. For example, the presence of shear-wave amplitudes on the full-waveform display is an indication of good acoustic coupling to the formation. Table 3C.9 lists the limitations of conventional cement-bond logs.

Formations with transit times less than casing (57 μsec/ft) can cause problems when interpreting the amplitude curves because the formation signal can arrive in the amplitude gate. The VDL should be examined to ensure that the formation arrival is impacting the amplitude curve.

The bond index (BI) is a qualitative measure of cement bond based on signal amplitude. This dimensionless quantity is the ratio of measured attenuation to maximum attenuation:


A BI value of 1.0 represents a perfect cement bond. A value of less than 1.0 indicates an incomplete bond. This technique requires attenuation measurements in zones with 100% bond and in free pipe.

Radial-Cement Evaluation. Radial-cement-evaluation devices were developed to overcome some limitations of conventional cement-bond tools and to permit more accurate evaluation of cement distribution behind casing by providing the precise location of partial bond and channeling. These tools use one or more azimuthally sensitive transducers to evaluate cement quality around the circumference of the casing. Data from these tools are presented as individual log curves or as azimuthal images ("maps") of cement quality generated by interpolating between the individual azimuthal measurements (Fig. 3C.17). In addition, each tool design also provides a conventional 5-ft VDL waveform measurement to provide information about the cement-to-formation bond.

There are four radial-evaluation-tool designs in current use: televiewer-types that use a single rotating ultrasonic transducer,[72][73] circular ultrasonic pulse/echo transducers arranged in a fixed helical pattern around the sonde,[74][75] a multipad device that provides six compensated attenuation measurements,[76] and an array of eight TR pairs, arranged azimuthally around the sonde, that provide compensated CBL amplitude.[77][78]

The ultrasonic tools compute the acoustic impedance of the material beyond the casing. To do this, repeated acoustic pulses are directed at the casing to make it resonate in its thickness mode and the energy level (attenuation) of the decaying reflected wave is measured. Good cement bond to casing produces a rapid damping (higher impedance) of this resonance; poor cement bond results in longer resonance decay (lower impedance). Measurements from these devices are influenced by the same factors as openhole televiewer devices.

The pad device makes multiple short-spaced, compensated, azimuthal-attenuation measurements. Because the pads are in direct contact with the casing—in contrast to ultrasonic measurements—measurements are unaffected by gas in the borehole, fast formations, heavy-mud conditions, or minor tool eccentricity. The attenuation in each segment is measured in two directions using a pair of acoustic receivers and two transmitters. The two measurements are combined to form a result that compensates for surface roughness and the effects of minor residual cement on the inside of the casing. Transmitting elements and the firing sequence are controlled to direct (steer) and enhance the acoustic-energy output of both the pad transmitters and the VDL transmitter. This has the effect of improving the signal strength of both the casing and cement-to-formation arrivals, respectively. This technique improves VDL interpretation, particularly in soft formations in which the standard VDL may wash out.

The use of new high-performance low-density, foam, and complex cements is increasing. However, the presence of gas in cement slurries, as an inert component or as contamination, may seriously affect ultrasonic-tool interpretation. New interpretation methods integrate ultrasonic and attenuation measurements from conventional tools to provide improved cement evaluation in these conditions.[79][80][81][82] The latest ultrasonic tool has a conventional pulse-echo transducer plus a flexural transmitter and two flexural receivers that provide greater depth of investigation. Interpretation techniques combining these different measurements provide improved evaluation in lightweight cements, especially in the annulus, beyond the casing-cement bond.[83] Table 3C.10 summarizes the capabilities and guidelines for running the different types of cement-bond evaluation tools.

Casing Evaluation. Preventing casing failure caused by deformation, physical wear, or corrosion is critical to maintaining well production. Ultrasonic radial-cement-evaluation devices and modified openhole-imaging devices are also used to evaluate casing for indications of potential collapse, thinning, and internal or external metal loss.[73][84][85][86] Echo amplitude and travel time provide images of the condition of the inside casing surface (e.g., buildup, defects, and roughness such as pitting and gouges) (Fig. 3C.18), and travel-time and resonant-frequency analysis provide casing thickness (Fig. 3C.19).

The acoustic caliper generated from the pulse/echo travel time provides the casing inside diameter (an average of all transducers or a single circumferential scan). An estimate of casing ovality is obtained using only the maximum and minimum measurements. Then, if the nominal value of the outside casing diameter is assumed, changes in thickness can be calculated and internal defects identified. Frequency analysis determines the casing resonant frequency from the acoustic waveform; casing thickness is inversely related to the resonant frequency. By combining travel time and resonant-frequency measurements and using data from all available transducers (or a single scan), presentations showing casing cross sections are used to highlight casing damage such as thinning, corrosion metal loss, and collapse (Fig. 3C.19).

Conventional Applications

Interpretation of acoustic-log data begins with the slowness values obtained from processing the recorded waveforms. Slowness, or porosity derived from slowness, may be corrected for additional factors (discussed below) before use in applications. Today, log analysis and interpretation is routinely performed by computers during data acquisition (in real time) or in post-acquisition processing in offices and computing centers. Modern interpretation software is built on algorithms derived from the empirical relationships originally used to create a variety of graphical solutions contained in crossplots and nomograms.[87] Because porosity tools vary in their sensitivity to lithology, porosity, and fluid properties, the combination of different measurements allows more-accurate determination of porosity, petrophysical, and geological characteristics. The logging service companies issue chartbooks with tool-specific charts to facilitate rapid manual determination of porosity, lithology, shaly-sand analysis, saturation, mechanical properties, and cement-bond evaluation. These charts, which are accompanied by instructions for their use, form the basis for quick-look interpretations and for quality control of computer interpretations.[88][89]

The earliest applications of acoustic-logging measurements made use of compressional slowness, used alone or in combination with resistivity logs and other porosity logs. This group of applications, which includes velocity, porosity, gas identification, lithology, fluid saturation, and rock strength, still comprises the basic set of applications for acoustic-log data. In the 1960s, laboratory studies indicated that shear-wave data could also prove useful in formation evaluation.[90] The development and introduction of reliable shear-wave acquisition and full-waveform logging in the late 1970s and 1980s resulted in improved accuracy in these conventional applications.[91] Further advances throughout the 1980s and 1990s, in both basic and applied research as well as in tool technology, led to new and advanced applications, e.g., permeability estimation, anisotropy determination, and direct hydrocarbon indicators, that use shear- and Stoneley-wave amplitude and attenuation (Table 3C.11).

The compressional velocity of sound in fluid is less than the velocity in rock. If there is pore space in the rock, and it is fluid-filled, the acoustic energy will take longer to get from the transmitter to the receiver (i.e., low velocity indicates high porosity). The recorded velocity or travel time represents the sum of the velocity of the solid part or framework of the rock (i.e., the rock matrix), the rock lining the pores, and the fluid filling the pore space. In turn, travel time in the rock matrix, Δtma , is influenced by variations in lithology (i.e., the chemical composition) and confining pore pressure (i.e., compaction).[92] These factors are related through an empirical relationship known as the Wyllie time-average equation.[93] When the velocity (transit time, Δt, or travel time, t) of the rock matrix and borehole fluids are known, porosity can be computed the following ways (Eq. 3C.4 to Eq. 3C.7).

In terms of velocity, v:


where ϕ = fractional porosity of the rock, v = velocity of the formation (ft/sec), vf = velocity of interstital fluids (ft/sec) and, vma = velocity of the rock matrix (ft/sec).

In terms of transit time (Δt):




where Δt = acoustic transit time (μsec/ft), Δtf = acoustic transit time of interstitial fluids (μsec/ft), and Δtma = acoustic transit time of the rock matrix (μsec/ft). (See Table 3C.3 for typical values of Δtma and Δtf.)

In terms of travel time:


The velocity of most borehole and reservoir fluids (except gas) does not vary greatly and a fluid velocity (Δtf) of 189 μsec/ft (5,300 ft/sec) is generally assumed for fresh drilling fluids; a slightly lower value, 185 μsec/ft, is used for salt muds. Fluid type becomes more of a concern when oil-based mud (OBM) is used if the formation of interest is not invaded or if invasion is very shallow. The lithology must be known or estimated in order to select the appropriate matrix velocity.

The Wyllie equation represents consolidated and compacted formations. In poorly consolidated or unconsolidated rocks, a correction factor is necessary (Eq. 3C.8). Also, the presence of shale or clay within the sand matrix will increase Δt by an amount proportional to the bulk-volume fraction of the clay. An empirical equation is used for calculating porosity in sandstones in which adjacent shale values (Δtsh) exceed 100 μsec/ft (Eq. 3C.9):


where the compaction correction factor Cp is


where Δtsh = specific acoustic transit time in adjacent shales (μsec/ft), and 100 = acoustic transit time in compacted shales (μsec/ft). The shale compaction coefficient (C) generally ranges from 1.0 to 1.3, depending on the regional geology.

The highest velocities observed in sandstones approach 20,000 ft/sec (50 μsec/ft), but most sandstones have a lower matrix velocity. Velocities in adjacent shales are used to adjust the matrix velocity for sands with velocities lower than 18,000 ft/sec. Table 3C.12 provides guidelines for selecting the appropriate value of Δtma. If the lithology of carbonate rocks can be reasonably estimated and if the porosity distribution is fairly uniform, the Wyllie time-average formula can provide reliable determination of porosity for this group.

A second empirical velocity/porosity relationship, the Raymer-Hunt-Gardner equation,[94] was introduced to correct for observed anomalies and shortcomings of the Wyllie time-average formula (Eq. 3C.10). It provides improved porosity correlation over the entire porosity range and is applicable to both consolidated and some unconsolidated formations, thus eliminating the need for a compaction correction. However, in high-porosity, unconsolidated, and uncemented (slow) rocks, neither of the empirical velocity/porosity transforms may be adequate[95]


where α = (Δtma/2Δtf) − 1.

Graphical solutions for both algorithms for a sandstone matrix are compared in Fig. 3C.20. One caveat regarding the use of empirically derived porosity transforms: they do not account for all the factors influencing acoustic velocity. Consequently, these relationships may not be valid for all reservoirs.

In fast formations, the shear velocity can also be used for porosity evaluation in a manner similar to that described above for compressional velocity.[91] Further, the combination of compressional and shear slowness can provide an enhanced porosity determination.[96] Using shear velocity for porosity determination offers several distinct advantages because shear velocity is: generally more sensitive to porosity than compressional velocity, insensitive to gas effects, less affected by borehole washout, can be used to replace nuclear porosity in some situations,[97] and porosity evaluation can be conducted in cased hole using dipole tools (or in some cases, monopole-array tools using special processing).[98][99]

These velocity/porosity methods are for clean (shale free), water-filled formations. The calculated apparent porosity must still be corrected for the volume of pore-filling material (shale). If the formation contains shale or dispersed-clay particles, or is hydrocarbon bearing and invaded to only a very shallow depth, corrections to the basic log data are necessary before reasonable porosity values can be calculated.

Because shale transit times range from 62 to 167 μsec/ft, failure to correct for the presence of shale may result in overly optimistic porosity calculations. The acoustic measurement is also influenced by the way the shale is distributed within the sandstone reservoirs. The fraction of shale, or shale volume, can be estimated using a combination of log measurements that are influenced by shale, such as neutron porosity, density, gamma ray, or spontaneous potential (SP). Chartbook nomograms developed for porosity determination include graphical solutions for both undercompaction and shale volume.

In some producing regions, producibility indexes based on the volume of shale in producing sandstone reservoirs have been developed. The fraction of total porosity occupied by dispersed clay (q factor) is empirically related to effective and total porosity and production characteristics. Local experience is used to create permeability cutoffs using the q factor (Fig. 3C.21).[87]

Acoustic travel time in gas and oil is higher than in water. The presence of unflushed hydrocarbons in an interval can result in high values of apparent formation porosity. Commonly used correction factors are 0.9 in oil zones and 0.7 in gas zones.[92] More recently, a gas-zone porosity-correction technique using shear slowness has been developed.[100]

An additional empirical velocity-porosity predictive model has recently been proposed and is still in the experimental phase.[101][102]

Carbonate and complex lithology reservoirs are generally comprised of varying proportions of limestone, dolomite, chert, quartzite, and occasionally, evaporites. The primary influences on porosity in these rocks are lithology and pore type. Generally, any shale present is in dispersed form and in small amounts that do not significantly impact porosity calculations. Acoustic porosity is a measure of the primary or intergranular (matrix) porosity. In dual-porosity reservoirs, the secondary porosity (e.g., isolated pores, vugs, and fractures) may significantly influence the rock-pore distribution, but may be overlooked by acoustic-log measurements. This topic is the subject of ongoing research.[103] In contrast, nuclear-porosity devices, such as density and neutrons, measure total porosity. The difference between the nuclear-porosity and acoustic-porosity measurements is an approximation of the secondary porosity.

Lithology Identification. Acoustic velocity is primarily a function of the rock matrix and can be used to identify different lithologies and for stratigraphic correlations. A variety of crossplot techniques, using acoustic measurements alone, or in combination with other porosity logs (neutron and density), have been devised to assist in lithologic identification (Fig. 3C.22). In particular, the M-N and mineral-identification-plot (MID) techniques use all three porosity logs in different combinations.[104][105] Before lithology determination, the individual log measurements must be corrected for influences of gas effect, secondary porosity, bad hole conditions, and shaliness. In general, the MID plot is more sensitivity to lithology, gas, and secondary porosity and provides superior results to M-N plots. Crossplots, using a variety of log measurements or combinations of measurements can be used to resolve specific lithologic problems related to local or regional geology.[87][106]

The ratio of compressional to shear velocity, Vp/Vs, is an effective lithology indicator because each lithology exhibits a defined trend that is independent of porosity and depth (Fig. 3C.23).[90][107][108] However, because the Vp/Vs ratio is affected by formation anisotropy, the ratio values may not be absolute indicators of a particular lithology.[109]

The addition of shear slowness to lithology identification provides a more robust result that can be particularly useful in cased-hole evaluations where density logs are not available. In Fig. 3C.24, the combined use of shear slowness and cased-hole neutron porosity results in enhanced-porosity determination in a complex lithology. Crossplots of Vp/Vs ratio vs. compressional travel time, Δtc, facilitate identification of lithology trends with respect to porosity and lithology (Fig. 3C.25). Recent studies of complex carbonate reservoirs indicate that the Vp/Vs ratio is a function of porosity and in some cases, can differentiate higher-permeability facies.[110][111]

Saturation Determination. The potential of acoustic velocity for determination of fluid saturation was recognized soon after development of the first logging devices and quickly became a staple input for log-interpretation methods and software. Acoustic-derived porosity serves as one variable, together with resistivity, in a variety of graphical and empirical methods used for solving the Archie saturation equation. Hingle and Pickett plots are the two most commonly used resistivity-porosity plots. Depending on the data available, the Hingle plot[113][114] can solve for Rw, Δtma, and water saturation (Sw). Pickett plots[115][116] (Fig. 3C.26) solve for Archie parameters a and m, formation factor, resistivity index, and Sw. A new technique using an empirical equation based on acoustic- and resistivity-log parameters is reported to successfully estimate water saturation in clean and shaly sandstones.[117]

Hydrocarbon Identification. Gas. Acoustic coupling between solid and gas or fluid and gas is poor, resulting in a high loss of energy. A sudden loss of energy (amplitude) in the measured acoustic signal, primarily in the compressional wave and only secondarily in the shear wave: (e.g., the cycle skipping or high slowness values) may indicate gas-filled pore space (gas effect). In the cased of gas-filled porosity, the acoustic-neutron crossplot can be useful for this purpose because neutron porosity is lower than acoustic porosity in gas zones.

Compressional velocities are affected (slowed) by the compressive fluids in the pore space, while shear velocity is affected only by the rock matrix. Consequently, the presence of gas is especially noticeable in compressional-wave slowness. The combination of compressional and shear slowness, either as a ratio or as a log overlay, provides a quick-look gas indicator (Fig. 3C.27).

The ratio of Vp/Vs offers a quicklook technique to distinguish between reservoir fluids[118][119][120][121] and is especially effective in identifying light hydrocarbons (gas).[122][123] When Δts is plotted against the Vp/Vs ratio, water-bearing sands and shales show a linear relationship and points falling below matrix lines result from the slowing effect of Δtp in light hydrocarbons (Fig. 3C.28). These relationships are used for correcting porosity in gas-bearing intervals.[100] Further, laboratory investigations suggest that the Vp/Vs ratio can be used for saturation determination in some situations[124] as well as time-lapse changes accompanying steam flood of heavy-oil reservoirs.[125]

Oil. Recent work suggests that the Vp/Vs ratio may also serve as an indicator of bypassed oil in cased wells.[126][127] Research on the acoustic properties of heavy oils indicates that under the proper conditions of temperature and viscosity, these oils may behave as solids and generate shear waves that may be detectable at logging-tool frequencies.[128]

Geophysical Applications

The higher operating frequency of acoustic-logging tools and the smaller TR distances allows for higher-quality velocity data and finer vertical resolution than surface reflection techniques. Acoustic-velocity logs were originally developed for calibrating surface seismic velocities and reflectors. Acoustic-log interval travel time or transit time, Δt, can be summed, i.e., integrated, over the entire logged interval to provide the equivalent of seismic one-way time which is compared to borehole seismic surveys and reflection seismic two-way time.

Acoustic-log data are commonly calibrated using checkshot (velocity) or vertical seismic profile (VSP) surveys prior to use in geophysical applications. Data from these surveys, which use downhole receivers and surface acoustic sources, are used to adjust the log data for drift and borehole conditions and result in improved time-depth correlation. Acoustic-log data are combined with density-log data, to generate an impedance log that in turn is used to produce a synthetic seismogram. Synthetic seismograms are artificial seismic records that tie seismic time to log depth and are also used to match well-log quantities to seismic attributes for distinguishing primary seismic events (geologic structure and stratigraphy). It is possible, however, that a synthetic seismogram may not provide a very good match to the seismic field data. Disagreements commonly result from the differences scale and acquisition physics used in seismic and well-log measurement; for example, operational frequency (wavelength), borehole condition, and angle of measurement (particularly in the presence of anisotropy).[129][130][131][132][133] Acoustic-log data provide a fundamental and essential element of modern seismic reservoir characterization.[134] The chapter on Fundamentals of Geophysics in this volume of the Handbook contains more information on the determination and use of these types of analyses.

Drilling and Reservoir Engineering Applications

Pore Pressure and Overpressure Detection and Evaluation. Abnormal pressure is defined as any departure from normal hydrostatic pressure at a given depth.[135] Abnormal subsurface pressures, either overpressure (geopressure) or underpressure, are encountered in hydrocarbon basins throughout the world in all lithologies, all geologic ages, and at all depths.[136] Early and reliable detection of geopressure is vital to avoid or mitigate potential drilling and safety hazards, e.g., shallow water flow, blowouts, and shale instability. During drilling, advanced warning of approaching geopressuring enables the mud weight to be adjusted to avoid well and reservoir damage and to determine casing points. This is a particular concern in deepwater wells in which the pressure difference; i.e., the operating window, between the hydrostatic gradient and the fracture gradient can be very narrow.

Geopressuring in hydrocarbon reservoirs may result from a variety of geologic and tectonic processes.[136][137][138] Borehole-acoustic detection methods using compressional and shear slowness can identify abnormally pressured zones before they are drilled and can quantify pressure gradients. These methods, discussed below, are used in conventional borehole logging (wireline and LWD), new seismic-while-drilling techniques, and more recently, surface seismic data.[37][56][137][139][140][141][142][143][144][145][146][147][148]

Undercompaction is the primary mechanism for creating overpressure, particularly in deltaic basins in which high rates of deposition commonly prevent the escape of pore water trapped in shales. Undercompacted shales have higher acoustic transit times (i.e., higher apparent porosity) than normally pressured shales at the same depth.[149][150][151][152] With the onset of overpressuring, a semi-logarithmic plot of acoustic slowness with depth will diverge from a normal (hydrostatic) straight-line trend of decreasing slowness (increasing velocity) with depth (Fig. 3C.29).

The "normal," or hydrostatic, trend for the well, which may vary with different geologic provinces, is defined by plotting slowness values for shale beds (> 10-ft thickness) in the well. A constant overburden gradient of 1.0 psi/ft is generally assumed. The difference in acoustic slowness between the normal and abnormal trends can be converted to an equivalent fluid-pressure gradient and formation pressure for a given depth (Fig. 3C.30). This method may not be applicable or effective in all areas or where undercompaction is not the mechanism for overpressuring.[153][154] More-general approaches to determination of pore pressure and fracture gradient use an effective-stress, rock-mechanics approach.[153][155][156]

Recent investigations into the effects of pressure on shale porosity suggest that the relationship is more complex than previously thought. While additional study is necessary, the results to-date suggest that it may be necessary to reconsider or revise the well-log methods currently used in pore pressure and exhumation analysis (see section on Geological Applications below).[148][157][158][159]

Fracture Identification. Locating fractures, recognizing fracture morphology, and identifying fluid-flow properties in the fracture system are important criteria in characterizing reservoirs that produce predominantly from fracture systems. However, fracture identification and evaluation using conventional resistivity and compressional-wave acoustic logs is difficult, in part because fracture recognition is very dependent on the dip angle of fractures with respect to the borehole.

Fractures are physical discontinuities that generate acoustic reflection, refraction, and mode conversion—all of which contribute to a loss of transmitted acoustic energy. In particular, compressional- and shear-wave amplitude and attenuation and Stoneley-wave attenuation are significantly affected by the presence of fractures. Compressional waves are primarily affected by oblique fractures—those with dip angles between 15° and 85°—while shear waves are primarily affected by horizontal or near-horizontal fractures.[160] On conventional-velocity logs, fracture-induced attenuation may be evidenced as cycle skipping, variations in the Vp/Vs ratio and on VDL presentations, or as chevron (crisscross) patterns caused by mode-conversion interference.[161][162] Borehole-televiewer-type imaging devices provide a higher degree of success in identifying fractures and determining whether or not they are open (producible) or closed. The development of reliable full-waveform shear- and borehole-imaging devices enabled enhanced fracture identification and evaluation.[62][163] Aguilera[164] summarizes the use of conventional acoustic-log methods for fracture identification.

Recently developed anisotropy-analysis methods use crossed-dipole shear, Stoneley-wave, and acoustic-imaging data—individually or in combination—to provide reliable identification and evaluation of in-situ and induced fractures (see the Crossed-Dipole Anisotropy Analysis section of this chapter).

Geological Applications

Estimates of Erosion and Uplift (Exhumation). The amount of erosion that has occurred in a region that has been uplifted can be estimated from the degree of shale compaction measured by acoustic travel time.[165][166][167] This technique assumes that shale compaction is irreversible and that the shale retains the degree of compaction it gained at its maximum burial depth. Uplift and erosion will result in lower porosities than expected for the current burial depth (i.e., a shale will appear to be overcompacted).[148][168][169][170][171][172][173][174][175][176][177][178]

Determination of Organic Richness and Source-Rock Potential. Acoustic slowness, used alone or in conjunction with formation resistivity, can provide qualitative indications and quantitative determination of source-rock potential (when calibrated to laboratory data). The identification of potential petroleum-source rocks and characterizing the thermal maturity of these rocks is important for assessing petroleum potential (risking) and for basin modeling.

Studies of coals and organic-rich shales have demonstrated that acoustic velocity is reduced by the presence of organic material, that changes in velocity are proportional to the volume of organic material present, and that increases in thermal maturity (largely a function of burial depth and temperature) are accompanied by increases in acoustic velocity (decreases in transit time, Δt). Total organic carbon and the level of organic thermal maturation, expressed in terms of vitrinite reflectance, are two key parameters used for determining the potential of a formation to source hydrocarbons, and each can be mathematically related to Δt.[179][180][181] Because acoustic velocity is influenced by a number of factors in addition to organic carbon content, a combination of log measurements can provide improved results when other factors do not mask responses. In particular, acoustic-resistivity crossplot techniques (Fig. 3C.31) and log overlays (Fig. 3C.32) have proved successful.[182][183][184]

Geomechanical Applications

Rock Mechanical Properties. The determination of a reservoir’s mechanical properties is critical to reducing drilling risk and maximizing well and reservoir productivity. Estimates of rock mechanical properties are central to drilling programs, well placement, and well-completion design.[185] Mechanical properties include the elastic properties (Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio) and the inelastic properties (fracture gradient and formation strength).

Elasticity is the property of matter that causes it to resist deformation in volume or shape. Hooke’s law describes the behavior of elastic materials and states that for small deformations, the resulting strain is proportional to the applied stress. Stress is the force applied per unit area, and strain is the fractional distortion that results because of the acting force. The modulus of elasticity is the ratio of stress to strain. Depending on the mode of the acting geological force and type of geological media the force is acting upon, three types of deformation can result as well as three elastic moduli that correspond to each type of deformation. Young’s modulus, E, is the ratio of uniaxial compressive (tensile) stress to the resultant strain. Bulk modulus, K, is the change in volume under hydrostatic pressure (i.e., the ratio of stress to strain). (K is the reciprocal of compressibility.) Shear modulus, μ, is the ratio of shearing (torsional) stress to shearing strain. An additional parameter, Poisson’s ratio, σ, is a measure of the geometric change of shape under uniaxial stress. These four elastic parameters are interrelated such that any one can be expressed in terms of two others and can also be expressed in terms of acoustic-wave velocity and density (Table 3C.13).

The data needed to compute mechanical rock properties are compressional and shear velocities (slowness) and density. Shear and compressional velocities are a function of the bulk modulus, shear modulus, and density of the formation being measured. The Vp/Vs ratio, combined with formation density, ρ, is used to calculate Poisson’s ratio, Young’s modulus, the bulk modulus, and the shear modulus. Whenever possible, log-derived, dynamic rock properties should be calibrated to core-derived static (laboratory) properties, because the static measurements more accurately represent the in-situ reservoir mechanical properties.[186][187][188][189][190] Rock mechanical properties can be determined using conventional empirical charts[191] or computer programs. The elastic moduli and Poisson’s ratio are used in a variety of applications.[192] These applications include predictions of formation strength,[193][194][195][196][197] well stimulation (fracture pressure and fracture height),[198][199][200][201] borehole and perforation stability,[202] sand production and drawdown limits in unconsolidated formations,[203][204][205] coal evaluation,[206] and determining the roof-rock-strength index for underground mining operations.[207][208] Rock-mechanics applications of modern multipole tools are discussed in the Anisotropy Analysis section following.

Near-Well Imaging

Acoustic data acquired using modern array tools can provide high-resolution (0.5 m), microscale "seismic" 2D and 3D images of structural features in the near-borehole region (10 to 15 m). Conventional seismic-processing techniques, including filtering and migration, are used to extract compressional and shear reflections from the acoustic data. The reflections are then used to image geological features near the borehole. This technique allows the imaging of bed boundaries, thin beds (stringers), fractures, and faults in openhole and cased wells (Fig. 3C.33).[32][209][210][211][1][212][213][214][215]

Advanced Data Analysis And Applications

Processing acoustic data downhole as well as at the surface is necessary to transform the raw acoustic signals recorded by modern logging instruments into data suitable for interpretation and analysis. Data processing takes place during acquisition, in the logging tool itself and in the surface acquisition unit, and also in post-acquisition processing at computing centers. There are a variety of sources of noise in the downhole environment that contaminate the recorded acoustic signal: tool ("road") noise, measurement error, reflection and scattering from rough borehole or bed boundaries, mode conversion, and interferences that occur in the downhole environment. The goal of acoustic-data processing is to minimize the data noise while maximizing the petrophysical information.[216] Data preprocessing reduces the influences of these sources, thus allowing extraction of the true formation signal.

Following the rapid theoretical advances in acoustic-wave propagation made during the 1980s and 1990s, significant advances in data processing provided improved quality in slowness measurements and enabled a number of new applications using Stoneley and dipole-shear wave in open and cased holes. The combined interpretation of Stoneley and dipole-shear acoustic measurements with NMR and borehole imaging enhances formation evaluation.

Slowness Analysis

One of the primary goals in borehole acoustic logging is to obtain formation slowness from array measurements. Accurate slowness analysis is vital to most petrophysical, geophysical, and seismic applications. A variety of techniques are used for computing slowness from array tools (Table 3C.14).

Semblace and Nth-Root Stacking. The two most commonly used techniques to determine slowness from borehole acoustic array are semblance[217][218][219] and Nth-root stacking[220][221]; both are cross-correlation, coherency techniques that compare signatures in an acoustic array and find the similarities that correspond to coherent wave types. Semblance has a direct physical interpretation, whereas Nth-root stacking is a purely mathematical solution. Although the semblance method is faster, the Nth-root stacking method is more tolerable to noise and ignores amplitude variations across the array and, in general, provides better results. Collecting the array data, either as receiver or transmitter (source) arrays (Fig. 3C.34), enhances the slowness output from both of these techniques.

The primary application of the receiver- and transmitter-array-derived slowness curves is to provide compensation (DDBHC) to the monopole compressional and shear slowness for borehole irregularities such as washouts or cave-ins. Borehole compensation is achieved by averaging the slowness estimates from the receiver and transmitter arrays. The dipole-shear wave does not require borehole compensation because the flexural-shear wave is not as sensitive to the borehole geometry although it is often used to improve results in rough boreholes.

The objective of the semblance technique is to find the slowness that maximizes the coherence (time domain) among the wave power spectra over the receiver array. The Nth-root stacking technique is very similar to the semblance technique, except that the waveform amplitudes are modified in a different way to produce a so-called "pseudo" power spectrum instead of the true power spectrum.

Although the algorithms used in semblance and Nth-root stacking differ, the processing procedure is similar. A time window of fixed length is set up on each signature in the array. The windows are offset by a specified time interval on the successive signatures and a correlation is computed over these windows. The windows on all but the first signature are then stepped a certain distance out in time and another correlation value is computed. The process continues for the range of anticipated slowness in the well. This process is repeated as the window is progressively stepped on the first signature.

The group of correlation values obtained is known as a correlogram, in which the waveform coherence or correlation values either from semblance or Nth root method are displayed as a function of slowness and arrival time creating a 3-D surface. The correlation values in a range of arrival times are further combined to form a "combined correlogram," which is a projection of the 3-D surface on the slowness axis. The correlogram peak at each measured-depth level is used to obtain the Δt slowness for the wave type. These individual slowness values are then displayed as a continuous log curve. Filtering for the compressional wave or for the dispersive shear wave is normally required before using either method. As a quality check, the slowness results of semblance or Nth-root stack processing can also be plotted in the combined correlogram together with a "computed travel time" which is plotted against the waveform. The computed travel time represents the sum of the transit-time measurements from the transmitter to the receiver along with the mud travel time. Dipole shear-slowness processing must also take into account dispersion of the flexural wave.[222] Depending on the frequency of the flexural mode, a correction may be required to obtain shear-wave slowness.

Resolution Enhancement. The aperture (vertical resolution) of array tools is typically 3.5 ft. This means that a bed must be at least that thickness to measure true acoustic slowness, although such tools can detect (resolve) beds down to 2-ft thickness. To meet the need for the higher resolution necessary for thin-bed evaluation, waveform-matching (multishot) processing techniques use the redundant information contained in overlapping receiver subarrays to improve vertical resolution (Fig. 3C.34).[223] Recently introduced processing techniques reduce the aperture to 0.5 ft and thus achieve a true vertical resolution of 1.0 ft (Fig. 3C.35).[112] However, reducing the aperture makes the measurements more susceptible to noise.

Anisotropy Analysis

Formation anisotropy—the directional variation of physical properties—can be the result of depositional processes (intrinsic) or tectonic processes (stress-induced). Formation anisotropy is evidenced through variations in permeability, rock strength, fractures, and borehole failure. In acoustic/seismic terms, intrinsic anisotropy is structural in nature and is commonly seen as transverse isotropy (TI or vertical transverse isotropy, VTI), in which properties differ in the vertical or horizontal planes, such as in shales or thinly bedded intervals.[224] Stress-induced anisotropy is known as azimuthal anisotropy (or horizontal transverse isotropy, HTI), in which acoustic parameters in a vertical borehole vary with azimuthal orientation, such as the case of fractures parallel to the borehole.

Analyses of in-situ anisotropy (primarily stress induced) are made using direct or derived shear-wave velocity and provide the magnitude and azimuth of anisotropy (i.e., direction of the maximum and minimum horizontal stresses as well as an indication of their difference). Anisotropy analysis has been widely used in solid-earth seismology, geothermal studies, and more recently, in exploration geophysics (see summaries in Crampin and Chastin[225] and Helbig and Thomsen[226]). In the petroleum industry, these results are used in well design and well placement for optimum reservoir drainage,[227] to detect and characterize faults and fractures in openhole and cased hole,[228] to predict borehole instability and sand production,[229] and for optimizing the design and evaluation of well completions (perforations and hydraulic fracturing) (see following section on Crossed-Dipole Anisotropy Analysis).

Compressional-, shear- and Stoneley-wave properties are each affected, to some degree, by the presence and type of formation anisotropy. While the shear-wave response to azimuthal anisotropy (see the following section on Crossed-Dipole Anisotropy Analysis) and Stoneley waves to VTI anisotropy is well known, the effect on compressional-wave energy is less well characterized.[230][231][232][233] In some situations, information from additional measurements, such as borehole images, dip logs, or both, may be necessary for relating the measured anisotropy to geological features.

Borehole acoustic azimuthal and VTI anisotropy analysis is an advance made possible by the recent introduction of new inversion methods.[234][235][236][237][238][239][240][241] These methods use the crossed-dipole shear to derive azimuthal anisotropy and the Stoneley wave to derive TI anisotropy in slow formations, or a combination of these modes in deviated wells. A reasonable shear velocity can be derived using inversion techniques with low-frequency Stoneley-wave dispersion which is sensitive to the horizontal shear (in contrast to the dipole’s sensitivity to the vertical shear).[8][23][242]

Several new applications have been made possible by anisotropy analysis: identification of formation alteration using dipole-shear dispersion,[33][236][243][244] stress estimation,[238] and distinguishing between intrinsic and stress-induced anisotropy using dispersion crossover.[245][246][247][248] Anisotropy analysis can also be conducted using shear-wave parameters derived from Stoneley-wave dispersion.[241][249]

Crossed-Dipole Anisotropy Analysis. In anisotropic media, shear waves (both monopole refracted and dipole flexural) split into orthogonally polarized components having different velocities. This is known as shear-wave splitting, shear-wave birefringence, or shear-wave velocity anisotropy.[250][251][252][253] The difference in fast and slow shear-wave slowness provides a measure of the magnitude of anisotropy. Shear-wave splitting is useful for evaluating fractures, faults, bedding planes that intersect the borehole at an angle, and unbalanced tectonic stresses perpendicular to the borehole.

Because the flexural waves induced by dipole-acoustic sources have a directional component, the use of mutually perpendicular (crossed) pairs of dipole transmitters and receivers can detect and measure dipole shear-wave splitting.[254][255][256][257] In isotropic formations, both receiver components (X and Y) will measure the same shear-wave arrival time. However, in an azimuthally anisotropic formation, the shear wave measured at the X-component of the receiver pair will be different from the one measured at the Y-component; one is called the fast shear component, the other, the slow shear component (Fig. 3C.36). To measure the fast and slow shear-wave slowness, four components are measured: two inline components, X-X and Y-Y, and two crossline components, XY and YX (Fig. 3C.37).

The dipole flexural shear mode is affected by a variety of factors including formation anisotropy. Significant borehole ellipticity (the result of borehole failure or breakouts)[258] and high relative inclination between the borehole and formation[259][260] may result in erroneous interpretation of dipole-derived anisotropy and must be accounted for during data processing.[261] Additionally, the presence of shale anisotropy in high-angle and horizontal wells, can significantly influence compressional velocity, which must be corrected for this effect.[262]

Initially, mathematical rotation methods originally developed for use in processing surface seismic data[263] were used to determine the fast-wave direction together with the slowness values for the fast and slow shear wave. More recently, inversion methods[264] are being applied to the four data sets to simultaneously determine the azimuth and magnitude of the anisotropy (Fig. 3C.38).

An anisotropy map (Fig. 3C.39) combines the derived average anisotropy and its azimuth to generate an azimuthal image. This display facilitates interpretation by allowing the analyst to quickly assess depth intervals of interest by looking at the brightness, direction, and continuation of the features on the map. The map also facilitates comparison with borehole-image logs. Rose diagrams (Track 3) provide an accurate indication of the fast shear azimuth over each labeled depth interval. The integration of monopole and dipole measurements yields improved estimates of anisotropy, magnitude of anisotropy, and permeability.[242][265]

Horizontal Stress and Hydraulic Fracturing. Fractures, both natural and hydraulically induced, develop in relation to regional or localized stress patterns and play a major role in optimizing production and reservoir drainage. An estimate of the magnitude and azimuth of the horizontal stresses surrounding a borehole is needed for accurately placing wells to take advantage of existing fracture patterns and for artificially inducing fracture patterns during well completion through hydraulic stimulation.[227][266]

The stresses operating on a rock formation are described by a triaxial coordinate system that consists of two principal horizontal stresses, σx and σy, and a vertical stress component, σz, which is the overburden. In a borehole, these downhole stresses are expressed as radial components at the borehole wall: the vertical component, σz, the radial component, σr, and the tangential component, σθ, and the (azimuthal) shear component, σ.

Unbalanced-formation-stress components produce distortion around the borehole (stress-induced anisotropy) that results in shear-wave splitting. The azimuth of the fast-shear wave parallels the direction of maximum horizontal stress and the azimuth of the slow-shear wave parallels the direction of the minimum horizontal stress. Hydraulic-fracture azimuth is parallel to the direction of maximum horizontal stress.[267]

Hydraulic well stimulation consists of perforating an interval, then packing and pressuring these perforations to create fractures behind casing to allow increased production. Crossed-dipole anisotropy logging can estimate the vertical extent of the formation-stress fracture along the borehole and its azimuth in the formation (Fig. 3C.40).[34][238][239][240][257][268][269][270][271][272][273]

Attenuation Analysis

Acoustic-wave attenuation correlates with a variety of petrophysical parameters, including formation lithology and pore-fluid permeability, the degree of fluid saturation, and fractures type.[274][275][276][277] A recent study suggests that the combination of compressional- and shear-wave attenuation logs may provide a potential formation-evaluation tool (Figs. 3C.41 and 3C.42).[277]

Stonely-Wave Analysis

Permeability. Stoneley-wave velocity and attenuation are sensitive to formation and fracture permeability, particularly at low frequencies.[3][278][279][280] Stoneley-wave velocity decreases, and its attenuation increases, as permeability increases. Initial efforts (begun in the 1970s) to derive permeability information from Stoneley data were unsuccessful because neither the necessary low-frequency tools nor the appropriate processing methods had been developed. The parallel development of modern multipole array tools and sophisticated semblance- and inversion-processing methods enable computation of continuous profiles of formation permeability from monopole Stoneley-wave data.[281][282][283] Typically, these methods first model the nonpermeability effects using the elastic-wave theory and then relate differences between the modeled and the measured data to formation permeability. One approach to Stoneley-wave processing is comprised of three parts[283][284]: slowness analysis, reflectance mapping, and permeability estimation (Fig. 3C.43).

Stoneley-wave data are typically presented as an interval transit time, Δtt and as a ratio of the amplitudes for the two receivers used. Both traces have been shown to correlate well with permeability changes and compare well with core data, when it is available. Stoneley-wave amplitude can be computed and used in conjunction with the slowness and the signatures to analyze dispersion and attenuation characteristics. Use of the attenuation (center-frequency shift) and dispersion (travel-time delay) provide good permeability indication and better quality control for permeability estimation.

Wave-separation processing minimizes the effects of nonpermeability-related influences (e.g., road noise and borehole scattering) and yields reflectance logs for the direct and reflected Stoneley-wave data. The center-frequency log for the reflected wave data characterizes the Stoneley-wave attenuation and can be used to indicate fractures, vugs, and bed boundaries. The center-frequency log for the direct (transmitted) data is used to estimate formation permeability. Knowledge of the formation-fluid properties (viscosity and compressibility from core or NMR) enables quantitative estimates. Without this information log-derived permeability estimates are only qualitative.

These models require sophisticated computer processing. A simplified, field-oriented technique based on Stoneley amplitude[285] has so far provided good results in ideal conditions and when calibrated to core or NMR data.

Stoneley-derived formation permeability compares well with estimates obtained by nonacoustic methods, including core analysis and NMR logs (Fig. 3C.44).[286][287] Additional improvement in permeability estimation is possible when anisotropy information is incorporated in the process.[288] Formation evaluation is further enhanced when these diverse measurements are integrated through joint interpretation.[289] As indicated by the plots in Fig. 3C.44, calibration of log responses to core data would improve log-predicted values in noncored intervals.

The Stoneley wave measures total permeability and NMR measures vuggy permeability. A comparison of these two measurements in carbonate formations makes it possible to evaluate the permeability contributions arising from fractures and vugs.[289] A combination of these two measurements calibrated using wireline formation-tester data enables improved permeability estimation in these reservoirs.[290]

Gas Detection. Stoneley-wave properties, used in combination with other data, facilitate identification of gas-bearing intervals. A gas-saturated formation interval has drastically different fluid mobility and compressibility compared to those of the surrounding formations. In the presence of gas, Stoneley-derived permeability is overestimated because of increased pore-fluid mobility (decreased viscosity) and compressibility, and NMR permeability may be underestimated because of a decreased hydrogen index. If first calibrated in a nongas-bearing interval, separation of the two permeability curves indicates the presence of gas (Fig. 3C.45).[289] The plot also shows the neutron-density crossplot is effective in detecting the gas zone and may be more sensitive in some intervals.

The significant contrast in fluid mobility and compressibility in a gas zone also generates a measurable Stoneley-wave reflection. The presence of these reflections, together with an increase in compressional slowness or a decrease in the Vp/Vs ratio, identifies a gas-bearing zone (Fig. 3C.46).[291] This type of joint interpretation is particularly effective in thin-bed evaluation.

Fracture Evaluation. The pressure-driven, fluid-borne nature of Stoneley waves makes them sensitive to fluid movement, and thus, to open fractures. The effects of open fractures on Stoneley waves are amplitude reduction, an increase in Stoneley slowness, the occurrence of mode conversion, and the occurrence of Stoneley reflections.[163][292][293]

The Stoneley wave responds to fracture permeability while NMR does not, thus, the Stoneley-wave permeability is greater in the presence of fractures than NMR permeability. The combined use of Stoneley- and NMR-derived permeability provides a fracture indicator in both sandstones (Fig. 3C.47) and carbonates (Fig. 3C.48).[289]


This chapter has summarized the characteristics and capabilities of acoustic-logging tools. Although determination of geophysical (seismic) and petrophysical (porosity) properties have traditionally been the most widely used applications for acoustic-log data, new and advanced applications in geomechanics (anisotropy, fracture, and stress evaluation) and petrophysics (permeability) have been made possible by the multiarray tools and inversion processing methods now available. Interpretation methods that combine acoustic data with core and other log data, such as resistivity, nuclear, NMR, and borehole images, facilitate determination of fluid saturation and typing when logging conditions provide reliable data. For all applications of acoustic logging careful planning is critical to ensure successful acquisition of the desired data.


a = Archie parameter
C = shale compaction coefficient
Cp = compaction correction factor
E = Young’s modulus
K = bulk modulus
m = Archie parameter
R = resistivity, ohm-m
R1 = receiver one in a two-receiver tool configuration
R2 = receiver two in a two-receiver tool configuration
Sw = water saturation, fraction
t = travel time
t1 = travel time between T2 and R1
t2 = travel time between T2 and R2
t3 = travel time between T1 and R1
t4 = travel time between T1 and R2
T = transmitter
TR = transmitter-to-receiver spacing (ft)
T1 = transmitter one in a two-transmitter tool (BHC) configuration
T2 = transmitter two in a two-transmitter tool (BHC) configuration
v = velocity of the formation
V = velocity, ft/sec
x = distance between R1 and R2
X12 = distance between R1 and R2
α = porosity correction factor
Δt = transit time, sec
Δtc = compressional travel time
ϕ = fractional porosity of rock
θ = angle, degrees
ρ = formation density, lbm/ft3
μ = shear modulus
σ = Poisson’s ratio
σr = borehole radial stress
σx = principal horizontal stress x-direction
σy = principal horizontal stress y-direction
σz = principal vertical stress z-direction
σθ = borehole tangential stress


c = compressional wave
= critical
f = fluid
ma = rock matric
p = compressional wave
s = shear wave
sh = shale
w = water


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SI Metric Conversion Factors

dB/ft × 3.048* E − 01 = dB/m
ft × 3.048* E − 01 = m
ft/sec × 3.048* E − 01 = m/sec
in. × 2.54* E + 00 = cm
psi/ft × 2.262 059 E + 01 = kPa/m
μsec/ft × 3.280 840 E + 00 = μsec/m


Conversion factor is exact.