Determining tubular eccentricity with sonic tool

Abstract

A method of determining eccentricity of a tubular within a wellbore includes transmitting a sonic signal and receiving sonic waveforms based on detecting the sonic signal with sonic receivers positioned azimuthally around a sonic measurement tool. The sonic waveforms each include a tubular interference mode reflected and / or refracted from the tubular, and a casing interference mode reflected and / or refracted from a casing of the wellbore. The method includes generating an eccentricity waveform plot by combining the sonic waveforms and removing a monopole component, and generating an arrival time curve of the sonic waveforms to determine an earliest arrival time of the casing interference mode of one of the sonic waveforms. An eccentricity direction is determined as the azimuthal position of the earliest arrival time, and an eccentricity magnitude is determined with a tubular-eccentricity model based on the earliest arrival time.

Description

DETERMINING TUBULAR ECCENTRICITY WITH SONIC TOOLCROSS REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims priority to US Provisional patent application No. 63 / 552366 that was filed on February 12, 2024, which is herein incorporated by reference in its entirety.BACKGROUND OF THE DISCLOSURE

[0002] Wellbores may be drilled into a surface location or seabed for a variety of exploratory or extraction purposes. For example, a wellbore may be drilled to access fluids, such as liquid and gaseous hydrocarbons, stored in subterranean formations and to extract the fluids from the formations. Wellbores used to produce or extract fluids may be formed in earthen formations using earth-boring tools such as drill bits for drilling wellbores and reamers for enlarging the diameters of wellbores.

[0003] In many cases, measurement tools are implemented in wellbores for various purposes such as for surveying or evaluating a formation, wellbore, reservoir, etc. This may be achieved through the use of acoustic tools which transmit acoustic signals into a surrounding formation with acoustic transmitters positioned at one location in a wellbore and detect the acoustic signals from the surrounding formation with acoustic receivers positioned at other locations in the wellbore. Based on evaluating the returning signals, information about the surrounding formation can be inferred.

[0004] In some cases, tubulars may be positioned within a wellbore having acoustic tools conveyed therein. For example, techniques for cement evaluation through tubing (CETT) may rely on taking acoustic measurements of the wellbore casing, cement, formation, etc., from within a tubular. Eccentricity of the tubular within the wellbore can affect the reliability of acoustic measurements for characterizing various borehole and / or formation properties. Accordingly, techniques for determining the eccentricity of a tubular within the wellbore may be advantageous.SUMMARY

[0005] In some embodiments, a method of determining eccentricity of a tubular positioned within a wellbore includes transmitting a sonic signal with a sonic transmitter of a sonic measurement tool positioned within the tubular, receiving a plurality of sonic waveforms based on detecting the sonic signal with a plurality of sonic receivers of the sonic measurement tool positioned at a plurality of azimuthal positions around the sonic measurement tool, wherein the plurality of sonic waveforms each include a tubular interference mode reflected and / or refracted from the tubular and a casing interference mode reflected and / or refracted from a casing of the wellbore, generating an eccentricity waveform plot based on combining the plurality of sonic waveforms and based on removing a monopole component of the sonic signal from the plurality of sonic waveforms, identifying an earliest arrival time of the casing interference mode of one of the plurality of sonic waveforms based on generating an arrival time curve of the plurality of sonic waveforms in the eccentricity waveform plot, determining an eccentricity direction of the tubular as the azimuthal position associated with the earliest arrival time, and determining an eccentricity magnitude with a tubular-eccentricity model based on the earliest arrival time in the eccentricity direction and based on a reference arrival time, wherein the tubulareccentricity model relates a difference in sonic signal travel times through an annulus of the wellbore to tubular displacement. In some embodiments, the method may be performed by a computer system, in some embodiments, the method may be performed as instructions stored on a computer-readable storage medium.

[0006] In some embodiments, a method of determining eccentricity of a tubular positioned within a wellbore includes the features of any one of the appended claims.

[0007] In some embodiments, a method for evaluating eccentering of a tubing comprises: transmitting an acoustic wave in an azimuthal direction from the tubing towards an annulus, wherein the acoustic wave reflects towards the tubing once the acoustic wave collides with the annulus; receiving the reflected acoustic wave from the annulus in the tubing; and measuring and visualizing receiving time of the reflected acoustic wave.

[0008] In some embodiments, the acoustic wave is an ultra-high frequency monopole sonic wave.

[0009] In some embodiments, the acoustic wave is of a frequency lower than 50 kHz

[0010] In some embodiments, the acoustic wave is transmitted from a monopole signal transmitter positioned within the tubing.

[0011] In some embodiments, the reflected acoustic wave is received by a monopole signal receiver positioned within the tubing.

[0012] This summary is provided to introduce a selection of concepts that are further described in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter. Additional features and aspects of embodiments of the disclosure will be set forth herein, and in part will be obvious from the description, or may be learned by the practice of such embodiments.BRIEF DESCRIPTION OF THE DRAWINGS

[0013] In order to describe the manner in which the above-recited and other features of the disclosure can be obtained, a more particular description will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings. For better understanding, the like elements have been designated by like reference numbers throughout the various accompanying figures. While some of the drawings may be schematic or exaggerated representations of concepts, at least some of the drawings may be drawn to scale. Understanding that the drawings depict some example embodiments, the embodiments will be described and explained with additional specificity and detail through the use of the accompanying drawings in which:

[0014] FIG. 1 illustrates an example of an acoustic tool implemented in a wellbore for collecting acoustic data, according to at least one embodiment of the present disclosure;

[0015] FIG. 2-1 illustrates an example environment in which a sonic evaluation system is implemented, according to at least one embodiment of the present disclosure;

[0016] FIG. 2-2 illustrates an example implementation of the sonic evaluation system as described herein, according to at least one embodiment of the present disclosure;

[0017] FIG. 3-1 illustrates an example of a sonic tool implemented in a wellbore for collecting sonic data, according to at least one embodiment of the present disclosure;

[0018] FIG. 3-2 illustrates a top view of a schematic of the sonic tool disposed in the wellbore, according to at least one embodiment of the present disclosure;

[0019] FIG. 4-1 illustrates example sonic signal data taken by a sonic tool, and FIG. 4- 2 illustrates a top view of a schematic of the sonic tool, according to at least one embodiment of the present disclosure;

[0020] FIG. 4-3 illustrates an example of generating a combined waveform plot according to at least one embodiment of the present disclosure;

[0021] FIG. 4-4 illustrates generating a combined monopole plot, according to at least one embodiment of the present disclosure;

[0022] FIG. 4-5 illustrates generating an eccentricity waveform plot, according to at least one embodiment of the present disclosure;

[0023] FIG. 5 illustrates an example of an eccentricity waveform plot, according to at least one embodiment of the present disclosure;

[0024] FIG. 6-1 illustrates an example scenario in which a first tubing-eccentricity model is applicable for determining an eccentricity magnitude, according to at least one embodiment of the present disclosure;

[0025] FIG. 6-2 illustrates an example scenario in which a second tubing-eccentricity model is applicable for determining the eccentricity magnitude, according to at least one embodiment of the present disclosure;

[0026] FIG. 6-3 illustrates an example scenario in which a third tubing-eccentricity model is applicable for determining the eccentricity magnitude, according to at least one embodiment of the present disclosure

[0027] FIG. 7-1 illustrates an example of determining a calibration coefficient for the first tubing-eccentricity model, according to at least one embodiment of the present disclosure;

[0028] FIG. 7-2 illustrates an example of determining a calibration coefficient for the second tubing-eccentricity model, according to at least one embodiment of the present disclosure;

[0029] FIG. 7-3 illustrates an example of determining a calibration coefficient for the third tubing-eccentricity model, according to at least one embodiment of the present disclosure;

[0030] FIG. 8 illustrates a flow diagram for a method or a series of acts for determining eccentricity of a tubular positioned within a wellbore as described herein, according to at least one embodiment of the present disclosure; and

[0031] FIG. 9 illustrates certain components that may be included within a computing system.DETAILED DESCRIPTION

[0032] This disclosure generally relates to systems and methods for determining eccentricity of tubulars positioned within wellbores. For example, the present disclosure describes a computer-implemented sonic evaluation system which leverages sonic measurements by a sonic measurement tool for determining an eccentricity direction and an eccentricity magnitude of the sonic measurement tool within the wellbore. In many cases, such as in production wellbores that have been completed and operated for producing reservoir fluids, a production tubing may be positioned and / or fixed in the wellbore such that downhole tools may be conveyed within the wellbore through the production tubing. The production tubing may often be eccentric or off-centered within the wellbore due to deviations of the wellbore. Accordingly, a sonic tool disposed within the wellbore inside of a tubular may be affected by the eccentricity of the tubular, and the sonic measurements taken by the sonic measurement tool may be limited in their reliability.

[0033] The sonic evaluation system described herein may facilitate transmitting and receiving one or more sonic signals with the sonic tool. Waveforms may be detected by receivers of the sonic tool based on the sonic signals propagating through the wellbore, tubing, casing, formation, etc. Accordingly, the waveforms may include various interference modes, which the sonic evaluation system may advantageously isolate in order to determine eccentricity. For example, by identifying a casing interference mode of the waveforms, and comparing arrival times for the casing interference mode across receivers at multiple azimuthal positions around the sonic tool, the sonic evaluation system may infer the direction of the eccentricity based on an earliest arrival time for the casing interference mode. Further, this earliest arrival time in the direction of the eccentricity may be utilized by a tubular-eccentricity model, which may relate a difference of this earliest arrival time to a reference arrival time for inferring the magnitude of the eccentricity. For instance, theearliest arrival time may be compared to a known arrival time for a centered-tubular condition, or in another case, the earliest arrival time may be compared to a known arrival time for a maximum eccentricity condition. In this way, the same sonic tool which may be implemented for taking cement evaluation measurements may advantageously determine its own eccentricity, for example, rather than relying on one or more other (e.g., dedicated) tools for determining eccentricity.

[0034] As will be discussed in further detail below, the present disclosure includes a number of practical applications having features described herein that provide benefits and / or solve problems associated with determining the eccentricity of a tubular within a wellbore. Some example benefits are discussed herein in connection with various features and functionalities provided by a sonic evaluation system implemented on one or more computing devices. It will be appreciated that benefits explicitly discussed in connection with one or more embodiments described herein are provided by way of example and are not intended to be an exhaustive list of all possible benefits of the sonic evaluation system.

[0035] For example, in some cases, conventional solutions may determine eccentricity by utilizing one or more tools in addition to a sonic evaluation tool implemented downhole. For example, ultrasonic tools may be particularly suited for taking high quality images of wellbores and may facilitate determining the eccentric position of a tubular. However, these solutions involve implementing this additional (e.g., ultrasonic) tool in the wellbore in addition to the sonic tool, or else as an alternative to the sonic tool through additional trips downhole.

[0036] The present techniques, however, advantageously utilize the sonic tool and its associated measurement capabilities to determine the eccentricity of the tubular in which the sonic tool is disposed. In this way, the eccentricity may be determined by the same tool which may already be implemented downhole for formation and / or cement evaluation purposes, obviating the need for packaging and conveying additional and / or dedicated tools for determining eccentricity. As is known, longitudinal tool length in a wellbore is an important consideration, and reducing the number of downhole tools (and accordingly the total length) can simplify the complexity of the downhole system, reduce potential failure points, and provide flexibility and adaptability.

[0037] Further, the systems and methods described herein facilitate determining eccentricity based on less data and / or less information. For example, because the eccentricity can be determined based on sonic measurements by the sonic tool, additional data (e.g., ultrasonic data) does not have to be transmitted and processed in order to determine the tubular eccentricity along with transmitting and processing sonic data associated with cement evaluation (e.g., after eccentricity is determined). Reducing the total information of this process may be particularly valuable when considering that sonic data may tend to be much higher resolution, and accordingly may comprise a much larger volume of data. Accordingly, by advantageously utilizing the sonic data (e.g., and only the sonic data) to determine eccentricity, the total transmission and processing demands of such an operation are reduced.

[0038] Further, in some cases the tubular eccentricity is determined based on the sonic data that is taken for wellbore evaluation purposes. For example, rather than taking sonic measurements for calibration purposes, determining eccentricity, and then performing cement evaluation with additional measurements, the present techniques may determine eccentricity based on processing and evaluating the same waveforms utilized for cement evaluation, and then calibrating / interpreting those waveforms based on the determined eccentricity. This further reduces the total volume of data to be transmitted and processed as well as simplifies the downhole operation. Accordingly, the sonic evaluation system described herein may advantageously utilize the sonic tool and its measurements to determine its own eccentricity.

[0039] Moreover, the systems and methods described herein provide the practical application of facilitating evaluating cement of a production wellbore as part of a plug-and- abandon operation of the wellbore. For instance, in order to plug and abandon a wellbore that has been completed and is finished producing, the cement must be evaluated to determine that it is of a quality such that the wellbore can be plugged and abandoned. For instance, cement evaluation in this way may be for the purposes of complying with governmental regulations. Sonic measurement tools are conveyed within the wellbore for evaluating the cement quality, which must typically be performed from within small diameter (e.g., less than 7 inches (17.8 cm) or less than 6 inches (15.2 cm)) production tubulars which are positioned and fixed within the wellbore. Eccentricity of the productiontubular can have a major influence on the ability of sonic measurements to reliably characterize cement quality, and as such it can be imperative to determine the eccentricity of the tubular, which can be advantageously determined by the sonic measurement tool itself based on the present techniques. Indeed, in many cases, other (e.g., ultrasonic) tools which may be equipped for determining eccentricity may not exist which can be implemented in such small diameter applications such as within production tubulars of 3- 7 inches (7.6-17.8 cm). Accordingly, the systems and methods described herein may facilitate confirming the cement quality of a production wellbore such that the wellbore may be plugged and abandoned.

[0040] Additional details will now be provided regarding systems described herein in relation to illustrative figures portraying example implementations. For example, FIG. 1 illustrates an example of an acoustic tool 111 implemented in a wellbore 102 for collecting acoustic data, according to at least one embodiment of the present disclosure. For example, the acoustic tool 111 may be a sonic tool which may operate within a sonic spectrum or a range of sonic wavelengths and frequencies. The wellbore 102 may be a wellbore formed in a formation 101 as part of a downhole system or operation. For instance, the wellbore 102 may be formed to facilitate locating, accessing, and / or producing downhole resources such as oil, gas, water, geothermal energy, etc. The formation 101 may be a subsurface formation including one or more geological layers.

[0041] The acoustic tool 111 may be implemented in the wellbore 102 in order to facilitate surveying, evaluating, measuring, and / or characterizing one or more downhole components, formations, implements, etc. For example, the acoustic tool may be utilized to evaluate the surrounding formation 101, to evaluate cement of a casing of the wellbore 102, etc. The acoustic tool 111 may be conveyed and / or positioned within the wellbore 102 via a conveyance line 104 such as a wireline or coiled tubing, for example, which may be controlled and administered via conveyance equipment at a surface of the wellbore 102. In this way, the acoustic tool 111 may be implemented in the wellbore for taking acoustic measurements which may facilitate a downhole operation.

[0042] In some cases, the wellbore 102 includes a casing 106 which may be positioned and secured in place in order to support the wellbore, contain a formation, position one or more components, etc. For example, the casing 106 may be cemented in place by a cement108. In some embodiments, a tubular 110 is positioned within the wellbore 102 (e.g., within the casing 106). The tubular 110 may be a production tubing for circulating fluid, producing formation fluids, etc. In some cases, the annulus between the casing 106 and the tubular 110 may be fdled with cement (e.g., to fix the tubular 110 in place) or may otherwise be vacant, such as for facilitating circulating fluid therein.

[0043] The acoustic tool 111 may include a transmitter tool or transmitter portion 113 having one or more acoustic transmitters 117, as well as a receiver tool or receiver portion 119 having one or more acoustic receivers 115. The acoustic transmitters 117 and acoustic receivers 115 may be implemented as piezoelectric transducers (or any other suitable component) for converting electrical signals into acoustic energy (e.g., sonic sound waves) and vice versa.

[0044] The acoustic tool 111 may operate by generating acoustic signals 121 and transmitting them into the surrounding formation 101. When the acoustic signals 121 are transmitted into the formation 101, they travel through the surrounding rock and fluids, reflecting and refracting depending on the material properties the acoustic signals 121 encounter. The reflected and / or refracted signals are then captured by the acoustic receivers 115, which convert the acoustic signals 121 back into electrical signals for analysis and for inferring information about the formation 101. For example, in some cases, properties of the formation 101 may be of interest, and the acoustic signals 121 that travel through the formation may be evaluated. In other cases, properties of the cement 108 (or other borehole or formation feature) may be of interest, and the corresponding acoustic signals 121 may be received and evaluated. By analyzing the speed at which the acoustic signals 121 travel through the formation 101 (or cement 108, etc.), as well as the amplitude and frequency of the received acoustic signals 121, information such as rock density, porosity, fluid content, cement fill, cement quality, cement imperfections, cavities, and other mechanical properties can be inferred. In other cases, acoustic data may relay information about formation boundaries, fluid types and the identification and location of fractures. Further, acoustic tools like that described herein may be implemented for downhole imaging purposes for creating detailed images of borehole walls, detecting fractures, casing deformation, and other anomalies. The acoustic tool 111 may implement monopole signal transmission, dipole signal transmission, quadrupole signal transmission, andcombinations thereof, for example, for taking detailed measurements of anisotropic and / or heterogenous formations.

[0045] In some cases, such as in CETT operations, the acoustic tool 111 is implemented within the tubular 110 rather than in the open wellbore 102. For instance, in some cases, the wellbore 102 may be completed (to a certain degree) and the tubular 110 may be positioned therein in furtherance of a production objective of the wellbore 102. Thus, in some embodiments, the acoustic tool 111 must be conveyed and positioned within the wellbore 102 from within the tubular 110. In a particular example, such a configuration of the acoustic tool 111 within the tubular 110 may be implemented for evaluating the cement 108 (e.g., CETT) by transmitting and receiving the acoustic signals 121 through both the tubular 110 and the casing 106.

[0046] In some cases, the tubular 110 can be eccentric (e g., no concentric), off-center, offset, or otherwise misaligned from the center of the wellbore 102. For example, given doglegs, tortuosity, or deviations in the wellbore trajectory, the tubular 110 may be positioned off-center in any azimuthal direction within the wellbore 102. Accordingly, the acoustic tool 111, by virtue of being positioned in the tubular 110, may also be positioned off-center in the wellbore 102. Eccentricity in this regard can have an adverse effect on the reliability of the acoustic measurements taken by the acoustic tool 111. For example, in many cases the acoustic measurements may rely on determining a slowness (e.g., arrival time) of the received acoustic signals 121 to infer properties of the various transmission media through which they travel, based on attenuation of the acoustic signals therein. An off-center positioning of the acoustic tool 111 even in the slightest can upset these delicate measurements. For instance, eccentricity can result in an uneven annular thickness around the acoustic tool 111, or can result in uneven path lengths of the acoustic signals 121 travelling from transmitters 117 to receivers 115. In a particular case, eccentricity can affect cement bond log (CBL) responses as determined by the acoustic tool. Accordingly, eccentricity of the tubular 110 can present challenges to evaluating wellbore features through acoustic signals.

[0047] In some cases, it is possible to calibrate and / or account for the eccentricity of the tubular 110 in order to reliably characterize one or more features based on the acoustic measurements. Such a calibration may be dependent, however, on determining theazimuthal direction of the eccentricity, as well as the extent, magnitude, or distance of the eccentricity. The present disclosure describes techniques for determining eccentricity of tubulars in wellbore.

[0048] The sonic measurement tool may include or may be associated with a client device 112 having a sonic evaluation system 120 implemented thereon (e.g., or with a client application implemented thereon for accessing the sonic evaluation system 120 as described herein). The sonic evaluation system 120 may facilitate determining the direction and magnitude of an eccentricity of the tubular 110 within the wellbore 102 such that sonic measurements may be taken (e.g., and calibrated) for evaluating various downhole properties, such as the cement 108, notwithstanding the tubular 110 being off-center in the wellbore 102. In some cases, the sonic evaluation system 120 may advantageously provide this functionality based on transmitting and receiving sonic signals with a sonic tool. For example, the eccentricity of the tubular 110 may be determined without implementing another (e.g., dedicated) tool, such as an ultrasonic tool, in addition to the sonic measurement tool.

[0049] FIG. 2-1 illustrates an example environment 200 in which a sonic evaluation system 120 is implemented in accordance with one or more embodiments described herein. As shown in FIG. 2-1, the environment 200 includes a server device 114. The server device 114 may include one or more computing devices (e.g., including processing units, data storage, etc.) organized in an architecture with various network interfaces for connecting to and providing data management and distribution across one or more client systems. As shown in FIG. 2-1, the server device 114 may be connected to and may communicate with (either directly or indirectly) a client device 112 through a network 116. The network 116 may include one or multiple networks and may use one or more communication platforms and / or technologies suitable for transmitting data. The network 116 may refer to any data link that enables transport of electronic data between devices of the environment 200. The network 116 may refer to a hardwired network, a wireless network, or a combination of a hardwired network and a wireless network. In one or more embodiments, the network 116 includes the internet. The network 116 may be configured to facilitate communication between the various computing devices via well-site information transfer standard markup language (WITSML) or similar protocol, or any other protocol or form of communication.

[0050] The client device 112 may be representative of one or multiple client devices, and may refer to various types of computing devices. For example, the client device 112 may include a mobile device such as a mobile telephone, a smartphone, a personal digital assistant (PDA), a tablet, a laptop, or any other portable device. Additionally, or alternatively, the client device 112 may include one or more non-mobile devices such as a desktop computer, server device, surface or downhole processor or computer (e.g., associated with a sensor, system, or function of the downhole system), or other nonportable device. In one or more implementations, the client device 112 includes graphical user interfaces (GUI) thereon (e.g., a screen of a mobile device). In addition, or as an alternative, one or more of the client device 112 may be communicatively coupled (e.g., wired or wirelessly) to a display device having a graphical user interface thereon for providing a display of system content. The server device 114 may similarly refer to various types of computing devices. Each of the devices of the environment 200 may include features and / or functionalities described below in connection with FIG. 9.

[0051] As shown in FIG. 2-1, the environment 200 may include the sonic evaluation system 120 implemented on the server device 114. While shown on the server device 114, the sonic evaluation system 120 may be implemented wholly or in part on the client device 112, across the server device 114 and the client device 112, or on or across one or more additional devices, such that different portions or components of the sonic evaluation system 120 are implemented on different computing devices in the environment 200. The client device 112 may include a client application 118. The client application 118 may include an application or interface for interacting with and / or receiving the features of the sonic evaluation system 120 as described herein. In some embodiments, one or more of the functionalities or features of the sonic evaluation system 120 may be carried out or performed on or by the client application 118. In this way, the environment 200 may be a cloud computing environment, and the sonic evaluation system 120 may be implemented across one or more devices of the cloud computing environment in order to leverage the processing capabilities, memory capabilities, connectivity, speed, etc., that such cloud computing environments offer in order to facilitate the features and functionalities described herein.

[0052] FIG. 2-2 illustrates an example implementation of the sonic evaluation system 120 as described herein, according to at least one embodiment of the present disclosure. The sonic evaluation system 120 may include a sonic signal manager 122, a sonic waveform manager 124, and an eccentricity manager 126 which may implement and / or interface with tubular-eccentricity models 128. The sonic evaluation system 120 may also include a data storage 130 having sonic signal data 132 and sonic waveform data 134 stored thereon. While one or more embodiments described herein describe features and functionalities performed by specific components 122-128 of the sonic evaluation system 120, it will be appreciated that specific features described in connection with one component of the sonic evaluation system 120 may, in some examples, be performed by one or more of the other components of the sonic evaluation system 120.

[0053] By way of example, sonic signals may be described herein as being transmitted and / or received based on the sonic signal manager 122, but one or more of these features may be delegated to other components of the sonic evaluation system 120. As another example, while sonic waveforms may be generated and / or modified by the sonic waveform manager 124, in some instances, some or all of these features may be performed by the eccentricity manager 126 (or other component of the sonic evaluation system 120). Indeed, it will be appreciated that some or all of the specific components may be combined into other components and specific functions may be performed by one or across multiple components 122-128 of the sonic evaluation system 120.

[0054] Additionally, while FIG. 1, for example, depicts the sonic evaluation system 120 implemented on a client device 112 of the downhole system, it should be understood that some or all of the features and functionalities of the sonic evaluation system 120 may be implemented on or across multiple client devices 112 and / or server devices 114. For example, data may be input and / or received on a (e.g., local) client device, and the tubular eccentricity may be determined on one or more of a remote, server, or cloud device. Indeed, it will be appreciated that some or all of the specific components 122-128 may be implemented on or across multiple client devices 112 and / or server devices 114, including individual functions of a specific component being performed across multiple devices.

[0055] FIG. 3-1 illustrates an example of a sonic tool 311 implemented in a wellbore 302 for collecting sonic data, according to at least one embodiment of the presentdisclosure. In a particular example, the wellbore 302 may be a cased wellbore including casing 306 cemented to the open wellbore with cement 308. However, the present techniques are not limited to cased wellbores, and may be applicable to determining eccentricity of tubulars in open wellbores. The sonic tool 311 and / or the wellbore 302 may include any of the features as described in FIG. 1. For example, the sonic tool 311 includes a sonic transmitter 317 (or multiple sonic transmitters) and a plurality of sonic receivers 315 for transmitting and receiving sonic signals that may travel or propagate through one or more components, features, or media of the wellbore system shown.

[0056] A tubular 310 may be positioned in the wellbore 302. For example, the wellbore 302 may be a completed and / or production wellbore and the tubular 310 may be a production tubing for producing formation and / or reservoir fluids from the wellbore 302. As mentioned above, in some cases the tubular 310 may be positioned eccentric within the wellbore 302, such as offset from a center of the wellbore 302.

[0057] As mentioned, the sonic evaluation system 120 may include a sonic signal manager 122. The sonic signal manager 122 may facilitate transmitting, receiving, and storing sonic signals via the sonic tool 311. For example, the sonic signal manager 122 may instruct or direct the transmitter 317 to emit, produce, or excite one or more sonic signals at one or more times. The transmitter 317 may be a monopole transmitter and may emit sonic signals 321 that are monopole sonic signals. For instance, the transmitter 317 may be a single, radially symmetric source that emits pressure waves equally in all (e g., azimuthal) directions. The (monopole) sonic signals 321 may include and / or produce compressional waves (P-waves), shear waves (S-waves), and / or Stoneley waves which may travel through tubing, casing, formation, etc.

[0058] The sonic signals 321 may be acoustic signals in the sonic domain, spectrum, or range. For example, the sonic signals 321 may be in a frequency range of up to 25 kHz, such as between 15 kHz and 25 kHz. In some cases, the frequency range may be as low as 10 kHz, or may be as high as 30 kHz. In one example, the sonic signals 321 may particularly have frequencies of around 20 kHz, which may correspond with a frequency range of typical sonic signals utilized by downhole sonic tools for sonic evaluation purposes, such as for performing CETT. For instance, the sonic signals may be generated as a range of frequencies that are centered at about 20 kHz. In some cases, this range offrequencies is centered at a central frequency which may be as low as 1 kHz, or may be as high as 25 kHz.

[0059] The techniques described herein may be implemented specifically by utilizing sonic measurement tools in order to advantageously determine tubular eccentricity with a sonic tool which may typically be implemented downhole for wellbore evaluation purposes. Sonic signals — and in particular, monopole sonic signals — may have one or more drawbacks associated with determining tubular eccentricity. For example, the techniques described herein may rely on identifying the casing mode of the received sonic signals and differentiating arrival times between different azimuthal positions of the casing mode. However, acoustic signals in the sonic spectrum may tend to be affected by the near field effect, which may lead to interference which may mask or dominate the casing mode. For example, receivers of the sonic tool may be positioned at a distance from the transmitter that is within a near field region of the transmitter, and accordingly the received signals may be subject to complex wave propagation and may be dominated by interference patterns from multiple wave components, making it difficult to identify and characterize the casing mode. In some cases, lower frequencies may be less susceptible to the near field effect in this manner. However, given the resolution needed to distinguish subtle differences in arrival times of the casing mode, it may be necessary to implement higher frequencies (e.g., 20 kHz) to achieve sufficient resolution. Accordingly, the sonic evaluation system 120 may be advantageously implemented to determine tubular eccentricity based on high frequency sonic signals notwithstanding the challenges associated with such frequencies of acoustic signals.

[0060] The sonic signals 321 transmitted by the transmitter 317 may be received by the receivers 315. The receiver 315 may be configured as an array positioned azimuthally around the sonic tool 311. For example, in some cases the receivers 315 includes 4 receivers, 6 receivers, 8 receivers, or more, in an azimuthal array. In this way, the receivers 315 may be positioned and configured to receive the sonic signals 321 from all directions (e.g., 360°) about the sonic tool 311. While just one array of receivers 315 is shown, it should be understood that the sonic tool 311 may include multiple, and often many, arrays of receivers 315 positioned longitudinally along the sonic tool 311. The techniquesdescribed herein may be performed based on a singular array of receivers 315, or may implement multiple receiver arrays.

[0061] The sonic signals 321 as transmitted by the transmitter 317 may travel or propagate through a variety of extensional modes or interference modes. For example, in some cases, a tool mode 321-1 (e.g., a tool extensional mode or a tool interference mode) of the sonic signals may be representative of a propagation of the sonic signals 321 from the transmitter 317 to the receivers 315 through the sonic tool 311 itself, such as through the tool body of the sonic tool 311. In some cases, the tool mode 321-1 may be a first interference echo of the sonic signals 321 and may have an earliest arrival time of the sonic signal. In some embodiments, the sonic tool 311 may be particularly configured to mitigate, eliminate, and / or attenuate the tool mode 321-1 such that these (e.g., earliest) arrivals of the sonic signals 321 do not interfere with signals arriving through the cement, formation, etc. For instance, the sonic tool 311 may include damping features, tool body acoustical properties, or other attenuation characteristics to attempt to reduce or minimize the tool mode 321-1. Thus, in some cases, the tool mode 321-1 may not be present in the received sonic waveforms, or may not be present to a substantial or degree from the purposes of the techniques described herein.

[0062] The sonic signals 321 may include a tubular mode 321-2 (e.g., a tubular extensional mode or tubular interference mode). The tubular mode 321-2 may be a portion of the sonic signals 321 which propagates through the tubular to arrive at the receivers 315. In some cases, the tubular mode 321-2 may be a second interference echo of the sonic signals 321 and may represent a second arrival time of the sonic signals 321 (e.g., after the tool mode arrivals). The sonic signals 321 may also include a casing mode 321-3 (e.g., a casing extensional mode or casing interference mode) of the sonic signals 321 which travel or propagate through the casing to arrive at the receivers 315. For example, the sonic signals of the casing mode 321-3 may penetrate through the tubular 310, along and / or through the casing, and may penetrate back through the tubular 310 to arrive at the receivers 315. The casing mode 321-3 may be a third interference echo of the sonic signals 321 and may represent a third arrival time of the sonic signals 321 (e.g., after the tool mode 321-1 and tubular mode 321-2). The sonic signals 321 may include other wave modes, arrivals,and / or interference echoes in addition to those just described, but for the purposes of this disclosure, discussion herein will be focused primarily on those modes just described.

[0063] FIG. 3-2 illustrates a top view of a schematic of the sonic tool 311 disposed in the wellbore 302, according to at least one embodiment of the present disclosure. As shown, the tubular 310 is eccentric, offset, or displaced from a center of the wellbore 302. As mentioned, this eccentricity can be problematic, as such can affect the ability or reliability of the sonic signals to accurately reflect characteristics of the cement 308, formation 301, etc. For ease of discission, only casing modes 321-3 are shown in FIG. 3- 2. Additionally, while FIG. 3-2 illustrates 4 instances of the casing mode 321-3 in 4 orthogonal directions, it should be understood that any number of instances of the casing mode 321-3 (e.g., 8) may be transmitted and received in any number of azimuthal directions around the sonic tool 311.

[0064] As shown, the casing mode 321-3 as transmitted in various azimuthal directions may take different travel paths having different “round trip” lengths from, and back to, the sonic tool 311. For instance, the tubular 310 in this example is displaced (e.g., eccentric) toward the bottom of the page and accordingly, the casing mode 321-3 that travels in the downward direction (with reference to the page) takes a shorter path than the casing mode 321-3 in the upward direction. The casing modes 321-3 that are directed laterally may also take different travel paths from that of the upward and downward direction. Accordingly, the receivers at the various azimuthal directions may detect or receive the casing modes 321-3 having different arrival times corresponding to the eccentricity direction and eccentricity magnitude of the tubular 310. The sonic evaluation system 120 may leverage this phenomenon in order to infer the direction and magnitude of eccentricity of the tubular 310.

[0065] In some embodiments, the sonic signal manager 122 may, in connection with the transmitter 317, cause one or more monopole sonic signals to be emitted from the sonic tool 311. For instance, the sonic signals 321 may be transmitted as part of an eccentricity calibration operation of the sonic tool 311. In some cases, the techniques described herein may be implemented without emitting dedicated sonic signals for calibration, but rather, may perform calibration and determine eccentricity based on the same sonic measurements taken during an evaluation operation (e.g., CETT) of the sonic tool 311.

[0066] FIG. 4-1 illustrates example sonic signal data 440 taken by a sonic tool 410 as illustrated in FIG. 4-2, according to at least one embodiment of the present disclosure. The sonic tool 410 in this example is equipped with 8 receivers positioned equidistant (e.g., 45° apart) around the perimeter of the sonic tool 410 and having receiver azimuth positions 1- 8. The sonic signal data 440 includes various waveforms 444 for sonic signals received by the receivers as the azimuthal positions 1-8. As shown, the measurement period (e.g., 1 millisecond in this case) over which the waveforms 444 of the sonic signal data 440 are measured may encompass many different modes, patterns, echoes, interferences, etc., which may vary from receiver to receiver (e.g., from azimuthal position to azimuthal position). For example, the transmitted sonic signals may bounce, echo, reverberate, or reflect, or refract may times within any of the spaces of the tubular, wellbore, etc. before arriving at the receiver.

[0067] As mentioned above, the sonic evaluation system 120 includes a sonic waveform manager 124. The sonic waveform manager 124 may facilitate isolating, manipulating, and / or generating one or more waveforms based on the sonic signal data 440. For example, in some cases the casing mode (e.g., and tubular mode) may arrive at the receivers within a threshold time period which may be less than the entirety of the measurement period. For example, the sonic waveform manager 124 may define a calibration window 442 within which the casing mode is expected or known to arrive, and after which further data of the waveforms 444 may represent other modes (not of interest) or interferences of the sonic signals. Accordingly, the sonic waveform manager 124 may extract calibration waveforms 446 by isolating the portion of the waveforms 444 that arrive within the calibration window 442, or by filtering, truncating, or otherwise removing any portion of the waveforms 444 occurring outside of the calibration window 442. In some cases, the sonic waveform manager 124 extracts the calibration waveforms 446 based on raw waveforms 444, such as without (or before) applying any filters, or otherwise processing the raw waveforms 444 (e.g., without processing that may typically be performed in downhole sonic measurement operations). For example, the eccentricity determination techniques described herein may operate based on the raw sonic data without utilizing any low-pass, high-pass, or other filters. In this way, artificial artifacts, stretching, magnification, attenuation, etc., may not be present in the calibration waveforms 446 inorder to facilitate identifying subtle differences in arrival times across the azimuthal positions as described herein.

[0068] In some embodiments, the sonic waveform manager 124 may determine the calibration window 442 based on the size and / or configuration of the sonic tool 410, the size and / or configuration of the tubular in which the sonic tool 410 is disposed, the casing, the wellbore, or other downhole features. For example, based on the size (e.g., diameter) of the tubular and the size (e.g., diameter) of the casing, the sonic waveform manager 124 may identify the time period over which the casing mode is expected to arrive, and may remove or ignore sonic data arriving after this time period. For instance, the casing mode arrival times for defining the calibration window 442 may be observed or determined for various tubular and casing size combinations through empirical studies or analyses, and the calibration window 442 may accordingly be determined based on the known or observed behavior of the casing mode for a given implementation. Similarly, the calibration window 442 may be determined by taking into account the thickness of the tubular and / or casing, the material of the tubular and / or casing, a composition of fluid (e.g., mud) in the tubular anulus and / or casing anulus, or other physical properties of the associated components.

[0069] Accordingly, the sonic waveform manager 124 may extract the calibration waveforms 446, which may correspond with the arrivals of the tool mode, the tubular mode, and / or the casing mode at the various azimuthally positioned receivers. As shown in FIG. 4-1, the calibration waveforms 446 may vary from receiver to receiver, which variations may be slight and / or not readily apparent.

[0070] FIG. 4-3 illustrates an example of generating a combined waveform plot 448, according to at least one embodiment of the present disclosure. Based on the calibration waveforms 446, the sonic waveform manager 124 may generate the combined waveform plot 448, which may represent the various calibration waveforms 446 together as a plot or image. For example, the combined waveform plot 448 may represent positive values (e.g., peaks) and negative values (e.g., valleys) of the underlying waveforms with a spectrum of colors, shades, dot densities, etc. As shown, the combined waveform plot 448 may indicate the various azimuthal receiver positions associated with the underlying calibration waveforms 446. In some cases, the sonic waveform manager 124 may interpolate between the calibration waveforms for adjacent receivers in order to fdl in the area of the combinedwaveform plot 448. In this way, the combined waveform plot 448 may conceptually be a representation of the calibration waveforms 446 stacked side-by-side and viewed from above (e.g., 90° from how the calibration waveforms 446 are represented in the sonic signal data 440). The combined waveform plot 448 may facilitate relating the waveforms (e.g., and arrival times as described herein) of the sonic signals at the various azimuthal receiver positions.

[0071] As shown in FIG. 4-3, the combined waveform plot 448 depicts the calibration waveforms as having various vertical bands 450. These vertical bands 450 may be indicative of the sonic waveforms 444 received at the various azimuthal receiver locations being substantially similar and / or having similar arrival times. In some cases, however, this observation may be due to the fact that the monopole component of the sonic signals are similar or the same for each of the waveforms. For instance, the monopole component may dominate the observable waveforms and may accordingly mask the subtle differences between the modes (e.g., casing mode) of the waveforms. To elaborate, the tool mode and / or the tubular mode may dominate the waveforms, and given that the tool mode and / or the tubular mode may be substantially the same for each receiver (e.g., the sonic tool may be positioned concentric in the tubular such that there are not variations in the tubular mode at different azimuthal positions), these modes may dominate the waveforms and / or mask the more subtle casing mode and associated differences therein.

[0072] FIG. 4-4 illustrates generating a combined monopole plot 452, according to at least one embodiment of the present disclosure. In some embodiments, the sonic waveform manager 124 may identify a dominant component of the calibration waveforms 446, such as identifying a monopole component, a tool mode, a tubular mode, or other waveform mode, pattern, or wave component. In one example, the sonic waveform manager 124 may determine an average waveform by averaging the various calibration waveforms 446. The average waveform may represent a component, mode, pattern, etc., of the calibration waveforms 446 which is common to each of the calibration waveforms 446. For instance, in some cases a tool mode and / or a tubular mode may be substantially similar in each of the calibration waveforms 446, and the average waveform may accordingly characterize these similar and / or common patterns in the calibration waveforms 446. In some embodiments, the sonic waveform manager 124 represents the average waveform bygenerating the combined monopole plot 452. For example, as shown, the combined monopole plot 452 may represent each azimuthal receiver position with the same waveform data, evidenced by the vertical bars presented in the combined monopole plot 452. In this way, the sonic waveform manager 124 may identify waveform data which may be common to each of the calibration waveforms 446 for each of the azimuthal receiver positions and which may tend to dominate the calibration waveforms 446 and / or mask features of the calibration waveforms 446.

[0073] FIG. 4-5 illustrates generating an eccentricity waveform plot 454, according to at least one embodiment of the present disclosure. In some cases, in order to identify, highlight, and / or accentuate subtle and / or masked features in the calibration waveforms 446, the sonic waveform manager 124 may apply the combined monopole plot 452 to the combined waveform plot 448. For example, the sonic waveform manager 124 may subtract the data of the combined monopole plot 452 from that of the combined waveform plot 448. For instance, the average waveform as described above may be subtracted from each of the calibration waveforms 446 of the sonic signal data 440. Accordingly, the eccentricity waveform plot 454 may be generated.

[0074] By removing the common (e.g., monopole) components from the calibration waveforms, the remaining modes, patterns, or features in the eccentricity waveform plot 454 may be representative of the casing mode. For example, by subtracting out the data of combined monopole plot 452, the arrivals which occur before the casing mode arrivals (e.g., the tool mode and the tubular mode) may be removed and / or attenuated from the measured waveforms. The eccentricity waveform plot 454 may accordingly be representative of the one or more subtle or less-dominant modes in the waveform data, which may facilitate identifying distinct differences therein. For instance, as shown in the example in FIG. 4-5, the eccentricity waveform plot 454 includes distinct azimuthal curves 456 in the time domain, which were not present or not apparent in the original combined waveform plot 448 (e.g., and in the calibration waveforms 446). These azimuthal curves 456 may represent differences in the arrival times of the casing mode across different azimuthally positioned receivers. For instance, the azimuthal curves 456 may be understood conceptually as curves following peaks and / or valleys that are similar between the waveforms of the azimuthal positions 1-8, but which arrived at the respective azimuthalpositions at different times. Accordingly, the sonic evaluation system 120 may leverage these features of the eccentricity waveform plot 454 in order to infer a direction and magnitude of eccentricity of the tubular.

[0075] FIG. 5 illustrates an example of an eccentricity waveform plot 554, according to at least one embodiment of the present disclosure. As shown, the eccentricity waveform plot 554 depicts various azimuthal curves 556, which may be representative of differences in arrival times of a (e.g., same) sonic signal mode (e.g., the casing mode) at different azimuthal positions. In some embodiments, the sonic waveform manager 124 may identify a ridge 558 of one or more of the azimuthal curves 556. For example, the sonic waveform manager 124 may utilize a ridge detection algorithm which may identify a corresponding peak or valley (e.g., depending on weather the relevant azimuthal curve 556 corresponds with a waveform peak or valley) for each azimuthal position of a selected azimuthal curve 556. For instance, the ridge detection algorithm may identify a peak or valley based on the color / shading spectrum of the eccentricity waveform plot 554, based on a minimum and / or maximum value of an underlying waveform, or other ridge detection technique. In this way, the sonic waveform manager 124 may identify a ridge 558 for characterizing an azimuthal curve 556 of the eccentricity waveform plot 554.

[0076] In some embodiments, the sonic waveform manager 124 may select an azimuthal curve 556 for determining an associated ridge 558. In some cases, the sonic waveform manager 124 may select an azimuthal curve 556 that is most complete, continuous, has a threshold amount of positive and / or negative data points, and / or has positive and / or negative data points of a threshold magnitude. In some cases, the sonic waveform manager 124 selects an azimuthal curve 556 that is earlier in time than one or more other azimuthal curves 556. In some embodiments, the sonic waveform manager 124 selects an azimuthal curve 556 that is associated with a peak (e.g., maximum positive values) or a valley (e.g., maximum negative values) of the underlying waveforms.

[0077] In some cases, the sonic waveform manager 124 selects an azimuthal curve 556 based on a specific time threshold or casing window 560. For example, the sonic waveform manager 124 may identify the casing window 560 which may correspond with an expected or known arrival time for the casing mode. For instance, as described above, a calibration window may be determined based on any number of properties of the casing, tubular, fluid,or other features of the downhole implementation, and the calibration window is selected based on isolating the casing mode and earlier arrivals. The casing window 560 may be identified by further narrowing the calibration window to isolate and distinguish a time window associated with just the casing mode arrivals. For instance, in the example of FIG. 5, the casing window 560 may be a time interval corresponding with about 210 ps to about 260 ps. Accordingly, the sonic waveform manager 124 may identify an azimuthal curve 556 which occurs during the casing window 560 and may employ the ridge detection techniques on this selected azimuthal curve 556.

[0078] Based on the detected ridge 558, the sonic waveform manager 124 may fit an arrival curve 562 to the ridge 558. For example, the sonic waveform manager 124 may utilize a best-fit algorithm for determining the arrival curve 562. The arrival curve 562 may be a specified type of curve. For instance, in some cases, the sonic waveform manager 124 fits a cosine (or other sinusoidal) curve to the ridge 558. The arrival curve 562 may accordingly approximate and relate the various arrival times across the azimuthal positions.

[0079] As mentioned above, the sonic evaluation system 120 includes an eccentricity manager 126. The eccentricity manager 126 may facilitate determining an eccentricity direction and an eccentricity magnitude for the eccentricity of the tubular (and the sonic tool). For example, the eccentricity manager 126 may determine the eccentricity direction based on the arrival curve 562. For instance, the eccentricity manager 126 may determine an earliest arrival point 564, or a peak of the arrival curve 562 which may correspond with an earliest point in time along the arrival curve 562. For example, the earliest arrival point 564 may be representative of an associated receiver and azimuthal position receiving or detecting the casing mode earlier and before all other receivers / azimuthal positions. Accordingly, the eccentricity manager 126 determines an eccentricity direction of the tubular to be the direction which corresponds with the azimuthal position of the earliest arrival point 564. For instance, in the example in FIG. 5, the earliest arrival point 564 corresponds with an azimuthal position 6, and the eccentricity manager 126 may accordingly determine that the tubular is displaced or eccentric within the wellbore in the azimuthal direction where the receiver 6 is position on the sonic tool.

[0080] In some embodiments, the eccentricity manager 126 determines the eccentricity magnitude of the tubular (and the sonic tool), or the amount (e.g., length) of displacementof the tubular from the center of the wellbore, in the eccentricity direction. The eccentricity manager 126 may determine the eccentricity magnitude based on one or more tubulareccentricity models. The tubular-eccentricity models may infer or estimate the eccentricity magnitude based on the associated arrival times of the casing mode at one or more azimuthal positions. For example, in some cases, the tubular-eccentricity models determine the eccentricity magnitude based on the arrival time of the earliest arrival point 564. In other cases, the tubular-eccentricity models determine the eccentricity magnitude based on the arrival time of a latest arrival point 566. For example, the eccentricity manager 126 may determine the latest arrival point 566 in a similar manner to determining the earliest arrival point 564, and the latest arrival point 566 may correspond with a receiver and azimuthal direction which received or detected the casing mode last and after all other receivers.

[0081] The tubing-eccentricity models may be one or more models, algorithms, or relationships which may characterize a displacement magnitude for the sonic tool based on one or more arrival times at one or more azimuthal positions. The tubing eccentricity models may include models that are applicable to specific downhole circumstances, or which may be utilized based on a certain set of given assumptions.

[0082] FIG. 6-1 illustrates an example scenario in which a first tubing-eccentricity model is applicable for determining an eccentricity magnitude 672, according to at least one embodiment of the present disclosure. In some cases, the first tubular-eccentricity model facilitates determining displacement based on a known central reference point corresponding with a tubular 610 being centralized in a wellbore 602 (e.g., centralized in the casing). For instance, the central reference point may define a reference casing arrival time 668 corresponding to the arrival time of the casing mode at a receiver when the tubular (and the sonic tool 611) is centralized. Because the tubular 610 is centered in the wellbore, the reference casing arrival time 668 may be the same or substantially similar as received at any receiver at any azimuthal position. In some cases, the reference casing arrival time 668 may be determined based on taking one or more sonic measurements at a point (e.g., measurement depth) in which it is known that the tubular is centered. In another example, the reference casing arrival time 668 is determined based on calculating a theoretical arrival time value for a centralized tubular of the given implementation characteristics (e.g.,tubular size / thickness, casing size / thickness, fluid type, etc.), such as with a mathematical model or simulation.

[0083] Based on the reference casing arrival time 668, the first tubing-eccentricity model may relate an active arrival time 670 to the reference casing arrival time 668 to estimate the displacement of the tubular 610 within the wellbore 602. For example, the active arrival time 670 may be an arrival time for an eccentricity of the tubular at a current or active operation, or otherwise an eccentricity of interest of the tubular. The active arrival time 670 may also represent an earliest arrival time as determined for the current operation in accordance with that described above. To elaborate, the active arrival time 670 may be an earliest arrival time as determined in an eccentricity direction and as detected for a casing mode as received by a receiver in the eccentricity direction based on an eccentricity waveform plot as described herein.

[0084] The first tubing-eccentricity model may be based on the following relationship or any other relationship, equation, algorithm:Eccentricity Magnitude = ATcsg * (coef csg ' mud slowness) * 12 Where:Eccentricity magnitude is measured in inches;ATcsg is the difference between the active arrival time 670 and the reference casing arrival time 668, measured in ps; coef csg is a unitless calibration coefficient for the first tubing-eccentricity model; and mud slowness is a coefficient characterizing the acoustic slowness of the fluid in the casing annulus, measured in ps / foot.

[0085] FIG. 6-2 illustrates an example scenario in which a second tubing-eccentricity model is applicable for determining the eccentricity magnitude 672, according to at least one embodiment of the present disclosure. In some cases, the second tubular-eccentricity model facilitates determining displacement based on a known maximum eccentricity reference point corresponding with the tubular 610 being displaced a maximum distance from the center of the wellbore 602, for example, contacting the casing. For instance, the maximum eccentricity reference point may define a maximum eccentricity arrival time 674corresponding to the arrival time of the casing mode at a receiver when the tubular (and the sonic tool 611) is displaced a maximum amount. For example, the maximum eccentricity arrival time 674 may correspond to the arrival time of the casing mode for a sonic signal that travels from the sonic tool 611, through the tubular 610, through little or none of the casing anulus, to and along the casing, and back to the sonic tool 611. In some cases, the reference casing arrival time 668 may be determined based on taking one or more sonic measurements at a point (e.g., measurement depth) in which it is known that the tubular is at maximum displacement. In another example, the reference casing arrival time 668 is determined based on calculating a theoretical arrival time value for a maximum displaced tubular of the given implementation characteristics (e.g., tubular size / thickness, casing size / thickness, fluid type, etc.), such as with a mathematical model or simulation. The maximum eccentricity reference point may also define a maximum eccentricity magnitude 676, or the displacement of the tubular 610 from the center of the wellbore 602 at its maximum. For example, the maximum eccentricity magnitude 676 may be:(Inner Diameter of Casing — Outer Diameter of Tubular)2The inner diameter of the casing may take into account the thickness of the casing at the corresponding measurement depth of the sonic tool 611, such as by accounting for one or more collars or other components which may be positioned on or at the casing at that measurement depth.

[0086] The second tubing-eccentricity model may be based on the following relationship or any other relationship, equation, algorithm:Eccentricity Magnitude = ecc max - (ATmax *coef max / mud slowness) * 12 Where:Eccentricity magnitude is measured in inches; ecc max is the maximum eccentricity magnitude 676;ATmax is the difference between the active arrival time 670 and the maximum eccentricity arrival time 674, measured in ps; coef max is a unitless calibration coefficient for the second tubing-eccentricity model; andmud slowness is a coefficient characterizing the acoustic slowness of the fluid in the casing annulus, measured in ps / foot.

[0087] FIG. 6-3 illustrates an example scenario in which a third tubing-eccentricity model is applicable for determining the eccentricity magnitude 672, according to at least one embodiment of the present disclosure. In some cases, the third tubular-eccentricity model facilitates determining displacement without relying on any known reference points. For example, the third tubing-eccentricity model may relate the active arrival time 670 to a latest arrival time 678 for determining the corresponding displacement. For instance, the latest arrival time 678 may be the latest arrival time as determined based on an eccentricity waveform plot as described herein. In some cases, the latest arrival time may be an arrival time as determined for an azimuthal direction that is opposite (e.g., 180°) from the eccentricity direction as determined above. To clarify, the active arrival time 670 is the earliest arrival time for the casing mode for an active measurement operation, and the latest arrival time 678 is the corresponding arrival time for the latest arrival of the casing mode.

[0088] The third tubing-eccentricity model may be based on the following relationship or any other relationship, equation, algorithm:Eccentricity Magnitude = ATwd * (coef wd mud slowness)' * 12 Where:Eccentricity magnitude is measured in inches;ATwd is the difference between the latest arrival time 678 and the active arrival time 670, measured in ps; coef wd is a unitless calibration coefficient for the third tubing-eccentricity model; and mud slowness is a coefficient characterizing the acoustic slowness of the fluid in the casing annulus, measured in ps / foot.

[0089] The tubing-eccentricity models described herein may relate casing mode arrival times to eccentricity magnitude based on characterizing how the sonic signals travel through the tubular, casing anulus (e.g., fluid in the anulus), and casing. Accordingly, the eccentricity magnitude is inferred based on relating a shortest arrival time in the determined eccentricity direction to a relevant reference point (or to a longest arrival time). Indeed, the tubing-eccentricity models may be based on characterizing the difference in time that ittakes the relevant signals to travel through the casing anulus, including accounting for fluid in the anulus. For example, the mud slowness coefficients may be known, established, and / or measurable slowness properties of the fluid in the anulus, and the sonic evaluation system may accordingly determine an appropriate coefficient based on identifying the type of fluid in the anulus. While this simplified approximation of inferring tubular displacement based on a difference in travel time of signals through the annulus has been observed to be substantially accurate, dynamics of the downhole system and the specific circumstances of each of the tubing-eccentricity models is better approximated by virtue of the calibration coefficients for each model. For instance, based on simulations and / or empirical studies, the various calibration coefficients have been determined in order to achieve a high level of accuracy by the tubing-eccentricity models in accordance with the techniques described.

[0090] FIG. 7-1 illustrates an example of determining a calibration coefficient 786-1 for the first tubing-eccentricity model, according to at least one embodiment of the present disclosure. Through simulations and / or empirical testing, a plurality of arrival times may be determined for a centralized tubular condition 780 which, as shown, remains relatively consistent. Additionally, a fastest arrival time may be determined for an offset tubular condition 782 at one or more known displacements which, as shown, decreases with increasing eccentricity magnitude. By taking the difference 784-1 between the reference casing arrival times and the shortest arrival times at each known displacement, a calibration coefficient 786-1 can be determined which relates the displacement to this difference 784- 1. To elaborate, the calibration coefficient 786-1 relates the difference 784-1 in travel times through the casing anulus to the eccentricity magnitude of the tubular. In some cases, the calibration coefficients 786-1 are determined based on assuming a linear relationship or fitting a linear curve to the arrival time differences 784-1, and the calibration coefficient 786-1 is the slope of the linear fitted line. In other cases, different types or orders of curves may be fit for approximating the calibration coefficient 786-1.

[0091] The calibration coefficient 786-1 may be determined in this way specific to a given downhole implementation, such as for a given combination of casing size, tubular size, materials, frequencies, etc. Accordingly, the calibration coefficients 786 for a given tubing-eccentricity model may be specific to the specific combination of components (e.g.,the specific downhole implementation), and a plurality of calibration coefficients 786 may be determined for representing a variety of possible downhole implementations.

[0092] The calibration coefficient 786-1 may relate displacement to the difference 784- 1 in arrival times based on the assumption that the sonic signals are travelling through the casing anulus through air. Accordingly, the tubular-eccentricity models as described above account for a fluid that may be present in the annulus by incorporating the mud slowness coefficient (e.g., dividing the calibration coefficient by the mud slowness coefficient). In this way, the tubular-eccentricity models may accurately characterize the physical properties of the system in order that the eccentricity magnitude may be reliably determined.

[0093] In a similar way to determining calibration coefficients for the first tubulareccentricity model, FIG 7-2 illustrates an example of determining a calibration coefficient 786-2 for the second tubular-eccentricity model, and FIG. 7-3 illustrates an example of determining a calibration coefficient 786-3 for the third tubular-eccentricity model, according to embodiments of the present disclosure. For instance, with reference to FIG. 7-2, earliest arrival times for a maximum eccentricity condition can be determined for a known maximum eccentricity, and earliest arrival times for a displaced tubular condition can be determined for one or more known displacements. Accordingly, a difference 784-2 between the earliest arrival times for the displaced tubular condition and the maximum eccentricity condition can be determined and the calibration coefficient 786-2 identified (e.g., the slope of the linear fit). As mentioned above, the calibration coefficient 786-2 may be applicable to the second tubular-eccentricity model and for a specific downhole implementation (e.g., combination of tubular size and casing size). Accordingly, a plurality of calibration coefficients 786-2 can be determined for representing any number of combinations or collections of downhole components for a given implementation.

[0094] Further, in a similar way, with reference to FIG. 7-3, arrival times can be determined for a displaced tubular condition of a known displacement. Specifically, an earliest and a latest arrival time can be determined for each known displacement, and a difference 784-3 determined. Based on the difference 784-3, the calibration coefficient 786-3 can be determined, applicable for the third tubular-eccentricity model.

[0095] Based on the determined eccentricity direction and eccentricity magnitude, the sonic evaluation system 120 may facilitate evaluating one or more downhole features. For example, the sonic evaluation system 120 may take sonic measurements which may facilitate characterizing the quality of the cement behind the casing of the wellbore, and may do so from within a production tubular. These measurements may be calibrated or interpreted based on the determined eccentricity of the tubular, which may facilitate the measurements reliably characterizing cement quality. In some cases, the quality of the cement may be determined as part of a plug and abandonment operation of the wellbore. For instance, based on validating that the cement is of sufficient quality, thickness, completeness, integrity, etc., the wellbore may be plugged, sealed off, or otherwise abandoned.

[0096] FIG. 8 illustrates a flow diagram for a method or a series of acts for determining eccentricity of a tubular positioned within a wellbore as described herein, according to at least one embodiment of the present disclosure. While FIG. 8 illustrates acts according to one embodiment, alternative embodiments may add to, omit, reorder, or modify any of the acts of FIG. 8. In some cases, the method 800 is performed by a computer system. In some embodiments, the method 800 is performed as instructions stored on a computer-readable storage medium.

[0097] In some embodiments, the method 800 includes an act 810 of transmitting a sonic signal with a sonic transmitter of a sonic measurement tool positioned within the tubular.

[0098] In some embodiments, the method 800 includes an act 820 of receiving a plurality of sonic waveforms based on detecting the sonic signal with a plurality of sonic receivers of the sonic measurement tool positioned at a plurality of azimuthal positions around the sonic measurement tool, wherein the plurality of sonic waveforms each include a tubular interference mode reflected and / or from the tubular and a casing interference mode reflected and / or from a casing of the wellbore.

[0099] In some embodiments, the method 800 includes an act 830 of generating an eccentricity waveform plot based on combining the plurality of sonic waveforms and based on removing a monopole component of the sonic signal from the plurality of sonic waveforms.

[0100] In some embodiments, the method 800 includes an act 840 of identifying an earliest arrival time of the casing interference mode of one of the plurality of sonic waveforms based on generating an arrival time curve of the plurality of sonic waveforms in the eccentricity waveform plot.

[0101] In some embodiments, the method 800 includes an act 850 of determining an eccentricity direction of the tubular as the azimuthal position associated with the earliest arrival time.

[0102] In some embodiments, the method 800 includes an act 860 of determining an eccentricity magnitude with a tubular-eccentricity model based on the earliest arrival time in the eccentricity direction and based on a reference arrival time, wherein the tubulareccentricity model relates a difference in sonic signal travel times through an annulus of the wellbore to tubular displacement.

[0103] In some embodiments, the method 800 further includes performing a cement evaluation through tubing (CETT) operation for a cement of the wellbore with the sonic measurement tool based on calibrating for the eccentricity direction and eccentricity magnitude.

[0104] In some embodiments, the method further includes determining to plug and abandon the wellbore based on determining a quality of the cement to be above a threshold quality.

[0105] In some embodiments, the sonic signal is between 10 and 30 kHz, optionally between 15 and 25 kHz.

[0106] In some embodiments, the sonic signal is centered around 20 kHz.

[0107] In some embodiments, the sonic signal is a monopole sonic signal.

[0108] In some embodiments, the tubular is 6 inches (17.8 cm) in diameter or less, optionally 6 inches (15.2) in diameter or less.

[0109] In some embodiments, the reference arrival time of the tubular-eccentricity model is a reference casing arrival time for a centered tubular condition.

[0110] In some embodiments, the reference arrival time of the tubular-eccentricity model is an earliest arrival time for a maximum eccentricity condition.[OHl] In some embodiments, the reference arrival time is a latest arrival time of the casing interference mode of one of the plurality of sonic waveform, or an arrival time ofthe casing interference mode of one of the plurality of sonic waveforms in a direction opposite the eccentricity direction.

[0112] In some embodiments, the eccentricity waveform plot represents the plurality of sonic waveforms on a spectrum and as viewed from a top view.

[0113] In some embodiments, generating the eccentricity waveform plot includes interpolating between sonic waveforms of adjacent azimuthal positions.

[0114] In some embodiments, the method 800 further includes identifying an azimuthal curve within a casing window of the eccentricity waveform plot, determining a ridge of the azimuthal curve with a ridge detection algorithm, and generating the arrival time curve includes fitting a cosine curve to the ridge.

[0115] In some embodiments, generating the eccentricity waveform plot includes isolating a plurality of calibration waveforms of the plurality of sonic waveforms within a calibration window, the calibration window corresponding with an expected arrival time of the casing interference mode for a diameter of the tubular and a diameter of the casing.

[0116] In some embodiments, removing the monopole component includes averaging the plurality of calibration waveforms to generate an average waveform, and removing the average waveform from each of the plurality of calibration waveforms.

[0117] In some embodiments, the average waveform includes one or more waveform modes that dominate the plurality of calibration waveforms and mask the casing interference mode in the plurality of calibration waveforms.

[0118] Turning now to FIG. 9, this figure illustrates certain components that may be included within a computer system 900. One or more computer systems 900 may be used to implement the various devices, components, and systems described herein.

[0119] The computer system 900 includes a processor 901. The processor 901 may be a general-purpose single- or multi-chip microprocessor (e.g., an Advanced RISC (Reduced Instruction Set Computer) Machine (ARM)), a special purpose microprocessor (e.g., a digital signal processor (DSP)), a microcontroller, a programmable gate array, etc. The processor 901 may be referred to as a central processing unit (CPU). Although just a single processor 901 is shown in the computer system 900 of FIG. 9, in an alternative configuration, a combination of processors (e.g., an ARM and DSP) could be used.

[0120] The computer system 900 also includes memory 903 in electronic communication with the processor 901. The memory 903 may include computer-readable storage media and can be any available media that can be accessed by a general purpose or special purpose computer system. Computer-readable media that store computerexecutable instructions are non-transitory computer-readable media (device). Computer- readable media that carry computer-executable instructions are transmission media. Thus, by way of example and not limitations, embodiment of the present disclosure can comprise at least two distinctly different kinds of computer-readable media: non-transitory computer-readable media (devices) and transmission media.

[0121] Both non-transitory computer-readable media (devices) and transmission media may be used temporarily to store or carry software instructions in the form of computer readable program code that allows performance of embodiments of the present disclosure. Non-transitory computer-readable media may further be used to persistently or permanently store such software instructions. Examples of non-transitory computer- readable storage media include physical memory (e.g., RAM, ROM, EPROM, EEPROM, etc.), optical disk storage (e.g., CD, DVD, HDDVD, Blu-ray, etc.), storage devices (e.g., magnetic disk storage, tape storage, diskette, etc.), flash or other solid-state storage or memory, or any other non-transmission medium which can be used to store program code in the form of computer-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer, whether such program code is stored or in software, hardware, firmware, or combinations thereof.

[0122] Instructions 905 and data 907 may be stored in the memory 903. The instructions 905 may be executable by the processor 901 to implement some or all of the functionality disclosed herein. Executing the instructions 905 may involve the use of the data 907 that is stored in the memory 903. Any of the various examples of modules and components described herein may be implemented, partially or wholly, as instructions 905 stored in memory 903 and executed by the processor 901. Any of the various examples of data described herein may be among the data 907 that is stored in memory 903 and used during execution of the instructions 905 by the processor 901.

[0123] A computer system 900 may also include one or more communication interfaces 909 for communicating with other electronic devices. The communicationinterface(s) 909 may be based on wired communication technology, wireless communication technology, or both. Some examples of communication interfaces 909 include a Universal Serial Bus (USB), an Ethernet adapter, a wireless adapter that operates in accordance with an Institute of Electrical and Electronics Engineers (IEEE) 802.11 wireless communication protocol, a Bluetooth® wireless communication adapter, and an infrared (IR) communication port.

[0124] The communication interfaces 909 may connect the computer system 900 to a network. A “network” or “communications network” may generally be defined as one or more data links that enable the transport of electronic data between computer systems and / or modules, engines, or other electronic devices, or combinations thereof. When information is transferred or provided over a communication network or another communications connection (either hardwired, wireless, or a combination of hardwired or wireless) to a computing device, the computing device properly views the connection as a transmission medium. Transmission media can include a communication network and / or data links, carrier waves, wireless signals, and the like, which can be used to carry desired program or template code means or instructions in the form of computer-executable instruction or data structures and which can be accessed by a general purpose or special purpose computer.

[0125] A computer system 900 may also include one or more input devices 911 and one or more output devices 913. Some examples of input devices 911 include a keyboard, mouse, microphone, remote control device, button, joystick, trackball, touchpad, and lightpen. Some examples of output devices 913 include a speaker and a printer. One specific type of output device that is typically included in a computer system 900 is a display device 915. Display devices 915 used with embodiments disclosed herein may utilize any suitable image projection technology, such as liquid crystal display (LCD), light-emitting diode (LED), gas plasma, electroluminescence, or the like. A display controller 917 may also be provided, for converting data 907 stored in the memory 903 into one or more of text, graphics, or moving images (as appropriate) shown on the display device 915.

[0126] The various components of the computer system 900 may be coupled together by one or more buses, which may include one or more of a power bus, a control signal bus,a status signal bus, a data bus, other similar components, or combinations thereof. For the sake of clarity, the various buses are illustrated in FIG. 9 as a bus system 919.

[0127] The techniques described herein may be implemented in hardware, software, firmware, or any combination thereof, unless specifically described as being implemented in a specific manner. Any features described as modules, components, or the like may also be implemented together in an integrated logic device or separately as discrete but interoperable logic devices. If implemented in software, the techniques may be realized at least in part by a non-transitory processor-readable storage medium comprising instructions that, when executed by at least one processor, perform one or more of the methods described herein. The instructions may be organized into routines, programs, objects, components, data structures, etc., which may perform particular tasks and / or implement particular data types, and which may be combined or distributed as desired in various embodiments.

[0128] Further, upon reaching various computer system components, program code in the form of computer-executable instructions or data structures can be transferred automatically or manually from transmission media to non-transitory computer-readable storage media (or vice versa). For example, computer executable instructions or data structures received over a network or data link can be buffered in memory (e.g., RAM) within a network interface module (NIC), and then eventually transferred to computer system RAM and / or to less volatile non-transitory computer-readable storage media at a computer system. Thus, it should be understood that non-transitory computer-readable storage media can be included in computer system components that also (or even primarily) utilize transmission media.

[0129] The embodiments of the sonic evaluation system have been primarily described with reference to wellbore drilling operations; the sonic evaluation system described herein may be used in applications other than the drilling of a wellbore. In other embodiments, the sonic evaluation system according to the present disclosure may be used outside a wellbore or other downhole environment used for the exploration or production of natural resources. For instance, the sonic evaluation system of the present disclosure may be used in a borehole used for placement of utility lines. Accordingly, the terms “wellbore,”“borehole,” and the like should not be interpreted to limit tools, systems, assemblies, or methods of the present disclosure to any particular industry, field, or environment.

[0130] One or more specific embodiments of the present disclosure are described herein. These described embodiments are examples of the presently disclosed techniques. Additionally, in an effort to provide a concise description of these embodiments, not all features of an actual embodiment may be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous embodiment-specific decisions will be made to achieve the developers’ specific goals, such as compliance with system-related and business-related constraints, which may vary from one embodiment to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.

[0131] Additionally, it should be understood that references to “one embodiment” or “an embodiment” of the present disclosure are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. For example, any element described in relation to an embodiment herein may be combinable with any element of any other embodiment described herein. Numbers, percentages, ratios, or other values stated herein are intended to include that value, and also other values that are “about” or “approximately” the stated value, as would be appreciated by one of ordinary skill in the art encompassed by embodiments of the present disclosure. A stated value should therefore be interpreted broadly enough to encompass values that are at least close enough to the stated value to perform a desired function or achieve a desired result. The stated values include at least the variation to be expected in a suitable manufacturing or production process, and may include values that are within 5%, within 1%, within 0.1%, or within 0.01% of a stated value.

[0132] A person having ordinary skill in the art should realize in view of the present disclosure that equivalent constructions do not depart from the spirit and scope of the present disclosure, and that various changes, substitutions, and alterations may be made to embodiments disclosed herein without departing from the spirit and scope of the present disclosure. Equivalent constructions, including functional “means-plus-function” clausesare intended to cover the structures described herein as performing the recited function, including both structural equivalents that operate in the same manner, and equivalent structures that provide the same function. It is the express intention of the applicant not to invoke means-plus-function or other functional claiming for any claim except for those in which the words ‘means for’ appear together with an associated function. Each addition, deletion, and modification to the embodiments that falls within the meaning and scope of the claims is to be embraced by the claims.

[0133] The terms “approximately,” “about,” and “substantially” as used herein represent an amount close to the stated amount that is within standard manufacturing or process tolerances, or which still performs a desired function or achieves a desired result. For example, the terms “approximately,” “about,” and “substantially” may refer to an amount that is within less than 5% of, within less than 1% of, within less than 0.1% of, and within less than 0.01% of a stated amount. Further, it should be understood that any directions or reference frames in the preceding description are merely relative directions or movements. For example, any references to “up” and “down” or “above” or “below” are merely descriptive of the relative position or movement of the related elements. Additionally, as used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items.

[0134] The present disclosure may be embodied in other specific forms without departing from its spirit or characteristics. The described embodiments are to be considered as illustrative and not restrictive. The scope of the disclosure is, therefore, indicated by the appended claims rather than by the foregoing description. Changes that come within the meaning and range of equivalency of the claims are to be embraced within their scope.

Claims

CLAIMSWhat is claimed is:

1. A method (800) of determining eccentricity of a tubular (310) positioned within a wellbore (302), comprising: transmitting a sonic signal (321) with a sonic transmitter (317) of a sonic measurement tool (311) positioned within the tubular (310); receiving (810) a plurality of sonic waveforms (444) based on detecting the sonic signal (321) with a plurality of sonic receivers (315) of the sonic measurement tool (311) positioned at a plurality of azimuthal positions around the sonic measurement tool (311), wherein the plurality of sonic waveforms (344) each include a tubular interference mode (321-2) reflected and / or refracted from the tubular (310) and a casing interference mode (321- 3) reflected and / or refracted from a casing (306) of the wellbore (302); generating (820) an eccentricity waveform plot (448) based on combining the plurality of sonic waveforms (444) and based on removing a monopole component of the sonic signal (321) from the plurality of sonic waveforms (444); identifying (830) an earliest arrival time (670) of the casing interference mode (321- 3) of one of the plurality of sonic waveforms (344) based on generating an arrival time curve (562) of the plurality of sonic waveforms (444) in the eccentricity waveform plot (448); determining (840) an eccentricity direction of the tubular (310) as the azimuthal position associated with the earliest arrival time (674); and determining (850) an eccentricity magnitude (672) of the tubular (310) with a tubular-eccentricity model based on the earliest arrival time (564) in the eccentricity direction and based on a reference arrival time (668, 674, 678), wherein the tubular-eccentricity model relates a difference in sonic signal travel times through an annulus of the wellbore (302) to tubular displacement.

2. The method of claim 1 , further comprising performing a cement evaluation through tubing (CETT) operation for a cement of the wellbore with the sonic measurement tool based on calibrating for the eccentricity direction and eccentricity magnitude.

3. The method of claim 2, further comprising determining to plug and abandon the wellbore based on determining a quality of the cement to be above a threshold quality.

4. The method of any of claims 1-3, wherein the sonic signal is a monopole sonic signal between 10 and 30 kHz.

5. The method of any of claims 1-4, wherein the tubular is 7 inches in diameter or less.

6. The method of any of claims 1-5, wherein the reference arrival time of the tubulareccentricity model is a reference casing arrival time for a centered tubular condition.

7. The method of any of claims 1-6, wherein the reference arrival time of the tubulareccentricity model is an earliest arrival time for a maximum eccentricity condition.

8. The method of any of claims 1-7, wherein the reference arrival time is: a latest arrival time of the casing interference mode of one of the plurality of sonic waveforms; or an arrival time of the casing interference mode of one of the sonic waveforms in a direction opposite the eccentricity direction.

9. The method of any of claims 1-8, wherein the eccentricity waveform plot represents the plurality of sonic waveforms on a spectrum and as viewed from a top view.

10. The method of any of claims 1-9, wherein generating the eccentricity waveform plot includes interpolating between sonic waveforms of adjacent azimuthal positions.

11. The method of any of claims 1-10, further comprising: identifying an azimuthal curve within a casing window of the eccentricity waveform plot; determining a ridge of the azimuthal curve with a ridge detection algorithm; and generating the arrival time curve includes fitting a cosine curve to the ridge.

12. The method of any of claims 1-11, wherein generating the eccentricity waveform plot includes isolating a plurality of calibration waveforms of the plurality of sonic waveforms within a calibration window, the calibration window corresponding with an expected arrival time of the casing interference mode for a diameter of the tubular and a diameter of the casing.

13. The method of claim 12, wherein removing the monopole component includes averaging the plurality of calibration waveforms to generate an average waveform, and removing the average waveform from each of the plurality of calibration waveforms.

14. A system (900), including: a processor (901); memory (903) in electronic communication with the processor (901); and instruction (905) stored on the memory (903) which, when executed by the processor (901) cause the processor (901) to perform the method of any of claims 1-13.

15. A computer-readable storage medium (903) including instructions (905) which, when executed by a processor (901), cause the processor (901) to perform the method of any of claims 1-13.

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