Single well anisotropy inversion using velocity measurements

At least one elastic parameter of a region of interest of a formation is modeled, and at least one velocity measurement acquired in a wellbore extending in the formation is predicted based on the modeling. The model is refined based on the predicted velocity measurement(s) and based on at least one actual measurement acquired from within a single wellbore.

BACKGROUND

Hydrocarbon fluids, such as oil and natural gas, are obtained from a subterranean geologic formation by drilling one or more wellbores and installing completion equipment in the wellbores to enable the extraction of fluids from the reservoir. Surface equipment is also provided to route or store the extracted fluids.

A variety of different operations may be performed for purposes of enhancing the extraction of fluid. For example, perforating operations may be performed to fire shaped charges to pierce the well casing (if any) and form perforating tunnels into the reservoir. Well stimulation operations, such as acidizing and hydraulic fracturing operations, which involve injecting a fluid at relatively high pressure through a wellbore into the reservoir to cause fracturing of the formation, may also be employed.

SUMMARY

In accordance with embodiments, at least one elastic parameter of a region of interest of a formation is modeled, and at least one velocity measurement acquired in a single wellbore extending in the formation is predicted based on the modeling. The model is refined based on the predicted velocity measurement(s) and based on at least one actual measurement acquired from within the single wellbore.

DETAILED DESCRIPTION

Reference throughout the specification to “one embodiment,” “an embodiment,” “some embodiments,” “one aspect,” “an aspect,” or “some aspects” means that a particular feature, structure, method, or characteristic described in connection with the embodiment or aspect is included in at least one embodiment. Thus, the appearance of the phrases “in one embodiment” or “in an embodiment” or “in some embodiments” in various places throughout the specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, methods, or characteristics may be combined in any suitable manner in one or more embodiments. The words “including” and “having” have the same meaning as the word “comprising.”

Moreover, inventive aspects lie in less than all features of a single disclosed embodiment. Thus, the claims following the Detailed Description are hereby expressly incorporated into this Detailed Description, with each claim standing on its own as a separate embodiment.

Knowledge of the mechanical rock properties, or elastic parameters, of a subterranean geologic formation may be used for a wide variety of purposes in the planning, drilling, completion and production phases of a well. In this manner, the formation's elastic parameters may be used for such purposes as well completion design, avoiding wellbore instability, designing hydraulic fractures and monitoring hydraulic fracturing from micro-seismic events.

The elastic parameters of a given formation may be directionally dependent, or exhibit anisotropy. More specifically, a given formation may exhibit vertical transverse isotropy (VTI). The physical properties of a VTI material are identical when measured with respect to a symmetry axis but otherwise vary with direction (i.e., otherwise are anisotropic in nature). In the case of many sedimentary layers, these layers are generally horizontal, and the resulting symmetry axis is vertical. Therefore, measurements acquired in radial directions about the vertical axis do not vary with respect to direction, but measurements acquired in other directions are dependent on the direction. For a VTI material, the elastic stiffness tensor may be described using a reduced set of five elastic constants, or parameters: C11, C33, C44, C66and C13.

The C11, C33, C44, C66and C13parameters describe the velocity variations for three different wave types: the quasi-compressional wave (qP), the quasi shear-wave polarized in the vertical plane (qSv) and a true shear-wave polarized in the horizontal plane (SH). The behaviors of the quasi-compressional waves qP and quasi shear-waves qSv are described by the C11, C33, C44and C13parameters. The behavior of the SH wave is described by the C44, and C66elastic parameters.

In accordance with embodiments that are disclosed herein, for purposes of determining the elastic parameters for a given formation (such as a formation that is assumed to be VTI, for example) a sonic measurement tool may first be deployed in a wellbore that extends into the formation for purposes of acquiring velocity measurements at several different angles. Thus, the measurements are associated with different directions, and in general, the deviation of the well at a given measurement site controls the direction of the measurement.

For a formation that formed from a material that is considered to be a VTI material and for a wellbore segment inside the formation, which is deviated (i.e., not vertical), the velocity measurements are, in general, acquired in various directions that are not orthogonal to the symmetry axis (the vertical axis, for example) of the formation. Therefore, due to the anisotropy that is exhibited by the VTI material, the wave speeds that are measured using the sonic measurement tool are, in general, directionally dependent.

In accordance with embodiments disclosed herein, a model (the C11, C33, C44, C66and C13parameters, for example) for the elastic parameters of a formation of interest is derived using the actual velocity measurements that are acquired by a sonic measurement tool from within a single deviated wellbore that extends in the formation.

Turning now to a more specific example, referring toFIG. 1, a well10may contain a wellbore14, which initially (from the Earth surface) extends vertically through an upper overburden formation20and then deviates from the vertical orientation to extend laterally in a lower formation24of interest. As an example, the upper overburden formation20may be generally isotropic, and the lower formation24may be a relatively low permeability shale formation that may be considered VTI. A deviation60of the wellbore14with respect to depth is illustrated inFIG. 2.

More particularly,FIG. 2depicts the deviation60of the wellbore14ofFIG. 1as a function of distance along the borehole. Referring toFIG. 2in conjunction withFIG. 1, near the Earth surface, the wellbore14extends from an Earth surface point30in a near vertical segment64to a point32at which the wellbore14begins deviating away from a vertical orientation. In this regard, from the point32to a point34(at the adjacent boundaries of the formations20and24), the deviation increases along segment66and continues to increase in a segment68between the point34and36. Near and extending past point36, the wellbore14becomes substantially horizontal for this example.

For purposes of determining elastic parameters for the formation24, a sonic measurement tool may be disposed in the wellbore14and used to acquire velocity measurements at several locations in the segment of the wellbore14between the points34and36. The velocity measurements may be measurements of vertically polarized shear waves; horizontally polarized shear waves; compressional waves; flexural waves, quadrupole waves, monopole head waves, and/or Stoneley waves, depending on the particular embodiment. As non-limiting examples, the velocity measurements may be acquired while the wellbore14is being drilled (using a logging while drilling (LWD) sonic measurement tool, for example); or the velocity measurements may be acquired after the drilling phase is complete using, for example, a sonic measurement tool that is deployed downhole on a wireline or on another type of conveyance mechanism.

Due to the anisotropy that is exhibited by the formation24, the sonic measurement tool acquires velocity measurements in directions at some angle to the symmetry axis (here, the “Z” axis). For example, the sonic measurement tool may acquire velocity measurements that are generally orthogonal with respect to the trajectory of the wellbore14, and therefore, the directions of the velocity measurements vary with the tool's location. Due to the VTI nature of the formation24, the velocity measurements vary with direction, even though the formation24may be homogeneous.

More specifically, referring toFIG. 3in conjunction withFIG. 1, a measured slowness80(the inverse of velocity) varies with the depth of the wellbore14. In this manner, a segment of the slowness80associated with the overburden formation20is relatively constant, i.e., the slowness80varies little from point30to the point34, due to the formation20being isotropic. However, in the formation24of interest, the slowness80varies with depth as the trajectory of the wellbore14changes (i.e., the measurement angle changes), as indicated by segment88(seeFIG. 3). It is noted that if the formation24were hypothetically isotropic instead of anisotropic, the slowness would be constant, as indicated by dashed lines89and90inFIG. 3.

Systems and techniques are disclosed herein, which analyze the velocity/slowness variations with respect to the well deviation to estimate one or more of the elastic parameters associated with the formation24. The determined elastic parameters may then be used for purposes of conducting and planning various oilfield activities, such as activities related to well completion, wellbore stability design, hydraulic fracturing design, hydraulic fracturing monitoring and pre-stack depth migration.

More specifically, referring toFIG. 4, a technique100in accordance with embodiments includes acquiring (block104) data indicative of actual velocity measurements at different measurement angles along a single wellbore, i.e., along a deviated wellbore section of a single wellbore, which extends in a region of interest of a given formation. The technique100includes modeling (block108) elastic parameters of the formation as a function of velocity for the region of interest and predicting (block110) velocity measurements acquired in the deviated wellbore section. The technique100includes refining (block112) the model based on the predicted velocity measurements and the actual velocity measurements.

Depending on the particular embodiment, the predicted velocity measurements may be derived using full waveform modeling or using samples of group velocity vectors in different directions.

As a first example, in accordance with some embodiments, a three-dimensional (3-D) finite difference technique may be used to determine the full waveform data, which may then be used in an objective function to match the observed waveforms to synthetically generated waveforms. As non-limiting example, the 3-D finite difference technique may be used that is disclosed in Mallan, R K, Jun Ma, and Carlos Torres-Verdin, 3D NUMERICAL SIMULATION OF BOREHOLE SONIC MEASUREMENTS ACQUIRED IN DIPPING, ANISOTROPIC, AND INVADED FORMATIONS SPWLA 50 Annual Logging Symposium, 2009. For purposes of reducing computation costs, the computation and velocity from a point source (i.e., “group velocities”) located in a homogeneous medium is sufficiently accurate and may be achieved using fewer computing resources. In the case of weak anisotropy, plane-wave velocities (i.e., “phase velocities”) located in a homogeneous medium may be appropriate.

As a second example, the model of the elastic parameters may be refined using samples of group velocity vectors in different directions. In this manner, for materials possessing transverse isotropy, analytical expressions exist for the plane-wave velocity (also called “phase velocity”) variations, such as the expressions that are set forth in Thomsen, Leon, WEAK ELASTIC ANISOTROPYGeophysics51 (October): 1954-1966. Such plane-wave velocity expressions are appropriate in the case that the source excites plane waves or the anisotropy is weak. In the case that the source is more accurately represented as a point source, the velocities that are measured are the group velocities for which no exact analytical expression exists to compute the quasi-compressional qP and quasi shear-wave qSV group velocities for a given group direction. These “point-source,” or group velocities may, however, be determined for a given plane-wave direction by solving the Kelvin-Christoffel equation and then computing the group velocity vector whose direction gives the group direction. As non-limiting examples, a technique such as the one disclosed in Musgrave, M. J. P., CRYSTALACOUSTICS(Holden-Day 1970) or the one disclosed in Auld, B. A., ACOUSTICFIELDS ANDWAVES INSOLIDS(Kreiger Publishing Co. 1990) may be used. For dipole sonic logs, the velocities that are measured are the group velocities.

In accordance with some embodiments, a model describing the relationship of the elastic parameters (the five constants of the stiffness tensor for a VTI formation, for example) is first estimated. From this model, group velocity vectors are sampled over different directions, such as directions in a range of possible directions given the trajectory of the wellbore14, for purposes of forming a lookup table of group velocities that are indexed by measurement trajectories. The look up table is then searched to find the point-source (group) directions that are close to the well deviations of the observed, or acquired, velocity measurements that are acquired by the sonic measurement tool. The acquired velocity measurements are then compared to corresponding velocity measurements in the look-up table for purposes of refining the model.

More specifically, in accordance with some embodiments, the predicted velocities from the look-up table and the actual, acquired velocity measurements are used to evaluate an objective function, such as an example objective function (called “f(m)”) that is set forth below:

f⁡(m)=∑i=1N⁢VObs,i-VSyn,iΔ⁢⁢Vi,Eq.⁢1
where “m” represents a model describing the formation's elastic properties (such as the five constants of the stiffness tensor for a VTI formation, for example); “N” represents the number of actual velocity measurements available from the sonic log; “i” represents an index; “VObs,i” represents the “ith” observed, or acquired velocity measurement; and “VSyn,i” represents the “ith” predicted velocity measurement from the look-up table that is closest in direction to the VObs,ivelocity measurement; and “ΔVi” represents the error associated with the VObs,ivelocity measurement. An iterative process is used to minimize the f(m) objective function for purposes of determining the elastic parameters.

More specifically, referring toFIG. 5, a technique150may be used for purposes of determining at least one elastic parameter for a formation of interest in accordance with embodiments. Pursuant to the technique150, an initial model describing at least one elastic parameter is estimated (block154) in a region of interest. Next, pursuant to the technique150, an iterative process begins in which the objective function is minimized for purposes of refining the model. In this manner, the technique150includes predicting (block158) velocities acquired in a single wellbore that extends in the region of interest for different directions based on the model and incorporating the predicted velocities into a look-up table, pursuant to block158.

Next, the technique150includes determining (block162) an objective function based on measured velocities in the region of interest and the predicted velocities (found in the look-up table) having similar associated directions. The objective function is then evaluated such that a determination may be made (decision block166) whether the objective function has been sufficiently minimized. In this manner, several iterations may be performed for purposes of evaluating the objective function, changing the model and then re-evaluating the objective function for purposes of minimizing the function. If the objective function has not been sufficiently minimized, the technique150includes refining (block170) the model (changing the C11, C33, C44, C66and C13parameters, for example) and returning to block158. Otherwise, the objective function has been minimized, thereby determining the elastic parameter(s).

Thus, in accordance with embodiments disclosed herein, the elastic parameters are determined from predicted velocity measurements and actual velocity measurements acquired with a single wellbore without relying on actual velocity measurements acquired from any other wellbore. The velocity measurements may be measurements of one or more of horizontal shear wave velocities, vertical shear wave velocities, Stoneley wave velocities and compression wave velocities or any wave generated by a sonic tool of any type of conveyance from which compressional or shear wave velocities may be inferred. Moreover, the measurements do not have to be made in a nearly horizontal or nearly vertical well; and weak anisotropy is not necessarily assumed.

The elastic parameters and model that are determined using the techniques that are disclosed herein may be used for a wide variety of purposes. For example, using the determined elastic parameters, a velocity model may be constructed for purposes of locating microseismic events that are produced by hydraulic fracturing operations. The determined anisotropic characteristics may be used to correct the velocity measurements to account for the well deviation as described by Hornby, B., Howie, J., and Ince, D., ANISOTROPYCORRECTION FOR DEVIATED-WELL SONIC LOGS: APPLICATION TO SEISMIC WELL TIE, SEG Expanded Abstracts., 1999; and Hornby, B., Howie, J., and Ince, D., ANISOTROPY CORRECTION FOR DEVIATED-WELL SONIC LOGS: APPLICATION TO SEISMIC WELL TIE, Geophysics 68(2), 2003.

Another way in which the elastic parameters may be used is for determining attributes related to the anisotropy. For example, a particularly useful attribute is the Bn/Bt ratio, which is related to the gas saturation in shales, Sayers, C. M., 2008, THE EFFECT OF LOW ASPECT RATIO PORES ON THE SEISMIC ANISOTROPY OF SHALES, SEG Expanded Abstract 2750-2754. Thus, the anisotropy measurement can potentially be used as a prediction of future production of the formation. The anisotropy parameters may be used to determine the total organic content (TOC) in shales as disclosed in Sondergeld, C. H., Chandra, S. R., Margesson, R. W., & Whidden, K. J., ULTRASONIC MEASUREMENT OF ANISOTROPY ON THEKIMMERIDGESHALE, SEG Annual Meeting Expanded Abstracts, 2000, a correlation exists between TOC and shale anisotropy parameters. Therefore, the techniques and systems that are disclosed herein may be used as an indicator or even a measure of TOC.

As another example, the elastic parameter(s) may be used for purposes of planning a perforation operation to be conducted in the formation24. In this manner, the orientations of the perforating charges, the clustering of the perforating charges, the locations of groups of perforating charges, distances between perforating charges, and so forth may be chosen based on the determined elastic parameters. Thus, many variations are contemplated and are within the scope of the appended claims.

Referring toFIG. 6, in accordance with some embodiments, a data processing system320, or computer, may contain a processor350for purposes of determining a model for at least one elastic parameter of a region of interest of a formation using velocity measurements acquired from within a single wellbore that extends in the region of interest. In this manner, using the processor350, the system320may contain a model, a predictor and an adjuster that models at least one elastic parameter of a region of interest of a formation as a function; predicts (via the predictor) at least one velocity measurement acquired in a wellbore extending in the formation based on the model; and refines (via the adjustor) the model based on the at least one predicted velocity measurement and at least one actual velocity measurement acquired from within the single wellbore.

In accordance with some embodiments, the processor350may be formed from one or more microprocessors and/or microprocessor processing cores. As non-limiting examples, the processor350may be disposed at a well site, may be disposed remotely from the well site or may, in general, be a processing system that may be at one location or may be spatially distributed at various locations, in accordance with the many possible different embodiments.

As depicted inFIG. 6, the processor350may be coupled to a communication interface360for purposes of receiving pressure and particle motion data. As examples, the communication interface360may be a Universal Serial Bus (USB) interface, a network interface, a removable media interface (a flash card, CD-ROM interface, etc.) or a magnetic storage interface (IDE or SCSI interfaces, as non-limiting examples). Thus, the communication interface360may take on numerous forms, depending on the particular embodiment.

In accordance with some embodiments, the processor350is coupled to a memory340, which stores program instructions344, which when executed by the processor350, may cause the processor350to perform various tasks of one or more of the techniques that are disclosed herein, such as the techniques100and/or150, as non-limiting examples. The memory340may store information characterizing the model and may use data for a look-up table of sampled, predicted velocity measurements.

The memory340is a non-transitory memory and may take on numerous forms, such as semiconductor storage, magnetic storage, optical storage, phase change memory storage, capacitor-based storage, etc., depending on the particular implementation. Furthermore, the memory340may be formed from more than one of these non-transitory memories, in accordance with some embodiments. When executing the program instruction344, the processor340may also, for example, store preliminary, intermediate and/or final results obtained via the execution of the program instructions344as data348in the memory340.

The data processing system320is merely an example of one out of many possible architectures for processing velocity measurements, modeling elastic parameters and predicting velocity measurements, in accordance with the techniques that are disclosed herein. Moreover, the data processing system320is represented in a simplified form, as the processing system320may have various other components (a display to display initial, intermediate or final results of the system's processing, as a non-limiting example), as can be appreciated by the skilled artisan. Thus, many variations are contemplated and are within the scope of the appended claims.

While a limited number of embodiments have been disclosed herein, those skilled in the art, having the benefit of this disclosure, will appreciate numerous modifications and variations there from. It is intended that the appended claims cover all such modifications and variations.