BR112018070720B1 - APPARATUS FOR INVESTIGATING A SUBSURFACE VOLUME OF INTEREST FROM A WELL BORE AND METHOD FOR INVESTIGATING A SUBSURFACE VOLUME OF INTEREST - Google Patents

Abstract

Apparatus, systems and methods for investigating a subsurface volume of interest in a borehole. The apparatus comprises a housing configured for transport along the borehole; an acoustic source in the enclosure configured to generate acoustic signals; a lens assembly disposed in the housing and beside the acoustic source, the lens assembly being formed by a plurality of lens elements; wherein each lens element comprises a plurality of cells arranged in a matrix of curvilinear cells, each cell formed as a column oriented transverse to a direction of travel of the acoustic signals. The plurality of cells can be arranged according to a conformal mapping geometry, including a Bipolar canonical conformal mapping transformation of constant contour lines [u, v] in [x, y] Cartesian coordinates. A portion of the cells is reduced in size by a scale factor. The scale factor corresponding to each cell of the portion varies non-monotonically along the periodicity lines.

Description

DISCLOSURE FIELD

[0001] This disclosure relates to acoustic sensors and methods of producing and using such acoustic sensors in various tools, including acoustic profiling tools.

FUNDAMENTALS OF DISCLOSURE

[0002] The downhole acoustic profiling tools, used to investigate subsurface resources, may include one or more transmitters or acoustic sources and several acoustic receivers. These tools may also include a transceiver that can function as both a transmitter and a receiver. In both cases, the transmitters emit acoustic energy into the subsurface environment surrounding the wellbore. Acoustic signals are reflected by interfaces associated with the wellbore, wellbore structures and/or the formation. The reflected acoustic signals are detected by receivers in the logging tool and processed to provide estimates of one or more wellbore properties, wellbore structures and/or formation. The present disclosure provides acoustic sensors that use a metamaterial lens to manipulate these acoustic waves.

DISCLOSURE SUMMARY

[0003] Aspects of the present disclosure include apparatus, systems and methods for investigating a subsurface volume of interest from a borehole. The apparatus may include a housing configured for transport along the bore; an acoustic source in the enclosure configured to generate acoustic signals; a set of lenses placed in the casing and next to the acoustic source. The lens assembly is formed of a plurality of lens elements, where each lens element comprises a plurality of cells arranged in a matrix of curvilinear cells. Each cell is formed as a column oriented transversely to a direction of travel of acoustic signals, and each cell having a cube, a plurality of spokes radiating from the cube, and a plurality of fingers circumferentially distributed around the cube, where the cube, the rays and fingers are oriented to cause the acoustic waves to travel at a different speed in each of the three orthogonal directions.

[0004] In general terms, the above apparatus can be implemented as an acoustic tool. The acoustic tool may include a transducer configured to generate and detect an acoustic wave in cooperation with the lens assembly. The lens assembly can be separated from the acoustic source. The plurality of cells can be arranged according to a conformal mapping geometry. The conformal mapping geometry may comprise a Bipolar canonical conformal mapping transformation of contour lines [u, v] constants in Cartesian coordinates [x, y]. A portion of the plurality of cells may each be reduced in size by a scale factor from the largest cell dimension applicable to at least one cell of the plurality to fit the conformal mapping. The scale factor corresponding to each cell of the portion can vary non-monotonically along the periodicity lines of the conformal mapping. Rectangular Cartesian coordinates [x, y] can be related to contour lines [u, v] by the relations:

[0005] In aspects, the present disclosure provides an apparatus for investigating a subsurface volume. The apparatus may include a housing configured to be carried down a shaft, an acoustic transducer disposed in the housing and generating acoustic signals, an electronic assembly disposed in the housing and controlling the acoustic transducer, and a set of lenses. The lens assembly can be placed in the housing and next to the acoustic transducer. The lens assembly may be formed from a plurality of lens elements. Each lens element may comprise a plurality of cells arranged in an array of curvilinear cells. Each cell can be formed as a column oriented transversely to a direction of displacement of the acoustic signals. Each cell may have a cube, a plurality of spokes radiating from the cube, and a plurality of fingers circumferentially distributed around the cube. The cube, spokes and fingers can be oriented to make the acoustic waves travel at a different speed in each of the three orthogonal directions.

[0006] In aspects, the present disclosure provides a method for investigating a subsurface volume. The method may include placing an acoustic tool in a pit. The apparatus may include a housing configured to be carried down a shaft, an acoustic transducer disposed in the housing and generating acoustic signals, an electronic assembly disposed in the housing and controlling the acoustic transducer, and a set of lenses. The lens assembly can be placed in the housing and next to the acoustic transducer. The lens assembly may be formed from a plurality of cells. Each cell can be formed as a column oriented transversely to a direction of displacement of the acoustic signals. Each cell may have a cube, a plurality of spokes radiating from the cube, and a plurality of fingers circumferentially distributed around the cube. The cube, spokes and fingers can be oriented to make the acoustic waves travel at a different speed in each of the three orthogonal directions. The method may include directing the acoustic waves through an adjacent aberrant medium that blocks, at least partially, the direction of travel of the acoustic waves and the volume of interest.

[0007] The examples of the disclosure features have been summarized fairly broadly so that the following detailed description can be better understood and so that the contributions they represent to the art can be appreciated.

BRIEF DESCRIPTION OF THE FIGURES

[0008] For a detailed understanding of the present disclosure, reference should be made to the following detailed description of embodiments, taken in conjunction with the attached figures, in which like elements have been given like numbers, in which: FIG. 1A schematically illustrates a downhole acoustic profiling system having a downhole tool configured to acquire information using a sensor; FIG. 1B is a cross-sectional graphical representation of well structures in place relative to the wellbore for operations in accordance with embodiments of the present disclosure; FIG. 1C is a graphical representation of a tool cut into the bipolar acoustic hyperlens within the well structures in accordance with embodiments of the present disclosure; FIG. 1D illustrates a geometric conformal mapping transformation in cross-section of the original rectangular hyperlenses using a bipolar conformal mapping coordinate transformation in accordance with embodiments of the present disclosure; FIG. 1E shows a schematic diagram of a lens element in accordance with embodiments of the present disclosure; FIG. 1F shows a projection of the cell locations and the corresponding scale factors mij; FIG. 2 is a schematic diagram of an acoustic tool according to the present disclosure that emits an emitted acoustic signal that is less distorted by an aberrant medium; FIGS. 3A-3D show exemplary metamaterial cells for manipulating an acoustic wave in accordance with the present disclosure; FIGS. 4A-4D illustrate downhole tools and tool components in accordance with embodiments of the present disclosure; FIGS. 5A and 5B illustrate a model simulating the performance of embodiments of apparatus in accordance with the present disclosure; FIG. 6 shows a graphical representation of illustrative theoretical projections of pressure transmission across the liner; FIG. 7 shows a graphical representation of theoretical projections illustrating intensity transmission across the coating; FIGS. 8A and 8B show contour projections illustrating the acoustic intensity of acoustic waves emitted by a transducer in a casing, fixed in a borehole, which are filled by a borehole fluid without and with a lens assembly of the present disclosure ; FIGS. 9A and 9B show an illustration of the comparison in resonant energy distribution with hyperlens and without hyperlens, respectively; FIG. 10 shows a graphical representation of illustrative theoretical projections of pressure transmission across the liner; FIGS. 11A and 11B show contour projections illustrating an acoustic intensity distribution for a signal received from an anomaly reflection at the casing cement bonding interface with the hyperlens and without hyperlens, respectively.

DETAILED DESCRIPTION

[0009] Aspects of the present disclosure include an ultrasonic hyperlens that can be employed in deployments of multi-column image sensors traversing the coating. In aspects, the present disclosure relates to acoustic devices and related methods for investigating a volume of interest when a signal transmission path to that volume of interest is partially or completely obstructed by an aberrant medium. In aspects, the present disclosure also relates to acoustic devices and related methods for investigating a volume of interest when a signal transmission path of that volume of interest is partially or completely obstructed by an aberrant medium.

[0010] There are several challenges that operators face during the plugging and abandonment ('P&A') phase of a well life. As an example, when a well is abandoned or plugged, permanent structures must be placed as barriers to ensure isolation of all zones with a potential for flow relative to each other and the surface or seafloor. The current method of achieving such isolation is to pour cement into the well to form plugs in the appropriate locations to create the seals needed for zonal isolation. Barrier plugs are attached by cutting and pulling the piping and casing to expose the capping rock to the grouting operation so that the cement plugs can form a permanent seal. The location for placement of these cement plugs is consequently quite important.

[0011] Commonly, the time-consuming task of removing the casing and cement is undertaken due to the lack of an ability to obtain data and knowledge about the quality of the cement behind the casing, from the assessment through the piping and casing. In the absence of such an understanding of the condition of the cement, prudence dictates that the casing be removed from the borehole to allow the placement of capping rock barriers in suitable locations for zonal isolation. This operation to remove the casing and cement is typically a significant expense.

[0012] Thus, the scarcity of effective technologies that can determine the quality of cement through tubes and casings is problematic. Cement is part of the well construction to provide structural support for the casing. A solid cement structure with good integrity also creates zonal isolation from surface or seabed hydrocarbons, as well as the underground water table. In this regard, a good cement-pipe connection guarantees the safe abandonment of a well. With the ability to obtain a highly reliable record of cement quality through tubes and casings, operations that require cutting and removing casing and cement can be significantly reduced.

[0013] For these and other downhole acoustic imaging applications, an acoustic lens that allows the transmission and reception of ultrasound through aberrant media, such as, for example, multiple steel tubes and fluid annular spaces, is highly desirable. Aspects of the present disclosure include a lens derived from an artificial cell matrix that imparts unusual dynamic properties to the lens, such as negative refractive indices and negative Poisson ratios, as well as anisotropic modulus and density. Certain combinations of density and anisotropic modulus can create hyperbolic frequency dispersion capable of sustaining the propagation of very high frequency (spatial) wave vectors.

[0014] US Patent Application No. 15/040,677, submitted by the same inventor, discloses a rectangular acoustic hyperlens. As demonstrated in the previous application, this hyperlens shows significant transmission across the casing, but for multiple tubular aberrant media the beam of transmitted acoustic intensity is over 40 mm wide at the casing-to-cement interface. For imaging cement bond traversing multi-column casing, a beam intensity of less than half this width would greatly improve results. In some implementations, a beamwidth of less than 15 mm is preferable. In addition, implanting a flat acoustic hyperlens inside a tool designed for 3” ID tubing - i.e., conforming the original rectangular cross section of the flat hyperlens to form an inside approximately 2” sensor diameter for a tool envelope wire while still retaining the unusual dynamic properties associated with hyperbolic frequency dispersion that creates transmission through aberrant media - is problematic.

[0015] Aspects of the present disclosure include techniques for meeting the dimensional specifications of a downhole tool for the lens while maintaining the hyperlens properties using a geometric conformal mapping transformation on the cross section of the original "flat" hyperlens. An example described here is using a bipolar conformal mapping coordinate transformation to create lattice periodicity flux lines that converge to a small focus from a set of nearly collimated lines at the lens output.

[0016] The general embodiments of the apparatus described herein include a lens assembly including a plurality of lens elements, wherein each lens element comprises a plurality of cells arranged in an array of curvilinear cells. In the array of curvilinear cells, the plurality of cells are arranged in a conformal mapping geometry. The conformal mapping geometry comprises a Bipolar canonical conformal mapping transformation of constant contour lines [u, v] into Cartesian coordinates [x, y].

[0017] Each cell may be formed as a column oriented transversely to a direction of displacement of acoustic signals, each cell having a cube, a plurality of spokes radiating from the cube, and a plurality of fingers circumferentially distributed around the cube, where the cube, spokes and fingers are oriented to make the acoustic waves travel at a different speed in each of the three orthogonal directions.

[0018] Embodiments may include using at least one acoustic sensor to produce acoustic information that responds to an acoustic wave from the earth formation. The sensor can include at least one hyperlens together with at least one acoustic transmitter and/or at least one acoustic receiver, which can be implemented as a transducer. In some implementations, the same transducer can serve as transmitter and receiver. The information is indicative of a parameter of interest. The term "information" as used herein includes any form of information (analog, digital, EM, print, etc.), and may include one or more of: raw data, processed data and signals.

[0019] The methods may include estimating a parameter of interest from the information, evaluating the formation using the parameter of interest, and performing other wellbore operations depending on the evaluation or parameter of interest. In particular embodiments, a state of drilling operations, characteristics of the borehole, casing, cement or formation, or a bond between cement and casing, can be estimated using the parameter of interest and then used in performing an operation as described above. .

[0020] FIG. 1A schematically illustrates a downhole acoustic profiling system 100 having a downhole tool 10 configured to acquire information using a sensor 20, comprising at least one acoustic transmitter and at least one acoustic receiver, while in a borehole 50 on a land formation 80 and estimate a parameter of interest. The parameter of interest may refer to the properties of the casing 40 or cement 45 within the borehole 50, or characterization of the connection between them.

[0021] The sensor 20 may include one or more transmitters and/or acoustic receivers. The system 100 may include a conventional turret 60 erected on a drilling deck 70. A transport device (conveyor 15), which may be rigid or non-rigid, may be configured to transport the downhole tool 10 in the well 50 that intersects earth formation 80. Drilling fluid ("mud") 90 may be present in the wellbore 50. Carrier 15 may be a drillstring, a coil, a piano wire, an e-line, a wire , etc. The downhole tool 10 may be coupled or combined with additional tools including, for example, some or all of the information processing (insertion) system. Thus, depending on the configuration, the tool 10 can be used during drilling and/or after the well 50 has been formed. While a land system is shown, the teachings of the present disclosure can also be used in marine or subsea applications. Conveyor 15 may include embedded power and/or data conductors to provide signal and/or power communication between surface and downhole equipment (e.g., a seven-conductor cable). Conveyor 15 may include a downhole assembly, which may include a drill motor for rotating a bit.

[0022] A surface control system 65 receives signals from the downhole sensor 20 and other sensors used in the system 100 and processes these signals according to programmed instructions provided to the surface control system 65. The control system surface 65 can display the desired parameters and other information on a display/monitor that is used by an operator. The surface control system 65 can further communicate with a downhole control system 30 at a suitable location on the downhole tool 10. The surface control system 65 can process data related to operations and sensor data 20, and may control one or more downhole operations performed by system 100.

[0023] In one embodiment, the electronics associated with the sensor 20 can be configured to record and/or process the information obtained. Certain embodiments of the present disclosure may be implemented with a hardware environment 21 that includes an information processor 17, an information storage medium 13, an input device 11, processor memory 9, and may include a peripheral information storage medium. 19. The hardware environment can be in the well, on the rig or at a remote location. Additionally, the various components of the hardware environment can be distributed across these locations. Input device 11 can be any data reader or user input device such as data card reader, keyboard, USB port, etc. The information storage means 13 stores information provided by the sensor(s). Data storage medium 13 may include any non-transient computer-readable medium for storing standard computer information, such as a USB drive, memory card, hard disk, removable RAM, EPROMs, EAROMs, flash memories and optical discs or the like. commonly used memory storage systems known to one skilled in the art, including network or internet based storage. Information storage means 13 stores a program that, when executed, causes information processor 17 to perform the disclosed methods. Information storage means 13 may also store training information provided by the user. The information may also be stored on a peripheral information storage medium 19, which may be any standard computer information storage device such as a USB drive, memory card, hard drive, removable RAM or other memory storage system. commonly used by someone skilled in the art, including Internet-based storage. Information processor 17 can be any form of computer or math processing hardware, including Internet-based hardware. When the program is loaded from the information storage medium 13 into the memory of the processor 9 (e.g., computer RAM), the program, when executed, causes the information processor 17 to retrieve sensor information from the medium. of information storage 13 or peripheral storage medium 19 and process the information to estimate a parameter of interest. The information processor 17 can be located at the surface or at the bottom of the well.

[0024] The term “information” as used in this document includes any form of information (analogue, digital, EM, printed, etc.). As used herein, a processor is any information processing device that transmits, receives, manipulates, converts, computes, modulates, transposes, transports, stores or otherwise uses information. In various non-limiting aspects of the disclosure, an information processing device includes a computer that executes programmed instructions to perform various methods. These instructions may provide for operation, control, data collection and analysis, and other functions of the equipment in addition to the functions described in this disclosure. The processor may execute instructions stored in computer memory accessible to the processor, or it may employ logic implemented as field-programmable gate arrays ('FPGAs'), application-specific integrated circuits ('ASICs'), other combinatorial or sequential logic hardware, and so on. on.

[0025] In one embodiment, the electronics associated with the transducers, described in greater detail below, can be configured to take measurements in a plurality of azimuthal orientations as the tool moves along the longitudinal axis of the wellbore (" axially") using sensor 40. These measurements can be substantially continuous, which can be defined as repeated in very small increments of depth and azimuth, so that the resulting information has sufficient range and resolution to provide a picture of the hole parameters (for example, acoustic properties of the fluid and formation in the borehole) or parameters relating to the casing, cement or bond between them (collectively, “downhole parameters”).

[0026] In other embodiments, the electronics may be located elsewhere (eg, on the surface, or remotely). To perform the treatments during a single maneuver, the tool can use a high bandwidth transmission to transmit the information acquired by the sensor 40 to the surface for analysis. For example, a communication line for transmitting the acquired information can be an optical fiber, a metal conductor, or any other suitable signal conducting medium. It should be appreciated that the use of a "high bandwidth" communication line can allow surface personnel to monitor and control operations in "near real time".

[0027] A surface control system or downhole control system can be configured to control the tool described above and any incorporated sensors and to estimate a parameter of interest according to the methods described herein. Mathematical models, look-up tables or other models that represent the relationships between the signals and the values of the formation properties can be used to characterize operations in the formation or in the formation itself, optimize one or more operational parameters of a production or development, etc. The system may perform these actions through notifications, advice and/or smart control.

[0028] FIG. 1B is a cross-sectional graphical representation of well structures in place relative to the wellbore for operations in accordance with embodiments of the present disclosure. The typical well cut includes production piping 101, an annular space filled with downhole fluid 102, casing 103, and cement 104 in a wellbore that intersects formation 105 (eg, capstone). Production pipe 101 can be a central steel pipe having an inside diameter as little as about three inches, with a wall thickness of about 0.25 inches, up to ten inches with a wall thickness of 0.50 inches. . The downhole fluid 102 may be an annular space of about 1 to 2 inches of mud and oil mixtures and brine. The skin 103 can be, for example, a 0.5 inch thick steel skin. The cement layer 104 can be approximately two centimeters thick.

[0029] FIG. 1C is a graphical representation of a tool cut into the bipolar acoustic hyperlens within the well structures in accordance with embodiments of the present disclosure. Sensor sleeve 106 lies eccentrically within production pipeline 101 and liner 103 in turn. A lens element 107 comprises a plurality of cells 108 arranged in an array of curvilinear cells. The lens element comprises part of an azimuthally directed lens assembly.

[0030] The hyperlens geometry is constructed from a set of bipolar constant coordinate contours with coordinates [x, y] located in the first and fourth quadrants of the Cartesian frame, as illustrated in the inset. The cell network is formed with curvilinear periodicity in both directions along the contours [u, v], with the scaling of the anisotropic cell geometry in order to adjust and align the cell axes with the tangent and normal contour vectors. The inherent flux lines of the lattice periodicity then converge to focus a nearly collimated set of lines, whose location and size are determined by the selection of the mathematical parameter R and the threshold values [u, v] that define the lens profile. To a closer approximation, these geometric focus lines translate into the propagation field of acoustic waves and increase the intensity transmission through the coating and the concentration in the spot size. The fundamental design of metamaterial artificial cells comprising metamaterial hypermedia is discussed in more detail below.

[0031] FIG. 1D illustrates a geometric conformal mapping transformation in the cross section of the original rectangular hyperlenses using a bipolar conformal mapping coordinate transformation in accordance with embodiments of the present disclosure.

[0032] The rectangular Cartesian coordinates can be related to the coordinates mapped by the relations: where [v, v] are the coordinates of the bipolar conformal domain, as illustrated in the constant [x, y] coordinate projection of FIG. 1C. See P. Moon and DE Spencer, Handbook of Field Theory, New York: Springer-Verlag, 1971.

[0033] FIG. 1E shows a schematic diagram of a lens element in accordance with embodiments of the present disclosure. Lens element 120 includes a plurality of cells 122. While cells 122 are depicted as the same shape as cells in FIG. 2B, below, lens element 120 can include any cellular configuration in accordance with the present disclosure. Cells 122 are arranged end to end. An acoustic wave 104 enters the lens element 120 primarily through an edge 126. The acoustic wave 134 travels through the lens element 120 in a direction that is perpendicular to the contours u. Cells 122 of lens element 120 manipulate acoustic wave 134 such that an engineered wave 138 exits an edge 130 of lens element 120. In a non-limiting embodiment, a substrate 121 can be used as a support from the which each of the cells 122 projects. For example, cells 122 can be grown from substrate 121 such that cells 122 and substrate 121 are integral. For example, substrate 121 can be a wafer. Cells 122 and the structurally independent features that make up each cell 122 can project from substrate 121 in a cantilevered fashion.

[0034] The hyperlens network geometry of a lens element is configured according to the Bipolar canonical conformal mapping transformation of constant contour lines [u, v] in Cartesian coordinates [x, y]. Configuration can be accomplished by building the network - that is, iteratively adding design elements to the mapping - as described in the workflow immediately below. Network formation begins with a “seed cell” that is generally anisotropic in scale and defines the reference cell building block for the lens array. The seed cell has a width of Xcell and height of Ycell. To start the matrix population, the seed cell is positioned at location (1) as identified in FIG. 1E, in the contour u = umin defined by the maximum desired curvature for the lens geometry. Maximum curvature can be iteratively determined from constraints related to tool diameter, transducer design, and housing transmission objectives. The seed cell is moved along the constant curvilinear coordinate u = u1 = umin to a position v = v1 corresponding to a y coordinate 5% more than half a seed cell spacing unit (Xcell) from the line of symmetry ( v = 0). This location (1) now fixes the first row of periodicity constant v lattice.

[0035] The next cell is fixed to have a geometric anisotropy factor S21, the same as the Seed Cell (S21= S11) and with a scale factor m21, where the scale factor mij is defined as mij = Ycellij / YcellSeed. The cell location is selected by searching along the first lattice periodicity line v = v1 in the direction of max. u = umax. until the first distance is found at the seed cell location [uminv1] that will allow the cell to fit with S21= S11. The scale factor required for the cell to fit the curvilinear contours is calculated and stored as m21 and the curvilinear coordinate line is stored as u = u2. The process is repeated for the remaining cells along the lattice periodicity line v = v1 up to location (8) and each scale factor calculated up to m81 and stored. These cell locations v = v1 now fix all lattice lines constant u.

[0036] Next, the seed cell is moved along the constant curvilinear coordinate u = u1 = umin to a position corresponding to a complete unit of seed cell Xcell spacing of v = v1. The process is repeated for the remaining cell locations along the u = u1 curvilinear contour up to the limit v = vmax with equal anisotropic factors Sij = S11 and scale factors mij = m11. These u = u1 cell locations now fix all lines of constant lattice periodicity v and, subsequently, all remaining matrix cell locations and associated cell orientations.

[0037] The other geometric anisotropy factors of cell Sij are all equal to seed cell S11 and mij scale factors are calculated under the constraint that each cell must fit within the set of constant curvilinear coordinate lines u = (u1, u 2, u3... u8), v = (v1v2, ... v5). The lens structure is symmetric about the contour v = 0, so the calculated cell locations are simply mirrored and the orientations are reversed to get the entire lens lattice.

[0038] FIG. 1F shows a projection of the cell locations and the corresponding scale factors mij. It is evident that the variation in the scale factors is not monotonous along the lattice periodicity lines [u, v], but they oscillate non-uniformly.

[0039] FIG. 2 illustrates a source 200 for generating a signal 202, which may be sonic or ultrasonic. An aberrant medium 204 may partially or completely obstruct the path of signal 202 to a volume of interest 206. By obstructing, it is meant that medium 204 has one or more properties or characteristics that may block, distort, refract, reflect, or otherwise way undesirably affect signal 202.

[0040] Embodiments of the present invention position a lens 210 formed of an acoustic metamaterial between the source 200 and the aberrant medium 204. The lens 210 is shaped and configured to manipulate the signal 202 in a manner that minimizes undesirable effects on the signal 202 due to to the aberrant medium 204. Specifically, lens 210 can have anisotropic properties and can transmit longitudinal acoustic waves at a different velocity in each of three orthogonal directions. The metamaterial constituting lens 210 can also deform with moduli of different volume in each of the same three orthogonal directions. As a result, lens 210 can be characterized by an anisotropic (diagonalized) density tensor and an anisotropic volume modulus tensor having terms that are highly frequency dependent. In certain cases, these characteristics can generate an unnatural manipulation of the incident acoustic energy that increases the evanescent wave vector components, or rapidly disappearing, of the incident energy. This manipulation of acoustic energy can lead to the formation of complementary or quasi-complementary wave vectors that transmit the acoustic energy through an adjacent aberrant medium with minimal loss or distortion relative to the incident energy.

[0041] The characteristics of such metamaterials derive from the basic dynamic mechanism of resonances, occurring in aggregate, to affect the creation of material properties beyond the limits of nature. In the particular case of acoustic metamaterials, these characteristics start directly from the behavior of the frequency response of the two basic parameters of the material: effective mass density and effective volume modulus. Both material parameters can assume negative attributes and even anisotropic behavior in the presence of particular types of resonance transition zones, specifically in the vicinity of anti-resonances. These anisotropic and negative properties can give rise to a wide range of spectral characteristics within certain frequency bands, including negative refraction and hyperlensing, which can open up possibilities for beam focusing and amplification in flat lenses. Actions such as focus and amplification will generally be called acoustic wave manipulation.

[0042] Negative index properties resulting from unit cell resonance within the frequency band can occur over a very narrow spectral bandwidth, the range of which is an effect of the unit cell resonance characteristics and the properties of the matrix fluid and/or or background. To affect these negative properties over a wider frequency range, a multiplicity of compatible resonances in the elementary cell must constructively couple. This can be accomplished through the metamaterial unit cell designs of the present disclosure.

[0043] There are several factors that determine whether a particular unit cell design can affect the dispersion characteristics of a propagating wave to the point of exhibiting anisotropic and negative index properties behavior necessary to make the hyperlensing. A particularly relevant factor is the creation of an aggregate of resonances in the transmission coefficient spectra that couple to form a broad wave manipulation band in the frequency range of interest. Whether the frequency band formed from the array will give rise to anisotropic and negative index responses is a function of other properties of resonance couplings. The extent to which a unit cell design exhibits a significant acoustic impedance mismatch, absorption loss, and/or significant volume modulus magnitude are dominant influences, as any of these can negate the hyperlensing effect in the frequency band. Cells according to the present disclosure can be referred to as elementary components in superlenses or hyperlenses, depending on their characteristics.

[0044] FIGS. 3A-3D show exemplary metamaterial cells for manipulating an acoustic wave in accordance with the present disclosure. Starting with FIG. 3A, in general, each cell 310 is a plate and disc-like member. Cell 310 has two opposing flat surfaces that are parallel. As illustrated, the visible planar surface 313 is parallel to the paper. The distance between the two surfaces, or thickness, can be in the range of 1 millimeter to 100 millimeters. The diameter of a circle surrounding the cell 310 can be in the range of 1 millimeter to 5 millimeters. These dimensions are generally selected to allow phenomena such as resonances to have a measurable influence on the behavior of cell 310 and affect wave manipulation in the particular frequency ranges of interest. Cells, such as cell 310, of the present disclosure can be formed of metals or non-metals. Suitable metals include, but are not limited to, steel, platinum, tungsten, gold and exotic options such as iridium, the material property important for manipulating acoustic waves being the mass density of the metal.

[0045] A non-limiting embodiment of a cell 310 may include a hub 312, a plurality of spokes 314 radiating from the hub 312, and a plurality of sheets 316 concentrically disposed. Cube 312 acts as a central support structure for spokes 314. In the embodiment shown, cube 312 is formed of four separate segments, one illustrative segment being marked with the numeral 318. Cube 312 may be circular or any other shape suitable geometric. Furthermore, while four segments 318 are shown, the cube 312 can be formed as a single integral body or have two or more segments 318. Each segment 318 is physically connected to one or more spokes 314.

[0046] The spokes 314 provide the framework for supporting the sheets 316. An illustrative spoke is labeled with the numeral 320. The spoke 320 may be formed as an elongated bar having one or more necks 322. A neck 322 is a section of the spoke 320 that has a cross-sectional area that is smaller than immediately adjacent cross-sectional areas. Thus, the spoke 320 is more flexible at the necks 322 and can more easily bend, twist, or deform at the necks 322 than at other locations along the spoke 320. In one arrangement, the necks 322 are formed immediately adjacent to and radially to within each junction 324 between spoke 320 and sheet 316. In addition, a neck 322 may be immediately radially outward from a junction 326 between spoke 320 and hub 312.

[0047] Each of the sheets 316 may include a circumferentially distributed array of fingers 328 arranged in the shape of a circle. Each finger 328 is cantilevered from joint 324. While two fingers 328 are shown at each joint 324 with an orientation transverse to radius 320, more or less fingers 328 and different orientations may be used. Finger 328 may be a curved element that includes one or more flared sections 330. One flared section 330 has more mass than an immediately adjacent section of finger 328. The flared mass is formed giving flared section 330 a greater width than others. sections of finger 328. Thus, there may be an asymmetrical mass distribution along the length of finger 328. To interleave fingers 328, the radial positions of finger 328 are staggered for each successive ray 314. Thus, a finger 328 of a finger 328 314 can fit radially between two fingers 328 of an adjacent spoke 314. While six sheets 316 are shown, more or less sheets 316 can be used.

[0048] Cell 310 of FIG. 3A has four segments 311a-d. Each segment 311a-d has two spokes 314 radiating from a hub segment 318. Each spoke 314 has three sets of fingers 328. Each set has two fingers 328a, b. Fingers 328 are distributed circumferentially to form six sheets 316. It should be noted that the four segments 311a-d are structurally independent of one another. Although the elements that make up each of the segments 311a-d have been described separately, it should be understood that each segment 311a-d may be manufactured as a unitary body as opposed to being assembled from discrete components. It should also be noted that while four segments are represented, cell 310 can use a smaller or larger number of segments.

[0049] The resonances and antiresonances within the cell 310 are affected by the interaction of the various structural features through the matrix or background fluid medium described above. Thus, the number, size, shape and orientation of features such as spokes 314, leaves 316, fingers 328 and flared sections 330 influence where and to what extent resonances and anti-resonances occur and how they complement or negate each other affecting manipulation and incident acoustic wave control.

[0050] Referring to FIG. 3B, another embodiment of a cell 340 for manipulating an acoustic wave is shown. The general shape and dimensions of cell 340 are similar to those of cell 310 (FIG. 3). Cell 340 may include a hub 342, a plurality of spokes 344 radiating from hub 342, and a plurality of sheets 346 concentrically disposed. Cell 340 is similar to cell 10 of FIG. 3A in many ways. Variations of cell 340 are discussed below.

[0051] As before, the spokes 344 provide the framework for supporting the sheets 346. An illustrative spoke is labeled with the numeral 350. In this embodiment, the spoke 350 may be formed as an elongated bar that does not include any reduced cross-sectional areas. Likewise, the sheets 46 may include a circumferentially distributed array of fingers 352, with each finger 352 being swung from a joint 354. In this arrangement, the fingers 352 are straight members that include one or more flared sections 356.

[0052] In FIG. 3B, sheets 346 are arranged as a plurality of concentric polygons. In the illustrated arrangement, each of the sheets 346 is octagonal in shape. However, other polygonal shapes can be used. As before, fingers 352 are interleaved by staggering the radial positions of fingers 352 for each successive ray 344. Cell 40 of FIG. 3B has four segments configured in the same manner as cell 310 of FIG. 3A. However, any number of threads can be used.

[0053] Referring to FIG. 3C, another embodiment of a cell 370 for manipulating an acoustic wave is shown. In a manner previously discussed, the fingers 372 of each sheet 374 are swung from a radius 376. In this embodiment, the fingers 372 have projections 378 that are oriented transversely to the fingers 372. Each of the projections 378 can be a spacer or elements similar to bars that can move independently in relation to each other. By moving is meant bending, twisting, vibrating, etc. While projections 378 are shown projecting radially outward from a hub 380, it should be appreciated that fingers 372 can be arranged so that projections 378 project radially outward, or both.

[0054] The shape, size, number and orientation of the projections 378 inside each sheet 374 and between the sheets 374 can vary so as to influence the resonant behavior of the cell 370. Thus, for example, the projections 378 can have different sizes along a finger 372 and each of the fingers 372 may have a different number of projections 378.

[0055] Furthermore, cells according to the present disclosure need not be symmetrical or nearly isotropic as shown in FIGS. 3A-3C.

[0056] Certain embodiments of the present disclosure can incorporate anisotropy in the form factor to influence the bandwidth and hyperlensing effect of resonant bandwidths with a negative index formed by a cell. In one methodology, anisotropy can be applied by invoking geometric modeling transformations that maintain the invariance of the Helmholtz wave equation; for example, a Joukowsky modeling transformation. For example, the transformation can be described by the relationship: with the coordinates of the original cell: Z =x+iy and the coordinates of transformed (modeled) cells: A Joukowsky modeling can transform the octagonal cell boundary of FIG. 3B that can be circumscribed by a circle of radius R in a modeled cell geometry that can be circumscribed by the ellipse with modeling factor S = a / b, where a and b are the elliptical dimensions collinear with the x and y axes, respectively. All remaining coordinates in the original geometry of the interleaf cell transform according to the same shaping factor S. Therefore, the Joukowsky transformation for an octagonal interleaf cell is:

[0057] These equations can be used to transform the 2D geometric coordinates [x, y] of the cross-section of the quasi-isotropic cell previously illustrated in FIG. 3B with an anisotropic Joukowsky transformation with shape factor S = 2 anisotropy in cell shape. The resulting anisotropic cell 390 is shown in FIG. 3D. The anisotropy S = 2 is merely an illustrative value. A feature of anisotropic modeling is that the thickness of at least two fingers varies non-linearly along the plane in which the cell lies. For example, finger thicknesses, 392, 394 and 396 are different and the difference is mathematically non-linear. Thickness comparison can be done by selecting the same feature (for example, a zoomed-in section) and measuring a distance along the same location along the same axis. For example, the edges 393, 395 and 397 can be used as a measure of the thickness of the transformed finger sections. Anisotropic shape can also be applied to the cells of FIGS. 3A or 3C, or other cell configurations in accordance with the present disclosure.

[0058] FIGS. 4A-4D illustrate downhole tools and tool components in accordance with embodiments of the present disclosure. Referring to FIG. 4A, an embodiment of an acoustic tool 420 in accordance with the present disclosure is shown. A perspective view is shown in FIG. 4B. The tool 420 may be conveyed by a suitable conveyor (not shown) along a hole 424 drilled into a clay formation 426. The conveyor may be a non-rigid conveyor such as wire, e-line, piano wire or coil, a rigid carrier such as a drill pipe, a drop tool, or a self-contained device. In a non-limiting embodiment, the tool 420 includes a housing 428 that has an acoustic source cavity 430 that receives an acoustic source assembly 432 and an electronics cavity 434 that receives an electronics assembly 436. A cavity sleeve 438 seals and surrounds acoustic source assembly 432 in acoustic source cavity 430. Window 438 may be constructed and formed to have a similar acoustic impedance with fluid filling lens cavity 442; for example, fabricating the window from Teflon material and using pure water as the lens cavity fluid. A shroud 440 seals and surrounds the electrical component assembly 436 within the electrical cavity 434. The acoustic source cavity 430 may have a lens section 442 and a source section 444. The pressure compensating cavity 446 and 448 equalizes the pressure between the outside of the housing 428 and the sections 442 and 444, respectively. The pressure compensation fluid in source section 444 will generally have different acoustic impedance properties than the fluid in lens section 442. The properties of the fluid in lens section 442 are variables dictated by the acoustic properties of the cell and the gamma of desired frequency.

[0059] The acoustic source assembly 432 generates and emits acoustic energy that can pass through an aberrant medium with reduced distortion. In some situations, the aberrant medium may be the metal constituting a tubular well, such as a housing 450. In one embodiment, the acoustic source assembly 420 includes a transducer 452 and a lens 454. The transducer 452 may be any device configured to generate and receive sonic or ultrasonic signals. An illustrative non-limiting source may include piezoelectric elements.

[0060] The lens 454, which is best illustrated in FIGS. 4C and 4D, includes a plurality of cells 460 arranged in a matrix as described above with respect to FIG. 1 AND. Each cell 460 may be in the form of a column extending orthogonally/transversely to a signal propagation direction, which is shown with arrow 462. The illustrated embodiment includes two lens elements 470, 472, each of which has a base 476 from which cells 460 project in a swinging-type manner. Sections 470, 472 are arranged to mirror each other. Furthermore, the cells 460 are aligned such that two facing cells 460 effectively form a column-like structure between the two bases 476. The facing cells 460 can be separated by a gap, enter in contact with each other or may be fixed to each other. In embodiments, one end of cell 460 can be fixed or both ends can be fixed. Cells 460 can have any cross-sectional shape and structures that have been discussed herein. It should be understood that lens array 454 is not limited to any particular distribution of cells 460 or that such distribution is symmetrical or conforms to a particular geometric shape, except as explicitly indicated above. It should also be understood that lens assembly 454 may include only one element (eg, section) 470 from which cells 460 project. Additionally, lens assembly 454 can include an arrangement where two bases 448 are traversed by one cell 460, as opposed to two sideways facing cells.

[0061] The set of electronic components 436 may include electronics, microprocessors, memory modules, algorithms, power supplies and circuits suitable for driving and detecting the acoustic transducer 452. The electronic set 436 may also include hardware for bidirectional communication so transmitting and/or receiving data signals.

[0062] Referring to FIGS. 4A-4D, an illustrative mode of operation of acoustic tool 420 involves evaluating a cement body 480 (FIG. 8), i.e., a volume of interest, surrounding a well casing 450. The well casing may be formed from a metal, such as steel. The evaluation may include estimating a quality of contact or bond between the cement and the well casing 450. During use, the electronics assembly 436 activates the acoustic transducer 452. In response, the acoustic transducer 452 emits acoustic waves through the lens. 454 along arrow 462. Acoustic waves can be sonic or ultrasonic and can have a narrow or wide frequency band. It should be noted that the waves enter the cells 420 along a surface facing the surface of the acoustic transducer and exit the cells 420 along a surface facing away from the acoustic transducer 452. Thereafter, the acoustic waves pass through borehole casing 450 and into cement body 480. As discussed earlier, lens 454 manipulates acoustic waves in a manner that allows these waves to pass through the metal of borehole casing 450 with reduced distortion. A reflected wave 430 returns from the formation and enters lens 454. After being manipulated by lens 454, wave 420 enters transducer 452 and is processed.

[0063] The lens 454 can reduce distortion in acoustic signals that have already traveled through the aberrant medium 204, as well as for acoustic signals that travel into the aberrant medium 204. That is, the lens 454 can manipulate an acoustic signal emitted in the medium aberrant medium 204 and also manipulate a reflected signal from the zone of interest 206 that has traveled through the aberrant medium 204. Thus, transducer 452 can act as both a signal emitter and a signal detector.

[0064] Generally, it is desirable to evaluate a parameter or feature, such as a cement bond, over a full circumference at a specified depth in the borehole. Thus, embodiments of the present disclosure can mount the tool 420 on a platform that is rotated by a suitable rotary device, such as an electric or hydraulic motor. In some embodiments, the transport device on which the tool 420 is mounted, for example, a drill string, can be rotated. In yet other embodiments, a stationary array of two or more tools 420 can be circumferentially distributed along a plane to achieve complete circumferential coverage.

[0065] FIGS. 5A and 5B illustrate a model simulating the performance of embodiments of apparatus in accordance with the present disclosure. A finite element model 500 was developed by having the bipolar hyperlens 502 completely immersed in a water bottom inside a teflon sleeve 510 (2 mm thick). The wellbore fluid within the production tube and casing is a typical mud 506. The fluid outside the casing is a semi-infinite cement domain 512. The acoustic source is an idealized (rigid) pressure source 501 that emits from of a cylindrical boundary of R27.5mm with a gap 550 of 1mm between the source and the hyperlens 502. The Teflon sleeve 510 is located eccentrically within the production tubing 504 to form a 1mm gap between the Teflon sleeve 504 and the pipe ID. Pipe 504 is concentric with casing 508.

[0066] FIG. 6 shows a graphical representation 600 of illustrative theoretical projections of pressure transmission across the liner. The graphical representation 600 was derived from simulation results for the dual column scenario with the idealized (rigid) source using finite element analysis. Curve 602 illustrates the pressure of an acoustic transmission over a range of frequencies for a signal through the double column section with a half-inch metal enclosure. This signal is transmitted directly to the half-inch casing. Curve 604 illustrates the pressure of an acoustic transmission over a range of frequencies for a signal through the half-inch metal clad dual column section. However, the 604 curve signal is first handled by a lens, as described above, which has a cell with geometries, as discussed above, before entering the double-column section. Peaks 606 can occur as shown at particular frequencies. It should be noted that the simulation that has the metamaterial hypermedia increases the transmission of acoustic pressure through the cladding with an ideal source pressure amplification of more than four times in the cladding-cement bond, at the hyperlens design resonance of 259 kHz.

[0067] FIG. 7 shows a graphical representation 700 of illustrative theoretical projections of intensity transmission across the coating. The graphical representation 700 was derived from simulation results for the dual column scenario with the idealized (rigid) source using finite element analysis. Curve 702 illustrates the pressure of an acoustic transmission over a range of frequencies for a signal through the one-half-inch metal clad dual-column section. This signal is transmitted directly to the half inch coated dual speaker section. Line 704 illustrates the strength of an acoustic transmission over a range of frequencies for a signal through the one-half-inch metal clad dual column section. However, this signal is first handled by a lens, as described above, which has a cell with geometries, as discussed above, before entering the double-column section. It should be noted that line 704 demonstrates increased signal strength over a relatively wide frequency range. A peak 706 may occur as shown at a particular frequency. It should be noted that the simulation of the signal altered by the set of lenses of the present disclosure shows an enhanced acoustic intensity transmission through the coating compared to the control case without the hyperlens by about +30 dB in the resonance design of hyperlens of 259 kHz. It should be appreciated that the increase in signal strength is achieved without increasing the amplitude of the voltage signal applied to the transducer.

[0068] FIGS. 8A and 8B show contour projections 800 and 850, respectively, illustrating the acoustic intensity of acoustic waves emitted by a transducer 452 in a casing 834 attached to a borehole that is filled by a borehole fluid 837. contour projections 800 and 850 are derived from simulation results for the double column scenario with the idealized (rigid) source using multiphysics modeling. Graphs 800, 850 represent an end view or top view; that is, along a longitudinal axis of a borehole 836. Also, for simplicity, tool modeling is done using a symmetrical half section. Dark blue areas 860 show regions of low acoustic intensity and dark red regions 861 show areas of high acoustic intensity. In FIG. 8A, the transducer 452 emits a signal directly onto the coating 834. The acoustic intensity in the region 838 along the radial direction of the transducer has a low magnitude diffused acoustic intensity, which is generally considered undesirable for acoustic imaging. In FIG. 8B, transducer 452 emits a signal through a lens 454. As can be seen, lens 454 creates a relatively focused acoustic intensity zone 840 along a radial direction of transducer 452, which is generally considered desirable for acoustic imaging. Numerical modeling suggests that the acoustic intensity in the 840 region may be an order of magnitude greater than the acoustic intensity in the 838 region. One can observe near-collimated intensity transmission through the pipe and into the cement domain. The transmit beam width (-6 dB) is approximately 15 mm wide at the cement bonding interface with the steel casing.

[0069] FIGS. 9A and 9B show contour projections 900 and 950, respectively, illustrating the respective degree of non-productive reverberation. Graphic representations 900 and 950 are derived from simulation results for the dual column scenario with the idealized (rigid) source using multiphysics modeling. An important feature of the transmission field traversing the double-column casing with the bipolar hyperlens, as disclosed herein, is the absence of significant piping and/or casing reverberations, as indicated in the line contour projection of FIGS. 8A and 8B. The energy intensity within the piping, casing and downhole fluid associated with the amplified transmission with the hyperlensing (FIG. 8A) is of a similar magnitude to the non-resonant quiescent distribution seen in the response without the hyperlensing (FIG. 8B). An illustration of the comparison in resonant energy distribution with hyperlens and without hyperlens shown in FIGS. 9A and 9B. The intrinsic resonant response of the dual column section at 252 kHz without the hyperlens (FIG. 9B) has a large reverberation in the pipe and also in the casing to a slightly lesser extent (reverberant columns 952). Looking at FIG. 9A, in comparison, the resonant response of the double column section with the hyperlens significantly reduced reverberation in the pipe (902 quiescent columns) and effectively zero reverberation in the casing. This quiescent phenomenon associated with hyperlensing is expected to create a low noise floor compatible with pulse-echo type imaging applications that require a quiescent environment for detection of very small cement bond echo reflection signals.

[0070] FIG. 10 shows a graphical representation 1000 of illustrative theoretical projections of pressure transmission across the cladding for reflected waves. The graphical representation 1000 was derived from a simulation similar to the finite element analysis of FIG. 6, but including a small circumferential pressure anomaly interface between the steel casing and the cement domain. FIGS. 11A and 11B show contour projections 1100 and 1150, respectively, illustrating an acoustic intensity distribution for a received signal 1102 from an anomaly reflection at the cladding-cement bonding interface 464. The projection 1100 shows results with the lens assembly . The 1150 projection shows the results without the lens assembly. As before, a transducer 452 is shown in a casing 434. A pressure emitter placed in the anomaly simulates a cement bond reflection having an arc length of 15 mm.

[0071] Implicit in this analysis is the assumption that the reflection coefficient for the interfacial anomaly is 1. A pseudo-pulse-echo transfer function is constructed by first normalizing the interface emitter pressure magnitude to equal the transmission of pressure for the simulations traversing the casing shown above. The average pressure magnitude that is transmitted back to the original source boundary due to reflection is normalized with respect to the amplitude of the original ideal source to provide a simulated (two-step) pulse echo transfer function. Curves 1002 and 1004 illustrate the frequency response spectrum for the simulated pulse echo transfer function. The pulse echo transfer function for the dual column without the lens assembly (curve 1002) indicates that the high transmission at the 252 kHz intrinsic dual column resonance does not proportionally reward the reflection back to the source boundary, with a net fraction of 6.6% of the original source pressure received. In contrast, the second hyperlensing resonance at 261 kHz for curve 1004 exhibits excellent reciprocity to the reflection emitter, with a net fraction of 45.7% of the original source pressure received.

[0072] Although the present disclosure is discussed in the context of a hydrocarbon producing well, it is to be understood that the present disclosure may be used in any wellbore environment (eg, a geothermal or water well). In addition, modalities can be used in acoustic tools used on the surface or in bodies of water.

[0073] "Curvilinear array", as used here, means that the cells of the array are arranged along curved lines on a surface to which the cells are connected, as opposed to a rectangular grid of cells.

[0074] "Conformation mapping geometry", as used herein, refers to a geometry of placing cells at intersections of contour lines of a non-Cartesian coordinate system mapped onto a surface. Here the surface can be a flat base from which each cell projects in a cantilevered fashion.

[0075] "Bipolar", as used herein, refers to a two-dimensional orthogonal coordinate system. "Canonical bipolar" refers to a bipolar coordinate system based on Apollonian circles in which the constant curves u and v are circles intersecting at right angles, where the coordinates have two foci F1 and F2, which can be mapped to (- R, 0) and (R, 0), respectively, on the x-axis of a Cartesian coordinate system.

[0076] The present disclosure is subject to modalities in different ways. Shown in the figures and described in detail herein are specific embodiments of the present disclosure with the understanding that the present disclosure is to be considered an exemplary of the principles of the disclosure, and is not intended to limit the disclosure to what is illustrated and described in this document. While the foregoing disclosure is directed to specific embodiments of the disclosure, various modifications will be apparent to those skilled in the art. All variations are intended to be covered by the foregoing disclosure.

Claims (10)

1. Apparatus for investigating a subsurface volume of interest from a borehole, characterized in that it comprises: a casing (428) configured for transport along the borehole; an acoustic source (432) in the housing (428) configured to generate acoustic signals; a lens assembly (454) disposed in the housing (428) and adjacent to the acoustic source (432), the lens assembly (454) being formed by a plurality of lens elements (470, 472); wherein each lens element (470, 472) comprises a plurality of cells (310, 340, 460) arranged in an array of curvilinear cells, each cell (310, 340, 460) formed as a column oriented transversely to one direction of acoustic signal displacement, each cell (310, 340, 460) having a hub (312, 342), a plurality of spokes (314, 344) radiating from the hub (312, 342), each spoke (314, 344 ) includes a plurality of fingers (328, 352) circumferentially distributed around the hub (312, 342), where the hub (312, 342), spokes (314, 344) and fingers (328, 352) are oriented to cause the acoustic waves to travel at a different speed in each of the three orthogonal directions. Apparatus according to claim 1, characterized in that the plurality of cells (310, 340, 460) are arranged according to a conformal mapping geometry. 3. Apparatus according to claim 2, characterized in that the conformal mapping geometry comprises a Bipolar canonical conformal mapping transformation of constant contour lines [u, v] in Cartesian coordinates [x, y]. 4. Apparatus according to claim 1, characterized in that: the hub (312, 342), the plurality of spokes (314, 344) and the plurality of fingers (328, 352) are divided to form a plurality of structurally independent cell segments (318); the plurality of fingers (328, 352) are radially staggered to nest together; and the hub (312, 342), the plurality of spokes (314, 344) and the plurality of fingers (328, 352) all lie along the same plane. 5. Apparatus according to claim 1, characterized in that a metamaterial created by the plurality of cells (310, 340, 460) deforms with a different volume module in each of the three orthogonal directions. 6. Method for investigating a subsurface volume of interest, characterized in that it comprises: positioning an acoustic tool (420) in a well, wherein the acoustic tool (420) includes: a casing (428) configured for transport along from the well hole; an acoustic source (432) in the housing (428) configured to generate acoustic signals; a lens assembly (454) disposed in the housing (428) and adjacent to the acoustic source (432), the lens assembly (454) being formed by a plurality of lens elements (470, 472); wherein each lens element (470, 472) comprises a plurality of cells (310, 340, 460) arranged in an array of curvilinear cells, each cell (310, 340, 460) formed as a column oriented transversely to one direction of acoustic signal displacement, each cell (310, 340, 460) having a hub (312, 342), a plurality of spokes (314, 344) radiating from the hub (312, 342), each spoke (314, 344 ) includes a plurality of fingers (328, 352) circumferentially distributed around the hub (312, 342), wherein the hub (312, 342), spokes (314, 344) and fingers (328, 352) are oriented to make the acoustic waves travel at a different speed in each of the three orthogonal directions; and directing the acoustic waves through an adjacent aberrant medium (204) that blocks, at least partially, the direction of travel of the acoustic waves to the volume of interest. 7. Method according to claim 6, characterized in that the aberrant medium (204) is a metal pipe. 8. Method according to claim 6, characterized in that it further comprises estimating the quality of a cement bond between the cement and the metal pipe. 9. Method according to claim 6, characterized in that it further comprises the use of the acoustic transducer (452) to detect a reflected signal from the volume of interest that has traveled through the aberrant medium (204) and the set of lenses (454). 10. Method, according to claim 6, characterized in that it further comprises: receiving an acoustic signal sensitive to acoustic waves comprising information regarding the volume of interest; and use the information to estimate a parameter of interest.