US20170241260A1

US20170241260A1 - Method and apparatus for downhole measurements of velocity anisotropy on sidewall cores

Info

Publication number: US20170241260A1
Application number: US15/051,781
Authority: US
Inventors: Hector Jose Gonzalez Perez; Guodong Jin; Gaurav Agrawal; Syed Shujath ALI; Ali A. Al Dhamen
Original assignee: Baker Hughes Inc
Current assignee: Baker Hughes Holdings LLC
Priority date: 2016-02-24
Filing date: 2016-02-24
Publication date: 2017-08-24

Abstract

A method for estimating, downhole, elastic properties of a subsurface material having a bedding plane includes extracting a core sample from the subsurface material into a downhole tool, the downhole tool comprising a measurement device having a first source and a first receiver opposing the first source, the first receiver configured to receive a signal from the first source, performing at least five acoustic wave velocity measurements on the core sample in situ within the downhole tool, the measurements including compressional acoustic wave velocities and shear wave acoustic velocities with certain directions of shear acoustic wave polarization using the measurement device, estimating, with a controller, elastic properties of the core sample using the at least five acoustic wave velocity measurements, and providing an output signal comprising the elastic properties to an output signal receiving device.

Description

BACKGROUND

Many reservoirs made up of unconventional rock such as shale source rock are being used today to produce hydrocarbons. Determination of elastic properties of shale source rock is crucial for reservoir characterization and development. Knowledge of these properties helps determine well spacing design and hydraulic fracturing design among other engineering design parameters. Hence, any improvements in methods and apparatuses for characterizing shale source rock would be well received in the hydrocarbon production industry.

BRIEF SUMMARY

Disclosed is a method for estimating, downhole, elastic properties of a subsurface material having a bedding plane. The method includes extracting a core sample from the subsurface material into a downhole tool, the downhole tool comprising a measurement device having a first source and a first receiver opposing the first source, the first receiver configured to receive a signal from the first source, performing at least five acoustic wave velocity measurements on the core sample in situ within the downhole tool, the measurements including compressional acoustic wave velocities and shear wave acoustic velocities with certain directions of shear acoustic wave polarization using the measurement device, estimating, with a controller, elastic properties of the core sample using the at least five acoustic wave velocity measurements, and providing an output signal comprising the elastic properties to an output signal receiving device.
Also disclosed is an apparatus for estimating, downhole, elastic properties of a subsurface material having a bedding plane. The apparatus includes a downhole device configured to extract a core sample from the subsurface material into the downhole tool, a measurement device disposed in the downhole tool having a first source and a first receiver opposing the first source, the first receiver configured to receive a signal from the first source, the measurement device configured to perform at least five acoustic wave velocity measurements on the core sample in situ within the downhole tool, the measurements including compressional acoustic wave velocities and shear wave acoustic velocities with certain directions of shear acoustic wave polarization using the measurement device, and a controller in communication with the measurement device and configured to estimate elastic properties of the core sample using the at least five acoustic wave velocity measurements.

BRIEF DESCRIPTION OF THE DRAWINGS

The following descriptions should not be considered limiting in any way. With reference to the accompanying drawings, like elements are numbered alike:

FIG. 1 is a cross-sectional view of an embodiment of a downhole drilling, monitoring, evaluation, exploration and/or production system in accordance with an embodiment of the present disclosure;

FIG. 2A depicts aspects of a transversely isotropic medium with a vertical symmetry axis;

FIG. 2B depicts aspects of the state of stress at an arbitrary point P in the medium of FIG. 2A;

FIG. 3A is an isometric illustration of a core sample having bedding layers therein and a measurement device in accordance with an embodiment of the present disclosure;

FIG. 3B is a top down plan illustrations of the core sample and measurement device of FIG. 3A shown in a first position;

FIG. 3C is a top down plan illustrations of the core sample and measurement device of FIG. 3A shown in a second position;

FIG. 3D is a top down plan illustrations of the core sample and measurement device of FIG. 3A shown in a third position;

FIG. 4A is an isometric illustration of a core sample having bedding layers therein and a measurement device in accordance with another embodiment of the present disclosure;

FIG. 4B is a top down plan illustrations of the core sample and measurement device of FIG. 4A shown in a first position;

FIG. 4C is a top down plan illustrations of the core sample and measurement device of FIG. 4A shown in a second position;

FIG. 5A is an isometric illustration of a core sample having bedding layers therein and a measurement device in accordance with another embodiment of the present disclosure;

FIG. 5B is a top down plan illustrations of the core sample and measurement device of FIG. 5A; and

FIG. 6 is a flow process for estimating a property of a subsurface material in accordance with an embodiment of the present disclosure.

DETAILED DESCRIPTION

A detailed description of one or more embodiments of the disclosed apparatus and method presented herein by way of exemplification and not limitation with reference to the figures.
Disclosed are methods and apparatuses for downhole estimation of properties of a subsurface material before bringing samples to the surface for testing. In one or more embodiments, the properties are elastic anisotropy constants of transversely isotropic reservoir rocks such as unconventional shale. A core sample of the unconventional shale is extracted from a formation using a downhole tool conveyed through a borehole. The core sample is housed within a testing device of the downhole tool. Once the core sample is housed in the testing device, the core sample is acoustically interrogated and properties are estimated therefrom. To fully characterize the elastic properties of the transversely isotropic reservoir rock, three Thomsen anisotropy parameters with five independent elastic constants are required. Accordingly, this translates to measuring at least three separate orientations relative to bedding planes of the core sample. That is, measurements may be taken parallel, perpendicular, and at 45 degrees to bedding planes within the core sample. The present methods and apparatuses for characterizing the elastic anisotropy of transversely isotropic reservoir rocks uses a single core sample housed within a testing device or chamber downhole. The testing device or chamber in a downhole tool enables inclusion of reservoir fluids in situ and thus accurate results for estimating properties of the formation may be achieved. Sets of acoustic transducers are positioned with respect to surfaces or planes of isotropy and held in contact with the core sample by the testing device. Acoustic velocity measurements are then performed and an elasticity value of the core sample (in downhole conditions), and thus the subsurface material, is determined from the measurements.
Most gas shales are considered to be intrinsically transversely isotropic, with a symmetry axis generally aligned with the vertical. In embodiments of the present disclosure, a core sample or a plug extracted parallel to the bedding layers or formation is analyzed. In one or more embodiments, the plug is non-destructively measured in multiple configurations to yield composite information similar to what would be obtained from three plugs of different bedding angles and/or similar to measurements obtained in a laboratory with simulated downhole conditions. That is, the core sample or plug of the core sample is analyzed downhole in situ surrounded by formation fluids, etc.
A core holder is configured as part of the testing device and is specifically designed to enable measurement using three, six, or nine wave velocities along the radial direction with the downhole conditions. By adjusting the relative position of the sample bedding to the radial velocity transducers or measuring a complete set of wave velocities, variation of measured velocities with angles is determined, yielding elastic constants and Thomsen parameters. In addition, because the testing device and core holder are located on a downhole tool and the methods and apparatuses described herein are used downhole, velocity measurements under in situ reservoir stress, pore pressure, temperature, etc.
Referring to FIG. 1, a non-limiting schematic illustration of a downhole drilling, monitoring, evaluation, exploration, and/or production system 100 associated with a borehole 102 is shown. A carrier 104 is run in the borehole 102, which penetrates one or more earth formations 106 a, 106 b, the carrier 104 configured to facilitate operations such as drilling, extracting matter from the formations 106 a, 106 b, sequestering fluids such as carbon dioxide, and/or making measurements of properties of the formations 106 a, 106 b, a formation interface 107 (i.e., the interface between the formations 106 a, 106 b), and/or the borehole 102 downhole. As shown, lower formation 106 b may have one or more bedding planes or layers 111 which may be of interest for analysis. In some formations the bedding planes may be formed as parallel or substantially parallel bedding planes. The formation 106 b and the bedding planes 111 thereof represent any subsurface material of interest that may be characterized using the methods and apparatuses disclosed herein.
The carrier 104 includes any of various tools, devices, components, etc. to facilitate subterranean operations. In various embodiments, the carrier 104 is constructed of, for example, a pipe, multiple pipe sections, flexible tubing, or other structures. In other configurations, the carrier 104 is constructed of an armored wireline, such as that used in wireline logging. The carrier 104 is configured to include, for example, a drilling system and/or a bottom-hole assembly (BHA) on a downhole end thereof.
The system 100 and/or the carrier 104 may include any number of downhole tools 108 for various processes including drilling, hydrocarbon production, and formation evaluation for measuring one or more physical properties, characteristics, quantities, etc. in and/or around the borehole 102. For example, in some embodiments, the downhole tools 108 include a downhole coring tool 110. Various measurement tools can be incorporated into the system 100 to affect measurement regimes such as wireline measurement applications, measurement-while-drilling (MWD), and/or logging-while-drilling (LWD) applications.
The downhole coring tool 110 is configured to extract a core sample from the second formation 106 b, and particularly of the bedding layers 111, through a sidewall of the borehole 102. In order to extract the core sample, the tool downhole coring tool 110 includes a hollow drill bit 112 that is operated by a motor or other controller and/or drive device 114. The drill bit 112 is configured to drill through the sidewall of the borehole 102 and into the bedding layers 111 of the second formation 106 b to obtain a core sample 116. The core sample 116 is contained in a hollow portion of the drill bit 112. Once the core sample 116 is extracted it is disposed within a testing device 118 that is part of the downhole coring tool 110. The testing device 118, in some embodiments, is configured having a testing chamber to house the core sample 116 or a plug thereof. Other techniques for extracting the core sample may also be employed and/or multiple separate or combined devices and/or components may be used to obtain a core sample. For example, in addition to a coring tool, a plug tool may be configured within the downhole coring tool 110 or in another tool or device that is configured to extract a plug from the core sample 116.
While the system 100 may operate in any subsurface environment, FIG. 1 shows the downhole tools 108 disposed in the borehole 102 penetrating the earth 109 (including a first formation 106 a and a second formation 106 b, the second formation 106 b having bedding layers 111). The downhole tools 108 are disposed in the borehole 102 at a distal end of the carrier 104. As shown, the downhole tools 108 include measurement tools (e.g., controller/motor 114, testing device 118, drill bit 112, etc.) and downhole electronics 120 configured to perform one or more types of measurements in LWD or MWD applications and/or operations. In a LWD or MWD configuration, the carrier 104 is a drill string. However, the coring processes and analysis as described herein may be performed separate from drilling operations, and in such embodiments the carrier may be a wireline or similar conveyance structure.
A drilling rig 122 is configured to conduct drilling operations such as rotating the carrier 104 (e.g., a drill string) and/or convey other downhole devices through the borehole 102. The downhole electronics 120 are configured generate data, i.e., collect data, at the downhole tools 108. Raw data and/or information processed by the downhole electronics 112 may be telemetered along telemetry 113 to the surface for additional processing or display by a computing system 124. In some configurations, drilling and/or positioning (e.g., movement) control signals are generated by the computing system 124 and conveyed downhole the downhole tools 108 or, in alternative configurations, are generated within the downhole electronics 120 or by a combination thereof. The downhole electronics 120 and the computing system 124 may each include one or more processors and one or more memory devices.
Turning to FIG. 2A, a schematic illustration of a core sample is shown, and FIG. 2B shows an arbitrary point of the core sample for demonstrating a stress tensor. The core sample 216 is formed of a plurality of bedding layers 211. A vertical axis of symmetry A_zis shown passing perpendicular through the bedding planes 211. Further, as shown, each bedding plane 211 extends in x- and y-directions.
Most gas shales are considered to be an intrinsically transversely isotropic (TI) medium. Such a medium is characterized by the existence of a single plane of isotropy (e.g., an x-y plane) and one single axis of rotational symmetry (e.g., vertical axis of symmetry A_z) normal to the isotropy plane (e.g., x-y plane) as illustrated in FIG. 2A.
The state of stress at an arbitrary point P of the medium, e.g., a point P in any plane of the bedding layers 211 of the core sample 216, can be defined by a stress tensor [σ]
$\begin{matrix} [σ] = σ_{ij} = [\begin{matrix} σ_{11} & σ_{12} & σ_{13} \\ σ_{21} & σ_{22} & σ_{23} \\ σ_{31} & σ_{32} & σ_{33} \end{matrix}], i, j = 1, 2, 3 & (1) \end{matrix}$
In Eq. (1), the stress component σ_ijis defined as acting on the i-plane and being oriented in the j direction. The point P is imagined as an infinitesimally small cube as illustrated in FIG. 2B. Components of the stress tensor with repeating indices, e.g., σ₁₁, σ₂₂, σ₃₃, are denoted as normal stress while a stress component with different indices (e.g., σ₁₂) is called a shear stress. By consideration of moment equilibrium of the medium, one can find that σ_ij=σ_ji. Therefore, only six independent stress components are required to define completely the state of stress at any point P.
When an elastic body is subjected to stress, changes in size and shape occur and these deformations are called strain. Using the same notation as shown in FIG. 2B, the strain at point P is determined by the strain tensor [ε]:
$\begin{matrix} [ɛ] = ɛ_{ij} = [\begin{matrix} ɛ_{11} & ɛ_{12} & ɛ_{13} \\ ɛ_{21} & ɛ_{22} & ɛ_{23} \\ ɛ_{31} & ɛ_{32} & ɛ_{33} \end{matrix}], i, j = 1, 2, 3 & (2) \end{matrix}$
Similar to stress, the components of the strain tensor [ε] with repeating indices are denoted as normal strain, all others as shear strain. Accordingly, the strain tensor [ε] has six independent components because ε_ij=ε_ji, as will be appreciated by those of skill in the art.
Stress and strain are related to each other by Hooke's Law where the strain is assumed to be sufficiently small that stress and strain depend linearly on each other. For a transversely isotropic media, it can be written as
$\begin{matrix} \begin{matrix} [\begin{matrix} σ_{11} \\ σ_{22} \\ σ_{33} \\ σ_{23} \\ σ_{31} \\ σ_{12} \end{matrix}] = [\begin{matrix} C_{11} & C_{12} & C_{13} & 0 & 0 & 0 \\ C_{12} & C_{11} & C_{13} & 0 & 0 & 0 \\ C_{13} & C_{13} & C_{33} & 0 & 0 & 0 \\ 0 & 0 & 0 & C_{44} & 0 & 0 \\ 0 & 0 & 0 & 0 & C_{44} & 0 \\ 0 & 0 & 0 & 0 & 0 & C_{66} \end{matrix}] [\begin{matrix} ɛ_{11} \\ ɛ_{22} \\ ɛ_{33} \\ γ_{23} = 2 ɛ_{23} \\ γ_{31} = 2 ɛ_{31} \\ γ_{12} = 2 ɛ_{12} \end{matrix}] with \end{matrix} & (3) \\ C_{12} = C_{11} - 2 C_{66} & (4) \end{matrix}$
From the above matrix equation, there are five non-zero independent elastic constants: C₁₁, C₃₃, C₁₃, C₄₄, and C₆₆. Here, C₁₁is the in-plane (parallel to the plane of isotropy) compressional modulus, C₃₃, is the out-of-plane (perpendicular to the plane of isotropy) compressional modulus, C₄₄, is the out-of-plane shear modulus, and C₆₆is the in-plane shear modulus, C₁₃is a constant that controls the shape of the wave surfaces.
To characterize the anisotropy degree of a medium, Thomsen (1986) introduced three anisotropy parameters ε, δ, and γ, which represent combinations of the five independent elastic constants:
$\begin{matrix} ε = \frac{C_{11} - C_{33}}{2 C_{33}} & (5) \\ γ = \frac{C_{66} - C_{44}}{2 C_{44}} & (6) \\ δ = \frac{{(C_{13} + C_{44})}^{2} - {(C_{33} - C_{44})}^{2}}{2 C_{33} (C_{33} - C_{44})} & (7) \end{matrix}$
where ε reflects the degree of anisotropy of the compressional wave propagating in the medium; δ reflects the degree of anisotropy of the shear wave. These parameters allow for a statement like “anisotropy is x %”; If they are less than 0.1, the medium can be assumed to be “weakly anisotropic”.
Determination of the five independent elastic constants above requires five independent wave measurements. One way is to measure the velocities on three core plugs cut from a single whole core sample in three different orientations. The three plugs are cut in three different orientations: one parallel to the bedding planes, one perpendicular to the bedding planes, and one at 45 degrees to the cylindrical symmetry axis in order to derive the five independent elastic constants.
Turning now to FIGS. 3A-3D, various schematic illustrations of a core sample 316 are shown. FIG. 3A is an isometric illustration of the core sample 316 illustrating bedding layers 311 existing therein. FIGS. 3B-3D are top down plan illustrations of the core sample 316 illustrating various positions of a measurement device 326 relative to the core sample 316. The measurement device 326, as shown, includes a source 328 and a receiver 330. The source 328 and the receiver 330 form a source/receiver pair of the measurement device 326.
In some embodiments, the source may be configured as an acoustic wave source or transducer that is configured to convert an electrical signal into an emitted acoustic wave. Any or all of the acoustic transducers (or other sources) described herein may be driven by piezoelectric operation, electromagnetic operation, or magnetostrictive operation as non-limiting examples. It will be appreciated that acoustic transducers for transmitting and receiving compression waves and/or shear waves having a desired direction or directions of polarization are commercially available.
The measurement device 326 is coupled, such as electrically connected by electrical conductors, to a controller within the downhole tool, such as downhole tool 108 in FIG. 1. However, in other embodiments, the controller may be configured on the surface and in communication with the measurement device 326. The controller has a structural configuration to enable the controller to control operation of the measurement device 326, and particularly the sources 328 and receivers 330, in order to measure the velocity of the different types of acoustic waves for interrogating the core sample 316. In one or more embodiments, the controller is implemented by electronics or by a computer processing system having computer-executable instructions and hardware for implanting those instructions for measuring the various acoustic wave velocities. In one or more embodiments, the controller is configured to measure the travel time of the acoustic wave as it travels from the source transducer to the receiver transducer and to calculate the acoustic wave velocity by dividing the known distance between the source and receiver transducers by the measured travel time. The controller may also be configured to calculate the Thomsen parameters using the various measured acoustic wave velocities and to output results to a user using an output interface connected to an output device such as a display, recorder, printer, or other processing system.
According to the wave polarization and propagation directions with respect to a bedding-parallel lamination (e.g., bedding layers 311), nine velocities can be measured. For propagation perpendicular to the bedding layers 311, there are a vertically propagating compressional wave (V_PV) and two vertically propagating shear waves (V_SV1and V_SV2), as shown in FIGS. 3A and 3B. For propagation at 45 degree relative to the axis of symmetry, there are a quasi-compressional wave (V_qP) with the same polarization direction as propagation direction, and two quasi-shear waves (V_qSVand V_qSH), as shown in FIG. 3C. For propagation parallel to the bedding layers 311, there are a horizontally propagating compressional wave (V_PH), a shear wave (V_SV) with horizontal propagation and vertical polarization, and a shear wave (V_SH) with horizontal propagation and polarization direction, as shown in FIG. 3D.
Only five wave velocities are required to calculate the five elastic constants: V_PV, V_SV1=V_SV2, V_PH, V_SH, and V_qP. They are related through the following equations:
$\begin{matrix} C_{11} = {ρ (V_{PH})}^{2} & (8) \\ C_{33} = {ρ (V_{PV})}^{2} & (9) \\ C_{44} = {ρ (V_{SV 1})}^{2} & (10) \\ C_{66} = {ρ (V_{SH})}^{2} & (11) \\ C_{13} = - C_{44} + \sqrt{4 {ρ^{2} (V_{qP})}^{4} - 2 {ρ (V_{qP})}^{2} (C_{11} + C_{33} + 2 C_{44}) + (C_{11} + C_{44}) (C_{33} + C_{44})} & (12) \end{matrix}$
The method and apparatus disclosed herein of characterizing the elastic anisotropy of transversely isotropic reservoir rocks uses only one core sample (or core sample plug) such as the one illustrated in FIGS. 3A-3D, as compared to prior laboratory solutions using three core plugs with different orientations relative to the bedding layers. The core sample is extracted parallel to the bedding layers in a formation. In one or more embodiments the core sample is non-destructively measured in multiple configurations to yield composite information similar to what would be obtained using three separate plugs while the core sample is maintained downhole and thus in downhole environments and conditions.
The core sample 316 is jacketed in a core holder or other chamber in a downhole tool (e.g., downhole tool 108 in FIG. 1), specifically designed to measure nine wave velocities at one or more pressure and/or temperature as illustrated in FIGS. 3A-3D. The core holder and/or testing chamber of the downhole tool enables acoustic wave velocity measurements under in situ reservoir conditions such as stress (i.e., pressure), pore pressure, temperature, etc. To accomplish this, the testing chamber or core holder is configured with the measurement device 326. The measurement device 326, in some non-limiting embodiments, is configured as an axial acoustic transducer set, with the source 328 being an axial acoustic wave source and the receiver 330 being an axial acoustic wave receiver. In some non-limiting embodiments, the measurements device 326 (and/or components thereof) are configured, installed, or housed without a housing or jacket of the core holder or other chamber.
As shown in FIG. 3B, a first measurement may be made with the measurement device 326 in a first position. In the first position of the measurement device 326, the source 328 and the receiver 330 are located such that acoustic waves propagating from the source 328 to the receiver 330 are traveling perpendicular to the bedding layers 311. That is, the receiver 330 is positioned opposite the source 328 about the core sample 316 along a diameter or radial line through the core sample 316. The first position of the measurement device 326 is indicated by first line 317 a. In the first position, the measurement device 326 is configured to measure a first measurement including the vertically propagating compressional wave (V_PV) and the two vertically propagating shear waves (V_SV1and V_SV2).
The measurement device 326 can be rotated 45°, as shown in FIG. 3C, to a second position and a second measurement is made. The rotation may be achieved by rotating the measurement device 326 relative to the core sample 316. In some embodiments, the measurement device 326 is rotated and the core sample 316 is held in a stationary or static position. That is, the downhole tool or a portion there of that contains or houses the measurement device 326 is rotated while the core sample 316 is not rotated. In an alternative configuration, the core sample 316 is rotated and the measurement device 326 is static or does not move. The movement can be achieved by rotation of a core holder or other device. Those of skill in the art will appreciate that the core sample 316 is rotated relative to the measurement device 326, and the means for doing do may be by any configuration and/or process, including those described above, combinations thereof, and/or variations thereon.
In the second position of the measurement device 326, the source 328 and the receiver 330 are located such that acoustic waves propagating from the source 328 to the receiver 330 are traveling 45 degrees relative to the axis of symmetry to the bedding layers 311. That is, the receiver 330 is positioned opposite the source 328 about the core sample 316 along a diameter or radial line through the core sample 316. The second position of the measurement device 326 is indicated by second line 317 b. In the second position, the measurement device 326 is configured to measure the second measurement including the quasi-compressional wave (V_qP) with the same polarization direction as the propagation direction, and the two quasi-shear waves (V_qSVand V_qSH).
The measurement device 326 can be rotated another 45° (90° relative to the first position), as shown in FIG. 3D, to a third position and a third measurement is made. In the third position of the measurement device 326, the source 328 and the receiver 330 are located such that acoustic waves propagating from the source 328 to the receiver 330 are traveling perpendicular relative to the axis of symmetry to the bedding layers 311 (i.e., parallel to the bedding layers 311). That is, the receiver 330 is positioned opposite the source 328 about the core sample 316 along a diameter or radial line through the core sample 316. The second position of the measurement device 326 is indicated by third line 317 c. In the third position, the measurement device 326 is configured to measure the third measurement including the horizontally propagating compressional wave (V_PH), the shear wave (V_SV) with horizontal propagation and vertical polarization, and the shear wave (V_SH) with horizontal propagation and polarization direction.
Thus, by rotating the measurement device 326 45° at a time through the first, second, and third positions, and taking measurements at each position, the wave velocities required to calculate the five elastic constants (e.g., V_PV, V_SV1=V_SV2, V_PH, V_SH, and V_qP) are measured. Accordingly, determination of elastic properties of the core sample 316, and thus the formation from which the core sample 316 was extract, may be made, as described above.
The different wave velocity measurements yield the elastic constants and thus the Thomsen parameters. In general, the acoustic wave velocity measurements are performed sequentially in order to avoid interference between the different types of wave velocity measurements. However, in some cases the order of measurements may be different than that described above, without departing from the scope of the present disclosure.
Advantageously, because the measuring process described above using the measurement device 326 is performed downhole, within or in connection with a downhole tool, the in situ properties and characteristics of the particular core sample 316 are present during the measurements and thus an accurate analysis may be obtained. Accordingly, methods and downhole instruments/tools for measuring the velocity anisotropy of sidewall cores immediately after extraction from a formation and before bringing the cores to the surface for testing are provided. Measuring the core anisotropy downhole keeps the reservoir fluids in place and enables accurate results, which are representative of the formation in reservoir conditions.
Further, in some embodiments, the measurement device 326 or other device/tool is configured to measure a diameter of sidewall cores downhole. That is, measurements of diameter may be made under downhole pressures, temperatures, and other downhole environmental conditions. Accordingly, the measurement device 326 may not be only configured to measure acoustic wave velocities, but may be configured to perform other tests and/or analyses on a core sample downhole, prior to bringing the core sample to the surface.
Turning now to FIGS. 4A-4C, an alternative configuration of a measurement device 426 in accordance with the present disclosure is shown. FIG. 4A is an isometric illustration of the measurement device 426 as installed about a core sample 416 having bedding layers 411. FIGS. 4B and 4C are a top down plan illustrations of the core sample 416 illustrating various positions of the measurement device 426 relative to the core sample 416. The measurement device 426, as shown, includes two sources 428 a, 428 b and two respectively paired receivers 430 a, 430 b. A first source 428 a and a first receiver 430 a form a first source/receiver pair and a second source 428 b and a second receiver 430 b form a second source/receiver pair of the measurement device 426. The first pair is configured 45° offset from the second pair. That is, a 45° rotational angle separates a line passing through the elements of the first pair from a line passing through the elements of the second pair.
As shown, the same measurements as achieved in the configuration of FIGS. 3A-3D are achieved with only one relative rotation between the measurement device 426 and the core sample 416. That is, in a first configuration of the measurement device 426, the first position 417 a and the second position 417 b are both available, and thus the first measurement and the second measurement can be made in the first configuration. Further, a single relative rotation (from FIG. 4B to FIG. 4C) enables measurement of the remaining characteristics, by rotating the measurement device 426 into the second position 417 b and the third position 417 c, as shown in FIG. 4C. As will be appreciated by those of skill in the art, in the second configuration of the measurement device 426 (FIG. 4C) the second position 417 b may be measured a second time, if desired. As shown, the relative rotation moves the first pair 428 a, 430 a from the first position 417 a to the second position 417 b, and the second pair 428 b, 430 b moves from the second position 417 b to the third position 417 c.
The different wave velocity measurements yield the elastic constants and thus the Thomsen parameters. In general, the acoustic wave velocity measurements are performed sequentially in order to avoid interference between the different types of wave velocity measurements. However, in some cases some of the acoustic wave velocity measurements may be performed simultaneously if interference or cross-talk does not substantially affect those measurements.
Turning now to FIGS. 5A and 5B, another alternative configuration of a measurement device 526 in accordance with the present disclosure is shown. FIG. 5A is an isometric illustration of the measurement device 526 as installed about a core sample 516 having bedding layers 511. FIG. 5B is a top down plan illustrations of the core sample 516 illustrating a position of the measurement device 526 relative to the core sample 516. The measurement device 526, as shown, includes three sources 528 a, 528 b, 5528 c and three respectively paired receivers 530 a, 530 b, 530 c. A first source 528 a and a first receiver 530 a form a first source/receiver pair, a second source 528 b and a second receiver 530 b form a second source/receiver pair, and third source 528 c and a third receiver 530 c form a third source/receiver pair of the measurement device 526. The first pair is configured 45° offset from the second pair, and the third pair is offset from the second pair by 45° and offset from the first pair by 90°. That is, a 45° rotational angle separates a line passing through the elements of the first pair from a line passing through the elements of the second pair, and a 45° rotational angle separates a line passing through the elements of the second pair from a line passing through the elements of the first pair.
As shown, the same measurements as achieved in the configuration of FIGS. 3A-3D are achieved with no relative rotation between the measurement device 526 and the core sample 516. That is, in a first configuration of the measurement device 526, all of the first position 517 a, the second position 517 b, and the third position 517 c are available, and thus the first, second, and third measurements can be made in the first configuration without any relative rotation. The different wave velocity measurements yield the elastic constants and thus the Thomsen parameters. In general, the acoustic wave velocity measurements are performed sequentially in order to avoid interference between the different types of wave velocity measurements. However, in some cases some of the acoustic wave velocity measurements may be performed simultaneously if interference or cross-talk does not substantially affect those measurements.
As will be appreciated by those of skill in the art, the exact orientation of the measurement device or parts thereof (as provided herein) and the bedding layers of the core sample may not be known. However, advantageously, the above described measurements can be carried out downhole, and then when the core sample is delivered to the surface, further testing may be performed to correct for any offsets from the assumptions made above. For example, if the initial measurement is made not exactly perpendicular to the bedding layers, this can be corrected by consideration of the other measurements, and knowing the position of the first measurement, which may be stored with the collected information.
FIG. 6 is a flow process of a method 600 for estimating, downhole, a property of a subsurface material having bedding plane in accordance with an embodiment of the present disclosure. Block 602 calls for extracting a core sample of the subsurface material into a downhole tool. The downhole tool can include a testing chamber or other sample housing having one or more sensors that are part of a measurement device. The core sample may be extracted as a cylinder or other shape and housed within the housing and rotated or adjusted to a position to be measured using the measurement device. In some embodiments, the measurement device includes a single source/receiver pair (e.g., FIGS. 3A-3D), although other configurations (e.g., FIGS. 4A-4C; FIGS. 5A-5B) may be used without departing from the scope of the present disclosure. When the core sample is extracted from the formation, surrounding fluids and other downhole conditions are present at the downhole tool, and thus any measurements performed downhole with the measurement device will be subject to the downhole environment and thus accurate measurements and accurate characteristics and/or properties may be obtained regarding the formation.
Block 604 calls for performing at least five acoustic wave velocity measurements on the core sample within the downhole tool using the measurement device. If the measurement device includes one or two pairs of source/receiver, the measurement step of Block 604 will include an optional rotating process wherein the core sample is rotated relative to the measurement device (e.g., rotating the core sample, rotating the measurement device, or both). If the measurement device includes only one pair of source and receiver, the optional rotating may occur twice, with a first rotation being a 45° rotation, and a second rotation being a 45° rotation. If the measurement device includes two source/receiver pairs, a single rotation of 45° may be needed. If the measurement device includes three source/receiver pairs, no rotation is needed.
Block 606 calls for estimating, with a controller, elastic properties of the core sample, and thus the formation from which the core sample was extracted. The estimation uses the at least five acoustic wave velocity measurements obtained at Block 604. The estimation may be performed using the mathematical relationships described herein. Further, in some embodiments the controller is part of the downhole tool, and thus the estimation is made downhole. In other embodiments, the controller may be located on the surface, and the measurements obtained at Block 604 are transmitted or otherwise communicated to the surface for making the estimation at the controller (e.g., computing system 124 shown in FIG. 1).
Block 608 calls for providing an output signal comprising the estimated elastic properties to an output signal receiving device.
The method 600 may also include conveying the downhole tool through a borehole penetrating the subsurface material, the downhole tool being configured to extract the core sample of the subsurface material. The method 600 may also include extracting the core sample from the subsurface material using the downhole tool and conveying the extracted core sample to the surface of the earth. At the surface of the earth, the method 600 may also include performing additional measurements and/or testing, extracting plug sample(s) from the core sample, etc.
The method 600 may also include using an output interface to provide the output signal. The output signal may be used for at least one of displaying on a display the estimated elastic properties, recording the estimated elastic properties on a non-transitory computer readable medium, and printing the estimated elastic properties using a printer.
Set forth below are some embodiments of the foregoing disclosure:

Embodiment 1

A method for estimating, downhole, elastic properties of a subsurface material having a bedding plane, the method comprising: extracting a core sample from the subsurface material into a downhole tool, the downhole tool comprising a measurement device having a first source and a first receiver opposing the first source, the first receiver configured to receive a signal from the first source; performing at least five acoustic wave velocity measurements on the core sample in situ within the downhole tool, the measurements including compressional acoustic wave velocities and shear wave acoustic velocities with certain directions of shear acoustic wave polarization using the measurement device; estimating, with a controller, elastic properties of the core sample using the at least five acoustic wave velocity measurements; and providing an output signal comprising the elastic properties to an output signal receiving device.

Embodiment 2

The method according to embodiment 1, further comprising conveying the downhole tool through a borehole penetrating the subsurface material.

Embodiment 3

The method according to embodiment 1, wherein performing the at least five acoustic wave velocity measurements comprises: performing a first measurement with the first source and first receiver in a first position; rotating the measurement device relative to the core sample by 45° such that the first source and the first receiver are in a second position; performing a second measurement with the first source and the first receiver in the second position; rotating the measurement device relative to the core sample by 45° such that the first receiver and the second receiver are in a third position, wherein the third position is not equal to the first position; and performing a third measurement with the first source and the first receiver in the third position.

Embodiment 4

The method according to embodiment 1, wherein the measurement device comprises a second source and a second receiver opposing the second source, the second receiver configured to receive a signal from the second source.

Embodiment 5

The method according to embodiment 4, wherein performing the at least five acoustic wave velocity measurements comprises: performing a first measurement with the first source and first receiver at a first position and the second source and second receiver at a second position; rotating the measurement device relative to the core sample by 45° such that the first source and the first receiver are in the second position and the second source and second receiver are in a third position; and performing a second measurement with at least the second source and the second receiver in the third position.

Embodiment 6

The method according to embodiment 1, wherein the measurement device comprises: a second source and a second receiver opposing the second source, the second receiver configured to receive a signal from the second source, wherein a line passing through the second source and second receiver is 45° offset from a line passing through the first source and first receiver; and a third source and a third receiver opposing the third source, the third receiver configured to receive a signal from the third source, wherein a line passing through the third source and third receiver is 45° offset from a line passing through the second source and second receiver and 90° offset from the line passing through the first source and first receiver.

Embodiment 7

The method according to embodiment 1, further comprising: conveying the extracted core sample to the surface of the earth; and performing a correction operation such that at least five acoustic wave velocity measurements are oriented to the bedding plane of the core sample.

Embodiment 8

The method according to embodiment 1, wherein the at least five acoustic wave velocity measurements comprise: a parallel compression wave velocity measurement (VPH) of a compression acoustic wave traveling parallel to the bedding plane; a parallel shear wave velocity measurement (VSH) of a shear acoustic wave traveling parallel to the bedding plane and polarized parallel to the bedding plane; a perpendicular compression wave velocity (VPV) of a compression acoustic wave traveling perpendicular to the bedding plane; a perpendicular shear wave velocity measurement (VSV1) of a shear acoustic wave traveling perpendicular to the bedding plane and polarized parallel to the bedding plane; and a quasi-compression wave velocity (VqP) of a compression acoustic wave traveling at a 45° angle with respect to a direction of the bedding plane.

Embodiment 9

The method according to embodiment 1, wherein providing an output signal comprises using an output interface.

Embodiment 10

The method according to embodiment 1, further comprising at least one of displaying on a display the estimated elastic properties, recording the estimated elastic properties on a non-transitory computer readable medium, and printing the estimated elastic properties using a printer.

Embodiment 11

An apparatus for estimating, downhole, elastic properties of a subsurface material having a bedding plane, the apparatus comprising: a downhole device configured to extract a core sample from the subsurface material into the downhole tool; a measurement device disposed in the downhole tool having a first source and a first receiver opposing the first source, the first receiver configured to receive a signal from the first source, the measurement device configured to perform at least five acoustic wave velocity measurements on the core sample in situ within the downhole tool, the measurements including compressional acoustic wave velocities and shear wave acoustic velocities with certain directions of shear acoustic wave polarization using the measurement device; and a controller in communication with the measurement device and configured to estimate elastic properties of the core sample using the at least five acoustic wave velocity measurements.

Embodiment 12

The apparatus according to embodiment 11, further comprising a carrier configured to convey the downhole tool through a borehole penetrating the subsurface material.

Embodiment 13

The apparatus according to embodiment 11, wherein the measurement device is configured to: perform a first measurement with the first source and first receiver in a first position; rotate relative to the core sample by 45° such that the first source and the first receiver are in a second position; perform a second measurement with the first source and the first receiver in the second position; rotate relative to the core sample by 45° such that the first receiver and the second receiver are in a third position, wherein the third position is not equal to the first position; and perform a third measurement with the first source and the first receiver in the third position.

Embodiment 14

The apparatus according to embodiment 11, wherein the measurement device comprises a second source and a second receiver opposing the second source, the second receiver configured to receive a signal from the second source.

Embodiment 15

The apparatus according to embodiment 14, wherein the measurement device is configured to: perform a first measurement with the first source and first receiver at a first position and the second source and second receiver at a second position; rotate relative to the core sample by 45° such that the first source and the first receiver are in the second position and the second source and second receiver are in a third position; and perform a second measurement with at least the second source and the second receiver in the third position.

Embodiment 16

The apparatus according to embodiment 11, wherein the measurement device comprises: a second source and a second receiver opposing the second source, the second receiver configured to receive a signal from the second source, wherein a line passing through the second source and second receiver is 45° offset from a line passing through the first source and first receiver; and a third source and a third receiver opposing the third source, the third receiver configured to receive a signal from the third source, wherein a line passing through the third source and third receiver is 45° offset from a line passing through the second source and second receiver and 90° offset from the line passing through the first source and first receiver.

Embodiment 17

The apparatus according to embodiment 11, wherein the controller is configured to perform a correction operation such that at least five acoustic wave velocity measurements are oriented to the bedding plane of the core sample.

Embodiment 18

The apparatus according to embodiment 11, wherein the at least five acoustic wave velocity measurements comprise: a parallel compression wave velocity measurement (VPH) of a compression acoustic wave traveling parallel to the bedding plane; a parallel shear wave velocity measurement (VSH) of a shear acoustic wave traveling parallel to the bedding plane and polarized parallel to the bedding plane; a perpendicular compression wave velocity (VPV) of a compression acoustic wave traveling perpendicular to the bedding plane; a perpendicular shear wave velocity measurement (VSV1) of a shear acoustic wave traveling perpendicular to the bedding plane and polarized parallel to the bedding plane; and a quasi-compression wave velocity (VqP) of a compression acoustic wave traveling at a 45° angle with respect to a direction of the bedding plane.

Embodiment 19

The apparatus according to claim 11, further comprising an output interface configured to output the estimation of the controller.

Embodiment 20

The apparatus according to claim 11, further comprising at least one of a display to display the estimated elastic properties, a recorder to record the estimated elastic properties on a non-transitory computer readable medium, or a printer for printing the estimated elastic properties.
The above disclosed techniques provide several advantages. One advantage is that only a single core sample of the subsurface material is required for testing in the downhole tool, thus providing in situ measurements (e.g., under downhole environmental conditions). This eliminates the difficulties in trying to simulate downhole conditions, extracting multiple plug samples at different angles from one brittle core sample, transporting and handling the core sample, etc. Another advantage is that the testing can be performed more efficiently and with more precision using the downhole tool when located downhole.
Embodiments provided herein enable measurement of velocity anisotropy of sidewall cores downhole immediately after coring, i.e., in situ. Various embodiments include methods, tools, processes, and/or sensors of marking the core (or bedding) orientation relative to the formation immediately after coring. Further, an instrument of measuring the diameter of the sidewall cores downhole is enabled herein, also configured to operate in situ. Further, in some embodiments, a measurement device or other downhole tool for extracting and housing sidewall cores is provided and configured such that a portion of the tool and/or the extracted core can be rotated.
Further, embodiments provided herein provide configurations of various numbers of downhole velocity source/receiver pairs. One source/receiver pair enables measuring one compressional and two shear wave velocities at the same time along the radial direction of one sidewall core. Further, depending upon the downhole tool configuration, the number of the source/receiver pair and their positions can be varied. For example, one set of source/receiver pair is provided, which can be (a) rotated if the device of holding the sidewall core is not rotated, or (b) fixed if the sidewall core is rotated, or both. Further, two sets of source/receiver pair are provided, which are positioned as shown and described above and can be rotated or fixed. Furthermore, three sets of source/receiver pair are provided, which are positioned as shown and described above and can be rotated or fixed.
Moreover, embodiments provided herein supply an instrument for moving the core samples into or out of a test chamber for velocity measurement. Furthermore, a process for correcting and computing the five elastic constants of sidewall cores is provided.
Advantageously, embodiments provided herein can provide accurate results, measurements, and/or estimations representative of a downhole formation and reduce uncertainties caused by unavoidable changes in pressure, temperature, and environment when bringing the cores to surface.
In support of the teachings herein, various analysis components may be used, including a digital and/or an analog system. For example, the downhole electronics, computer processing systems, or controllers as used herein may include digital and/or analog systems. The system may have components such as a processor, storage media, memory, input, output, communications link (wired, wireless, optical or other), user interfaces, software programs, signal processors (digital or analog) and other such components (such as resistors, capacitors, inductors and others) to provide for operation and analyses of the apparatus and methods disclosed herein in any of several manners well-appreciated in the art. It is considered that these teachings may be, but need not be, implemented in conjunction with a set of computer executable instructions stored on a non-transitory computer readable medium, including memory (ROMs, RAMs), optical (CD-ROMs), or magnetic (disks, hard drives), or any other type that when executed causes a computer to implement the method of the present invention. These instructions may provide for equipment operation, control, data collection and analysis and other functions deemed relevant by a system designer, owner, user or other such personnel, in addition to the functions described in this disclosure.
Further, various other components may be included and called upon for providing for aspects of the teachings herein. For example, a power supply, cooling component, heating component, magnet, electromagnet, sensor, electrode, transmitter, receiver, transceiver, antenna, controller, optical unit, electrical unit or electromechanical unit may be included in support of the various aspects discussed herein or in support of other functions beyond this disclosure.
The term “carrier” as used herein means any device, device component, combination of devices, media and/or member that may be used to convey, house, support or otherwise facilitate the use of another device, device component, combination of devices, media and/or member. Other exemplary non-limiting carriers include drill strings of the coiled tube type, of the jointed pipe type and any combination or portion thereof. Other carrier examples include casing pipes, wirelines, wireline sondes, slickline sondes, drop shots, bottom-hole-assemblies, drill string inserts, modules, internal housings and substrate portions thereof.
Elements of the embodiments have been introduced with either the articles “a” or “an.” The articles are intended to mean that there are one or more of the elements. The terms “including” and “having” are intended to be inclusive such that there may be additional elements other than the elements listed. The conjunction “or” when used with a list of at least two terms is intended to mean any term or combination of terms. The term “configured” relates one or more structural limitations of a device that are required for the device to perform the function or operation for which the device is configured. The terms “first,” “second” and the like do not denote a particular order, but are used to distinguish different elements.
The flow diagram depicted herein is just an example. There may be many variations to this diagram or the steps (or operations) described therein without departing from the spirit of the invention. For instance, the steps may be performed in a differing order, or steps may be added, deleted or modified. All of these variations are considered a part of the claimed invention.
While one or more embodiments have been shown and described, modifications and substitutions may be made thereto without departing from the spirit and scope of the invention. Accordingly, it is to be understood that the present invention has been described by way of illustrations and not limitation.
It will be recognized that the various components or technologies may provide certain necessary or beneficial functionality or features. Accordingly, these functions and features as may be needed in support of the appended claims and variations thereof, are recognized as being inherently included as a part of the teachings herein and a part of the invention disclosed.
While the invention has been described with reference to exemplary embodiments, it will be understood that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications will be appreciated to adapt a particular instrument, situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims

What is claimed is:

1. A method for estimating, downhole, elastic properties of a subsurface material having a bedding plane, the method comprising:

extracting a core sample from the subsurface material into a downhole tool, the downhole tool comprising a measurement device having a first source and a first receiver opposing the first source, the first receiver configured to receive a signal from the first source;

performing at least five acoustic wave velocity measurements on the core sample in situ within the downhole tool, the measurements including compressional acoustic wave velocities and shear wave acoustic velocities with certain directions of shear acoustic wave polarization using the measurement device;

estimating, with a controller, elastic properties of the core sample using the at least five acoustic wave velocity measurements; and

providing an output signal comprising the elastic properties to an output signal receiving device.

2. The method according to claim 1, further comprising conveying the downhole tool through a borehole penetrating the subsurface material.

3. The method according to claim 1, wherein performing the at least five acoustic wave velocity measurements comprises:

performing a first measurement with the first source and first receiver in a first position;

rotating the measurement device relative to the core sample by 45° such that the first source and the first receiver are in a second position;

performing a second measurement with the first source and the first receiver in the second position;

rotating the measurement device relative to the core sample by 45° such that the first receiver and the second receiver are in a third position, wherein the third position is not equal to the first position; and

performing a third measurement with the first source and the first receiver in the third position.

4. The method according to claim 1, wherein the measurement device comprises a second source and a second receiver opposing the second source, the second receiver configured to receive a signal from the second source.

5. The method according to claim 4, wherein performing the at least five acoustic wave velocity measurements comprises:

performing a first measurement with the first source and first receiver at a first position and the second source and second receiver at a second position;

rotating the measurement device relative to the core sample by 45° such that the first source and the first receiver are in the second position and the second source and second receiver are in a third position; and

performing a second measurement with at least the second source and the second receiver in the third position.

6. The method according to claim 1, wherein the measurement device comprises:

a second source and a second receiver opposing the second source, the second receiver configured to receive a signal from the second source, wherein a line passing through the second source and second receiver is 45° offset from a line passing through the first source and first receiver; and

a third source and a third receiver opposing the third source, the third receiver configured to receive a signal from the third source, wherein a line passing through the third source and third receiver is 45° offset from a line passing through the second source and second receiver and 90° offset from the line passing through the first source and first receiver.

7. The method according to claim 1, further comprising:

conveying the extracted core sample to the surface of the earth; and

performing a correction operation such that at least five acoustic wave velocity measurements are oriented to the bedding plane of the core sample.

8. The method according to claim 1, wherein the at least five acoustic wave velocity measurements comprise:

a parallel compression wave velocity measurement (V_PH) of a compression acoustic wave traveling parallel to the bedding plane;

a parallel shear wave velocity measurement (V_SH) of a shear acoustic wave traveling parallel to the bedding plane and polarized parallel to the bedding plane;

a perpendicular compression wave velocity (V_PV) of a compression acoustic wave traveling perpendicular to the bedding plane;

a perpendicular shear wave velocity measurement (V_SV1) of a shear acoustic wave traveling perpendicular to the bedding plane and polarized parallel to the bedding plane; and

a quasi-compression wave velocity (V_qP) of a compression acoustic wave traveling at a 45° angle with respect to a direction of the bedding plane.

9. The method according to claim 1, wherein providing an output signal comprises using an output interface.

10. The method according to claim 1, further comprising at least one of displaying on a display the estimated elastic properties, recording the estimated elastic properties on a non-transitory computer readable medium, and printing the estimated elastic properties using a printer.

11. An apparatus for estimating, downhole, elastic properties of a subsurface material having a bedding plane, the apparatus comprising:

a downhole device configured to extract a core sample from the subsurface material into the downhole tool;

a measurement device disposed in the downhole tool having a first source and a first receiver opposing the first source, the first receiver configured to receive a signal from the first source, the measurement device configured to perform at least five acoustic wave velocity measurements on the core sample in situ within the downhole tool, the measurements including compressional acoustic wave velocities and shear wave acoustic velocities with certain directions of shear acoustic wave polarization using the measurement device; and

a controller in communication with the measurement device and configured to estimate elastic properties of the core sample using the at least five acoustic wave velocity measurements.

12. The apparatus according to claim 11, further comprising a carrier configured to convey the downhole tool through a borehole penetrating the subsurface material.

13. The apparatus according to claim 11, wherein the measurement device is configured to:

perform a first measurement with the first source and first receiver in a first position;

rotate relative to the core sample by 45° such that the first source and the first receiver are in a second position;

perform a second measurement with the first source and the first receiver in the second position;

rotate relative to the core sample by 45° such that the first receiver and the second receiver are in a third position, wherein the third position is not equal to the first position; and

perform a third measurement with the first source and the first receiver in the third position.

14. The apparatus according to claim 11, wherein the measurement device comprises a second source and a second receiver opposing the second source, the second receiver configured to receive a signal from the second source.

15. The apparatus according to claim 14, wherein the measurement device is configured to:

perform a first measurement with the first source and first receiver at a first position and the second source and second receiver at a second position;

rotate relative to the core sample by 45° such that the first source and the first receiver are in the second position and the second source and second receiver are in a third position; and

perform a second measurement with at least the second source and the second receiver in the third position.

16. The apparatus according to claim 11, wherein the measurement device comprises:

17. The apparatus according to claim 11, wherein the controller is configured to perform a correction operation such that at least five acoustic wave velocity measurements are oriented to the bedding plane of the core sample.

18. The apparatus according to claim 11, wherein the at least five acoustic wave velocity measurements comprise:

19. The apparatus according to claim 11, further comprising an output interface configured to output the estimation of the controller.

20. The apparatus according to claim 11, further comprising at least one of a display to display the estimated elastic properties, a recorder to record the estimated elastic properties on a non-transitory computer readable medium, or a printer for printing the estimated elastic properties.