Patent Description:
Production of hydrocarbons involves forming one or more wells in a subterranean formation. Generally, in connection with formation of a well, a wellbore is drilled and a casing is passed down the wellbore. The casing often includes sections with differing diameters, eccentricities, and/or bonding with surrounding material. In some regions, there may be concentric casing. In many instances, a casing or outer casing forms an annular space with surrounding rock. The annular space is commonly filled with cement or a similar material over at least part of its length when the well is created. Production tubing is passed through the casing, and the hydrocarbons are produced through the production tubing. In this context, the casing supports the wellbore and prevents collapse of the well.

Wellbores may be plugged and abandoned at the end of the wellbore useful life to prevent environmental contamination, among other benefits. At the end of the useful life, a wellbore commonly includes cemented casing with the production tube passed down the casing. In connection with plug and abandon, an effective seal is created across a full diameter of the wellbore. Conventionally, production tubing is removed and casing is milled away, along with cement exterior to the casing, before setting a continuous new cement plug across the full diameter of the wellbore, from rock to rock. Alternatively, the casing can be left in place, provided that the quality of original cement and cement bond to the exterior of the casing are confirmed. If the cement and cement bond to the exterior of the casing is adequate, a new cement plug can be set inside the casing, thereby effectively creating a barrier across the full diameter of the wellbore.

Thousands of meters of production tubing are typically removed to identify isolation corresponding to regions of cement having seal integrity suitable for plug and abandon. Stated differently, identifying one or more locations of isolation provided by exterior cement during plug and abandon activities conventionally involves removal of internal completion to permit logging tools free access to casings. Through-tubing plug and abandonment may theoretically be performed without removing the production tubing, saving considerable expense. The tubing may simply be cut or perforated and cement passed down the tubing and back up the annulus between tubing and casing to form a plug across the full casing diameter. However, this would involve assessment of the cement bond with casing from a location within the production tubing, and conventional techniques are unable to detect an integrity of a cement bond with a casing through the production tubing, casing, and any material, such as water, air, and/or gas. Isolation detection is thus time and resource extensive. It is with these observations in mind, among others, that various aspects of the present disclosure were conceived and developed.

<CIT> discloses a method and downhole tool that uses beamforming to localize acoustic energy at a desired zone-of-interest within a wellbore traversing a subterranean formation.

<CIT> discloses a downhole tool for operation with a wellbore and including a transmitter array and first and second receiver arrays, the transmitter array including a plurality of transmitters azimuthally distributed around a longitudinal axis of the downhole tool at a first axial location of the downhole tool.

Implementations described and claimed herein address the foregoing problems by providing a computer-implemented method for isolation detection in a wellbore according to appended claims <NUM> to <NUM> and one or more tangible non-transitory computer-readable storage media according to appended claim <NUM>.

Further, while multiple implementations are disclosed, still other implementations of the presently disclosed technology will become apparent to those skilled in the art from the following detailed description, which shows and describes illustrative implementations of the presently disclosed technology. As will be realized, the presently disclosed technology is capable of modifications in various aspects, all without departing from the scope of the claims. Accordingly, the drawings and detailed description are to be regarded as illustrative in nature and not limiting, the invention being solely defined by the appended claims <NUM>-<NUM>.

Described herein are systems and methods for analyzing a structure, such as a cylindrical structure and/or a subterranean structure, using acoustic waves. An acoustic logging tool having one or more acoustic sensors is deployed in a production tube to detect cement integrity around a casing in a downhole environment of a wellbore. The one or more acoustic sensors include a radial sensor. The radial sensor located inside the production tube generates a forward Rayleigh wave traveling around an outer surface of the casing. The wave is reflected from any asymmetries, such as in cement surrounding the casing and/or in the cement bonding with the casing. For example, an air gap adjacent the casing may reflect the wave. By analyzing spectral information from the forward and reflected waves, isolation region(s) may be identified. The isolation region(s) correspond to regions in the wellbore where bonded cement is free from anomalies and suitable for plug and abandon. Accordingly, the radial sensor provides isolation detection through both the production tube and the casing, without removal of internal completion, thereby reducing the time and resources expended for plug and abandon operations, among other advantages.

In the description, phraseology and terminology are employed for the purpose of description and should not be regarded as limiting. For example, the use of a singular term, such as "a", is not intended as limiting of the number of items. Also, the use of relational terms are used in the description for clarity in specific reference to the figure and are not intended to limit the scope of the appended claims.

To begin a detailed discussion of an example isolation detection system for characterizing a subterranean structure, reference is made to <FIG>. In one implementation, an acoustic logging tool <NUM> including one or more acoustic sensors is deployed into the subterranean structure. Examples of the various systems and methods described herein reference the subterranean structure including a production tube and casing in connection with isolation detection for plug and abandon operations. However, it will be appreciated by those skilled in the art that the presently disclosed technology is applicable to various types of structures, systems, and operations, including outside the oil and gas context. For example, the acoustic logging tool <NUM> may be used to determine a condition of pipes in connection with pigging operations in the oil and gas industry, the water industry, and/or the like. As another example, the acoustic logging tool <NUM> may be used in oil and gas applications to inspect structures deployed outside of downhole environments. Additionally, the acoustic logging tool <NUM> may be used to inspect fabricated pipes, storage tanks, and/or cylindrical structures to determine an integrity of structure containment and/or identify materials and connections outside and/or inside the structures.

As can be understood from <FIG>, in one implementation, the acoustic logging tool <NUM> includes a radial sensor <NUM>, an axial sensor <NUM>, and one or more centralizers <NUM>. The centralizers <NUM> may be positioned above and below the acoustic sensors <NUM>-<NUM> to maintain the acoustic logging tool <NUM> in a centralized coaxial position inside a length of production tubing, which is vertically oriented and located coaxially within a length of casing. The casing or an outer casing forms an annular space with a surrounding subterranean formation of a well. The annular space may be filled with cement or a similar material over at least part of its length when the well is created, and upon filling, the cement is intended to bond with the casing or outer casing to provide a seal.

In one implementation, the radial sensor <NUM> and the axial sensor <NUM> are independent sensors operating in orthogonal directions. The radial sensor <NUM> confirms a presence of radial symmetry in an isolation region, and the axial sensor <NUM> confirms a presence of axial symmetry in the isolation region. The axial sensor <NUM> scans in an axial direction along a length of the production tube, while the radial sensor <NUM> scans in a radial direction that is orthogonal to a general axis of the length of the production tube. As such, the axial sensor <NUM> detects changes in waves traveling along the casing reflected from anomalies in the materials beyond the casing, as well as changes in the production tube and casing collars, while the radial sensor <NUM> detects changes in waves travelling around the casing reflected from anomalies in the materials beyond the casing. Thus, referring to <FIG>, an axial log <NUM> is captured using the axial sensor <NUM> and a radial log <NUM> is captured using the radial sensor <NUM>. In some implementations, each of the radial sensor <NUM> and the axial sensor <NUM> may capture both the axial log <NUM> and the radial log <NUM>. The acoustic sensors <NUM>-<NUM>, alone or together, provide an approximate measure of acoustic impedance <NUM> of the material surrounding the casing, which may be used in cement classification. Combining the axial log <NUM>, the radial log <NUM>, and the acoustic impedance <NUM>, a characterization of isolation <NUM> may be generated. As shown in the characterization of isolation <NUM>, isolation occurs when the axial log <NUM> includes an axial symmetry, the radial log <NUM> includes a radial symmetry, and the acoustic impedance <NUM> is high.

Generally, the axial sensor <NUM> senses short, thick features or anomalies on the casing, while the radial sensor <NUM> senses long, thin features or anomalies on the casing. The axial sensor <NUM> and the radial sensor <NUM>, alone or in combination, may be used to determine whether material in contact with the casing is cement or another material. Stated differently, both the radial sensor <NUM> and the axial sensor <NUM> may detect axial symmetry and radial symmetry and classify a material in contact with the casing in terms acoustic impedance.

In one implementation, the acoustic logging tool <NUM> is deployed along the length of the production tube as the radial sensor <NUM> and/or the axial sensor <NUM> scans. Using the axial log <NUM> acquired from the scans, a determination may be made regarding whether there is axial symmetry, such that the material in contact with the casing is homogeneous. Similarly, using the radial log <NUM> acquired from the scans, a determination may be made regarding whether there is radial symmetry, such that the material in contact with the casing is homogeneous in a radial plane. Thus, based on the axial symmetry and/or the radial symmetry, there is confirmation that for the length of travel of the acoustic logging tool <NUM> along the production tube during the scan, the material in contact with the casing is axially and/or radially the same. Accordingly, the material is free from anomalies, whether short and thick or long and thin, and isolation is present. In other words, the acoustic logging tool <NUM> senses whether the material surrounding the casing is bonded with the casing around an entirety of the casing. Additionally, the acoustic logging tool <NUM> may be used to identify the material surrounding the casing. For example, the material may be cement, a fluid, a gas, and/or the like.

In some instances, reliance on the axial log <NUM> alone may result in a false isolation determination. For example, a channel in the material around the casing may be axially symmetrical. In this case, the axial log <NUM> suggests that the material surrounding the casing is axially symmetric and thus, isolation is present, but there would not be isolation in this case due to the presence of the channel. On the other hand, as the radial sensor <NUM> detects anomalies in the radial direction, the radial log <NUM> would identify radial asymmetries due to the presence of the channel. Therefore, the radial sensor <NUM> may be used to supplement or in place of the axial sensor <NUM> to detect isolation with a higher level of confidence. Indeed, the radial sensor <NUM> in general is more sensitive than the axial sensor <NUM>.

In one example implementation, the acoustic logging tool <NUM> is deployed to evaluate isolation between the casing and subterranean formation, such as bedrock, around a hole from inside the production tube. The casing may be approximately nine to ten inches in diameter, with the hole being approximately sixteen inches and the production tubing being approximately four inches in diameter. The acoustic logging tool <NUM> provides <NUM>° of coverage sufficient to identify anomalies that are of approximately one inch of diameter or greater at the casing-cement/barrier interface. As described here, the acoustic logging tool <NUM> discriminates between a vertically continuous anomaly and a vertically discontinuous anomaly, as well as between different types of materials, such as liquid (gas, seawater, brine, water-based mud, oil-based mud, etc.) and solid (e.g., cement, creeping shale, salt, etc.). The acoustic logging tool <NUM> tolerates the casing and/or the production tube being non-concentric, such that isolation detection may be provided despite the presence of eccentricity. Additionally, the acoustic logging tool <NUM> is able to cope with variable tubing conditions, such as the presence of oil, scale, corrosion, and/or the like. In addition to the logging capabilities of the acoustic logging tool <NUM>, the physical features provide that the acoustic logging tool <NUM> may be run on a wireline, fit through a small (e.g., <NUM> (<NUM> inch) diameter) restriction, and operate in an environment of approximately <NUM> MPa (<NUM>,<NUM> PSI) with a wellbore temperate of approximately <NUM> and in various inclinations due to mechanical deployment downhole.

As discussed above, the acoustic logging tool <NUM> tolerates eccentricity using the radial sensor <NUM>. Downhole, the production tube is often eccentric with the casing. The radial log <NUM> may be sensitive to the production tube eccentricity. For example, production tube eccentricity may be detected by convolution, which obtains data from a particular point and generates a reverse dataset. The dataset from the particular point and the reverse dataset are multiplied together and summed to generate a value. The multiplication and summation of the two datasets is repeated by sliding the data and plotting the numbers through shifting, multiplying, and integration to extract axes of symmetry. Accordingly, the radial sensor <NUM> is capable of detecting isolation, even in the presence of eccentricity.

Turning to <FIG>, the radial sensor <NUM> is shown deployed in a downhole environment <NUM>. As shown in <FIG>, in one implementation, a controller <NUM> obtains data from the radial sensor <NUM> in the downhole environment <NUM>. The radial sensor <NUM> may record signals using a recorder integrated with the acoustic logging tool <NUM> and/or transmit the signals up wires for recording at the surface. Once the data is recorded, the controller <NUM> obtains the data for processing.

In one implementation, the radial sensor <NUM> includes a body, which may be cylindrical in shape and made from electrically insulating material with staves arranged on an outer surface of the body. The radial sensor <NUM> may be maintained in a centralized, coaxial position inside a length of a production tube <NUM> using one or more spacers <NUM>, which may be the centralizers <NUM>. The spacers <NUM> may be made from electrically insulating material and disposed at a proximal end and a distal end of the radial sensor <NUM>. The production tube <NUM> may be made from steel or a similar metal and is vertically oriented and disposed coaxially within a length of casing <NUM>. The casing <NUM> may similarly made from steel and/or the like. Between the casing <NUM> and the production tube <NUM> is an annular gap <NUM>, which may be filled with water. Surrounding the casing <NUM> is a layer of cement <NUM>, which is further surrounded by a subterranean formation <NUM>. The subterranean formation <NUM> may include various types of rocks disposed about the wellbore. In some cases, an anomaly <NUM> may be present in the cement <NUM>, such that there is no isolation at the region including the anomaly <NUM>.

The radial sensor <NUM> is movable axially within the production tube <NUM>. In one implementation, the radial sensor <NUM> is connected at the distal end to a shaft <NUM> that is engaged to an advancing system <NUM> having a motor to advance and retract the radial sensor <NUM> downhole. It will be appreciated, however, that the radial sensor <NUM> may be translated along a length of the production tube <NUM> in various manners.

As described in more detail herein, the controller <NUM> obtains data captured using the acoustic logging tool <NUM>, including the radial sensor <NUM>, and processes the recorded data. The radial sensor <NUM> transmits waves at a known angular velocity and captures the waves at the same angular velocity. The radial sensor <NUM> may record the captured signal or transmit the signal to a computing device, such as the controller <NUM>, at the surface for recording. In either case, the controller <NUM> may obtain the recorded data that is captured using the radial sensor <NUM> directly or indirectly. The recorded data may be communicated to the controller <NUM> from the radial sensor <NUM> or via another computing device and/or data storage device using a wireless connection (e.g., for communication over a network) or a wired connection (e.g., wired connection <NUM>).

In some implementations, the controller <NUM> or another computing device may include a display <NUM>, at least one power source <NUM>, at least one processor <NUM>, a signal generator <NUM>, controls <NUM>, and/or the like for controlling the radial sensor <NUM>, recording signal data, displaying signal data, and/or processing the signal data as described herein. The controller <NUM> may be present on-site or remote from the downhole environment <NUM>. It will further be appreciated that the same or separate computing devices may be used to control the radial sensor <NUM> in connection with capturing and recording signals and to process the captured signals. The example implementations described herein will reference the controller <NUM> in connection with processing the recorded signals. However, this reference is for discussion purposes only and is not intended to be limiting.

Referring to <FIG>, the radial sensor <NUM> may be mounted to a bar <NUM> (e.g., a made from ploy(methyl methacrylate, acrylic, acrylic glass, etc.) using a coupling <NUM> and disposed between the centralizers <NUM> and translated within the production tube <NUM>. Generally, the radial sensor <NUM> is sensitive to waves traveling around the production tube <NUM> and the casing <NUM> but not to waves traveling axially along the lengths of the production tube <NUM> and the casing <NUM>. The radial sensor <NUM> includes a plurality of staves <NUM> disposed about the body of the radial sensor <NUM>. The example implementations discussed herein reference the staves <NUM> including sixteen staves. However, it will be appreciated that any number of the staves <NUM> may be used for spatial sampling depending on a size of the radial sensor <NUM>, the production tube <NUM>, the casing <NUM>, and/or the like.

In one implementation, the radial sensor <NUM> includes a plurality of plates <NUM> arranged on a backing <NUM>. The backing <NUM> may be made from a high-impedance material, such as an epoxy-tungsten mix. Each of the plates <NUM> is a sensitive plate configured to transmit and receive signals. While separate plates may be used for transmitting and receiving, utilizing the plates <NUM> for both transmitting and receiving reduces an overall size of the radial sensor <NUM>, thereby conserving resources and increasing mobility while maintaining sensitivity. As can be understood from <FIG>, each of the staves <NUM> extends along a longitudinal line formed by a plurality of the plates <NUM> (e.g., ten plates) wired in parallel and operating at frequencies well below resonance. The plates <NUM> taper in size longitudinally along a length of the radial sensor <NUM>, such that the plates <NUM> are longer in a middle of the radial sensor <NUM> and shorter at ends of the radial sensor <NUM>. This tapering configuration of the plates <NUM> forms a truncated hanning window to minimize longitudinal sensitivity of the radial sensor <NUM>. Stated differently, the tapering configuration provides that the radial sensor <NUM> is sensitive to waves traveling around the production tube <NUM> and the casing <NUM> but not to waves traveling axially along the lengths of the production tube <NUM> and the casing <NUM>. Dimensions of the plates <NUM> may vary based on the hanning window or other weighting function utilized to form the tapering configuration. For example, each of the plates <NUM> may be approximately <NUM> thick, <NUM> wide, and include a spacing <NUM> from a center of one plate to another plate of approximately <NUM>. The radial sensor <NUM> may have a width <NUM> of approximately <NUM>, a length <NUM> of approximately <NUM>, and the bar <NUM> may be approximately <NUM> wide in this example.

Each of the staves <NUM> acts as both a transmitter and receiver. In one implementation, the radial sensor <NUM> transmits on one of the staves <NUM> at a time, while receiving each time at all the staves <NUM>. Stated differently, a first stave of the staves <NUM> is pinged and transmits a first signal, which is recorded on each of the staves <NUM>. Then a second stave of the staves <NUM> is pinged and transmits a second signal, which is recorded on each of the staves <NUM>. Each of the staves <NUM> transmits in turn while all the staves <NUM> record.

In one implementation, with each of the staves <NUM> both transmitting and receiving, the radial sensor <NUM> includes transmit and receive switches on a chip for each of the staves <NUM>. The switches may be linear analogue switches configured to generate chirp pulses. While high-voltage switches may be used, such switches generate square waves, which may excite the plates <NUM> at their resonant frequency, thereby involving high-speed sampling and additional dynamic range. The linear analogue switches provide close control of amplitude and bandwidth in the chirp pulses. In one implementation, a pair of linear analogue switches are utilized. During transmission, both the first and second switches are closed, such that the inhibit lines go low and current flows through the first switch to the plates <NUM> and a capacitor which are arranged in parallel. No voltage appears at an amplifier input because it is shorted to ground via the second switch. After transmission, both the first and second switches are open, such that inhibit goes high and received signals from the plates <NUM> flow through the capacitor, which is now in series, to the amplifier input. Address lines on each of the chips facilitate selection of a transmission channel for each of the staves <NUM> with only one of the staves <NUM> acting as a transmitter at a time and each of the staves <NUM> acting as a receiver each time. The receive amplifier has a gain of approximately +30dB.

As described above, the linear analogue switches of the staves <NUM> transmit a chirp pulse or other waveform covering a wide bandwidth. The transmitted waveform of the chirp pulse may be approximately <NUM> from approximately <NUM> to <NUM>. In one implementation, the chirp has a slightly asymmetrical envelope providing zero DC offset to ensure that the plates <NUM> and the parallel capacitor have no charge after transmission, thereby avoiding a transient with the switches are open. The chirp may have an amplitude of approximately +/-8V or other voltage for overcoming any frictional noise generated by the centralizers <NUM> as the radial sensor <NUM> is translated within the production tube <NUM> with continuous movement.

Referring to <FIG>, an example radial endfire sensing configuration is illustrated. In one implementation, the staves <NUM> are disposed about an axis of the radial sensor <NUM> with equidistant spacing. For example, the staves <NUM> may each be space from each other by an angle <NUM>. When a wave is transmitted by one of the staves <NUM>, the wave travels around the casing <NUM> in a first direction (e.g., clockwise). When the anomaly <NUM>, such as a channel, is not present in the cement <NUM>, the wave will continue to travel around the casing <NUM> without interruption. When the anomaly <NUM> is present, the anomaly <NUM> reflects the wave in a second direction, such as counterclockwise. Accordingly, as described in more detail herein, the radial sensor <NUM> identifies the anomaly <NUM> based on the reflected wave.

As will be understood by those skilled in the art and described in more detail herein, waves are not transmitted or received directly. Instead, the waves are reconstructed from data recorded from the signals received by the staves <NUM>. As illustrated in <FIG>, recorded waves <NUM> are obtained from signals captured by the staves <NUM>. The recorded waves <NUM> are traveling in both the first direction and the second direction. In the example of <FIG>, the first direction is clockwise and the second direction is counterclockwise. Because the recorded waves <NUM> are traveling in both directions, the recorded waves <NUM> are separated into counterclockwise waves <NUM> and clockwise waves <NUM>. The counterclockwise waves <NUM> are shifted into shifted counterclockwise waves <NUM>, and the clockwise waves <NUM> are shifted into shifted clockwise waves <NUM>. The counterclockwise waves <NUM> and the clockwise waves <NUM> are shifted based on the angle <NUM>. For example, the angle <NUM> may be defined as θ, and the waves are shifted in angle: <NUM>, - θ, -2θ, etc., such that multiplication in the frequency domain is by ei<NUM>, eikθ, e<NUM>ikθ, etc. The shifted counterclockwise waves <NUM> are added to together to form reflected waves <NUM>, and the shifted clockwise waves <NUM> are added together to form forward waves <NUM>. As described in more detail herein, the reflected waves <NUM> may be used to detect the anomaly <NUM>. As will be appreciated, a time delay method and/or a reconstruction method may be utilized in connection with radial sensing.

To begin a detailed discussion of a time delay method for radial sensing, reference is made to <FIG>, which illustrate a representation <NUM> of radial sensing in the absence of a target. <FIG> shows a representation of a timing sequence of part of a transmit and receive sequence. In one implementation, a forward wave <NUM> is transmitted with time delays to define an angular velocity. More particularly, a pulse, such as a chirp pulse is emitted from each stave <NUM> and received by all of the staves <NUM>. Stated differently, the staves <NUM> each capture signals from the transmitted pulse as it propagates around the casing <NUM>. After a receiving time period during which the staves <NUM> capture signals from the transmitted pulse following transmission, another of the staves <NUM> is excited, followed by the receiving time period until each of the staves <NUM> has transmitted.

In one implementation, the forward wave <NUM> is created by sequentially firing pulses from the staves <NUM> with a controlled time interval between pulses, controlled frequency of the pulses, and/or a controlled phase of the pulses. By firing the staves <NUM> sequentially, the forward wave <NUM> is built up, traveling radially and consistent with the firing sequence. Thus, the forward wave <NUM> may be formed by adding the pulses together, even if each of the staves <NUM> is omnidirectional. Once the forward wave <NUM> is formed, the staves <NUM> are switched to receive energy and sense the forward wave <NUM> as it interacts with structures surrounding the casing <NUM>, such as the cement <NUM>. The forward wave <NUM> may propagate in a counterclockwise direction as illustrated in <FIG>. On the other hand, the forward wave <NUM> may be formed by firing one of the staves <NUM>, listening on all of the staves <NUM>, firing another of the staves <NUM> and listening again of all of the staves <NUM>, and so on until each of the staves <NUM> has transmitted. During processing the captured signals are added together as described herein. In either case, during processing the received signals are shifted in time to remove the time interval <NUM> between the transmitted pulses. The forward wave <NUM> may be sensed at one or more axial positions along the production tube <NUM> as the radial sensor <NUM> is moved.

The received signals may be filtered to provide the same time delays. For illustration purposes, traces from five of the staves <NUM> are shown with time on a horizontal axis and signal on a vertical axis for each trace. As shown, the traces are arranged on the same time axis and displaced from each other on the vertical axis to highlight the relative timing of the pulses <NUM>. The uniform time interval between transmission of the pulses <NUM> means that the pulses are arranged on a notional line with a positive gradient. The radial sensor <NUM> provides a dispersive system in which the velocity of acoustic waves change depending on its frequency. Transmission of the pulses <NUM> comprising multiple frequencies results in the forward wave <NUM>, whose frequency components are separated in time.

Accordingly, the forward wave <NUM> has an overall pattern that is generally the same for each of the staves <NUM> in the absence of asymmetry due to the presence of any anomalies. The overall pattern of the forward wave <NUM> is offset by the same time intervals between the staves <NUM> as the transmitted pulses <NUM>. Thus, the received signals may be filtered to provide the same time delays. Distinctive peaks in the traces (e.g., peaks <NUM>, <NUM>, and <NUM>) are thus arranged on notational lines having approximately the same positive gradient as the pulses <NUM>. The forward signals including the peaks <NUM>, <NUM>, and <NUM> may be combined together and converted from the time domain to the frequency domain to provide a forward spectrum, as illustrated in a plot <NUM> shown in <FIG>. The signals may be converted from the time domain to the frequency domain using a Fourier transform or similar transform.

In other words, the forward wave <NUM> has a spectrum of frequencies retumed at different times. The pulses <NUM> are transmitted to generate Rayleigh waves traveling around the casing <NUM>. As described in more detail herein, the Rayleigh waves may be formed when the forward wave <NUM> has a wavenumber distributed around the circumference of the radial sensor <NUM> for a frequency at a center of a range of interest. For example, the wavenumbers may be <NUM>, <NUM>, <NUM>, or <NUM>. The received signals from the forward wave <NUM> at each stave <NUM> over a period of time are processed to remove the time interval and summed and transformed into the forward spectrum. As shown in the example plot <NUM>, certain frequencies in the forward wave <NUM> may be strong with a relatively large amplitude, for example approximately <NUM>-<NUM>, <NUM>-<NUM>, etc..

Turning to <FIG>, an asymmetric feature <NUM> is present outside the casing <NUM>, which may be the anomaly <NUM>. The forward wave <NUM> interacts with the asymmetric feature <NUM> to create a reflected wave <NUM>. The reflected wave <NUM> travels in a direction opposite to the forward wave <NUM>. In the example shown in <FIG>, the reflected wave <NUM> travels in the clockwise direction. Accordingly, the reflected wave <NUM> is received by the staves <NUM> in a reverse order from the forward wave <NUM>. Thus, signals from the reflected wave <NUM> is superimposed in the traces. Distinctive peaks (e.g., peaks <NUM>, <NUM>, and <NUM>) corresponding to the reflected wave <NUM> are disposed on notational lines with a negative gradient. As such, the forward wave <NUM> may be distinguished from the reflected wave <NUM>. The reflected signals including the peaks <NUM>, <NUM>, and <NUM> may be combined together and converted from the time domain to the frequency domain to provide a reflected spectrum, as illustrated in a plot <NUM> shown in <FIG>. The signals may be converted from the time domain to the frequency domain using a Fourier transform or similar transform.

<FIG> illustrates a comparison of an effect of eccentricity on the forward and reflected spectra. Results for an eccentric configuration <NUM> of the production tube <NUM> within the casing <NUM> is compared with results for a concentric configuration <NUM> of the production tube <NUM> within the casing <NUM>. The results for each of the configurations includes plots of the forward spectrum, as well as plots of the reflected spectrum where the asymmetrical feature <NUM> is included (labeled as "Target") and not included (labeled as "No Target"). Each of the plots includes angular velocity on the vertical axis and frequency on the horizontal axis with amplitude being depicted on a color intensity scale.

It will be understood that the production tube <NUM> generally always provides some form of eccentricity within the casing <NUM>. For example, the production tube <NUM> may be resting against one side of an inner surface of the casing <NUM>, such as in an inclined well, or an axis of the production tube <NUM> may be at an angle relative to the casing <NUM>. This is particularly true since spacers are often not used to maintain the production tube <NUM> in the concentric configuration <NUM>, wells are rarely truly vertical, and/or the like. As shown in <FIG>, the transmitted pulses <NUM> of the forward wave <NUM> are chirps with a range of frequencies. The forward wave <NUM> is the result of interaction of the transmitted pulses <NUM> with material surrounding the casing <NUM> and includes a spectrum of frequencies at different amplitudes. Stronger amplitudes are shown by darker areas in red. In the example of <FIG>, the forward wave <NUM> has strong amplitude components at approximately <NUM>-<NUM> and at approximately <NUM> over a range of angular velocities. Thus, the forward spectrum for both configurations <NUM> and <NUM> contains many modes that propagate at different frequencies and angular velocities, which is characteristic of a dispersive system.

The reflected spectrum of the reflected wave <NUM> is shown for each of the configurations <NUM> and <NUM>. Where there is no target (no asymmetric features), the reflected wave <NUM> and thus the reflected spectrum is minimal (with only weak signals present, if any), as the forward wave <NUM> encounters no features that reflect the forward wave <NUM> sufficient to form the reflected wave <NUM>. Where the asymmetric feature <NUM> is present, the different acoustic impedance of the asymmetric feature <NUM> relative to the cement <NUM> forms the reflected wave <NUM> with different frequencies and amplitudes depending on the angular velocity of the forward wave <NUM> and the reflected wave <NUM>. In the example of <FIG>, only one mode reflects from the asymmetric feature <NUM>, with the mode having a large displacement on the surface of the casing <NUM>. This strong reflection is received at approximately <NUM>-<NUM> when the angular velocity is approximately <NUM> and <NUM> krad/s.

As can be understood from <FIG>, the forward spectrum for both the eccentric configuration <NUM> and the concentric configuration <NUM> are generally the same. Similarly, the reflected spectrum for both the configuration <NUM> and the concentric configuration <NUM> are generally the same when the asymmetrical feature <NUM> is present and not present. Accordingly, the radial sensor <NUM> may be used to detect the presence of the asymmetrical <NUM>, regardless of whether there is eccentricity of the production tube <NUM> relative to the casing <NUM>.

To begin detailed description of the reconstruction method, reference is made to <FIG>. Turning first to <FIG>, recorded waveforms from a single transmission of one of the staves <NUM> is shown. In one implementation, a data recorder, for example integrated with or in communication with the controller <NUM>, utilizes dedicated electronics to record the signals as raw data <NUM> at a wide bandwidth. For example, the data recorder may be set to <NUM>,<NUM> points at <NUM> per point (<NUM>/s). The raw data <NUM> may be compressed into compressed data <NUM> and saved. Every transmission produces a dataset containing receiving waveforms for each of the staves <NUM>. In the example described herein where there are sixteen of the staves <NUM>, each transmission would produce sixteen receiving waveforms. The raw data <NUM> may be saved, for example, at every fourth point giving <NUM> points at <NUM> sampling.

Each of the staves <NUM> may be numbered (e.g., <NUM>-<NUM>). In the example shown in <FIG>, Stave <NUM> was the transmitting stave. The raw data <NUM> shows the output of Stave <NUM>, as well as adjacent Stave <NUM>. During a first period (e.g., approximately <NUM>), Stave <NUM> approximates zero voltage due to the short to ground. As shown in the raw data <NUM>, voltage across the resistance, amplified by approximately +30dB, shows a chirp of approximately +/-4V. Stave <NUM> also shows a similar chirp due to electrical pickup from the transmitting voltage as a result of the wires having a close proximity. The raw data <NUM> may be four times oversampled to focus on frequencies up to approximately <NUM> as frequencies of interest. The oversampling of the raw data <NUM> improves signal-to-noise ratio. The raw data <NUM> is saved as the compressed data <NUM> for all of the staves <NUM> receiving the signal (e.g., Staves <NUM>-<NUM>). The colors shown in the compressed data <NUM> have a logarithmic scale and show decay to -40dB by approximately <NUM>. To generate the compressed data <NUM> from the raw data <NUM>, data corresponding to an initial time period (e.g., the initial <NUM>) was blanked to zero to remove the transmission pulse, and the waveforms were band-limited to the frequencies of interest (e.g., band-limited to <NUM>), and the waveforms were saved at every fourth point giving <NUM> points at <NUM> sampling.

Turning to <FIG>, the compressed data <NUM> is processed to obtain forward and reflected waves. As described herein, each of the staves <NUM> acts as a transmitter in transmitting a signal, and for each transmission by one of the staves <NUM>, all of the staves <NUM> record the signal. A single measurement by the radial sensor <NUM> consists of the data recorded for all of the transmissions by the staves <NUM>. For example, when one of the sixteen staves transmits, all sixteen staves record the transmission, and one measurement consists of sixteen transmissions, one on each stave. The single measurement is converted into a single result, as illustrated with <FIG>.

Generally, recorded waves are separated, shifted, and combined to obtain forward and reflected waves. Separation of the recorded waves in the compressed data <NUM> is illustrated in <FIG>. Separation of the waves is impractical in the time domain due to the radial sensor <NUM> creating a dispersive system with different frequencies traveling at different velocities. The radial sensor <NUM> includes the staves <NUM> arranged radially, such that the signal is traveling in both a first direction and a second direction, opposite the first direction, around the radial sensor <NUM> and that the signal completes itself arriving back at the transmission location. Accordingly, unlike the linear array, separation of the signals in the time domain is impractical.

In one implementation, the recorded waves in the compressed data <NUM> are converted to the frequency domain using a Fourier transform. Referring to <FIG>, the compressed data <NUM> as a single transmission in time and frequency for all of the staves <NUM> (e.g., transmission by one stave recorded on all sixteen staves). The single transmission of the compressed data <NUM> may be taken as an Nth transmission and is a function of time and angle, which may be described as m(t,θ,N). <FIG> illustrates separated waves <NUM> resulting from the Fourier transform of the compressed data <NUM>. The Fourier transform is a function of frequency and wavenumber, which may be described as M(f,k,N), as complex quantity of which only the amplitude is shown.

More particularly, the Fourier transform decomposes the compressed data <NUM> into its constituent frequencies. Stated differently, the Fourier transform of the compressed data <NUM>, which is a function of time, is a complex-valued function of frequency that provides wavenumbers corresponding to how many waves fit around the casing <NUM>. For example, in the implementation having sixteen of the staves <NUM>, there may be sixteen wavenumbers, with wavenumbers <NUM> to <NUM> propagating in a clockwise direction and wavenumbers -<NUM> to -<NUM> propagating in a counterclockwise direction. For wavenumber <NUM>, each wave has four wavelengths around the casing <NUM> with different signal strengths. In the example shown in <FIG>, a strong wave at approximately <NUM> had four wavelengths around the casing <NUM>, but at <NUM>, a wave is not present because there is not a mode of propagation that would provide four wavelengths around the casing <NUM> at a frequency of <NUM>. Angular velocity is a ratio of the wavenumber to the frequency, which is illustrated in color. The red color demonstrates that there is primarily one angular velocity of the wave but the other colors show that there are other velocities at which the wave will propagate a well. Thus, the Fourier transform of the compressed data <NUM> from the time domain to the frequency domain separates the waves into the separated waves <NUM>. The separated waves <NUM> include clockwise waves and counterclockwise waves. The clockwise waves and the counterclockwise waves each appear twice in the separated waves <NUM> as complex conjugates.

Turning to <FIG>, the clockwise waves and the counterclockwise waves of the separated waves <NUM> are shifted in opposite directions to generate shifted waves. The shift function <NUM> may be defined as S(f,k). The sections of the shift function <NUM> correspond to the clockwise waves and counterclockwise waves, as well as their complex conjugates. The counterclockwise waves are shifted -<NUM> and the clockwise waves are shifted +<NUM>. Stated differently, the clockwise waves are forward shifted and the counterclockwise waves are backshifted.

In the example with sixteen staves, the wavenumber k ranges from -<NUM> to +<NUM> and the angular step size in radians between the staves is <MAT>. To find the angular rotation α for each point the complex plane, S is multiplied by the wavenumber k, the angular step size θ, and a number of steps corresponding to the transmission number N. The angular rotation may thus be given by: <MAT>.

The shift is given by multiplying the transmission by eiα: <MAT>.

This provides the result for the Nth transmission. The result contains shifted versions of both the clockwise and counterclockwise waves, with the amplitude having the same relationship and the phases changing with the shift. The calculation is repeated for all the transmissions for each of the staves <NUM> (e.g., all sixteen transmissions) and the results are added: <MAT>.

By adding the shifted counterclockwise waves together, a reflected wave is formed, and the shifted clockwise waves are added together to form a forward wave. The results <NUM> for a region of interest are illustrated in <FIG>. In one implementation, the region of interest may be limited to the positive frequencies of the forward and reflected waves and their amplitudes. Stated differently, the waves having negative frequencies are complex conjugates of the waves having positive frequencies, the complex conjugates may be discarded, with the region of interest focusing on the positive frequencies of the forward and reflected waves and their amplitudes. For clarity, the region of interest of the results <NUM> may be shifted vertically such that the zero wavenumber appears in the middle with the forward waves located at the top and the reflected waves at the bottom of the results <NUM>.

As shown in <FIG>, generally the compressed data <NUM> for each of the staves <NUM> is converted from the time domain to the frequency domain, shifted, and combined into the result <NUM>. Each horizontal line corresponds to a spectrum, and reading from zero wavenumber, the forward spectra are F1 to F7 and the reflected spectra are R1 to R7. The horizontal lines of <NUM> and <NUM> do not have a direction. As described herein, the wavenumbers are integers corresponding to a number of wavelengths fitting around the production tube <NUM> and/or the casing <NUM>. For example, R2 has long waves with just two fitting around the production tube <NUM> and/or the casing <NUM>, and R6 has shorter waves with six fitting around.

Referring to <FIG>, an analysis of eccentricity and orientation of the production tube <NUM> inside the casing <NUM> is provided. Turning first to <FIG>, modeling <NUM> provides an analysis <NUM> of the production tube <NUM>, and analysis <NUM> of the casing <NUM>, and an analysis <NUM> of the production tube <NUM> within the casing <NUM> are provided for comparison of wave propagation. For each analysis <NUM>-<NUM>, forward waves obtained as described with respect to <FIG>, with the results including the amplitudes of the forward waves. The configurations associated with the analyses <NUM>-<NUM> do not include any asymmetrical features, such that there is no reflected wave.

With respect to the analysis <NUM>, the results include a bright red diagonal corresponding to a primary mode propagating with a primary angular velocity around the production tube <NUM> corresponding to the blue line. In other words, a diagonal in the frequency domain corresponds to a velocity. The angular velocity may be converted to a linear velocity. For example, the angular velocity for the analysis <NUM> may be approximately <NUM> krad/s, which is approximately <NUM>/s as a linear velocity. The angular velocity for the analysis <NUM> may be approximately <NUM> krad/s, which converts to a linear velocity of approximately <NUM>/s. The group velocities of <NUM>/s and <NUM>/s illustrate a correspondence to Lamb waves in the production tube <NUM> due to fluid being present on both sides and a correspondence to Rayleigh waves in the casing <NUM> due to a solid being present on one side due to the cement <NUM>.

As illustrated by the blue line not intersecting the origin, the analysis <NUM> and <NUM> are characteristic of a dispersive system, where different frequencies travel with different modes. Tangents to the upper and lower ends of the blue line, shown in red, are at <NUM> krad/s and <NUM> krad/s for the analysis <NUM> and at <NUM> krad/s and <NUM> krad/s for the analysis <NUM>. The red lines are phase velocities, which are higher than a group velocity shown in blue. In terms of angular frequencyω = 2πf, the group velocities are <MAT> and <MAT>. In other words, a peak or a trough at the back of a wave group will move gradually towards the front.

As shown with a comparison between the analyses <NUM>-<NUM>, the blue lines in each are very similar because the difference in the angular velocities of the production tube <NUM> and the casing <NUM> is roughly the same as the difference in their radii. Accordingly, separation of the production tube <NUM>, which is not of interest, from the casing <NUM>, which is of interest appears to be impractical in this manner according to the modeling <NUM>.

However, turning to <FIG>, in practice, measured results <NUM> including an analysis <NUM> of the production tube <NUM> in the casing <NUM> in a concentric configuration and an analysis <NUM> of the production tube in the casing <NUM> in an eccentric configuration. Both the forward and reflected spectra are included for each of the analyses <NUM>-<NUM>. Conceptually, the concentric configuration would not include reflected spectra due to the concentricity, as detailed herein. However, in practice, true concentricity is typically not achieved, for example due to the centralizers <NUM> being loose enough to allow free movement inside the production tube <NUM>. As such, the small amount of eccentricity present in the concentric configuration corresponding to the analysis <NUM> results in faint a reflected spectrum.

The analysis <NUM> shows a strong amplitude in the middle in red that was predicted by the modeling <NUM>. This amplitude is unsuitable for anomaly detection as discussed above. However, there is a fainter amplitude above the strong amplitude that is marked with the blue line in the angular velocity plot. The blue line is a different propagation mode having an angular velocity of approximately <NUM> krad/s and a linear velocity of approximately <NUM>/s. The blue line is a non-dispersive velocity that is traveling in what would otherwise be a dispersive system. Using the non-dispersive velocity, the production tube <NUM> may be separated from the casing <NUM> for analysis of the casing <NUM>. Further, it will be appreciated that other dispersive velocities may exist that can be utilized to separate the production tube <NUM> from the casing <NUM>.

The analysis <NUM> shows that eccentricity results in a strong reflected wave, even if there are no anomalies present outside the casing <NUM>. Generally, the spectra do not provide useful information. However, the boxes around portions of the forward spectrum and the reflected spectrum identify useful information. The boxes identifying portions of the forward spectra generally provide information on eccentricity and orientation of the production tube <NUM> within the casing <NUM>, and the boxes identifying portions of the reflected spectra generally provide information regarding isolation and material type, as well as eccentricity. The portions of the forward spectrum that may provide information regarding eccentricity and orientation include F2, F3, F4, and F7, for example. The portions of the reflected spectrum that may provide useful information regarding orientation R2, R3, and R5, for example. It will be appreciated that the number of the staves <NUM> can be in any order based on eccentricity of the production tube <NUM> and the casing <NUM>. As such the reference to the numbering is for illustration purposes only and not intended to be limiting. Each box in this example has a <NUM> bandwidth, and Table <NUM> below provides more detail for each of the boxes:.

As can be understood from the table, F2 and R2 may be used as a reference. For example, because F2 is almost completely independent of any other changes, where environmental changes in the downhole environment <NUM> occur (e.g., temperature, pressure, etc.), F2 may be used as a reference or calibration. While F3 may be used to indicate material type, such as cement, R3 and R5 are highly sensitive to isolation detection and material type identification. F4 provides may be used to detect eccentricity, and F7 may be used in combination with F4. Orientation may be found using convolution to detect the axis of symmetry, followed by phase comparison with a known reference to determine axis alignment.

For a more detailed discussion on isolation detection and material type identification, reference is made to <FIG>. In the example of <FIG>, results <NUM> including forward and reflected spectra are shown for a wellbore including a water lining. The top of the forward and reflected spectra are results corresponding to the presence of an anomaly, and the bottom of the forward and reflected spectra are results corresponding to the absence of an anomaly. As shown in the results <NUM>, the forward spectra show almost no change with the presence of the anomaly <NUM>, and R4 and R6 remain unchanged as well. However, R3 and R5 differ significantly with the presence and absence of the anomaly <NUM>, such that R3 and R5 provide isolation detection.

Turning to <FIG>, various example configurations showing reflected spectra are illustrated. A first configuration <NUM> includes air surrounding the casing <NUM>, a second configuration <NUM> includes water surrounding the casing <NUM>, and a third configuration <NUM> includes the cement <NUM> surrounding the casing <NUM> for comparison. The first configuration <NUM> includes a water filled channel configuration <NUM> and an air filled channel configuration <NUM>. Similarly, the second configuration <NUM> includes an air filled channel configuration <NUM> and a water filled channel configuration <NUM>. The third configuration <NUM> includes a cement channel configuration <NUM>, a water filled channel configuration <NUM>, and an air filled channel configuration <NUM>.

Results <NUM> are shown for each of the configurations <NUM>-<NUM> of the first, second, and third configurations <NUM>-<NUM> for differing levels of eccentricity represented by C, F, D, and E. As can be understood from the representations in <FIG>, C is generally concentric, and F-E increase in eccentricity from very slight in F to high eccentricity in E. The results <NUM> further include different orientations of the production tube <NUM>, as shown in the representations along the top. The orientation is defined clockwise relative to the channel at <NUM>° in this example. For each orientation and eccentricity, the results <NUM> are provided at R3 and R5 for the configurations <NUM>-<NUM>. For the first configuration <NUM>, the configuration <NUM> corresponds to the top of each plot of the results <NUM> for each orientation and eccentricity, and the configuration <NUM> corresponds to the bottom of each plot. Similarly, for the second configuration <NUM>, the configuration <NUM> corresponds to the top of each plot of the results <NUM> for each orientation and eccentricity, and the configuration <NUM> corresponds to the bottom of each plot. Finally, for the third configuration <NUM>, the configuration <NUM> corresponds to the top of each plot of the results <NUM> for each orientation and eccentricity, the configuration <NUM> corresponds to a middle of each plot, and the configuration <NUM> corresponds to the bottom of each plot. As can be understood from the results <NUM>, the channel in a lining around the casing <NUM> in each of the configurations <NUM>-<NUM> is detected, with it being visible in R3 and/or R5. The eccentricity is also visible in the spectra.

Referring to <FIG>, example configurations including the formation <NUM> disposed outside the cement <NUM> are illustrated. As discussed herein, the formation <NUM> may include rock layers, voids, and is acoustically reflective. Configuration <NUM> includes the formation <NUM> and the cement <NUM>, where the cement <NUM> has de-bonded from the casing <NUM>. Configuration <NUM> includes the formation <NUM> and the cement <NUM>, where the cement <NUM> has remained bonded to the casing <NUM>. In each of the configurations <NUM>-<NUM>, the radial sensor <NUM> was translated axially within the production tube <NUM> to generate a log from a bottom to a top with positions labeled as <NUM>-<NUM>. As such, in this example, there were <NUM> steps of approximately <NUM>, and a total travel distance of <NUM>, such that each log consists of <NUM> spectra in the results <NUM>. As shown in the results <NUM>, the radial sensor <NUM> is highly sensitive to impedance where the results <NUM> readily show a difference between bonded cement in the configuration <NUM> and de-bonded cement in configuration <NUM>. Even in the forward spectra, the difference when cement is present is apparent. Broad blurred spectra indicates presence of the cement <NUM>.

Turning to <FIG>, representations <NUM> of wave penetration into the cement <NUM> illustrate signal decay. The representations <NUM> in the example of <FIG> show only waves corresponding to F5. The grey disk at the center of each representation <NUM> corresponds to the radial sensor <NUM> and the thick black line corresponds to the casing <NUM>. In the representations <NUM>, the production tube <NUM> is omitted for clarity. Outside the casing <NUM> is the cement <NUM>. In the example of <FIG>, the cement <NUM> is a <NUM> lining. The top row of the representations <NUM> has air outside the cement <NUM> and the bottom row includes the formation <NUM> outside the cement <NUM>, which may be approximated as a high impedance material extending to infinity. As shown in each of the representations <NUM>, most of the energy from the wave is confined between the radial sensor <NUM> and the casing <NUM>, as shown with the bright colors.

As described herein, when waves traveling the casing <NUM> with fluid on one side (i.e., on an inside of the casing <NUM>) and solid on the other side (i.e., the cement <NUM> and the formation <NUM> outside the casing <NUM>), the propagating waves are Rayleigh waves. As can be understood from <FIG>, where air exists beyond the cement <NUM>, the energy cannot easily escape, with the waves being reflected back into the cement <NUM> at the cement-air boundary. Where the formation <NUM> exists beyond the cement <NUM>, the waves are not reflected back into the cement <NUM> at the cement-formation boundary, instead dissipating into the formation <NUM>. The representations <NUM> show that the wave propagation may characterize the cement <NUM> and the relationship with the formation <NUM>, without providing unnecessary detail about the characteristics of the formation <NUM> itself.

In the example of <FIG>, the representations <NUM> show that at <NUM>, the Rayleigh waves are outside the casing <NUM> and by <NUM>, the Rayleigh waves have travelled to <NUM>. As shown in the representations <NUM>, at this point, the Rayleigh waves start to reflect from the air in the top row and decay as energy radiates away as the Rayleigh waves propagate into the formation <NUM> in the bottom row. Generally, the Rayleigh waves penetrate about one wavelength from a boundary, such as the casing <NUM>, into a solid medium, such as the formation <NUM>. For F5, there are five wavelengths around the casing <NUM>. For a casing circumference of approximately <NUM>, λ=<NUM>. The color scale of the representations <NUM> is logarithmic. From a surface of the casing <NUM> to an edge of the representations <NUM>, the pressure decreases by approximately 6dB in the bottom row. As such, an object placed at <NUM> would have an amplitude of -12dB compared with when the object is placed close to the casing <NUM>. This detection threshold of approximately -12dB corresponds to the threshold at which detection of a presence or absence of a target may occur. Thus, the spectra in F5 and R5 may be focused on features within the detection threshold (e.g., <NUM> from the casing <NUM>). This is slightly farther than one wavelength.

As shown in the representations <NUM>, a signal that continues for a long time provides narrow spectral lines, as shown in the top row. Rapid decay of amplitude, as shown in the bottom row, creates wide spectral lines. The high impedance of the formation <NUM> thus causes spectra that are not only fainter due to low amplitude but also appear blurred. Further higher wavenumbers decay more rapidly, with the reflected spectra becoming more blurred, such as from R3 to R6 in <FIG> for example. Gas or fluid outside the casing <NUM> would thus provide narrow spectral lines, and the cement <NUM> would provide wider lines where the cement <NUM> is bonded to the formation <NUM>. On the other hand, isolation regions will appear blurred. R3 has narrower line but a longer wavelength, such that it penetrates farther into the formation <NUM>, and R5 has blurred lines with a lower penetration. As such, R3 and R5 combined provide enhanced isolation detection.

As can be understood from <FIG>, the acoustic waves may be recorded during continual movement of the radial sensor <NUM> along the production tube <NUM>. A transmission sequence <NUM> includes the staves <NUM> being pinged in a sequential order as the radial sensor <NUM> moves axially within the production tube <NUM>. The transmitted signals are reflected off collars on both the production tube <NUM> and the casing <NUM> used to join axial sections together. These axially reflected waves from the collars will be received by the radial sensor <NUM> and may interact with radially reflected waves producing false spectral lines. Accordingly a transmission sequence <NUM> utilizes a non-sequential order (e.g., a random order), where the recorded signals are rearranged based on the known firing sequence of the non-sequential order, thereby avoiding false spectral lines arising from axial waves reflected from the collars.

Turning to <FIG>, an example log <NUM> of an isolation region. The isolation region of the example in <FIG> is approximately <NUM> long. A configuration <NUM> includes the cement <NUM> outside the casing <NUM> and the production tube <NUM>. No channel is present. A diagram <NUM> illustrates the cement <NUM> with the formation <NUM> made from different types of rock. The cement <NUM> is continuous in some regions and includes the anomalies <NUM> in some regions where it is filled with air or water. The continuous regions of the cement <NUM> that are unbroken give a continuous log and show isolation in spectra <NUM> of R3 and R5. The spectra <NUM> of R3 and R5 has low penetration and shows cement, while R3 penetrates farther and provides addition formation details in addition to cement. For example, if R3 is continuous, the formation <NUM> has no features, and may include salt or a similar material which flows. As such, in the isolation region, R5 shows no changes, as R5 penetrates only into the cement <NUM>. R3 has a longer wavelength and this propagates into the formation <NUM> and detects formation features, such as salt. Knowing that salt is present may be helpful in isolation detection because salt may flow to form a right seal around the casing <NUM>. In the presence of salt, R3 will similarly show no features in the spectra <NUM>. The spectra <NUM> will vary in the presence of a channel, as detailed herein.

It will be appreciated that in some implementations, multiple casings may be utilized. As described herein, the presently disclosed technology separates the production tube <NUM> from the casing <NUM> mathematically using angular velocity. Similarly, multiple casings may be separated based on a difference in the angular velocities. An outer casing will have a similar linear velocity to the casing <NUM> but because the radius is much larger, the outer casing will have a different angular velocity. Further, each casing may have different sensitive reflection.

Referring to <FIG>, example operations <NUM> for analyzing a subterranean structure are illustrated. In one implementation, an operation <NUM> obtains radial acoustic waves transmitted and recorded for a target area, and an operation <NUM> separates the radial acoustic waves into clockwise waves and counterclockwise waves. An operation <NUM> shifts the counterclockwise waves into shifted counterclockwise waves and shifts the clockwise waves into shifted clockwise waves. An operation <NUM> generates forward waves from the shifted clockwise waves and reflected waves from the shifted counterclockwise waves, and an operation <NUM> identifies characteristics of the target area using the forward waves and the reflected waves.

Referring to <FIG>, a detailed description of an example computing system <NUM> having one or more computing units that may implement various systems and methods discussed herein is provided. The computing system <NUM> may be applied to the controller <NUM>, data recorder, and/or the like and may be used in connection with processing, as described herein. It will be appreciated that specific implementations of these devices may be of differing possible specific computing architectures not all of which are specifically discussed herein but will be understood by those of ordinary skill in the art.

The computer system <NUM> may be a computing system is capable of executing a computer program product to execute a computer process. Data and program files may be input to the computer system <NUM>, which reads the files and executes the programs therein. Some of the elements of the computer system <NUM> are shown in <FIG>, including one or more hardware processors <NUM>, one or more data storage devices <NUM>, one or more memory devices <NUM>, and/or one or more ports <NUM>-<NUM>. Additionally, other elements that will be recognized by those skilled in the art may be included in the computing system <NUM> but are not explicitly depicted in <FIG> or discussed further herein. Various elements of the computer system <NUM> may communicate with one another by way of one or more communication buses, point-to-point communication paths, or other communication means not explicitly depicted in <FIG>.

The processor <NUM> may include, for example, a central processing unit (CPU), a microprocessor, a microcontroller, a digital signal processor (DSP), and/or one or more internal levels of cache. There may be one or more processors <NUM>, such that the processor <NUM> comprises a single central-processing unit, or a plurality of processing units capable of executing instructions and performing operations in parallel with each other, commonly referred to as a parallel processing environment.

The computer system <NUM> may be a conventional computer, a distributed computer, or any other type of computer, such as one or more external computers made available via a cloud computing architecture. The presently described technology is optionally implemented in software stored on the data stored device(s) <NUM>, stored on the memory device(s) <NUM>, and/or communicated via one or more of the ports <NUM>-<NUM>, thereby transforming the computer system <NUM> in <FIG> to a special purpose machine for implementing the operations described herein. Examples of the computer system <NUM> include personal computers, terminals, workstations, mobile phones, tablets, laptops, personal computers, multimedia consoles, gaming consoles, set top boxes, and the like.

The one or more data storage devices <NUM> may include any non-volatile data storage device capable of storing data generated or employed within the computing system <NUM>, such as computer executable instructions for performing a computer process, which may include instructions of both application programs and an operating system (OS) that manages the various components of the computing system <NUM>. The data storage devices <NUM> may include, without limitation, magnetic disk drives, optical disk drives, solid state drives (SSDs), flash drives, and the like. The data storage devices <NUM> may include removable data storage media, non-removable data storage media, and/or external storage devices made available via a wired or wireless network architecture with such computer program products, including one or more database management products, web server products, application server products, and/or other additional software components. Examples of removable data storage media include Compact Disc Read-Only Memory (CD-ROM), Digital Versatile Disc Read-Only Memory (DVD-ROM), magneto-optical disks, flash drives, and the like. Examples of non-removable data storage media include internal magnetic hard disks, SSDs, and the like. The one or more memory devices <NUM> may include volatile memory (e.g., dynamic random access memory (DRAM), static random access memory (SRAM), etc.) and/or non-volatile memory (e.g., read-only memory (ROM), flash memory, etc.).

Computer program products containing mechanisms to effectuate the systems and methods in accordance with the presently described technology may reside in the data storage devices <NUM> and/or the memory devices <NUM>, which may be referred to as machine-readable media. It will be appreciated that machine-readable media may include any tangible non-transitory medium that is capable of storing or encoding instructions to perform any one or more of the operations of the present disclosure for execution by a machine or that is capable of storing or encoding data structures and/or modules utilized by or associated with such instructions. Machine-readable media may include a single medium or multiple media (e.g., a centralized or distributed database, and/or associated caches and servers) that store the one or more executable instructions or data structures.

In some implementations, the computer system <NUM> includes one or more ports, such as an input/output (I/O) port <NUM> and a communication port <NUM>, for communicating with other computing, network, or vehicle devices. It will be appreciated that the ports <NUM>-<NUM> may be combined or separate and that more or fewer ports may be included in the computer system <NUM>.

The I/O port <NUM> may be connected to an I/O device, or other device, by which information is input to or output from the computing system <NUM>. Such I/O devices may include, without limitation, one or more input devices, output devices, and/or environment transducer devices.

In one implementation, the input devices convert a human-generated signal, such as, human voice, physical movement, physical touch or pressure, and/or the like, into electrical signals as input data into the computing system <NUM> via the I/O port <NUM>. Similarly, the output devices may convert electrical signals received from computing system <NUM> via the I/O port <NUM> into signals that may be sensed as output by a human, such as sound, light, and/or touch. The input device may be an alphanumeric input device, including alphanumeric and other keys for communicating information and/or command selections to the processor <NUM> via the I/O port <NUM>. The input device may be another type of user input device including, but not limited to: direction and selection control devices, such as a mouse, a trackball, cursor direction keys, a joystick, and/or a wheel; one or more sensors, such as a camera, a microphone, a positional sensor, an orientation sensor, a gravitational sensor, an inertial sensor, and/or an accelerometer; and/or a touch-sensitive display screen ("touchscreen"). The output devices may include, without limitation, a display, a touchscreen, a speaker, a tactile and/or haptic output device, and/or the like. In some implementations, the input device and the output device may be the same device, for example, in the case of a touchscreen.

The environment transducer devices convert one form of energy or signal into another for input into or output from the computing system <NUM> via the I/O port <NUM>. For example, an electrical signal generated within the computing system <NUM> may be converted to another type of signal, and/or vice-versa. In one implementation, the environment transducer devices sense characteristics or aspects of an environment local to or remote from the computing device <NUM>, such as, light, sound, temperature, pressure, magnetic field, electric field, chemical properties, physical movement, orientation, acceleration, gravity, and/or the like. Further, the environment transducer devices may generate signals to impose some effect on the environment either local to or remote from the example computing device <NUM>, such as, physical movement of some object (e.g., a mechanical actuator), heating or cooling of a substance, adding a chemical substance, and/or the like.

In one implementation, a communication port <NUM> is connected to a network by way of which the computer system <NUM> may receive network data useful in executing the methods and systems set out herein as well as transmitting information and network configuration changes determined thereby. Stated differently, the communication port <NUM> connects the computer system <NUM> to one or more communication interface devices configured to transmit and/or receive information between the computing system <NUM> and other devices by way of one or more wired or wireless communication networks or connections. Examples of such networks or connections include, without limitation, Universal Serial Bus (USB), Ethernet, Wi-Fi, Bluetooth®, Near Field Communication (NFC), Long-Term Evolution (LTE), and so on. One or more such communication interface devices may be utilized via the communication port <NUM> to communicate one or more other machines, either directly over a point-to-point communication path, over a wide area network (WAN) (e.g., the Intemet), over a local area network (LAN), over a cellular (e.g., third generation (<NUM>), fourth generation (<NUM>), or fifth generation (<NUM>)) network, or over another communication means. Further, the communication port <NUM> may communicate with an antenna or other link for electromagnetic signal transmission and/or reception.

In an example implementation, radial logs, axial logs, impedance information, spectra, characterizations, and software and other modules and services may be embodied by instructions stored on the data storage devices <NUM> and/or the memory devices <NUM> and executed by the processor <NUM>.

The system set forth in <FIG> is but one possible example of a computer system that may employ or be configured in accordance with aspects of the present disclosure. It will be appreciated that other non-transitory tangible computer-readable storage media storing computer-executable instructions for implementing the presently disclosed technology on a computing system may be utilized.

In the present disclosure, the methods disclosed may be implemented as sets of instructions or software readable by a device. Further, it is understood that the specific order or hierarchy of steps in the methods disclosed are instances of example approaches. Based upon design preferences, it is understood that the specific order or hierarchy of steps in the method can be rearranged while remaining within the disclosed subject matter. The accompanying method claims present elements of the various steps in a sample order, and are not necessarily meant to be limited to the specific order or hierarchy presented.

Claim 1:
A computer-implemented method for isolation detection in a wellbore, the computer-implemented method comprising:
obtaining recorded data including radial acoustic waves transmitted and received using a radial sensor (<NUM>) of an acoustic logging tool (<NUM>) deployed in the wellbore, wherein the radial acoustic waves are transmitted and received by the radial sensor using a plurality of staves (<NUM>), the plurality of staves disposed about an axis of the radial sensor and spaced apart by an angle;
separating a first set of waves of the radial acoustic waves from a second set of waves of the radial acoustic waves by converting the recorded data from a time domain to a frequency domain, the first set of waves corresponding to a first direction of radial propagation and the second set of waves corresponding to a second direction of radial propagation;
shifting the first set of waves into a first set of shifted waves and the second set of waves into a second set of shifted waves;
generating a forward wave by combining the first set of shifted waves and a reflected wave by combining the second set of shifted waves; and
identifying one or more isolation regions in the wellbore using the forward wave and the reflected wave, wherein each of the one or more isolation regions corresponds to an area of bonded cement free from anomalies.