ESTIMATION OF MECHANICAL PROPERTIES OF TRANSVERSE ISOTROPIC MEDIA

专利摘要:
The present invention discloses systems and methods for determining the mechanical properties of anisotropic media. A method for determining the mechanical properties of an anisotropic medium includes obtaining anisotropic medium log data, log data corresponding to measurements of the anisotropic medium collected with a logging tool; determining values for a plurality of first stiffness components of a stiffness matrix based on horizontal and vertical speeds derived from the log data; determining an upper limit for a second rigidity component of the stiffness matrix based on the values for the plurality of first stiffness components; estimating a value for the second stiffness component based on the determined upper limit; determining a mechanical property of the anisotropic medium based on the estimated value of the second stiffness component and providing the determined mechanical property.
公开号:FR3067746A1
申请号:FR1855103
申请日:2018-06-12
公开日:2018-12-21
发明作者:Mehdi Eftekhari Far
申请人:Halliburton Energy Services Inc；
IPC主号:

专利说明:

ESTIMATION OF MECHANICAL PROPERTIES OF TRANSVERSE ISOTROPIC MEDIA
Cross reference to related applications [0001] The present application claims priority over the provisional American application no. 62 / 520,402 entitled "ESTIMATION OF MECHANICAL PROPERTIES OF TRANSVERSE ISOTROPIC MEDIA", filed on June 15, 2017, all of which are incorporated herein by reference.
TECHNICAL FIELD This description generally relates to the determination of mechanical properties, and more particularly, for example, without limitation, systems and methods for the extraction of gas and petroleum involving the determination of mechanical properties of anisotropic media based on training measures.
BACKGROUND OF THE DISCLOSURE The polar anisotropic media, which are commonly known as transversely isotropic media (TI), have an axis of rotation with closed loop and an infinite set of double axes perpendicular thereto. A plane of symmetry exists perpendicular to the closed loop axis. The media types are known as transversely isotropic (TI), with alternative names like vertical transverse isotropic (VTI), horizontal transverse isotropic (HTI) and inclined transverse isotropic (TTI). The VTI is a suitable model for describing unfractured stratified media and in particular shale. The shale formations constitute approximately 75% of the sedimentary basins, and this makes the VTI the most common anisotropic model in exploratory seismology. Shales play an important role in fluid flow and seismic imagery due to their low permeability and anisotropic properties.
A TI stiffness tensor contains five elastically independent constants and provides useful information to aid in various well operations, such as determining locations for drilling a horizontal well or identifying intervals for drilling. Unfortunately, it is difficult to reliably obtain the stiffness tensor using conventional methods, or obtaining it requires measurements that are not available at all depths in a well.
BRIEF DESCRIPTION OF THE FIGURES [0005] Figure IA is a diagram of an example of a drilling system which can use the principles of this disclosure.
Figure IB is a diagram of an example of a wired system that can use the principles of this disclosure.
Figure 2 is a diagram of an exemplary logging tool that can use the principles of this disclosure.
Figure 3 is a diagram illustrating an example of polar anisotropic symmetry.
Figure 4 is a diagram illustrating examples of reports of
Fish.
Figures 5A to 51 are graphs illustrating an example of input data and resulting errors.
Figures 6A to 6D are graphs illustrating examples of sensitivities of G.3 at different speeds.
Figures 7A to 7C are diagrams illustrating examples of Poisson reports.
Figure 8 is a graph illustrating an example of plotting as a function of G.3 · [0014] Figure 9 is a graph illustrating examples of upper and lower limits.
FIG. 10 is a graph illustrating examples of details of the estimate ^ 13 · [0016] FIGS. 11A to 111 are graphs illustrating an example of input data and the resulting errors.
Figures 12A to 12F are diagrams illustrating examples of Poisson reports.
Figures 13A to 13F are graphs illustrating examples of Thomson parameters.
Figure 14 is a graph illustrating an example of estimating δ using regression analysis.
Figure 15 is a flowchart illustrating an example of a method for calculating the mechanical properties of an anisotropic medium.
In one or more implementations, all the components illustrated in each figure would not be necessary, and one or more implementations may include additional components which are not illustrated in a figure. Variations in the arrangement and type of components may be made without departing from the spirit or scope of this disclosure. Additional components, different components, or a smaller number of components may be used within the scope of this disclosure.
DETAILED DESCRIPTION The detailed description presented below is intended to be a description of various implementations and it is not intended to represent only those implementations in which the technology described can be practiced. As will be understood by those skilled in the art, the implementations described can be modified in a number of different ways, without departing from the scope of this disclosure. Consequently, the figures and the description should be considered as illustrative in nature and not restrictive.
The present description generally relates to the determination of mechanical properties, and more particularly, for example, without limitation, systems and methods for the extraction of gas and petroleum involving the determination of the mechanical properties of anisotropic media, such as than transversely isotropic, orthotropic and / or orthotropic medium, based on the measurements of a formation.
Systems and methods for determining the mechanical properties of anisotropic media.
The principles of this disclosure can be used, e.g., in various types of well systems, such as drilling systems, completion systems, and wired systems for wells which may be useful for extraction. gas and / or petroleum. FIG. IA is a diagram of an example of a drilling system 100 which can use the principles of the present disclosure, according to one or more embodiments. As illustrated, the drilling system 100 may include a drilling platform 102 positioned at the surface of the earth and a wellbore 104 which extends from the drilling platform 102 to one or more underground formations 106. In other embodiments, such as in an offshore or underwater drilling operation, a volume of water can separate the drilling platform 102 and the wellbore 104.
The drilling system 100 may include a derrick 108 supported by the drilling platform 102 and comprising a movable block 110 making it possible to raise and lower the drilling column 112. A kelly 114 can support the drilling column 112 when it is lowered through a rotary table 116. A drilling bit 118 can be coupled to the drilling column 112 and powered by a motor at the bottom of the well and / or by rotation of the drilling column 112 by the rotary table 116. When the drill bit 118 rotates, it creates the well 104, which penetrates the underground formations 106. A pump 120 can circulate drilling fluid through a supply pipe 122 and the kelly 114, towards the bottom of the hole inside the drill string 112, through orifices in the drill bit 118, and back to the surface through the ring defined around the drill string 112, and in a retention basin 124. The The drilling fluid cools the drill bit 118 during operation and transports the cuttings from the wellbore 104 into the retention basin 124.
The drilling system 100 may also include a downhole assembly (BHA) coupled to the drill string 112 near the drill bit 118. The BHA may include various downhole measurement tools such as, without limitation, measurement during drilling (MWD) and logging during drilling (LWD) tools, which can be designed to take downhole measurements of well-related parameters, such as drilling conditions, properties training, etc. The MWD and LWD tools may include at least one logging tool 126, which may include one or more sensors having a plurality of sensing elements capable of collecting measurements or log data useful for determining wellbore parameters , including the mechanical properties of the formation. In some embodiments, the logging tool 126 is implemented as or otherwise includes a sonic logging tool having one or more acoustic transmitters and / or one or more acoustic receivers designed to measure and collect data that can be analyzed to provide measurements of the elastic wave velocity of an anisotropic medium in formation 106. In the present context, a "sonic logging tool" describes any logging tool designed to collect waveform data elastic based on acoustics, which can be in audible and / or inaudible frequencies. The transmitters and / or receivers may be designed to transmit and / or receive waves propagating in multiple different directions (e.g. vertical, horizontal and / or off-axis) and / or propagating in multiple different modes (e.g. e.g. monopoly, dipole, quadrupole). Analysis of the different modes using standard methods can provide the desired elastic wave measurements, such as compression and shear rates, through the formation of interest.
When the drill bit 118 extends the well 104 through the formations 106, the logging tool 126 can collect measurements which can be used to estimate the mechanical properties of the formations 106. The logging tool 126 and other sensors of the MWD and LWD tools can be coupled in communication to a telemetry module 128 used to transfer measurements and signals from the BHA to a surface receiver (not illustrated) and / or to receive commands from of the surface receiver. Telemetry module 128 may include any known means of downhole communication including, without limitation, a pulse-through-mud telemetry system, an acoustic telemetry system, a wired communication system, a wireless communication system wire, or any combination thereof. In some embodiments, the telemetry module 128 may be omitted and the drill string 112 may instead include a wired drill pipe or a wired wound tube used to transfer data through wired conductors to a receiver in area. In some embodiments, some or all of the measurements taken by the logging tool 126 can be stored inside the logging tool 126 or the telemetry module 128 for later retrieval at surface level during recovery of the drill string 112.
At various times during the drilling process, the drill string 112 can be removed from the well bore 104 as shown in Figure IB, to perform measurement / logging operations. More particularly, FIG. 1B illustrates a diagram of an example of a cable drilling system 200 which can use the principles of the present disclosure, according to one or more embodiments. Similar numbers used in Figures IA and IB refer to the same components or elements and, therefore, may not be described again in detail. As illustrated, the wired system 200 may include a wired instrument probe 202 which can be suspended in the wellbore 104 by a means of transport 204. Even if the means of transport 204 is illustrated as a cable in Figure IB, in various embodiments, a means of transportation may include, e.g., a wired line, a smooth cable, a drill pipe, coiled tubing, a downhole tractor, or a combination of them. The wired instrument probe 202 can include the logging tool 126, which can be coupled in communication to the transport means 204. In various embodiments, the transport means 204 can transport the telemetry and / or the current or not . For example, the transport means 204 may include conductors for transporting current to the wired instrument probe 202 and also to facilitate communication between the surface and the wired instrument probe 202. A logging unit 206, illustrated in FIG. 1B in the form of a truck, can collect the measurements coming from the logging tool 126, and can include computer components 208 for controlling, processing, storing and / or viewing the measurements collected by the logging tool 126 The computer components 208 can be coupled in communication to the logging tool 126 with the transport means 204.
Even if the computer components 208 are illustrated at the top of the hole in FIG. 1B, in various embodiments of the present disclosure, the methods described here can be implemented at the top of the hole, at the bottom of the hole, or both . For example, a processing system comprising one or more processors and / or memories designed to implement any of the methods for calculating the mechanical properties described here can be placed at the bottom of the hole in the borehole 104 (e.g., in the logging tool 126 or the instrument probe 202), at the top of the hole in the logging unit 206, or a combination thereof, may be designed to implement these methods using techniques of distributed treatment.
FIG. 2 is a diagram of an example of a logging tool 126 in more detail, according to certain embodiments. The logging tool 126 illustrated in FIG. 2 generally comprises one or more TX transmitters and one or more RX receivers. TX transmitters are generally designed to transmit waves in an anisotropic medium of interest, eg, formation 106 (see Figures IA to IB), while RX receivers are generally designed to measure a response corresponding to the waves emitted after interaction of the waves with the medium of interest. As an example, the TX transmitter (s) may include one or more acoustic transmitters (e.g., piezoelectric transmitters) that act as a source of audible and / or inaudible sounds to generate elastic waves in the anisotropic medium, and the receptor (s) RX can include one or more acoustic receivers (eg, piezoelectric receivers) that pick up the returned waves emitted by the acoustic transmitter (s). In some embodiments, the TX transmitters include a plurality of transmitters of two or more different types (e.g., selected from monopole transmitters, dipole transmitters and quadrupole transmitters) to allow determination of the various different speeds disclosed herein . Even if only one TX transmitter is illustrated in Figure 2, in various embodiments the logging tool 126 may include any suitable number of transmitters. For example, the logging tool 126 may include 2, 3, 4, 5 or more transmitters. Although only two RX receivers are illustrated in Figure 2, in various embodiments the logging tool 126 may include any suitable number of receivers. For example, the logging tool 126 may include 2, 3, 4, 5 or more receivers.
As shown in Figure 2, the logging tool 126 may generally be in the form of an elongated component defining a longitudinal axis 127, which can be placed at the bottom of the hole in a well bore 104 (see figures IA to IB). The TX transmitter (s) are generally axially spaced along the longitudinal axis with respect to the RX receivers to allow the capture of the desired data. In the example illustrated, multiple receivers are included, which are also axially spaced from each other, to allow the capture of delay time information from the transmitted waves.
i In some embodiments, the data from the logging tool 126 can be used to predict the mechanical properties of the formation. Predicting the correct values of Poisson's ratio (v) and Young's modulus (E), which can be used to calculate the fracture gradient and minimum horizontal stress, is useful for mechanical geometry, hydraulic fracturing and the completion. The minimum horizontal constraint is useful for selecting where to install and punch. With improved predictions of the moduli of elasticity, the minimum and maximum horizontal stress can be better evaluated. A stress versus depth profile associated with the brittleness of the rock predicted from the profiles of the moduli of elasticity is useful to help choose the "ideal points" for drilling a horizontal well, and also to determine the perforation intervals.
In some embodiments, a method is proposed for the precise calculation of the Young's moduli, the Poisson ratio and other mechanical and seismic properties of the medium with superposition (or stratification or fractures). In some embodiments, the methods described here provide highly accurate estimates while reducing the number of entries, which can be difficult to obtain even from core measurements. In some applications, carrots are not acquired at all depths; therefore, there is a need for a process which is less affected by the lack of core data.
Conventional approaches to calculating these properties use measurements at angles of 0, 90 and 45 degrees (the third may also be an arbitrary off-axis angle, between 0 and 90) relative to the axis of symmetry of the middle. In some embodiments, the methods described here do not require 45 ° measurements (or other off-axis measurements).
The characterization of the elastic properties of the VTI medium has been of great interest during the past three to three decades for several applications such as seismic imaging, drilling and geomechanics of completion. Even though there has been good progress in taking into account IT models for seismic applications, these models are still poorly understood for other applications such as geomechanics. For geomechanical and drilling applications, the assumptions idealized for IT models such as homogeneity, elasticity and dependence on scale, are violated more than in seismic applications. For seismic applications, many of these problems are less important, in part because of the larger seismic wavelengths that can ignore small-scale heterogeneities and in part because rocks remain in the elastic range, unlike geomechanical applications .
When taking into account the TI models, according to at least some embodiments disclosed here, the so-called dynamic mechanical properties (eg, Young's modules and Poisson ratios) derived from the measurements of the speed d waves in rocks may be related to static mechanical properties, which are more relevant to engineering applications. This can be called a static correction problem. Ignoring the anisotropy caused by stratification and thin layer organization (TTI) can lead to errors and significant problems in understanding the true relationship between dynamic and static properties. This problem seems to be more serious for Poisson ratios since it is defined as a fraction and the dynamic values obtained can be very different from the real values. As described here, small uncertainties in the measured velocities can lead to very large errors in the calculation of Poisson ratios.
In some embodiments, ignoring the VTI model for rocks that actually have VTI symmetry will affect the investigation of the dynamic-static property. There is an important difference between the VTI and the isotropic mechanical properties, which could have prevented the earlier observation of any significant relationship for Poisson ratios (and perhaps Young's moduli). The only property, which seems to be least affected by ignoring the VTI, is the estimate of the Young Ey modulus, which appears to be close to what would be observed by the isotropic assumption.
The concept of the Poisson ratio (isotropic definition and generally calculated from wave velocities) has been a controversial subject in geophysics, some suggesting that it should not be used for geophysical applications due to the fact that it is calculated using velocities while the true value of the Poisson ratio must be measured by the real mechanical load and the use of strain gauges. However, the Poisson ratio can be a useful tool for characterizing the mechanical properties of rock through, for example, friability. In some embodiments, careful measurement of dynamic Poisson ratios can preserve the relative relationships between Poisson ratios VTI and even provide dynamic results, which are close to static measurements. A basic assumption here is that various effects such as the assumption of dispersion and elasticity will be canceled out when calculating Poisson ratios.
According to certain embodiments, using the relationships which must be maintained for the Poisson reports in the VTI medium, a variation range for £ 13 can be defined. The limits for Çt3 are relatively narrow for several rock samples. For the measures in which the relationships between the Poisson ratios VTI are violated, this can be attributed to errors in £ 13 since the other four components of the stiffness matrix VTI are measured directly while C ₁₃ is calculated from other speeds and involves 45 ° measurements. As described here, C ₁₃ is very sensitive to errors in other speeds, especially 45 ° speed measurements.
The Thomsen notation and the parameters ε, γ and δ were used for several applications, because of their simplicity. Thomsen's notation and parameters are described, eg, in Thomsen, L., 1986, “Weak Elastic Anisotropy,” Geophysics 51 (10), 1954-1966. Although it is widely accepted that ε and γ are closely related (γ in several cases slightly higher than ε), there has not been any significant relationship between δ and the other two parameters. As described here, this ambiguity lies in the complications in the measurement of off-axis speeds (and subsequently C ₁₃ ) used to calculate δ but also due to the complicated definition of δ itself. If C ₁₃ is calculated with precision, δ seems to have a significant relation to ε and γ.
Theory [0041] Linear elasticity can describe the behavior of a variety of materials, such as the media constituting shales and other formations. The stress-stress relationships for a linear elastic material in 3D are complex since the material can be subjected to a variety of different compressive and shear stresses in different directions around any given point.
The generalized Hooke's law captures this complexity by modeling stress (σ) and stress (ε) as second-order tensors (σ ^, ε ^ ·) in which each stress component depends linearly on each component of constraint. This relationship between stress and stress is characterized by a material constant called stiffness (C) which can be represented by a fourth order tensor C _i7fei which defines the linear mapping between the two second order tensors corresponding to stress and to the constraint (σ ^ · = C _i7fci f _i7 ). It should be noted that the inverse of the stiffness is called the elasticity (S), and it should be understood that any calculation of the elasticity can generally be considered equivalent to the calculation of the stiffness within the framework of this description.
Mathematically, the stress and stress tensors can be represented in a Cartesian coordinate system as follows, in which the indices 1, 2, 3 correspond to the 3 axes in the coordinate system (eg, x = 1, y = 2, z = 3):
' ^σ 11 12 ^σ 13 ' ' ^ε ιι ^ε 12 ^ε 13 ^σ 21 ^σ 22 ^σ 23 > ^£ ij ^ε 21 ^ε 22 ^ε 23 . ^σ 31 ^σ 32 ^σ 33.^ε 31 ^ε 32 ^ε 33.
As a mapping between 3 by 3 matrices, the stiffness tensor Cij _kl can be represented by a 3 by 3 by 3 by 3 matrix having 81 components. The inherent symmetries of these mechanical properties make it possible to considerably simplify these equations and relationships. Voigt notation provides a standard mapping for tensor indices and allows the reduction of symmetric tensors for stress, stress and stiffness into two first-order tensors and a second-order tensor, respectively. This mapping is illustrated in the following equation, which omits the redundant stress and stress components due to the symmetry (σ ₂₃ = σ ₃₂ , ε ₁₃ = ε ₃₁ , ...):
-σ _χ = σγγ- 'Gi C ₁₂ C ₁₃ C ₁₄ C ₁₅ C ₁₆ ^ε ι - ε _χ1 - ^σ 2 ^{= σ} 22 Gi c ₂₂ c ₂₃ c ₂₄ c ₂₅ c ₂₆ ^ε 2 ^{= ε} 22 ^σ 3 ^{= σ} 33 Gl G2 C ₃ 3 £ 34 Gs Gô^ε 3 ^{= ε} 33 ^σ 4 ^{= σ} 23 Gi G2 G3 G4 Gs Ge^ε 4 - ^ε 23 ^σ 5 ^{= σ} 13 Gi G2 G3 G4 Gs Ge^ε 5 ^{= ε} 13 - ^σ 6 ^{= σ} 12- -Gi G2 G3 G4 Gs Gô- - ^ε 6 ^{= ε} 12-
components are illustrated for the previous stiffness matrix, which are sometimes called stiffness coefficients or elastic constants. While 36 stiffness components are illustrated, the symmetry of the stiffness matrix means that only 21 of its components are independent for the most general case of anisotropic elasticity.
The stiffness matrix can be further simplified for a variety of types of isotropy and anisotropy. For example, for isotropic media the stiffness matrix can be reduced to only two independent components corresponding to volume changes and shear deformations. For various types of anisotropy (transverse isotropy, orthotropic, orthothrombic, and others), the stiffness matrix can be simplified to less than 21 independent components.
The polar anisotropic media, which are commonly called transversely isotropic media (TI), have an axis of rotation with closed loop and an infinite set of double axes perpendicular thereto. A plane of symmetry exists perpendicular to the closed loop axis. The media types are known as transversely isotropic (TI), with alternative names like vertical transverse isotropic (VTI), horizontal transverse isotropic (HTI) and inclined transverse isotropic (TTI).
FIG. 3 illustrates an example of a TI medium 351 in which the axis of rotation with closed loop corresponds to the axis of symmetry 353 and extends in a vertical direction, perpendicular to the direction of stratification 355 of the medium. A stiffness tensor TI contains five elastically independent constants. The VTI is a suitable model for describing unfractured stratified media and in particular shale. The shale formations constitute approximately 75% of the sedimentary basins, and this makes the VTI the most common anisotropic model in exploratory seismology. Shales play an important role in fluid flow and seismic imagery due to their low permeability and anisotropic properties. It will be understood that even if examples are described here with reference to the VTI medium, the principles of this disclosure can be extended to various other types of medium, if necessary.
The stiffness matrix for the medium VTI in a coordinate system in which the directions xi and% 2 are in a horizontal plane and x ₃ is in the
vertical direction (see Figure 3) has the form of: G. C „-2C ₆₆ C, 3 0 0 0 ' C „-2C ₆₆ C _u Cu 0 0 0 C = C _I3 vs^ 13 Cu 0 0 0 VTI 0 0 0 Cu 0 0 0 0 0 0 Cu 0 0 0 0 0 0 Q ₆ _
The components of the stiffness matrix VTI, C _{11 (} C ₃₃ , C ₅₅ and Qo can be defined in terms of vertical and horizontal compression and shear rates. It should be noted that C ₄₄ = C ₅₅ for the medium VTI, and, consequently, the preceding matrix can equivalently be expressed using C _44. C ₁₃ , on the other hand generally requires measurements of speed off axis. For reasons of simplicity, the speed of the 45 ° compression wave is used in the equation to calculate (4) C ₁₃ .
c ₁₃ = V (2pP _P ² 45 - c _ir - C ₅₅ ) (2pV _p ² 45 - C ₃₃ - C ₅₅ ) - C ₅₅ (4) The parameters of Thomsen are also defined in terms of
Eyelash - ^ 33
2C ₃₃
C66-C55 ^2C 5S fi (Cl3 + ^ 55) ² - (^ 33- ^ 55) ^{2 2C} 33 (C33- ^C S5) (5) (6) (7) [0051] Anisotropic Poisson ratios (v _i; ·) For the VTI medium are defined by the following general equation:
^v ü = (8) By replacing the marking of the axes of 1.2 by H, h and 3 by V, the axes define:
(9)
Vhh = Γ (10) ^fc / l
V “V = - r (11) £ h The three Poisson ratios in a VTI medium are illustrated in FIG. 4, in each case, the first arrow indicates the direction of the stress applied and the following arrow illustrates the direction of expansion, orthogonal to applied stress. It should be noted that in the case v _HH , s _h is used to distinguish directions 1 and 2 because the values of horizontal stress are different during the evaluation v _HH , if not one would obtain v _HH = 1 which is not not fair.
In terms of Q, ·, the Poisson ratios VTI as well as the vertical Young's modulus (E _v ) and the horizontal Young's modulus (F _H ) are,
C11C · (12) _ C33 (Gl ~ ² ^ 66) ~ ^ 13 '' HH rr · z-2 (13)
Vy =
E _v =
2 (Ch-C ₆₆ ) ^C 33t ^C li ~ C66) ~ ^C 13 (14) (15) (16)
E _h =
6nC ₃₃ —Cf ₃ As the preceding equations demonstrate, C ₁₃ enters into the calculation of all these mechanical properties as well as the Thomsen parameter δ. Therefore, the uncertainties in 613 will affect all of its properties. Calculation 613 using equation (4) is very sensitive to uncertainties in speeds, particularly at speed at 45 °.
Referring to Figures 5A to 51, a simple MonteCarlo simulation reveals the effects of small errors in the speed measurements for the calculation of C ₁₃ , δ, and Poisson ratios. Figures 5A through 51 illustrate sample graphs 500a-500i to demonstrate sensitivities based on measurements from a dataset for a rock sample. Graphs 500a-500i illustrate an example of how parameters and mechanical properties are sensitive to variations or inaccuracies in speeds. Graphs 500a to 500i illustrated in Figures 5A to 51 illustrate the results of an experiment performed using data from a rock sample, but it should be noted that this experiment was repeated for many others rock samples and that the same observations were made for all experiments.
The graphs 500a-d illustrated in FIGS. 5A to 5D contain histograms based on four speed values measured for the sample, respectively (ie, vertical compression speed Vp0 = 3350 m / s , horizontal compression speed Vp90 = 5533 m / s, compression speed at 45 ° Vp45 = 4360 m / s and horizontal shear speed Vs90 = 3246 m / s). The horizontal bars 590a-d illustrate these measured speed values. 100 noise values were generated for each speed, the maximum added noise being equal to 1% of each speed quantity. These values are illustrated in the form of vertical bars in FIGS. 5A to 5D and have been taken as inputs for the analysis.
In FIGS. 5E to 51, the equations (4, 7, 12, 13 and 14) were used to calculate C _i3 , Poisson and the Poisson ratios VTI for each of the 100 permutations. The results of these calculations are reported in Figures 500e-i. In FIG. 5E, the graph 500e illustrates the values of G.3 calculated for each permutation in the form of vertical bars and illustrates the value of G.3 expected in the form of a horizontal bar 590e. The results are represented in the same way in FIGS. 5F to 51 in the graphs 500f-i for δ and the Poisson ratios VTI. In Figure 5F, graph 500f illustrates the values of δ calculated for each permutation in the form of vertical bars and illustrates the true value of δ in the form of horizontal bar 590f. In Figure 5G to 51, graphs 500g-i illustrate the calculated values of v _HV , v _HH , and the values v _v for each permutation in the form of vertical bars and illustrate the true values of v _HV , v _HH , and the values of v _v as horizontal bars 590g-i, respectively.
As shown in Figure 5E, even a small maximum error of 1% can cause C ₁₃ values which are different from 10 gigapascals (GPa). The difference for δ can be as high as 0.5 (see Figure 5F), and about 0.3 for Poisson ratios (see Figures 5G to 51). The same error rate as Çl3, can be observed for dynamic Young's modules (not illustrated). These differences can give completely different results and conclusions regarding the elastic properties of rock. In some applications, 45 ° measurements are the main causes of error in the estimation of C ₁₃ , and therefore, the mechanical properties of δ and VTI.
Figures 6A to 6D illustrate an example of how the parameters and mechanical properties are sensitive to different speeds. In particular, Figures 6A to 6D illustrate graphs 600a-d containing examples of results of a sensitivity analysis demonstrating how errors in the off-axis speed Vp45 can have a greater effect on Cj ₃ values in comparison at other speeds.
In this example, the ultrasonic data measured on approximately 450 rock samples were used for the analysis. A variation range for the velocities was defined for each sample. The range of variation for the n ^'th sample was [V - V 600' + 600] meter per second m / s. In particular, for each speed measurement, 1201 values were generated, of which the average value in the generated series was the measured value coming from the data. The vertical axis shows the number of the rock sample for the dataset that was used. There are approximately 450 rock samples (therefore the vertical axis is from 1 to approximately 450). Going along a horizontal line from left to right, the first value is V ¹ - 600 m / s and the last value indicated is V '+ 600 m / s. The measured values for the velocities are given by the white curve which passes through the middle of each cloud.
Referring to graph 600a illustrated in FIG. 6A, to see the effect of VpO on ^ 13 in this example, Ul3 was calculated using equation (4) by varying VpO for each sample in the range [V'pO - 600 to V 'p0 + 600], while using only the values measured for the rest of the velocities (V'p90, Vp45 and Vs90) for the sample f ^me (in which i is the rock sample number). This was repeated for graphs 600b (figure 6B), 600c (figureôC) and 600d (figure 6D) to calculate the sensitivities of ^ 13 to V'p90, Vp45 and Vs90, respectively, in each case defining a range of variation for the given speed, while keeping the other speeds unchanged. In order to be able to see significant trends, for each plot, the data was sorted based on the given speed which was varied. For example, in Cl3: the plot VpO illustrated in FIG. 6A, C ₁₃ is sorted by increasing VpO.
The hatching shows the value of £ -13 in this sensitivity analysis. Therefore, a more lateral variation (if it is consistent for the majority of the 450 samples) in each plot means that ^ 13 is more sensitive than the specific parameter. The results in this example show that C ₁₃ is more sensitive to Vp45 than other velocities because ^ 13 changes the most when the Vp45 is changed. This can be seen in Figure 6B, going from left to right, a much more abrupt change in C ₁₃ values for Vp45 is observed. This is consistent for almost all 450 samples. ^ 13 also has a relatively high sensitivity to VsO or C55 · Even if they are not as apparent, these conclusions can also be drawn from equation (4).
In some applications, Vp45 is the most problematic speed for the measurement for several reasons such as the difficulties in preparing the sample with an exact angle of 45 ° and in some cases problems of beam speed versus group . Adding to the complexity, Figures 6A to 6D demonstrate that C ₁₃ can be greatly affected by small errors in Vp45. FIGS. 5A to 51 show that these errors in ^ 13 can give elastic properties of the rock which are completely different from reality. Consequently, in certain applications, unless all the velocities (particularly the 45 °) are measured very precisely, major errors in the calculation of the properties of the rock and the characterization of the anisotropy (δ) can occur. Problems associated with Vp45 measurements, and therefore C ₁₃ , are sometimes attributed to group / phase velocity problems, particularly when point transducers are used. However, in some applications, the correction of the phase speed to the group speed does not always solve the problem of inaccurate measurements £ -13 ·
The limits of Poisson ratios and C _Î3 The relations among Poisson ratios VTI can be used to define practical upper and lower limits for 0.3 · A set of examples of upper and lower limits for Q3 is illustrated in l inequality (17). The lower limit comes from the fact that: 1) £ -13 must be positive, and 2) 0 <v _HH <v _HV . The upper limit comes from the fact that 0 <v _HH , however, it will be shown here that this is not the correct upper limit for C ₁₃ .
VC33C12 + ^ 66 - £ -66 <Cl ₃ <VC33C12 (17) One reason why the upper limit of equation (17) is not right is that there is a relation which must be considered in the VTI environment and which, to date, has been ignored by previous approaches. The missing relationship is illustrated in inequality (18).
v _V <v _HH (18) One reason why this relationship exists is hidden in the way that Poisson relationships are defined, as shown in equations (8-11). Figures 7A to 7C are diagrams of the VTI medium, which illustrate how Poisson relationships are defined and are provided to help demonstrate the reason why the relationship illustrated in inequality (18) exists.
FIG. 7A illustrates a representation of the static Poisson ratio v _v in the medium VTI 351. As shown in FIG. 7A, during the calculation of v _v , the medium VTI 351 is compressed in the vertical direction. The VTI 351 medium is more elastic in the vertical direction because the planes of weakness make it easier to compress the VTI 351 medium in the vertical direction. Therefore, a high stress in the vertical direction (ε _ν ) is felt. However, the resulting lateral stress (ε _Η ) is much lower because the VTI 351 medium is more rigid in the horizontal direction and is not much expanded in the horizontal direction due to stress acting in the vertical direction. Therefore, ε _ν "> ε _Η . Furthermore, when v _v is calculated, the vertical stress ε _ν goes to the denominator (v _v = - -), making v _v very small. This shows that v _v must be the smallest Poisson ratio in VTI rocks. Consequently, what remains in the search for the relationship between the three Poisson ratios VTI is to determine if v _HH <v _HV ° UVfiH> ^V HV [0069] FIG. 7B illustrates a representation of the static Poisson ratio v _HH in VTI 351 medium. When calculating v _HH , VTI 351 medium is compressed in the horizontal direction h. h is used as the first horizontal direction to distinguish it from H which is the second horizontal direction. It is important to make this distinction because when the rock is compressed in the direction h, e _h and ε _Η will be different, otherwise v _HH = 1, which has no physical meaning. When calculating v _HH , the rock is less elastic in the horizontal direction because this time the rocks are not pushed against the planes of weakness. Consequently, an average stress in the direction h (ε _Λ ) is observed, and an even smaller stress (compared to h) in the direction H (ε _Η ) is observed.
Therefore, ε _κ »ε _Η . When calculating v _HH , e _h goes to the denominator (v _HH = - but it ^£ h is not as large as ε _ν when calculating v _v . Consequently, v _HH will be larger than v _v .
FIG. 7C illustrates a representation of the static Poisson ratio v _HK in the medium VTI 351. When calculating v _HV , if the medium VTI 351 is compressed in the direction H, ε _Η will be greater than ε _ν ( to have a Poisson ratio less than 1). However, ε _ν , in this case, is relatively large (and goes to the numerator) due to the properties of the medium VTI and it is easy to expand them in the vertical direction when they are compressed in the horizontal direction. Consequently, v _HV must be the greatest Poisson ratio in a medium VTI, and it becomes obvious that v _HH <v _HV .
In summary, the following relationship must be true for all VTI rocks:
<v _v <v _HH <v _HV (19) The newly defined relation v _v <v _HH gives us an opportunity to establish a practical upper limit of C ₁₃ . This inequality (equation 18) gives the following inequality:
C ^ 3 + bCf + cC 3 + d> 0 (20) in which the coefficients b, c, d can include the stiffness components, as follows (21) c - - C11C33 (22) d - 2C ₃ 3 ( C ₁₁ - C ₆₆ ) (C _{1; l} - 2C ₆₆ ) (23) If inequality (18) is treated as an equation:
C ^ 3 + bCfi + cCi3 + d = 0, (24) Referring now to Figure 8, to see the behavior of the inequality (20), the data from a rock sample were taken, and while keeping the other Cfi unchanged, we varied, C ₁₃ . Figure 8 is a graph 800 illustrating the results of this analysis, which shows the inequality (20) reported as a function of C ₁₃ . The left vertical line 871 is the measured value of C ₁₃ , and the vertical line 873 to the right is the second root of equation (24).
With reference to FIG. 8, as an example, the acceptable range for G 3 always seems to be between the first and the second root of equation (24) and the measured values of C ₁₃ seem to be always very close to the second root (to the left of the second root). This experiment was repeated on several rock samples and the same behavior was observed.
According to some embodiments, this provides a method for determining a practical upper limit or estimating a value for C ₁₃ based on equation (24). For example, the three roots of the cubic function (24) can be solved using, among other methods, the trigonometric method. The general solution has the following form:
t _k - 2 - -cos
for k = 0,1,2 or
The solutions are (25)
3ac-b ²
3a ²
2b ³ -9abc + 27a ² d
27a ³ (26) (27)
C = t _k ~ - ^{13 K} 3a (28) The acceptable upper limit of C ₁₃ as mentioned previously, always seems to occur on the left of the second root (Gl); therefore, a practical upper limit of C ₁₃ can be defined as:
^{13 1} 3a (29) As previously discussed, the lower limit for ^ 13 can be based on equation (17); therefore a practical lower limit of can be defined as:
^ 13 ⁼ s / ^ 33 ^ 12 + ^ 66 ^- ^ 66 Οθ) [0079] FIG. 9 illustrates an example of graph 900 in which these limits for £ 13 are determined for the example of data set coming from FIGS. 5A to 51 corresponding to a rock sample. In Figure 9, the determined limits are reported with the measured values of Cl3 · In Figure 9, curve 947 shows the measured values of C ₁₃ from the data set. Curve 949 represents the lower limit calculated using equation (30) and curve 943 represents the newly defined upper limit calculated using equation (29). Curve 941 represents the upper limit defined in equation (17). As can be seen in figure 9, all the C ₁₃ measurements in this example, with the exception of one measurement (the I5 ^th data point), lie within the limits 943 and 949 defined in the equations (29 and 30). Advantageously, the upper and lower limits (curves 943 and 949) are very close to each other. Therefore, this provides an alternative method for estimating Cl3 (and other properties such as δ) simply by averaging the upper and lower limits, which do not need the Vp45 measurements. This average is represented by represented by the following equation:
_{Ci3 =} çh ± çii (31) In some embodiments, this method of calculating C ₁₃ is only used if the C ₁₃ measured (eg calculated from Vp45 using l equation 4) is not within the defined limits (equations 29 and 30). According to at least certain embodiments disclosed here, a method for controlling the quality of the C ₁₃ calculations can also or alternatively be used as a method for estimating C ₁₃ , without having to measure the Vp45 and use the equation ( 4). For example, the new upper limit corresponding to equation (29) can provide a parameter for the quality control of the measured C ₁₃ (calculated from Vp45 using equation 4), and the same upper limit may further or otherwise be used to estimate C ₁₃ without using the measured Vp45 to calculate the estimate using equation (31).
Results and Applications FIG. 10 is a graph 1000 containing an example of a histogram for demonstrating the precision of the estimate C ₁₃ using equation (31). Graph 1000 is based on approximately 450 rock samples from the data used in Figures 6A to 6D. In order to generate graph 1000, C ₁₃ was estimated using equation (31) for each of the approximately 450 rock samples. Each bar corresponds to a given precision of the estimated ^ 13 compared to the measured value from the data set, while the height of each bar shows the number of data points (i.e., the number estimated O.3 values) with the given precision. As can be seen in Figure 10, an accuracy of ± 0.5 GPa is observed for 135 of the approximately 450 rock samples, an accuracy of ± 1 GPa is observed for 100 samples, an accuracy of ± 1.5 GPa is observed for 125 samples and an accuracy of ± 2 GPa is observed for 40 samples. Consequently, in this example, G.3 can be estimated by calculating the average of the limits, with an accuracy of ± 2 GPa for 90% of the data and ± 1.5 GPa for 80% of the data.
FIGS. 11A to 111 illustrate another example of a graphics game 1 lOOa-i based on the Monte-Carlo simulation. Graphs 1100a-i demonstrate how the estimation of C ₁₃ by averaging the limits, as described above, can provide a process that is robust against errors in velocities. In particular, graphs 1100a-i show the determined values of ^ 13 'of δ, and the mechanical property values which are less scattered than what is shown in Figures 5A to 51.
The results shown in Figures 11E to 111 are based on the same inputs as those used in Figures 5E to 51. Therefore, the graphs 11OOa-lOOd illustrated in Figures 11A to 11D contain histograms which are the same graphs 500a-500d illustrated in Figures 5A to 5D. The horizontal bars 590a-d illustrate the same measured speed values as the horizontal bars in FIGS. 5A to 5D. The same noise values were generated 100 for each speed, the maximum added noise being equal to 1% of each speed quantity, as shown by the vertical bars in figuresl 1A at 1 ID and are taken as inputs for the analysis .
In Figures 11E, equation (31) was used to estimate C13 for each of the 100 permutations. In Figures 11F to 111, equations (7, 12, 13 and 14) were used to calculate δ and the Poisson ratios VTI for each of the 100 permutations, based on the estimated values of C13 from Figure 11E. The expected values based on the data for C ₁₃ , δ and the Poisson ratios VTI are illustrated as vertical bars 1190e to 1190i. As can be seen in Figure 11E to 111, more robust calculation results for all properties are observed. Although not illustrated in Figures 11A to 111, the same behavior (more robust calculation results using equation 31) was observed for the other data from different rock samples.
In order to further study the performance of the example of the previous averaging method ("averaging method" in Table 1) it was compared to a number of other methods. Data from the same rock sample in Figures 5A to 51 were used as a reference. C ₁₃ we assume that δ, and the dynamic Poisson ratios measured from these data are fair values.
One of the methods (“1 ^st method” in Table 1) which was used for the comparison, comes from the linear slip theory G.3 can be calculated by solving equation (32) .
C _i} C ₃₃ -C _{} 3} ² = 2C ₆₆ (C ₃₃ + C _{} 3} ) (32) The following method (“2 ^nd method has.” In Table 1) is a recent empirical method for estimating 0.3 in addition, the so-called "Modified Annie" ( "3 ^rd method has." in Table 1) was used for comparison. After calculating C ₁₃ using these methods, δ, and Poisson ratios were calculated. The performance statistics for G3 and δ are given in Table 1. As can be seen in the performance statistics, the averaging method demonstrates better performance than the other methods in predicting all the parameters. The same performance is found for Poisson reports.
Δ G.3 Coefficient ofcorrelation RMS error Coefficient ofcorrelation RMS error Process, avg. .9648 0.0289 .9958 .9668 ^1st process. .8749 .0898 .9916 2.9604 ^2nd process. .6780 0.0867 .9418 3.2092 3 ^th is process. .8464 0.01594 .9306 3.6264
Table 1: Correlation coefficient and errors in the prediction of the quadratic mean (RMS) C ₁₃ and of δ.
Figures 12A to 12F illustrate another example of a set of graphics 1200a-f. In this example, data from the same 450 rock samples were used in Figures 6A to 6D were corrected using equation (31) each time the measured C ₁₃ was found at the outside the limits given in equations (29 and 30). Therefore, for these data points, in addition to C ₁₃ , δ and Poisson ratios have also been recalculated. This correction, however, did not affect the Thomsen parameters ε and γ because C ₁₃ is not used in their definition. Data for rock samples that met the limits in equations (29 and 30) were not affected in this experiment.
The results of this analysis, before the correction, are given in the graphs 1200a-c in FIGS. 12A to 12C, and the results after correction are given in the graphs 1200d-f in FIGS. 12D to 12F. For all the plots illustrated, the hatches illustrate the value of the Thomsen ε data, which have not been modified by the correction. As can be seen in Figure 12B, the fact that v _HV has the highest value among the Poisson ratios VTI and v _v has the lowest values (implying v _v <<v _HV ) is so pronounced that it can be seen in the data without any correction. As can be seen in figure 2A, 12C, 12D and 12F, the other relationships illustrated in inequality (19) are not observed in the data before the correction, but are brought to the data after the correction. One observation is the fact that after correction, the data from almost isotropic rocks (dark hatching corresponding to very small values of ε) are aligned along line one on one (isotropic line), and when anisotropy increases the data starts to deviate from the line one by one.
An effect of this correction is on the δ, which reveals a fundamental physical phenomenon which was previously hidden due to measurement errors and problems associated with 45 ° measurements. Figures 13A through 13F illustrate another example of a graphics set 1300a-f. In this example, the data from the same 450 rock samples were used in Figures 6A to 6D were corrected using equation (31) each time the measured C ₁₃ was found at the The limits given in equations (29 and 30) and the Thomsen parameters for the data have been determined. The results of this analysis, before correction, are given in graphs 1300a-c of FIGS. 13A to 13C, and the results after correction are given in graphs 1300d-f of FIGS. 13D to 13F. In Figures 13A and 13D, the hatching of the graphs ε versus δ 1300a and 1300d indicates the values γ. In Figures 13B and 13E, the hatching of the graphs γ versus δ 1300b and 1300e indicates the values ε. In Figures 13C and 13F, the hatching of the graphs γ versus ε 1300c and 1300f indicate the values δ.
As illustrated in FIGS. 13A to 13F, after the correction, δ is positively correlated to ε, and negatively correlated to γ. Another way to interpret this relationship between ε, γ and δ, is to say, for example, that for a constant value of γ, ε and δ have a linear relationship. Furthermore, for a constant value of δ, ε and γ have a linear relationship. This relationship between ε, γ and δ gives us the opportunity, for example, to estimate δ from ε and γ using regression analysis.
FIG. 14 illustrates a graph 1400 showing the results of an example of linear regression analysis, once again using the same data as that used in FIGS. 6A to 6D. In this example, ε, γ and the corrected values of δ are used in a linear regression analysis. A relation, in the form illustrated below, is obtained δ = a ₀ + atE + a ₂ y (33) in laquellea _o = -0.003282; a ₁ = 1.527 and a ₂ = -1.055. Ignoring the small interception, this relation can be written in the following form δ = 1.5ε - γ (34), suggesting that ε contributes more to the estimation of δ than γ. In Figure 14, equation (34) was used to estimate the value of δ from ε and γ. The estimation results are reported with respect to the corrected δ in Figure 14, showing a close correlation between the two sets of values.
FIG. 15 is a flow diagram illustrating an example of a method 1500 for determining the mechanical properties of an anisotropic medium, according to certain embodiments. The method 1500 can use various principles described above. Process 1500 illustrates an example of how the determination of mechanical properties can be applied in the context of a drilling system and used to facilitate operations in a formation that contains anisotropic media. One or more of the steps illustrated in the figure may include processing operations implemented by one or more processors of a processing system, such as, for example, computer units 208 (Figure IB). In some embodiments, the method 1500 may include direct or indirect interactions with the anisotropic media of the present invention, using, for example, one or more tools of a well system, such as a drilling system 100 (Figure IA) or a 200 cable system (Figure IB).
It will be understood that a processing system can be designed to implement any of the methods described here using programming in hardware, software, or a combination of hardware and software. For example, in certain software embodiments, a non-transient computer-readable medium may contain instructions which, when executed by the processor, entail the implementation by the processing system of one or more steps of the disclosed methods. here. As an example, the computer readable non-transient storage medium may include disk drives, flash memory, optical disks, static RAM memory (SRAM), dynamic RAM memory (DRAM), and / or other memories volatile and / or non-volatile. As an example, the processor may include one or more microprocessors, microcontrollers, an application-specific integrated circuit (ASIC), user programmable pre-broadcast circuits (FPGA), digital logic circuit blocks, and / or other suitable processing circuit which can be implemented in one or more integrated circuits.
Referring now to Figure 15, a process 1500 is illustrated which involves determining an upper limit for the stiffness component C ₁₃ based on other stiffness components which might not use off-axis measurements . The upper limit can be used to estimate a value for C ₁₃ without requiring measurements off an axis.
The 1500 method can generally include obtaining measurement data from an anisotropic medium. More particularly, as shown in FIG. 15, the method 1500 can comprise obtaining the logging data at 210 corresponding to the measurements of the anisotropic medium collected with one or more logging tools, for example, the logging tool or tools 126 (see Figures IA to 2). The anisotropic medium can form or otherwise be part of a formation which is to be evaluated for a drilling operation or other well operation, such as, for example, an underground formation 106 (see Figures IA to IB). In various embodiments, the anisotropic medium can include, e.g., layering, layering, layering and / or fractures.
In some embodiments, the log data can be obtained by collecting real-time measurements, eg, by collecting the data using real-time measurements with the logging tool (s) and by transmitting them for other treatments. Furthermore, all or part of the log data obtained at 210 may correspond to the data which has been separately collected. In both cases, raw data from measurements of the anisotropic medium can be entered into, or received by, or otherwise obtained by a processing system for further data processing operations. In some embodiments, the measurements may include measurements of the wave speed (or "slowness measurements") for waves propagating in the anisotropic medium. Wave velocity measurements can be obtained, e.g., by transmitting waves through training with one or more transmitters of a sonic logging tool and receiving the corresponding waves with one or more receivers of the sonic logging tool to measure a corresponding response.
According to various embodiments, the velocities or the measurement speeds can be obtained or otherwise determined for the waves propagating in multiple different directions. A "horizontal velocity" or "horizontal velocity measurement" can correspond to waves propagating in a horizontal direction with respect to an axis of symmetry of an anisotropic medium (eg, perpendicular to the axis of symmetry). A "vertical velocity" or "vertical velocity measurement" may correspond to waves propagating in a vertical direction with respect to the axis of symmetry of the anisotropic medium (eg, parallel to the axis of symmetry). An “off-axis speed” or “off-axis measurement” can correspond to waves propagating in an off-axis direction (or oblique direction) with respect to the axis of symmetry of the anisotropic medium (eg, between 0 and 90 degrees relative to the axis of symmetry). The off-axis direction can be considered off-axis in that it is neither aligned with the horizontal axis nor with the vertical axis corresponding to the horizontal and vertical directions. In some embodiments, the off-axis measurements correspond to an angle of 45 ° relative to the axis of symmetry of the anisotropic medium. In addition or otherwise, another off-axis direction between 0 and 90 degrees can be used for the off-axis measurement (s).
At 212, the method 1500 comprises determining the values for a plurality of stiffness components. In particular, as shown in FIG. 15, the values for a stiffness component C _llt C ₃₃ , C ₅₅ and C ₆₆ of a stiffness matrix Cy can be determined based on the vertical speeds and the horizontal speeds measured or otherwise from log data, and more particularly, for example, based on vertical velocities and horizontal velocities involving compression waves and shear waves.
As a general rule, each of the stiffness components determined at 212 can be based directly or indirectly on the speeds derived from the log data. For example, in some embodiments a vertically propagated measured compression rate (VpO) from log data may provide a value for the stiffness component C ₃₃ directly, and a vertically polarized measured shear rate (VsO) from log data can provide a value for the stiffness component directly C55 · A horizontally polarized shear rate (Vs90) can then be estimated from the analysis of the sonic data of the complete waveform, including the d shape data Stoneley wave and possibly dipole waveform data, with other parameters. The stiffness component C ₆₆ is then directly calculated from Vs90. By knowing VsO and Vs90, we can have a parameter, γ, and if we decide that ε (the anisotropy of the P wave) is related to γ (eg, ε = γ), then we can in turn estimated the horizontally propagating compression speed Vp90, which can give the stiffness component Cn- It will be understood that these methods are only examples, and in various embodiments, any suitable method for determining the velocities or components of rigidity from log data can be used, as it should be.
Referring again to Figure 15, at 220, an upper limit for the stiffness component C ₁₃ is determined based on one or more of the stiffness components determined at 212. More particularly, as shown in the figure 15, both the upper limit and the lower limit can be set to 220, which can be used to estimate a value of C ₁₃ without requiring the use of off-axis measurements for estimation, as described here . For example, in some embodiments the upper limit can be determined based on the determination of a root of a cubic equation having stiffness components from 212 included in the coefficients of the cubic function. More particularly, the upper limit C ^ ₃ (or “upper limit”) can be determined based on the preceding equation (29). In some embodiments, the lower limit (or "lower limit") can be determined based on the above equation (30). On the other hand, when desirable results are given above for the upper limit based on equation (29), in other embodiments any other suitable method can be used to determine the upper and / or lower limits, like it should be.
At 232, a value of the stiffness component ^ 13 is estimated based on the determined upper limit. In particular, the value can be estimated at 232 by averaging the upper and lower limits, eg, based on equation (29) above. On the other hand, when desirable results are given above for the estimation based on the averaging of the upper and lower limits, in other embodiments any other suitable method for the estimation of Cj.3 can be used at 232. For example, other suitable methods for estimating the value of the stiffness component based on the upper and / or lower limits, and / or based on the other stiffness components (eg Ai, C ₃₃ , C ₅₅ and / or Qô) can be used.
At 236, one or more mechanical properties of the anisotropic medium are determined based on the estimated value of the stiffness component C ₁₃ . In particular, the mechanical property can be determined based on the stiffness component C ₁₃ and other parameters (eg, Cu, C33, C ₅₅ , C ₆₆ ) of the stiffness matrix C ^. Any one or more of a variety of mechanical properties can be calculated at this point. For example, one or more values of one or more Poisson ratios v _L j can be calculated, eg, based on one or more of equations (12) to (14). In addition or otherwise, one or more values of one or more Young E modules can be calculated, eg, based on one or more of equations (15) to (16). In addition or otherwise, one or more values of a fracture gradient can be calculated, e.g., based on a Poisson ratio and / or a Young's modulus. In addition or otherwise, one or more values of a minimum and / or maximum horizontal stress can be calculated, e.g., based on a Poisson ratio and / or a Young's modulus. Additionally or otherwise, one or more other mechanical properties dependent on 0.3 can be calculated to 236. The mechanical property (s) can then be provided for use in controlling an operating parameter of a drilling or drilling system. 'another well system.
According to certain embodiments, at 240, an operating parameter for a well system, such as the drilling system 100 (see FIG. IA), is controlled based on the mechanical property originating from 236. For example, the processing system can be designed to generate one or more control signals for controlling a tool of the drilling system based on the calculated mechanical property, or an operator can otherwise control an operating parameter of the drilling system based on the property mechanical. In some embodiments, a point (eg, an "ideal point" or location) for digging a horizontal well can be determined to 240. Additionally or otherwise, an interval for drilling into a well can be determined by based on mechanical property at 240. Additionally or otherwise, a fracturing pressure for formation fracturing can be determined based on mechanical property (and also based on a depth of formation, for example) . In addition or otherwise, one or more other operating parameters of a drilling system can be determined at 240 which can be influenced by a mechanical property of an anisotropic medium.
One or more operations can then be performed in accordance with the operating parameters from 240 using a tool from a well system. One or more operations may involve interaction with the anisotropic medium directly or indirectly with a tool. For example, in some embodiments a horizontal well can be dug using a drill bit or other drilling tool from a drilling system. Additionally or otherwise, a gap can be punched into a casing or lining of an oil well using a punch gun or other punch tool. In addition or otherwise, a formation can be fractured using a hydraulic tool or another fracturing tool according to a determined fracturing pressure based on the mechanical property.
While Figure 15 illustrates a method for estimating C ₁₃ based on the upper and lower limits determined from the log data, in some embodiments, the upper and lower limits may further or by elsewhere be used for quality control of measured values of C ₁₃ .
For example, in certain embodiments, the measurement data may also or moreover comprise coring data, corresponding to the measurements of one or more samples of the anisotropic medium extracted with one or more coring tools. Coring data can be obtained, e.g., by extracting one or more samples from the anisotropic medium with one or more coring tools, and by performing other laboratory analyzes or measurements on the extracted core sample (s). In various embodiments, any coring tool can be used. For example, in some embodiments, the coring tool may include or otherwise be implemented in the form of a coring drill bit used in coring bit 118 (Figure 1).
A measured value of 0.3 can be determined based on an off-axis speed from the coring data (eg, compression wave speed at 45 ° Vp45). The measured value of O3 can then be compared to the upper and lower limits as a quality control. The upper and lower limits can be determined based on the horizontal and vertical velocities from the core drilling data or other measurement data, in a manner similar to that previously described. When the measured value 0.3 is within the upper and lower limits, the measured value of O3 can be considered reliable and used for other upstream processing, e.g. to calculate one or more useful mechanical properties in controlling the operating parameters of a well system in a manner similar to that previously described. In addition, when the measured value C ₁₃ is outside the upper and lower limits, the measured value can be corrected, for example, using an estimate based on other speed stiffness components horizontal / vertical, as previously described.
The results of the tests demonstrate that the methods described here for predicting the mechanical properties of rocks surpass the other methods. This is indicated, for example, in Table 1. This study also provides the only method for achieving dynamic to static correction for mechanical properties for anisotropic media (eg, TI, VTI, HTI). Other methods may only be appropriate for Young's isotropic modules. In this disclosure, a more complete correction is proposed which corrects Young's horizontal and vertical modules and three Poisson ratios which are useful for calculating the fracture gradient and / or horizontal stresses. This disclosure also revealed a relationship between Thomsen's anisotropy parameters, which are widely used for seismic, geomechanical and drilling applications. This provided a way to predict or estimate the Thomsen Delta. Advantageously, the methods described here can be used to determine the mechanical properties for the evaluation of a formation and the choice of the ideal point, to determine a stiffness matrix to calculate the stresses and the fracture gradient, to identify the Thomsen Delta for seismic imaging, to identify mechanical properties and anisotropy parameters for the calculation of mud density, wellbore stability and other parameters.
The prediction of the fair values of the Poisson ratios and of the Young's moduli, which can be used to calculate the gradient of the fracture and the minimum horizontal stress, is useful for geomechanics, hydraulic fracturing and completion. For unconventional, the methods described here can be used and can be of greater value than predicting porosity, saturation and kerogenic volume. The profiles of the elastic modules can be used to predict the friability of the rock and / or to determine a stress profile versus the depth to help choose the "ideal points" for digging a horizontal well, but also to determine the perforation intervals .
Illustration of the present technology in the form of clauses [0111] Various examples of the aspects of disclosure are described in the form of numbered clauses (1, 2, 3, etc.) for reasons of convenience. These are provided as examples, and do not limit the present technology. The identifications of the figures and the reference numbers are provided below only as examples and for illustrative purposes, and the clauses are not limited to these identifications.
Clause 1. A method for determining the mechanical properties of an anisotropic medium, the method comprising: obtaining log data from the anisotropic medium, the log data corresponding to the measurements of the anisotropic medium collected with a logging; determining values for a plurality of first stiffness components of a stiffness matrix based on the horizontal and vertical velocities derived from the log data; determining an upper limit for a second stiffness component of the stiffness matrix based on the values for the plurality of first stiffness components; estimating a value for the second stiffness component based on the determined upper limit; determining a mechanical property of the anisotropic medium based on the estimated value of the second stiffness component and providing the determined mechanical property.
Clause 2. A system for determining the mechanical properties of an anisotropic medium, the system comprising: a logging tool designed to collect measurements of the anisotropic medium; and a processing system having a processor and a memory, the processing system configured to: obtain log data from the anisotropic medium from the logging tool, the log data corresponding to measurements of the anisotropic medium; determining values for a plurality of first stiffness components of a stiffness matrix based on the horizontal and vertical velocities derived from the log data; determining an upper limit for a second stiffness component of the stiffness matrix based on the values for the plurality of first stiffness components; estimate a value for the second stiffness component based on the determined upper limit and determine a mechanical property of the anisotropic medium based on the estimated value of the second stiffness component.
Clause 3. A non-transient computer-readable medium storing instructions which, when executed, entail the carrying out by a processing system of a process for determining the mechanical properties of an anisotropic medium, the process comprising : obtaining log data from the anisotropic medium, the log data corresponding to the measurements of the anisotropic medium collected with a logging tool; determining values for a plurality of first stiffness components of a stiffness matrix based on the horizontal and vertical velocities derived from the log data; determining an upper limit for a second stiffness component of the stiffness matrix based on the values for the plurality of first stiffness components; estimating a value for the second stiffness component based on the determined upper limit; determining a mechanical property of the anisotropic medium based on the estimated value of the second stiffness component and providing the determined mechanical property.
Clause 4. A method for determining the mechanical properties of an anisotropic medium, the method comprising: obtaining measurement data of the anisotropic medium; determining values for a plurality of first stiffness components of a stiffness matrix based on the horizontal and vertical velocities derived from the measured data; determining a measured value for a second stiffness component of the stiffness matrix based on an off-axis speed derived from the measurement data; determining an upper limit and a lower limit for the second stiffness component based on the values for the plurality of first stiffness components; comparing the measured value for the second stiffness component to the upper limit and the lower limit determined for the second stiffness component; determining a mechanical property of the anisotropic medium based on the estimated value of the second stiffness component when the measured value is determined to be within the upper limit and the lower limit and providing the determined mechanical property.
Clause 5. A system for calculating the mechanical properties of an anisotropic medium, the system comprising: a coring tool designed to collect a sample of the anisotropic medium; and a processing system having a processor and a memory, the processing system adapted to: obtain coring data from the anisotropic medium corresponding to the sample collected with the coring tool; determining values for a plurality of first stiffness components of a stiffness matrix based on the horizontal and vertical velocities; determining a measured value for a second stiffness component of the stiffness matrix based on an off-axis speed derived from the core data; determining an upper limit and a lower limit for the second stiffness component based on the values for the plurality of first stiffness components; comparing the measured value for the second stiffness component with the upper limit and the lower limit determined for the second stiffness component; determine a mechanical property of the anisotropic medium based on the estimated value of the second stiffness component when the measured value is determined to be within the upper limit and the lower limit and the supply of the determined mechanical property.
Clause 6. A non-transient computer-readable medium storing instructions which, when executed, cause a process to carry out a process for determining the mechanical properties of an anisotropic medium, the process comprising : obtaining data for measuring the anisotropic medium; determining values for a plurality of first stiffness components of a stiffness matrix based on the horizontal and vertical velocities derived from the measured data; determining a measured value for a second stiffness component of the stiffness matrix based on an off-axis speed derived from the measurement data; determining an upper limit and a lower limit for the second stiffness component based on the values for the plurality of first stiffness components; comparing the measured value for the second stiffness component to the upper limit and the lower limit determined for the second stiffness component; determining a mechanical property of the anisotropic medium based on the estimated value of the second stiffness component when the measured value is determined to be within the upper limit and the lower limit and providing the determined mechanical property.
Clause 7. According to any one of clauses 1 to 6, in which the determined mechanical property comprises a Poisson ratio, in which a fracturing pressure must be determined based on the Poisson ratio.
Clause 8. According to any one of clauses 1 to 3, in which the log data is designed to be collected by emitting a plurality of waves in the anisotropic medium and by measuring a corresponding response, in which the plurality of waves involves a plurality of different propagation directions and a plurality of different propagation modes.
Clause 9. According to any one of clauses 1 to 3, 7 or 8, in which the logging tool is designed to be placed at the bottom of the hole in a wellbore, in which the logging tool includes one or more transmitters adapted to transmit a plurality of waves and one or more sensors adapted to measure a corresponding response, wherein the one or more transmitters are axially spaced from one or more receivers.
Clause 10. According to any one of clauses 1 to 3 or 7 to 9, in which one or more transmitters are designed to emit acoustic waves, in which one or more receivers are designed to measure the corresponding response after interaction acoustic waves emitted with the anisotropic medium, and in which the log data includes acoustic waveform data.
Clause 11. According to any one of clauses 1 to 10, in which the upper limit is designed to be determined based on a root of a cubic function, in which the plurality of the first stiffness components is included in the coefficients of the cubic function.
Clause 12. According to any one of clauses 1 to 11, in which the plurality of the first stiffness components corresponds to the components _C115 C ₃₃ , C ₅₅ and C ₆₆ of the stiffness matrix, and in which the second stiffness component corresponds to a component C ₁₃ of the stiffness matrix.
Clause 13. According to any one of clauses 1 to 12, in which the upper limit is designed to be determined on the basis of (¾ = ti - in which: (¾ is the upper limit, b = —2 (C _{1; l} - C ₆₆ ), c = —C ₁₁ C ₃₃ , d = 2C ₃₃ (Cn - C ₆ 6) (Cn ^- 2C ₆₆ ), and t _x is the second root (¾ + bCi ₃ + cC ₁₃ + d = 0.
Clause 14. According to any one of clauses 1 to 13, in which the value of the second stiffness component is designed to be estimated based on an average of the upper limit and of a lower limit for the second. stiffness component.
Clause 15. According to any one of clauses 1 to 3 or 7 to 14, in which the logging tool comprises: one or more transmitters designed to emit a plurality of waves in the anisotropic medium, the plurality of the waves being designed to involve a plurality of different propagation directions and a plurality of different propagation modes; and one or more receivers axially separated from one or more transmitters and adapted to measure a corresponding response with respect to the plurality of transmitted waves.
Clause 16. According to any one of clauses 4 to 7, in which the measurement data are designed to include coring data corresponding to a sample of the anisotropic medium obtained using a coring tool, and wherein the off-axis speed is derived from the core data.
Clause 17. According to any one of clauses 4 to 7, 11 to 14 or 16, in which the coring data are designed to be collected by extracting the sample with the coring tool and by measuring the sample extracted.
Clause 18. A method for calculating the mechanical properties of an anisotropic medium, the method comprising: estimating a value of C ₁₃ ; and calculating a mechanical property of the anisotropic medium using the estimated C ₁₃ value.
Clause 19. According to any one of clauses 1 to 18, in which the mechanical property is a Young's modulus, a shear modulus, a Poisson ratio, a Thomsen anisotropy parameter δ, a horizontal stress or a fracture gradient.
Clause 20. According to any one of clauses 1 to 19, in which the anisotropic medium comprises a vertically transverse isotropic medium, a horizontally transverse isotropic medium, a transverse inclined isotropic medium, an orthotrobic medium or an orthotropic medium.
This disclosure introduces an improved technique for calculating mechanical properties (Young's and shear moduli, Poisson's ratios), Thomsen's anisotropy parameters δ, C ₁₃ , and any other parameter that uses C ₁₃ as an entry in anisotropic media such as VTI, HTI and TTI. This disclosure introduces methods which use only vertical and horizontal velocities (slowness) to estimate certain mechanical properties and do not require 45 ° measurements or any other off-axis measurements. This disclosure introduces a way of correcting data in which 45 ° measurements or any off-axis measurements are not acquired or cannot be acquired with high precision. This disclosure defines new relationships between the Poisson ratios for VTI, HTI, TTI, orthotropic and orthorhombic (equations 18 and 19, Figure 10) which give a new upper limit for G.3 (equations 20 to 29). This disclosure proposes a method for estimating Cl3 by calculating the average of the upper and lower limits of Cl3 (equation 31). This disclosure allows the computation of the Thomsen parameter δ, Poisson ratios TI and improved Young's moduli and any other mechanical properties such as horizontal stresses, fracture gradients, and other mechanical properties in anisotropic media. This disclosure allows dynamic to static correction of Poisson ratios in anisotropic media. A new relationship between the Thomsen parameter δ and the other parameters ε and γ is defined (equations 33 and 34). A new empirical relationship for dynamic to static correction of anisotropic Young's moduli is proposed (equation 35).
[0133] A reference to an element in the singular is not intended to mean "one and only one" except in the case of specific mention, but rather "one or more". For example, "a" module can describe one or more modules. An element preceded by "a", "an", "the" or "said" does not exclude, without other constraints, the existence of other similar elements.
The headers and subtitles, if any, are used for convenience only and do not limit the invention. The word "for example" is used to mean an example or an illustration. To the extent that the term "includes", "a", or etc., is used, such a term is intended to be inclusive in a manner similar to the term "include" since "include" is interpreted when it is used as a transitional word in a claim. Relational terms such as "first" and "second", etc., can be used to distinguish one entity or action from another without necessarily requiring or implying any real relationship or order of this type between such entities or actions .
Sentences such as: one aspect, the aspect, another aspect, some aspects, one or more aspects, an implementation, the implementation, another implementation, some implementations, one or more implementations, an embodiment , the embodiment, another embodiment, certain embodiments, one or more embodiments, a configuration, the configuration, another configuration, certain configurations, one or more configurations, the present technology, the disclosure, the this disclosure, other variations thereof, etc., are used for convenience and do not imply that a disclosure relating to such phrase (s) is / are essential ( s) to this technology or that such disclosure applies to all configurations of this technology. A disclosure relating to such phrase (s) may / may apply to all configurations, or one or more configurations. A disclosure relating to such phrase (s) may / may provide one or more examples. A sentence such as an aspect or certain aspects can relate to one or more aspects and vice versa, and this applies in a similar way to the preceding sentences.
A sentence "at least one of" which precedes a series of elements, with the terms "and" or "or" to separate any one of these elements, modifies the entire list, rather than each member of the list. The phrase "at least one of" does not require the selection of at least one element; instead, the sentence allows a meaning that includes at least one of any of the elements and / or at least one of a combination of the elements and / or at least one of each of the elements . As an example, each of the phrases "at least one of A, B and C" or "at least one of A, B or C" describe only A, only B or only C; any combination of A, B and C and / or at least one of each of A, B and C.
It is understood that the specific order or hierarchy of the disclosed steps, operations or processes is an illustration of the examples of approaches. Unless specifically mentioned, it is understood that the specific order or hierarchy of steps, process operations can be carried out in a different order. Some of the steps, operations or processes can be carried out simultaneously. The attached process claims, if any, present elements of the various steps, operations or processes in an example order, and are not intended to be limited to the specific order or hierarchy presented . These can be performed in series, linear, parallel or different order. It should be understood that the instructions, operations and systems described can generally be integrated together into a single software / hardware product or grouped into multiple software / hardware products.
In one aspect, a term "coupled" or a similar term can describe a direct coupling. In another aspect, a term "coupled" or a similar term may describe an indirect coupling.
Terms such as "above", "below", "front", "rear", "lateral", "horizontal", "vertical", etc., describe an arbitrary frame of reference, rather than the ordinary gravitational frame of reference. Therefore, a term can extend up, down, diagonally or horizontally in a gravitational frame of reference.
This disclosure is provided to enable any specialist in the field to practice the various aspects described here. In some cases, well known structures and components are illustrated in the form of flowcharts in order to avoid obscuring the concepts of the present technology. This disclosure provides various examples of the present technology, and the present technology is not limited to these examples. Various modifications of these aspects will be apparent to those skilled in the art, and the principles described herein can be applied to other aspects.
All the structural and functional equivalents to the elements of the various aspects described through the disclosure which are known or which will be known in the future to specialists in the field are expressly incorporated here for reference and are intended to be encompassed by claims. Furthermore, nothing disclosed herein is directed to the public regardless of whether such disclosure is explicitly described in the claims. No claimed element may be interpreted according to the provisions of section 35 USC §112, 6th paragraph, unless the element is explicitly described using the phrase "means for" or, in the case of a claim process, the item is described using the phrase "step to".
The title, background, brief description of the figures, the abstract and the figures are hereby incorporated into the disclosure and are provided as illustrative examples of the disclosure, not as restrictive descriptions . These are submitted with the idea that they will not be used to limit the scope or meaning of the claims. Furthermore, in the detailed description, it can be seen that the description provides illustrative examples and the various features are grouped together in various implementations for the purpose of simplifying the disclosure. The disclosure process is not to be construed as reflecting an intention that the claimed object requires other features which are expressly described in each claim. Instead, as the claims reflect, the inventive object is found in less than all of the features of a disclosed single configuration or operation. The claims are hereby incorporated into the detailed description, each claim being autonomous as a separately claimed object.
The claims are not intended to be limited to the aspects described here, but should be granted in full in consistency with the language of the claims and to encompass all legal equivalents. None of the claims, however, is intended to adopt subject matter which does not meet the requirements of applicable patent law, and which should not be interpreted in that way either.
MODIFIED CLAIMS GAME

权利要求:
Claims (15)
[1" id="c-fr-0001]
1. A method for determining the mechanical properties of an anisotropic medium, the method comprising:
obtaining anisotropic medium log data, the log data corresponding to the anisotropic medium measurements collected with a logging tool;
determining values for a plurality of first stiffness components of a stiffness matrix based on the horizontal and vertical velocities derived from the log data;
determining an upper limit for a second stiffness component of the stiffness matrix based on the values for the plurality of first stiffness components;
estimating a value for the second stiffness component based on the determined upper limit;
determining a mechanical property of the anisotropic medium based on the estimated value of the second stiffness component; and the provision of the specified mechanical property.
[2" id="c-fr-0002]
2. Method for determining the mechanical properties of an anisotropic medium, the method comprising:
obtaining data for measuring the anisotropic medium; determining values for a plurality of first stiffness components of a stiffness matrix based on the horizontal and vertical velocities derived from the measurement data;
determining a measured value for a second stiffness component of the stiffness matrix based on an off-axis speed derived from the measurement data;
determining an upper limit and a lower limit for the second stiffness component based on the values for the plurality of the first stiffness components;
comparing the measured value for the second stiffness component to the upper limit and the lower limit determined for the second stiffness component;
determining a mechanical property of the anisotropic medium based on the measured value of the second stiffness component when the measured value is determined to be within the upper limit and the lower limit; and the provision of the specified mechanical property.
[3" id="c-fr-0003]
The method of claim 1, further comprising collecting log data by emitting a plurality of waves into the anisotropic medium and measuring a corresponding response, wherein the plurality of waves involves a plurality of directions of propagation. different and a plurality of different propagation modes.
[4" id="c-fr-0004]
4. The method of claim 3, further comprising placing the logging tool at the bottom of the hole in a wellbore, wherein the logging tool comprises one or more transmitters adapted to transmit the plurality of waves and a or more receivers designed to measure the corresponding response, wherein the one or more transmitters are axially spaced from the one or more receivers.
[5" id="c-fr-0005]
5. Method according to claim 4, in which one or more transmitters are designed to emit acoustic waves, in which one or more receivers are designed to measure the corresponding response after interaction of the acoustic waves emitted with the medium anisotropic, and wherein the log data includes acoustic waveform data.
[6" id="c-fr-0006]
6. Method according to claim 2, in which the measurement data comprise coring data corresponding to a sample of the anisotropic medium obtained using a coring tool, and in which the off-axis speed is derived from the data of coring.
[7" id="c-fr-0007]
7. The method of claim 6, further comprising collecting the coring data by extracting the sample with the coring tool and measuring the extracted sample.
[8" id="c-fr-0008]
8. The method of claim 1 or 2, wherein the determined mechanical property comprises a Poisson ratio, wherein the method also comprises determining a fracturing pressure based on the Poisson ratio.
[9" id="c-fr-0009]
9. The method of claim 1 or 2, wherein the upper limit is determined based on a root of a cubic function, wherein the plurality of first stiffness components is included in the coefficients of the cubic function.
[10" id="c-fr-0010]
10. The method of claim 1 or 2, wherein the plurality of first stiffness components corresponds to components C ₄₁ , C ₃₃ , C ₅₅ and C ₆₆ of the stiffness matrix, and wherein the second stiffness component corresponds to a component Cl3 of the stiffness matrix.
[11" id="c-fr-0011]
11. The method of claim 10, wherein the upper limit is determined based on C ₄₃ = ig - in which: C ₄₃ represents the upper limit, b = -2 (C _X1 - C ₆₆ ), c = -CHC33 , d = 2C ₃₃ (C ₁₁ - C ₆₆ ) (Cn - 2C ₆₆ ), and t _x is the second root of C ₄₃ + bC ₄₃ + cC ₁₃ + d = 0.
[12" id="c-fr-0012]
12. The method of claim 1 or 2, also comprising: estimating the value of the second stiffness component based on an average of the upper limit and a lower limit for the second stiffness component.
[13" id="c-fr-0013]
13. System for determining the mechanical properties of an anisotropic medium, the system comprising:
a logging tool designed to collect measurements of the anisotropic medium; and a processing system having a processor and a memory, the processing system being adapted to implement the method according to any of claims 1, 3 to 5 or 8 to 12, wherein the log data is from the tool logging.
[14" id="c-fr-0014]
14. The system as claimed in claim 13, in which the logging tool comprises:
one or more transmitters designed to transmit a plurality of waves into the anisotropic medium, the plurality of waves being designed to involve a plurality of different propagation directions and a plurality of different propagation modes; and one or more receivers axially separated from one or more transmitters and adapted to measure a corresponding response with respect to the plurality of transmitted waves.
[15" id="c-fr-0015]
15. System for calculating the mechanical properties of an anisotropic medium, the system comprising:
a coring tool designed to collect a sample of the anisotropic medium; and a processing system having a processor and a memory, the processing system being adapted to implement the method according to any of claims 2 or 6 to 12, wherein the measurement data comes from the coring tool.

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US20200096659A1|2020-03-26|

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WO2018231594A1|2018-12-20|

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2021-03-12| ST| Notification of lapse|Effective date: 20210206 |

优先权:

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申请号 | 申请日 | 专利标题

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US201762520402P| true| 2017-06-15|2017-06-15|

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US62520402|2017-06-15|

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PCT/US2018/036136|WO2018231594A1|2017-06-15|2018-06-05|Estimation of mechanical properties of transversely isotropic media|

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