Method of using dipole compressional data to determine properties of a subterranean structure

To determine properties of a subterranean structure, information relating to dipole compressional data is collected based on measurements by a logging tool in a borehole. The information relating to the dipole compressional data is analyzed in multiple dimensions (e.g., multiple borehole axial planes) to determine the properties of the subterranean structure through which the borehole extends.

BACKGROUND

Mechanical disturbances can be used to establish acoustic waves in earth formations surrounding a borehole, and the properties of these waves can be measured to obtain information about the formations through which the waves have propagated. Parameters of compressional, shear and Stoneley waves, such as their velocity (or its reciprocal, slowness) in the formation and in the borehole, can be indicators of formation characteristics that help in evaluation of the location and/or producibility of hydrocarbon or other resources.

Typically, a logging tool is run into the borehole, where the logging tool includes one or more sonic (acoustic) sources (transmitters) and multiple spaced apart receivers. Measurements are made by the receivers as the logging tool is moved slowly in the borehole. The sonic signals from the one or more transmitters enter the formation adjacent the borehole, and the arrival times and possibly other characteristics of receiver responses are used to find formation parameters.

Conventionally, shear wave signals (S-waves) detected by the receivers are analyzed. The shear wave data processed can include dipole shear data (two-dimensional in shear) or dipole shear data plus Stoneley data (three-dimensional in shear).

However, performing conventional multi-dimensional analyses of shear data to determine formation properties may not provide accurate results.

SUMMARY

In general, according to an embodiment, a method of determining properties of a subterranean structure includes receiving information relating to dipole compressional data collected based on measurements by a logging tool in a borehole. The information relating to the dipole compressional data is analyzed in multiple dimensions to determine the properties of the subterranean structure through which the borehole extends.

DETAILED DESCRIPTION

To determine properties of a subterranean structure through which a borehole extends, dipole compressional data collected based on measurements by a logging tool run in the borehole is analyzed in multiple dimensions (e.g., multiple borehole axial planes). Understanding of the properties of the subterranean structure allows an operator to ascertain whether the subterranean structure contains a fluid of interest (e.g., hydrocarbons, fresh water, etc.) or whether the subterranean structure has other desirable or target characteristics.

Traditionally, shear data is analyzed in multiple dimensions for understanding properties of a subterranean structure. However, no effort has been directed at efficiently quantifying subterranean structure properties based on analyzing dipole compressional information in multiple dimensions (multiple borehole axial planes). Conventional interpretation of compressional data typically involves one-dimensional interpretation.

Techniques according to some embodiments capitalize on the observation that dipole compressional velocities (or their inverse, slownesses) behave in an isotropic manner much the same way as dipole shear velocities (or their inverse, slownesses). Slowness represents the inverse of velocity. However, under certain conditions, performing analysis to understand subterranean structure properties based on multi-dimension shear data interpretation and one-dimensional compressional data interpretation may be insufficient or may not produce accurate results. For example, in slow formations, it is possible that a shear wave signal cannot be detected via receivers. A “slow” formation refers to a formation having a sonic shear velocity that is slower than the velocity of the drilling mud (or other fluid) in the borehole.

Referring toFIG. 1, an overall schematic illustration of a well logging system that incorporates some embodiments is depicted. A logging tool10is lowered on a multi-conductor cable12(which can be armored, for example) into a borehole14(cased or un-cased) to take sonic (acoustic) logs of a subsurface formation (more generally referred to as a “subterranean structure”)16. The logging tool10is provided with at least one sonic dipole source or transmitter50, and a plurality of sonic receivers52.

The dipole source50generates flexural waves (associated with dispersive borehole flexural modes). In some embodiments, the logging tool10can also include a monopole transmitter51that transmits a Stoneley wave as well as a compressional headwave in all directions. The receivers52can include both monopole and dipole receivers.

In some embodiments, the logging tool10can also include a downhole controller54that is able to receive measurements from the receivers52. The downhole controller54can be implemented with a computer or a processor. The downhole controller54is able to determine shear and compressional wave data (e.g., shear and compression slownesses) based on the measurement data from the receivers52. In alternative embodiments, instead of performing the processing downhole by the downhole controller54in the logging tool10, the processing can be performed by a surface controller32, which can be implemented with a computer (server computer, desktop computer, notebook computer, multiprocessing computer, personal digital assistant, etc.).

The receivers52are spaced along the length of tool10from each other and from the transmitter(s), and typically the distance between each transmitter and the receiver closest thereto is much greater than the inter-receiver distance.

The logging tool10is configured for movement up and down the borehole14on the cable12, and as the tool10is moved, the transmitters50,51, intermittently or continuously generate sonic (acoustic) signals. The generated sonic signals travel through the borehole14and/or through the formation16, and the receivers52detect energy which results from the generated signals.

The mechanism for moving the tool10in the borehole includes the cable12which extends to the sheave wheel18at the surface of the formation, and then to a suitable drum and winch mechanism20which raises and lowers the tool10in the borehole as desired. Electrical connection between the transmitter and receivers on the one hand, and the surface equipment on the other hand, is made through suitable multi-element slipping and brush contact assembly22associated with the drum and winch mechanism20. A unit24contains tool control and preprocessing circuits which send electrical signals to tool10and receive other electrical signals (sonic logs) over cable12and assembly22. Unit24cooperates with a depth recorder26that derives depth level signals from depth measuring wheel28so as to associate the signals from receivers54with respective depth levels z in borehole14. The outputs of sonic receivers54, after optional pre-processing in unit24, are sent to storage30(implemented with storage media such as disk-based storage media or semiconductor storage media), which can also receive signals from or through depth recorder26so as to associate sonic receiver outputs with respective depth levels z in borehole14.

Storage30can store the outputs of receivers52in analog or digital form, a set for each respective depth level z. The processing of the log measurements is then accomplished by the surface controller32which processes the information according to the techniques set forth below. The output of the processing can include one or more dispersion curves.

In alternative implementations, as noted above, instead of performing processing at the surface controller32, the processing can be performed by the downhole controller54in the logging tool10. In such alternative implementations, the storage30is used to store the output of the downhole controller54(along with depth information recorded by the depth recorder26).

The response of a receiver52in the logging tool10to a sonic signal from a transmitter is a waveform of a general type as depicted inFIG. 2. As seen inFIG. 2, the responses of a receiver in different dipole compressional modes are depicted.FIG. 2illustrates on the vertical axes slowness data and amplitude data as a function of frequency (horizontal axis). The plot shown inFIG. 2is an example of a slowness dispersion plot. Curves200and202inFIG. 2illustrate responses in the two corresponding different dipole compressional modes. Each curve200,202shown inFIG. 2is illustrative of a dispersive wave that is responsive to the dipole transmitter50.

The two dipole compressional modes refer to dipole firings along the maximum and minimum horizontal stress directions, respectively. A dipole firing along a particular horizontal stress direction refers to activation of a dipole transmitter that is parallel to the particular horizontal stress direction.

The maximum and minimum horizontal stress directions are illustrated inFIG. 3.FIG. 3is a schematic diagram of a fluid-filled borehole14in a porous formation16subject to the three principal stresses. Ppand Pwdenote the pore pressure and wellbore pressure, respectively. The presence of a wellbore of radius a, causes near-wellbore stress distributions that can be obtained based on the theory of elasticity and are shown inFIGS. 4 and 5. A pressure difference, ΔP, is calculated as ΔP=Pw−Pp.

InFIG. 3, TXX(or SHmax) represents the maximum horizontal stress direction, while TYY(Shmin) represents the minimum horizontal stress direction. TZZ(SV) represents the vertical stress direction. The maximum horizontal stress and minimum horizontal stress directions lie in two borehole axial planes, where each borehole axial plane is generally perpendicular to each other and to the longitudinal axis of the borehole.

FIG. 4shows several stress distributions from the near-field to the far-field along the maximum horizontal stress direction (parallel to SHmax). Three curves402,404, and406are shown inFIG. 4. Curve402represents the principal stress (σzzas a function of r/a, where r represents the distance from the borehole14inFIG. 3, and a represents the radius of borehole14inFIG. 3). A larger r/a value indicates a further distance from the borehole14, and represents the far field. A r/a value represents a closer distance to the borehole14, with r/a=1 representing the interface of the borehole14and formation16. The principal stress σzzis axial at the wellbore and vertical at the far-field. In between the wellbore and the far-field, the principal stress σzzhas a different orientation between axial and vertical.

Curve404represents another principal stress σrras a function of r/a. Curve406represents principal stress σθθas a function of r/a. Principal stresses σrrand σθθalso change orientations between the wellbore and the far field. As noted above, the stresses represented by curves402,404, and406are at an azimuth parallel to the maximum horizontal stress direction (SHmax) at a given depth. Curves402,404,406illustrate how the three different stresses vary in magnitude as they approach the borehole14.

FIG. 5, on the other hand, depicts curves502,506, and504, which represent the stress σzz, stress σrrand stress σθθ, respectively, as a function r/a, along the minimum horizontal stress direction (Shmin).

Generally, the stresses σzzand σθθexhibit larger magnitudes in the near-wellbore region along the minimum horizontal stress direction (seeFIG. 5) than those along the maximum horizontal stress direction (seeFIG. 4). The differences between such stresses in the minimum horizontal stress direction and the maximum horizontal stress direction cause dipole dispersion crossovers in the presence of such stress distributions. The dipole dispersion crossover is an indicator of stress-induced anisotropy dominating any intrinsic anisotropy that may be present. The foregoing is consistent with the observation that dipole compressional slownesses behave in an anisotropic manner much the same way as dipole shear slownesses. Therefore, the measurement of dipole compressional slownesses can be used in diagnosing and evaluating formation properties and geomechanical behavior.

In addition to stress-induced anisotropy, other causes of formation anisotropy also exist. Other sources of anisotropy include bedding induced anisotropy and fracture induced anisotropy. These other sources of anisotropy provide intrinsic anisotropy. Some embodiments of the invention are applicable to formations exhibiting intrinsic anisotropy.

In accordance with some embodiments, the dipole compressional data is processed for the two orthogonal dipole transmitter orientation for compressional slownesses. The differences in the dipole compressional modes are used for dipole firings along the maximum and minimum horizontal stress directions, respectively. In accordance with some embodiments, both monopole and dipole compressional modes are excited and recorded in slow formations. Dipole compressional waves can also be excited in some faster formations. While their amplitude is relatively small, the dipole compressional waves are often much larger than the background noise and thus they can be quantified. Note that the monopole compressional mode is generated at lower frequencies than in the case with dipole compressional modes. Monopole compressional modes respond to azimuthal averages of formation properties. In contrast, dipole compressional modes are capable of discriminating formation properties in two adjacent quadrants, as depicted inFIG. 6.

FIG. 6is a stress contour polar plot of the sum of two principal stresses in a cross-sectional plane.FIG. 6shows stress contours resulting from far-field formation stresses in the presence of a fluid-filled borehole. The maximum and minimum horizontal stress directions are also displayed in the stress contour plots. A dipole transmitter that is parallel to the maximum horizontal stress direction insonifies two opposite quadrants indicated by602and604, whereas a dipole transmitter parallel to the minimum horizontal stress direction largely probes two opposite quadrants depicted by606and608.FIG. 6shows that the acoustic properties of the formation16are sensitive to stress.

Compressional and dipole compressional modes are radiating or leaky modes because their slownesses are smaller than the formation shear slownesses. As a result, recorded waveforms containing these leaky compressional modes exhibit amplitude attenuation along a receiver array (such as the array of receivers54depicted inFIG. 1).

The dipole compressional mode is largely affected by stress-induced changes in the compressional modulus C33for propagation along the X3-direction. Based on an acoustoelastic model, changes in the effective compressional modulus C33can be related to corresponding changes in the effective stresses σ33, σ11, and σ22in the propagating medium as shown in Eq. 1. Note that σ33, σ11, and σ22, respectively, denote σv, σHmax, and σhminin the propagating medium.

Briefly, according to the theory of elasticity, the elastic response of a body to an applied load may be obtained using the principle of energy conservation, where the applied stress causes deformations, which changes the strain energy within the body. Mathematically, the stress (τ) at each point of a body is expressed as the change in strain energy associated to the change in the displacement gradient. This in turn, is proportional to the resulting strain. The resulting expressions (E1 and E2, below) correspond to the generalized Hooke's law (in tensorial notation), and indicate a proportional relationship between stress (τij) and strain (εij).

The coefficient of proportionality in (E1) and (E2) is the elastic-tensor or stiffness-tensor. For heterogeneous bodies, Cijklis a function of the position in the body; for homogeneous bodies, Cijklis a constant and independent of position. Mathematically Cijklis a fourth-order tensor that has 34=81 independent components. However, symmetry properties and conditions of positive definiteness reduce the number of independent components to 21. The number of independent components of the tensor may be reduced further, depending on material symmetries. For orthotropic symmetry, the material response is characterized by nine independent stiffness coefficients, namely, C11, C22, C33, C44, C55, C66, C12, C13, C23.

For transverse isotropic behavior (i.e., rotational symmetry) the material response is characterized by five independent material constants, namely, C11=C22, C33, C44=C66, C12, C13=C23; where C66is a function of the others. For isotropic symmetry, there is no directional bias. Accordingly, the material response for isotropic symmetry may be characterized with only two independent material constants (C11=C22=C33, C12=C13=C23, where C44=C55=C66are functions of the others).

Based on the aforementioned symmetries, the stiffness matrix for anisotropic materials with orthotropic symmetry may be expressed as follows:

For a given set of formation material parameters, it is clear from Eq. 1 and typical near-wellbore stress distributions shown inFIGS. 4 and 5, that dipole compressional slownesses will be smaller at higher frequencies for dipole oriented along the minimum horizontal stress direction than the case when the transmitter is oriented along the maximum horizontal stress direction. Therefore, dipole compressional slownesses at higher frequencies can be used to determine the azimuth of the maximum or minimum horizontal stress directions. If radial depths of investigation at low frequencies are essentially the same for the monopole compressional and the two orthogonal dipole compressional modes, low frequency asymptotes of these leaky compressional modes coincide with the far-field compressional slowness of the formation in the presence of triaxial stresses.

Analyses of dipole compressional mode also provide a way to estimate one of the three nonlinear elastic constants C111that is essential for estimating all nine stress coefficients (C11, C22, C33, C44, C55, C66, C12, C13, C23) of plane wave velocities. Recall that changes in the Stoneley and cross-dipole dispersions and associated changes in shear moduli enable estimation of the other two nonlinear constants C144and C155.

The dipole compressional arrivals in this example are dominated by C11and C22. Thus, when quantified and combined with the compressional measurement of C33and shear measurements of C44, C55and C66, techniques according to some embodiments now measure 6 of the 9 orthorhombic unknowns. In fact, with this technique there are fewer unknowns percentage wise in an orthotropic formation (3 out of 9) than a TI (transverse isotropic) formation (2 out of 5) with current technology.

Another aspect of some embodiments of the invention is the observation that horizontal velocities can be measured on cores taken by a Mechanical Sidewall Coring Tool (MSCT) (developed by Schlumberger) or other core sampling tool from vertical wells with non-dipping beds. The MSCT is designed to retrieve multiple, high quality sidewall cores in hard formations. Recovery depends more on grain cementation than on formation porosity, and is possible for porosities as high as 30 P.U. provided the grains are well cemented.

The results from the dipole compressional evaluation of C11and C22can be checked and verified using horizontal side core taken by the MSCT or horizontal plugs in conventional cores.

FIG. 7is a flow diagram of a workflow according to an embodiment. The geological environment is evaluated (at702). Evaluating the geological environment includes one or more of the following: evaluating the structural geology of the formation16; evaluating the petrophysicals of the formation16; evaluating the geology of the borehole14; and evaluating the geomechanics of the formation16.

In addition, the logging environment is evaluated (at704). Evaluating the logging environment includes one or more of the following: evaluating the directional survey; evaluating the hardware and software configuration; evaluating the mud system; evaluating the mud logs; evaluating the mud resistivity log; evaluating the borehole temperature log; evaluating the Stoneley log; evaluating the FMI (formation micro imager) log; evaluating the CDF (Calibrated Downhole Force) log; evaluating the differential pressure log; evaluating caliper data; evaluating the bulk density data; and evaluating the drilling reports.

The mud slowness is also estimated (at706). Mud slowness (slowness of the fluid in the borehole14) is determined based on mud density, dispersion analysis, and Stoneley and flexural inversion. The mud density is then correlated with the mud slowness, and the variability in the mud slowness is estimated based on temperature, pressure, and salinity. All the data is then integrated into a mud slowness log.

Next, the sonic waveforms collected by the logging tool10are processed (at708), where the sonic waveforms include dipole (and possibly monopole) compressional wave and shear wave data. Thus, processing the sonic waveforms include processing compressional slowness, dipole compressional slownesses in the maximum and minimum stress directions, processing dipole shear slownesses, processing Stoneley slowness, and processing the 3D (three-dimensional) anisotropy module.

The three shear moduli are then evaluated (at710). Following evaluation of the three shear moduli, the mud slowness is then re-evaluated, and the process returns to step708if the mud slowness requires refinement.

The tasks708-712of the workflow ofFIG. 7are then repeated (at714) until the estimate of the mud slowness is stable.

Various tasks according to some embodiments can be performed by an electronic device such as the downhole controller54or the surface controller32shown inFIG. 1. An example electronic device800is shown inFIG. 8. The electronic device800includes a processor802that is connected to storage media804. The electronic device800also includes analysis software806that is executable on the processor802. In addition, a network interface808connects the electronic device800to a communications medium to receive information from the logging tool10shown inFIG. 1.

Although analysis software806is shown in the electronic device800, it is noted that in alternative implementations, the various processing tasks according to some embodiments can be performed entirely in hardware, or by a combination of hardware and firmware.

Instructions of software806are loaded for execution on the processor802. The processor can include one or more microprocessors, one or more microcontrollers, one or more processor modules or subsystems (including one or more microprocessors or microcontrollers), or other control or computing devices or integrated circuit devices. As used here, a “processor” refers to a single component or to plural components (e.g., one CPU or multiple CPUs).