Eccentricity correction algorithm for borehole shape and tool location computations from caliper data

The subject disclosure provides for a method of eccentricity correction of a borehole shape computation. The method includes deploying a caliper tool into a borehole penetrating a subterranean formation and acquiring field measurements with the deployed caliper tool. The method includes applying, in a processor circuit, an eccentricity correction algorithm to one or more standoff samples from the obtained field measurements, wherein the eccentricity correction algorithm produces a shape fitted curve that represents a measured borehole with a least number of points outside of the shape fitted curve and a least amount of error. The method includes determining eccentricity-corrected borehole coordinates with the applied eccentricity correction algorithm and determining a borehole shape from the eccentricity-corrected borehole coordinates. The method includes determining tool location coordinates relative to the borehole with the determined borehole shape.

TECHNICAL FIELD

The present description relates in general to downhole measurement systems, and more particularly to, for example, without limitation, eccentricity correction algorithm for borehole shape and tool location computations from caliper data.

BACKGROUND

Modern oil field operations demand a great quantity of information relating to the parameters and conditions encountered downhole. Such information typically includes characteristics of the earth formations traversed by the borehole, and data relating to the size and configuration of the borehole itself. The collection of information relating to conditions downhole, which commonly is referred to as “logging,” can be performed by several methods including wireline logging and “logging while drilling” (LWD).

During exploration and recovery operations, the standoff data of the borehole may be used as an indication of formation stress, compaction, and other mechanisms that operate to deform the borehole. In these and other logging environments, an image of the borehole wall can be constructed with the standoff data. Among other things, such images reveal the fine-scale structure of the penetrated formations. However, assessing the standoff data of the borehole rapidly and accurately, especially when the logging tool acquiring the associated data moves off-center, can be difficult.

DETAILED DESCRIPTION

Borehole standoff measurements can be made in many ways. Traditional approaches include mechanical devices that follow the contour of the borehole and acoustic/ultrasonic devices that measure the time it takes pressure waves to travel from the tool to the formation wall and back. Caliper logs can provide information about borehole geometry, which is important in petrophysical and geomechanical analyses. When using a caliper device for borehole standoff measurement for both wireline and logging-while-drilling, it is common that the tool string is off-centered. It is important to have a robust algorithm to correct the tool eccentricity in order to recover the correct hole shape.

The disclosed system addresses a problem in traditional borehole shape computation algorithms tied to computer technology, namely the technical problem of computing a borehole shape when a borehole wall perimeter is irregular. One of the challenges of LWD ultrasonic borehole imaging is to correct the eccentricity of the tool. It is important to determine the accurate tool location with respect to the borehole during each data acquisition and from which recover the borehole shape. A robust algorithm is crucial for this technology because an accurate tool center and borehole shape is expected to correct the amplitude of an image due to eccentricity. Traditional methods use least-square circle fitting or elliptical fitting, which yield an inaccurate borehole shape when the borehole is irregular (e.g. breakout, keyseat).

The present disclosure provides for computing the borehole shape with more accuracy over conventional approaches with the eccentricity correction borehole shape computation algorithm of the subject technology, especially for irregular borehole shapes such as keyseat or breakout. For example, the subject eccentricity correction algorithm is robust in handling irregular borehole shapes and is able to recover irregular hole shape with relatively high accuracy. In some implementations, the subject eccentricity correction borehole shape algorithm can be used for ultrasonic imager, ultrasonic caliper, mechanical caliper and other types of calipers. In some implementations, the eccentricity correction borehole shape algorithm can be used for calipers with more or less than 4 transceivers (or mechanical arms). The subject eccentricity correction borehole shape algorithm also works for wireline calipers and LWD calipers, for example, a 6-arm wireline caliper.

Conventional methods such as circle fitting or elliptical fitting methods only employ minimization of error. However, the subject algorithm employs a comprehensive list of assumptions and criteria to compute borehole shape from caliper data with high accuracy. For example, 1) a portion of intact borehole exists, where borehole irregularity is caused by attachment or removal of material from a gauge hole while part of the gauge hole remains intact, 2) adjacent firings are stacked, where the borehole shape remains unchanged within a small depth interval and the fitted borehole radius from several adjacent firings is a constant, 3) points out of the fitted circle shape are minimized, where the correct fitted circular borehole minimizes the number of points out of the circle or maximizes the number of points on the circle, and 4) the error is minimized, where the correct fitted circular borehole minimizes the difference between the square of the corrected radius and the square of the circular borehole radius.

The disclosed system further provides improvements to the functioning of the computer itself because it saves data storage space, reduces system processing latency and reduces the cost of system resources. Specifically, the eccentricity-corrected borehole shape computations helps reduce the system processing latency by computing the borehole shape with standoff measurements produced by adjacently stacked transducer firings without the need to execute individual computations for each transducer firing while logging and/or after the logging has been completed. The borehole shape computations can be stored and indexed by depth interval with minimal storage required due to the lesser amount of data generated from the adjacently stacked transducer firings. The process of adjacently stacking transducer firings for a given depth interval also helps to reduce the cost of system resources by minimizing the need to reallocate additional memory bandwidth for processing standoff measurements after each individual transducer firing.

The subject disclosure provides for a method of eccentricity correction of a borehole shape computation. In some implementations, the method includes deploying a caliper tool into a borehole penetrating a subterranean formation and acquiring field measurements with the deployed caliper tool. The method includes applying, in a processor circuit, an eccentricity correction algorithm to one or more standoff samples from the obtained field measurements, wherein the eccentricity correction algorithm produces a shape fitted curve that represents a measured borehole with a least number of points outside of the shape fitted curve and a least amount of error. The method includes determining eccentricity-corrected borehole coordinates with the applied eccentricity correction algorithm and determining a borehole shape from the eccentricity-corrected borehole coordinates. The method also includes determining tool location coordinates relative to the borehole with the determined borehole shape.

As used herein, the terms “firing” or “transducer firing” generally refer to a transmitted signal pulse by a transducer to produce a signal reflection with a borehole wall for measurement. In some aspects, the signal pulse and signal reflection are acoustic wave signals, where the transducer may be an acoustic transducer. In other aspects, the signal pulse and signal reflection are gamma ray signals, where the transducer may be a nuclear transducer. As used herein, the term “adjacent firing” refers to the adjacency of the transmitted transducer signal pulses in space and time. As used herein, the term “borehole shape” refers to the shape outline of the borehole wall perimeter.

FIG. 1Aillustrates an example of a data plot100depicting an eccentricity correction algorithm using a traditional approach. The traditional eccentricity correction algorithm uses mainly two assumptions. First, the borehole is stationery and the caliper tool moves at different acquisitions. Second, the borehole is approximately circular in shape. The hole center can be estimated using circle fitting and the radii are corrected by shifting the hole center to the origin of the circle fitted shape.

InFIG. 1A, the circles (e.g.,102,104,106,108) are raw data computed from borehole standoff data and the angle of firing. The point (e.g.,110) is the estimated hole center based on circle fitting. The triangles (e.g.,112,114,116,118) are eccentricity-corrected radii and the point (e.g.,120) is an eccentricity-corrected hole center.

In the traditional eccentricity correction algorithm, the circle fitting can be achieved in various ways such as least-squared circle fitting or chord method. For a caliper tool with more than four transceivers (or arms for mechanical caliper), an ellipse fitting method can be used. However, these fitting methods work best for a near-circular or near-elliptical borehole. When the borehole shape is irregular, the assumption fails and the method would result in an inaccurate hole shape.

To implement the mechanisms described for determining a borehole caliper measurement, a variety of apparatus, systems, and methods may be used. For example,FIG. 1Billustrates a caliper measurement apparatus150according to various implementations of the subject technology. In some implementations, the caliper measurement apparatus150may include one or more sensors194(e.g., ultrasound sensors) to receive signals190. In the subject disclosure, a 4-transceiver ultrasonic caliper tool is used as an example. However, the subject disclosure also applies to other types of caliper tools with more or less number of transceivers or mechanical calipers.

The caliper measurement apparatus150may include acquisition logic160(e.g., acquisition logic circuitry) to acquire data172, such as azimuthal location data, signals190, and/or borehole standoff distance data representing the standoff distance between a transducer194and a borehole192. That is, the acquisition logic160may acquire the ultrasonic signals190directly as borehole standoff data, or digitize the signals190to provide digital borehole standoff data, to record information representing borehole standoff distance measurements. The sensor194may include a single rotating transducer to couple to the acquisition logic160to provide the borehole standoff data. In some implementations, the caliper measurement apparatus150may include a gamma-ray density tool196to couple to the acquisition logic160to provide the borehole standoff data. In some aspects, the transducer194is an acoustic transducer. In particular, the transducer194may be an ultrasonic acoustic transducer. In implementations, the transducer194includes an array of transducers. In this respect, the array of transducers can be deployed and fire simultaneously at different angles of firing in a depth interval.

The caliper measurement apparatus150may also include a memory174to store the data172. The caliper measurement apparatus150may also include processing logic166to perform the steps of process200(FIG. 2). In some implementations, the processing logic116may operate to calibrate caliper measurement values. The processing logic116may be included in a downhole tool, or above-ground (e.g., as part of an above-ground computer workstation, perhaps located in a logging facility), or both.

In some implementations, the caliper measurement apparatus150may include one or more transmitters168, such as telemetry transmitters, to transmit the data172to an above-ground computer184. For example, one or more transmitters may be used to transmit caliper measurements, including corrected caliper measurement data, to the surface (e.g., above ground), where the above-ground computer184is located. The caliper measurement apparatus150may also include one or more displays182to display visual representations of caliper measurements, including corrected caliper measurement data and/or uncorrected caliper measurement data.

The process200will be discussed in reference toFIG. 1Bfor brevity and explanation. Further for explanatory purposes, the blocks of the sequential process200are described herein as occurring in serial, or linearly. However, multiple blocks of the process200may occur in parallel. In addition, the blocks of the process200need not be performed in the order shown and/or one or more of the blocks of the process200need not be performed. In some aspects, the process200is performed during a logging operation (e.g., LWD, MWD, wireline logging). In other aspects, the process200is partially performed during a logging operation (e.g., transducer firings deployed, field measurements are obtained) and the processing of the measurement data is performed on a surface as a post-processing operation.

As shown inFIG. 2, the caliper measurement apparatus150may cause deployment of a predetermined number of firings in a depth interval with a particular angle of firing (202). In some aspects, the angle of firing may be in a range of 0 to 360 degrees, and the angle of firing of each adjacent firing may be different from one another. The depth interval may include a range of depth values in some implementations, or may include a single depth value in other implementations.

In some aspects, the caliper measurement apparatus150obtains field measurements from the acquisition logic160. In particular, the caliper measurement apparatus150may acquire a standoff measurement for each transducer firing in the depth interval from the obtained field measurements. In other aspects, the caliper measurement apparatus150may acquire an angle of firing measurement for each transducer firing in the depth interval from the obtained field of measurements.

The caliper measurement apparatus150also computes uncorrected coordinates of a plurality of points of the measured borehole for each transducer firing (204). In some aspects, the uncorrected coordinates are computed using the standoff measurements and angle of firing measurements in the depth interval.

In some implementations, the caliper measurement apparatus150applies an eccentricity correction algorithm. The eccentricity correction algorithm employs two main assumptions: (1) the presence of a partial intact borehole, and (2) the stacking of adjacent transducer firings. With regard to the assumption of the presence of a partial circular intact hole, the borehole irregularity is assumed to be caused by attachment or removal of material from an intact gauge hole, such as keyseat, breakout, drilling-induced fracture, mudcake attachment, etc. A portion of the circular gauge hole remains intact, which can be used to calculate the hole diameter. With regard to the assumption of the stacking of adjacent firings, the borehole shape is assumed to remain unchanged within a small depth interval. In this respect, the borehole radius of the intact section from several adjacent firings is a constant. When only one firing is considered, the intact hole radius cannot be identified when two or more transceivers fire onto the non-intact section of the borehole. The stacking of adjacent firings improves the rate of finding the correct borehole radius and enables the corrected borehole shape to reveal more detailed features by including more data points.

The caliper measurement apparatus150performs circle fitting of every first predetermined number of points to generate a list of corresponding radius values (206). In particular, the caliper measurement apparatus150applies a shape fitting algorithm (e.g., circle fitting algorithm). In some aspects, the list of radius values correspond to an intact section of the measured borehole. In some aspects, the measured borehole includes an intact section and a non-intact section, where part of the borehole is enlarged or shrunk due to a downhole event (e.g., breakout, keyseat, mudcake attachment, etc.).

The caliper measurement apparatus150performs circle fitting of all combinations of second predetermined number of points with a given radius value (208). In particular, the caliper measurement apparatus150applies a shape fitting algorithm (e.g., circle fitting) to all combinations of every 2 points with a radius value of the listing of radius values to compute a plurality of hole centers.

The eccentricity correction algorithm also employs the following criteria to find the best fitting circular intact borehole: (1) by minimizing points out of the circle, and (2) by minimizing the error. Regarding the first criterion, the correct fitted circular borehole minimizes the number of points out of the circle or maximizes the number of points on the circle.

This is the main objective function and can be expressed using an L0-norm optimization algorithm, which is expressed as shown in Equation (1):

where i is the transceiver number, j is the firing number, (xij,yij) is the point on the borehole corresponding to ith transceiver in jth firing, (x0j,y0j) is the coordinate for the fitted hole center for jth firing, R is the hole radius of the intact circular section where Cj is the number of points on the circle for jth firing. However, the value of the function (number of points) is discrete. There are possibly multiple solutions with the same number of points out of circle. Hence the second minimization condition is used to arrive at a unique solution.

In some implementations, in maximizing the number of points on the shape fitted curve (i.e., minimizing the number of points out of the shape fitted curve using the L0-norm optimization algorithm, the caliper measurement apparatus150determines a first magnitude measurement (e.g., xij) of a transducer firing along a first axis (e.g., x-axis) for each of a plurality of transducers (e.g., ith transceiver) associated with one of a plurality of transducer firings (e.g., jth firing). The caliper measurement apparatus150also determines a first hole center estimation of the shape fitted curve along the first axis (e.g., x0j) for each of the plurality of transducers associated with the one of the plurality of transducer firings. The caliper measurement apparatus150also determines a first difference between the first magnitude measurement and the first hole center estimation (e.g., xij−x0j). The caliper measurement apparatus150also determines a second magnitude measurement (e.g., yij) of a transducer firing along a second axis (e.g. y-axis) orthogonal to the first axis for each of the plurality of transducers associated with the one of the plurality of transducer firings. The caliper measurement apparatus150also determines a second hole center estimation of the shape fitted curve along the second axis (e.g., y0j) for each of the plurality of transducers associated with the one of the plurality of transducer firings. The caliper measurement apparatus150also determines a second difference between the second magnitude measurement and the second hole center estimation (e.g., yij−y0j). The caliper measurement apparatus150also determines a sum of a square of the first difference and a square of the second difference (e.g., (xij−x0j)2+(yij−y0j)2). The caliper measurement apparatus150also determines a third difference between the determined sum and a square of a hole radius of an intact section of the shape fitted curve to produce a first solution vector (e.g., (xij−x0j)2+(yij−y0j)2−R2)). The caliper measurement apparatus150also applies an L0-norm optimization algorithm to the first solution vector for each of the plurality of transducer firings to maximize the number of points on the shape fitted curve (or minimize the number of points on the shape fitted curve). In some aspects, the determined number of points corresponds to the maximized number of data points on the shape fitted curve (e.g., circle).

Regarding the second criterion, the correct fitted circular borehole minimizes the difference between the square of measured radius and the square of circular borehole radius, which is expressed as shown in Equation (2):

In some implementations, other optimization methods can be employed to solve (x0j,y0j) and R based on the above conditions.

In some implementations, in minimizing the amount of error for each transducer firing, the caliper measurement apparatus150determines a first magnitude measurement (e.g., xij) of a transducer firing along a first axis (e.g., x-axis) for each of a plurality of transducers (e.g., ith transceiver) associated with one of a plurality of transducer firings (e.g., jth firing). The caliper measurement apparatus150also determines a first hole center estimation of the shape fitted curve along the first axis (e.g., x0j) for each of the plurality of transducers associated with the one of the plurality of transducer firings. The caliper measurement apparatus150also determines a first difference between the first magnitude measurement and the first hole center estimation (e.g., xij−x0j). The caliper measurement apparatus150also determines a second magnitude measurement (e.g., yij) of a transducer firing along a second axis (e.g. y-axis) orthogonal to the first axis for each of the plurality of transducers associated with the one of the plurality of transducer firings. The caliper measurement apparatus150also determines a second hole center estimation of the shape fitted curve along the second axis (e.g., y0j) for each of the plurality of transducers associated with the one of the plurality of transducer firings. The caliper measurement apparatus150also determines a second difference between the second magnitude measurement and the second hole center estimation (e.g., yij−y0j). The caliper measurement apparatus150also determines a sum of a square of the first difference and a square of the second difference (e.g., (xij−x0 j)2+(yij−y0j)2). The caliper measurement apparatus150also determines a third difference between the determined sum and a square of a hole radius of an intact section of the shape fitted curve to produce a second solution vector (e.g., (xij−x0 j)2+(yij−y0j)2−R2)). The caliper measurement device applies a square to an absolute value of the second solution vector for each of the plurality of transducer firings to minimize the amount of error on the shape fitted curve.

Referring back toFIG. 2, the caliper measurement apparatus150selects one of the hole centers for each corresponding radius value that minimizes the number of points outside of the shape fitted curve (e.g., circle) and minimizes the error for each of the transducer firings (210). In other words, the shape fitted curve with its origin at the selected hole center that has the least number of points outside the curve and least amount of error is selected. This process would be repeated for each round of transducer firing.

The caliper measurement apparatus150selects a radius value from the listing of radius values associated with the selected hole center having the least sum of points outside the shape fitted curve for all transducer firings and a least sum of errors for all transducer firings (212). With the selected radius value and the selected hole center, the caliper measurement apparatus150determines coordinates of eccentricity-corrected points on a representation of the measured borehole (214). The caliper measurement apparatus150interpolates additional data points using the eccentricity-corrected points in order to compute a representation of the borehole shape for the measured borehole (216).

InFIG. 2, two criteria are used for the optimization of the eccentricity correction algorithm. In some implementations, a selection of the two criterion in any number or order can be used while effectiveness of the algorithm may be affected. For example, criterion1(minimizing points out of the circle) can be satisfied first before criterion2(minimizing error). The reverse may also work but with a higher rate of error.

FIG. 3Aillustrates an example of a plot310depicting a keyseat borehole shape with synthetic caliper measurements. To compare results of the eccentricity correction shape-fitting algorithm with the traditional circle-fitting algorithm, a synthetic example is used to illustrate a keyseat borehole shape, with an enlarged section (e.g.,312) on one side. It is desirable for the eccentricity-correction algorithm of the subject disclosure to estimate the contour shape of the borehole including the enlarged section312as closely as possible given that traditional borehole shape algorithms typically fail to correctly estimate an irregularly shaped borehole. In some aspects, the enlarged section may refer to a non-intact section, and the terms may be used interchangeably without departing from the scope of the subject disclosure. The tool center is randomly generated and four firings are used in the example. Two out of four firings has one transceiver pointing at the enlarged section312.

FIG. 3Billustrates an example of a plot320depicting a keyseat borehole shape computation with a traditional borehole shape algorithm. The traditional circle-fitting algorithm computed the wrong hole center when one of the points falls in the enlarged area (e.g.,312). In particular, the points do not lie on the contour line of the enlarged section312. In this respect, the corrected hole shape transfers part of the enlarged feature to the other side of the borehole. This is a typical error caused by the traditional circle-fitting algorithm for the keyseat borehole shape.

FIG. 3Cillustrates an example of a plot330depicting a keyseat borehole shape computation with the eccentricity correction shape-fitting algorithm for a given depth interval in accordance with one or more implementations of the subject technology. The eccentricity correction shape-fitting algorithm computed the exact hole center with all of the corrected points with correct coordinates. For example, the points on the non-intact section (e.g.,312) of the shape fitted curve (illustrated by the dashed line) align with the non-intact section of the measured borehole (illustrated by the solid line). In this example, the plot330includes eccentricity-corrected points based on a hole center having a least number of points outside of the shape fitted curve and least amount of error, and a radius value having a least sum of points outside the shape fitted curve and least sum of errors for all transducer firings in a depth interval.

FIG. 4Aillustrates an example of a plot410depicting a breakout borehole shape with synthetic caliper measurements. The breakout borehole shape depicts the borehole enlarged on two opposite sides. All firings have one or two transceivers facing the enlarged section (e.g.,412). The tool center is randomly generated and six firings are used in the example. To evaluate the robustness of the improved algorithm, 150 firings are generated with random tool centers. Every 6 firings are considered to be in the same depth interval for computation. The rate of error of the algorithm is related to the proportion of non-intact section. This is because the non-intact section does not contain information of the intact borehole.

FIG. 4Billustrates an example of a plot420depicting a breakout borehole shape computation with a traditional borehole shape algorithm. The traditional circle-fitting algorithm generates an inaccurate hole shape on most of the points, especially on the enlarged section412.

FIG. 4Cillustrates an example of a plot430depicting a breakout borehole shape computation with an eccentricity corrected borehole shape algorithm for a given depth interval in accordance with one or more implementations of the subject technology. In contrast to theFIG. 4B, the eccentricity correction shape-fitting algorithm ofFIG. 4Ccomputed the exact hole center with all of the corrected points with correct coordinates. For example, the points on the non-intact section (e.g.,412) of the shape fitted curve (illustrated by the dashed line) align with the non-intact section of the measured borehole (illustrated by the solid line). In this example, the plot430includes eccentricity-corrected points based on a hole center having a least number of points outside of the shape fitted curve and least amount of error, and a radius value having a least sum of points outside the shape fitted curve and least sum of errors for all transducer firings in a depth interval.

FIG. 5Aillustrates an example of a plot510depicting a keyseat borehole shape computation with an eccentricity corrected borehole shape algorithm over multiple depth intervals in accordance with one or more implementations of the subject technology. InFIG. 5A, the keyseat borehole shape depicts one side of the borehole enlarged, where 23% of the borehole section is enlarged. In this example, acquisition data was obtained with 150 firings in 25 depth intervals (e.g., about 6 firings in a depth interval). InFIG. 5A, two firings out of the 150 firings resulted in incorrect coordinates, where the corresponding points were located outside of the keyseat borehole shape. In some aspects, the number of firings deployed may be programmed according to a target resolution of the borehole shape. In this respect, the higher the number of firings, the higher the number of data points for estimating the contour shape of the borehole circumference.

FIG. 5Billustrates an example of a plot520depicting a breakout borehole shape computation with an eccentricity corrected borehole shape algorithm over multiple depth intervals in accordance with one or more implementations of the subject technology. InFIG. 5B, the breakout borehole shape depicts two opposite sides of the borehole enlarged, where 46% of the borehole section is enlarged. In this example, acquisition data was obtained with 150 firings in 25 depth intervals (e.g., about 6 firings in a depth interval).

InFIG. 5B, seven firings out of the 150 firings resulted in incorrect coordinates, where the corresponding points were located outside of the breakout borehole shape. Since the eccentricity corrected borehole shape algorithm produces a high percentage of correct results for borehole shape computation with a significant proportion of enlarged area, its robustness is proven and incorrect results can be picked out as outliers.

FIGS. 6A to 6Cillustrate examples of plots depicting a breakout borehole shape computation with an eccentricity corrected borehole shape algorithm for different number of firings in a given depth interval in accordance with one or more implementations of the subject technology. For cases with a significant portion of non-intact borehole, stacking more number of firings in the same depth interval helps to reduce the error rate.FIGS. 6A-6Cshow a breakout example with 120 firings, with 4, 6 and 8 firings in a depth interval, respectively. The number firings with incorrect coordinates is 19, 7 and 4, respectively.

InFIG. 6A, the acquisition logic160acquired field measurements from 30 depth intervals, where 4 firings were deployed per depth interval for a total of 120 transducer firings with 19 incorrect coordinates detected. InFIG. 6B, the acquisition logic160acquired field measurements from 20 depth intervals, where 6 firings were deployed per depth interval for a total of 120 transducer firings with 7 incorrect coordinates detected. InFIG. 6C, the acquisition logic160acquired field measurements from 15 depth intervals, where 8 firings were deployed per depth interval for a total of 120 transducer firings with 4 incorrect coordinates detected.

FIG. 7Adepicts a schematic view of a logging operation deployed in and around a well system700ain accordance with one or more implementations. The well system700aincludes a logging system708and a subterranean region720beneath the ground surface706. The well system700acan also include additional or different features that are not shown inFIG. 7A. For example, the well system700acan include additional drilling system components, wireline logging system components, or other components.

The subterranean region720includes all or part of one or more subterranean formations or zones. The subterranean region720shown inFIG. 7A, for example, includes multiple subsurface layers722. The subsurface layers722can include sedimentary layers, rock layers, sand layers, or any combination thereof and other types of subsurface layers. One or more of the subsurface layers can contain fluids, such as brine, oil, gas, or combinations thereof. A borehole704penetrates through the subsurface layers722. Although the borehole704shown inFIG. 7Ais a vertical borehole, the logging system708can also be implemented in other borehole orientations. For example, the logging system708may be adapted for horizontal boreholes, slant boreholes, curved boreholes, vertical boreholes, or any combination thereof.

The logging system708also includes a logging tool702, surface equipment712, and a computing subsystem710. In the shown inFIG. 7A, the logging tool702is a downhole logging tool that operates while disposed in the borehole704. The surface equipment712shown inFIG. 7Aoperates at or above the surface706, for example, near the well head705, to control the logging tool702and possibly other downhole equipment or other components of the well system700a. The computing subsystem710receives and analyzes logging data from the logging tool702. A logging system can include additional or different features, and the features of an logging system can be arranged and operated as represented inFIG. 7Aor in another manner.

All or part of the computing subsystem710can be implemented as a component of, or integrated with one or more components of, the surface equipment712, the logging tool702, or both. For example, the computing subsystem710can be implemented as one or more computing structures separate from but communicative with the surface equipment712and the logging tool702.

The computing subsystem710can be embedded in the logging tool702(not shown), and the computing subsystem710and the logging tool702operate concurrently while disposed in the borehole704. For example, although the computing subsystem710is shown above the surface706inFIG. 7A, all or part of the computing subsystem710may reside below the surface706, for example, at or near the location of the logging tool702.

The well system700aincludes communication or telemetry equipment that allows communication among the computing subsystem710, the logging tool702, and other components of the logging system708. For example, each of the components of the logging system708can include one or more transceivers or similar apparatus for wired or wireless data communication among the various components. The logging system708can include, but is not limited to, one or more systems and/or apparatus for wireline telemetry, wired pipe telemetry, mud pulse telemetry, acoustic telemetry, electromagnetic telemetry, or any combination of these and other types of telemetry. In some implementations, the logging tool702receives commands, status signals, or other types of information from the computing subsystem710or another source. The computing subsystem710can also receive logging data, status signals, or other types of information from the logging tool702or another source.

Logging operations are performed in connection with various types of downhole operations at various stages in the lifetime of a well system and therefore structural attributes and components of the surface equipment712and logging tool702are adapted for various types of logging operations. For example, logging may be performed during drilling operations, during wireline logging operations, or in other contexts. As such, the surface equipment712and the logging tool702can include or operate in connection with drilling equipment, wireline logging equipment, or other equipment for other types of operations.

In some implementations ofFIG. 7A, the logging tool702is provided with a caliper device730. The caliper device730may include a set of distance sensors that measure borehole standoff data or radial distance. The caliper device730is configured to perform two or more sets of standoff measurements per acquisition. Acquisitions are performed once per capture interval. Each standoff measurement set includes borehole standoff data that corresponds to standoff measurements obtained substantially simultaneously by the set of distance sensors. The borehole standoff data in turn includes standoff values associated with individual acquisitions. A capture interval can occur periodically, such as at predetermined time intervals, at predetermined length intervals as the caliper730is advanced along a length of the borehole704, and/or in response to a control signal. The control signal can be triggered by, for example, user activation, a sensor output exceeding a predetermined threshold value, or a processing determination, such as by the computing subsystem710.

Examples of calipers that may be used include ultrasound transducers, electromagnetic transducers, mechanical arms and/or fingers, such as with pressure sensors, etc. An example suitable caliper device730can include a cylindrical body (not shown) and the set of distance sensors disposed on the body. The set of distance sensors can include four ultrasonic transducers (not shown) that are located at about the same distance along the length of the body of the caliper device730and evenly spaced about the circumference of the body.

The set of distance sensors perform standoff measurements by emitting an ultrasonic signal directed at an angle normal to the body of the caliper device730towards an inner surface of a borehole wall surrounding the borehole704. Reflected ultrasonic signals are detected by the set of distance sensors. The time interval between the emission and detection is measured and output as borehole standoff data that can be used to determine the standoff distance between the set of distance sensors and the borehole wall. The set of distance sensors can perform standoff measurements substantially simultaneously as the logging tool702moves within the borehole704in a rotational, non-rotational, or translational motion.

In some implementations, standoff data acquisition is performed over the course of a single logging tool rotation. During the acquisition, multiple standoff measurement sets are acquired. As explained above, each standoff measurement set includes a standoff measurement performed by all of the set of distance sensors simultaneously. In an example, four measurement sets are acquired by the set of distance sensors simultaneously during an acquisition. For example, the caliper device730may include four (4) distance sensors performing four measurement sets per acquisition, in which the set of distance sensors would generate sixteen (16) standoff measurements per acquisition.

The eccentricity-corrected fitted shape may then be used as an estimation of a shape of the borehole704at the location where the data points were acquired. The shape of the borehole704at different locations along the borehole704can thereafter be used to determine and/or monitor characteristics of the borehole704, such as changes in the shape of the borehole704, stability of the borehole704, or volume of the borehole704.

The determining and/or monitoring can be performed in real time during a drilling operation. This allows the drilling operation to be controlled in real time to cause or prevent changes in the borehole shape as needed in response to the estimated shape of the borehole704. For example, accurate borehole size and shape can be used to perform environmental correction of LWD sensors, provide real-time assessment of borehole stability, and calculate cement volume for filling the borehole.

The determining and/or monitoring can also be performed after a drilling operation based on the estimated shape of the borehole704along the length of the borehole704. Determinations can be made about available and/or feasible usage and/or treatment of the borehole704based on the estimated shape of the borehole704along its length. For example, the estimated shape of the borehole704along its length can be used to determine a volume of a material to insert in the borehole704, e.g., to fill and/or reinforce the borehole704. The estimated shape of the borehole704along the length of the borehole704can be used to generate a model of the borehole704, such as for making predictions, e.g., of the borehole's stability over time, and/or determining the need for an intervention, such as changing a characteristic of a drilling fluid, e.g., mud weight or mud type.

FIG. 7Bdepicts a schematic view of a wireline logging operation deployed in and around a well system700bin accordance with one or more implementations. The well system700bincludes the logging tool702in a wireline logging environment. The surface equipment712includes, but is not limited to, a platform701disposed above the surface706equipped with a derrick732that supports a wireline cable734extending into the borehole704. Wireline logging operations are performed, for example, after a drill string is removed from the borehole704, to allow the wireline logging tool702to be lowered by wireline or logging cable into the borehole704.

FIG. 7Cdepicts a schematic view of a well system700cthat includes the logging tool702in a logging while drilling (LWD) environment in accordance with one or more implementations. logging operations is performed during drilling operations. Drilling is performed using a string of drill pipes connected together to form a drill string740that is lowered through a rotary table into the borehole704. A drilling rig742at the surface706supports the drill string740, as the drill string740is operated to drill a borehole penetrating the subterranean region720. The drill string740can include, for example, but is not limited to, a kelly, a drill pipe, a bottom hole assembly, and other components. The bottomhole assembly on the drill string can include drill collars, drill bits, the logging tool702, and other components. Exemplary logging tools can be or include, but are not limited to, measuring while drilling (MWD) tools and LWD tools.

The logging tool702includes a tool for acquiring measurements from the subterranean region720. As shown, for example, inFIG. 7B, the logging tool702is suspended in the borehole704by a coiled tubing, wireline cable, or another structure or conveyance that connects the tool to a surface control unit or other components of the surface equipment712.

The logging tool702is lowered to the bottom of a region of interest and subsequently pulled upward (e.g., at a substantially constant speed) through the region of interest. As shown, for example, inFIG. 7C, the logging tool702is deployed in the borehole704on jointed drill pipe, hard wired drill pipe, or other deployment hardware. In other example implementations, the logging tool702collects data during drilling operations as it moves downward through the region of interest. The logging tool702may also collect data while the drill string740is moving, for example, while the logging tool702is being tripped in or tripped out of the borehole704.

The logging tool702may also collect data at discrete logging points in the borehole704. For example, the logging tool702moves upward or downward incrementally to each logging point at a series of depths in the borehole704. At each logging point, instruments in the logging tool702perform measurements on the subterranean region720. The logging tool702also obtains measurements while the logging tool702is moving (e.g., being raised or lowered). The measurement data is communicated to the computing subsystem710for storage, processing, and analysis. Such data may be gathered and analyzed during drilling operations (e.g., LWD operations), during wireline logging operations, other conveyance operations, or during other types of activities.

The computing subsystem710receives and analyzes the measurement data from the logging tool702to detect properties of various subsurface layers722. For example, the computing subsystem710can identify the density, material content, and/or other properties of the subsurface layers722based on the measurements acquired by the logging tool702in the borehole704.

FIG. 8is a block diagram illustrating an exemplary computer system800with which the computing subsystem710ofFIG. 7Acan be implemented. In certain aspects, the computer system800may be implemented using hardware or a combination of software and hardware, either in a dedicated server, integrated into another entity, or distributed across multiple entities.

Computer system800(e.g., computing subsystem710) includes a bus808or other communication mechanism for communicating information, and a processor802coupled with bus808for processing information. By way of example, the computer system800may be implemented with one or more processors802. Processor802may be a general-purpose microprocessor, a microcontroller, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA), a Programmable Logic Device (PLD), a controller, a state machine, gated logic, discrete hardware components, or any other suitable entity that can perform calculations or other manipulations of information.

Computer system800can include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them stored in an included memory804, such as a Random Access Memory (RAM), a flash memory, a Read Only Memory (ROM), a Programmable Read-Only Memory (PROM), an Erasable PROM (EPROM), registers, a hard disk, a removable disk, a CD-ROM, a DVD, or any other suitable storage device, coupled to bus808for storing information and instructions to be executed by processor802. The processor802and the memory804can be supplemented by, or incorporated in, special purpose logic circuitry.

Computer system800further includes a data storage device806such as a magnetic disk or optical disk, coupled to bus808for storing information and instructions. Computer system800may be coupled via input/output module810to various devices. The input/output module810can be any input/output module. Exemplary input/output modules810include data ports such as USB ports. The input/output module810is configured to connect to a communications module812. Exemplary communications modules812include networking interface cards, such as Ethernet cards and modems. In certain aspects, the input/output module810is configured to connect to a plurality of devices, such as an input device814and/or an output device816. Exemplary input devices814include a keyboard and a pointing device, e.g., a mouse or a trackball, by which a user can provide input to the computer system800. Other kinds of input devices814can be used to provide for interaction with a user as well, such as a tactile input device, visual input device, audio input device, or brain-computer interface device. For example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback, and input from the user can be received in any form, including acoustic, speech, tactile, or brain wave input. Exemplary output devices816include display devices such as a LCD (liquid crystal display) monitor, for displaying information to the user, or diagnostic devices such as an oscilloscope.

According to one aspect of the present disclosure, the computing subsystem110can be implemented using a computer system800in response to processor802executing one or more sequences of one or more instructions contained in memory804. Such instructions may be read into memory804from another machine-readable medium, such as data storage device806. Execution of the sequences of instructions contained in the main memory804causes processor802to perform the process steps described herein. One or more processors in a multi-processing arrangement may also be employed to execute the sequences of instructions contained in the memory804. In alternative aspects, hard-wired circuitry may be used in place of or in combination with software instructions to implement various aspects of the present disclosure. Thus, aspects of the present disclosure are not limited to any specific combination of hardware circuitry and software.

FIG. 9illustrates a flowchart of a process900for a downhole operation using a borehole shape prediction based on an eccentricity correction algorithm in accordance with one or more implementations of the subject technology. Further for explanatory purposes, the blocks of the sequential process900are described herein as occurring in serial, or linearly. However, multiple blocks of the process900may occur in parallel. In addition, the blocks of the process900need not be performed in the order shown and/or one or more of the blocks of the process900need not be performed.

The process900starts at step902, where a caliper tool is deployed into a borehole penetrating a subterranean formation. Next, at step904, field measurements are obtained with the deployed caliper tool. Subsequently, at step906, an eccentricity correction algorithm is applied, in a processing circuit, to one or more standoff samples from the obtained field measurements. In some aspects, the eccentricity correction algorithm produces a shape fitted curve that represents a measured borehole with a least number of points outside of the shape fitted curve and a least amount of error. Subsequently, at step908, a borehole shape is determined with the applied eccentricity correction algorithm. Next, at step910, tool location coordinates relative to the borehole are determined with the determined borehole shape.

Various examples of aspects of the disclosure are described below. These are provided as examples, and do not limit the subject technology.

Clause A. A method includes deploying a caliper tool into a borehole penetrating a subterranean formation; acquiring field measurements with the deployed caliper tool; applying, in a processor circuit, an eccentricity correction algorithm to one or more standoff samples from the obtained field measurements, wherein the eccentricity correction algorithm produces a shape fitted curve that represents a measured borehole with a least number of points outside of the shape fitted curve and a least amount of error; determining eccentricity-corrected borehole coordinates with the applied eccentricity correction algorithm; determining a borehole shape from the eccentricity-corrected borehole coordinates; and determining tool location coordinates relative to the borehole with the determined borehole shape.

Clause B. A system includes a caliper tool; and a caliper measurement device operably coupled to the caliper tool and having a memory and a processor, wherein the memory comprises commands which, when executed by the processor, cause the caliper measurement device to acquire field measurements from the caliper tool; apply an eccentricity correction algorithm to one or more standoff samples from the obtained field measurements, wherein the eccentricity correction algorithm produces a shape fitted curve that represents a measured borehole with a least number of points outside of the shape fitted curve and a least amount of error; determine eccentricity-corrected borehole coordinates with the applied eccentricity correction algorithm; determine a borehole shape from the eccentricity-corrected borehole coordinates; and determine tool location coordinates relative to the borehole with the determined borehole shape.

Clause C. A non-transitory computer-readable medium storing instructions which, when executed by a processor, cause a computer to acquire field measurements from a caliper tool deployed into a borehole penetrating a subterranean formation; apply an eccentricity correction algorithm to one or more standoff samples from the obtained field measurements, wherein the eccentricity correction algorithm produces a shape fitted curve that represents the borehole with a least number of points outside of the shape fitted curve and a least amount of error; determine eccentricity-corrected borehole coordinates with the applied eccentricity correction algorithm; determine a borehole shape from the eccentricity-corrected borehole coordinates; and determine tool location coordinates relative to the borehole with the determined borehole shape.

In one or more aspects, examples of clauses are described below.

A method comprising one or more methods, operations or portions thereof described herein.

An apparatus comprising one or more memories and one or more processors (e.g.,800), the one or more processors configured to cause performing one or more methods, operations or portions thereof described herein.

An apparatus comprising one or more memories (e.g.,804, one or more internal, external or remote memories, or one or more registers) and one or more processors (e.g.,802) coupled to the one or more memories, the one or more processors configured to cause the apparatus to perform one or more methods, operations or portions thereof described herein.

An apparatus comprising means (e.g.,800) adapted for performing one or more methods, operations or portions thereof described herein.

A processor (e.g.,802) comprising modules for carrying out one or more methods, operations or portions thereof described herein.

A hardware apparatus comprising circuits (e.g.,800) configured to perform one or more methods, operations or portions thereof described herein.

An apparatus comprising means (e.g.,800) adapted for performing one or more methods, operations or portions thereof described herein.

An apparatus comprising components (e.g.,800) operable to carry out one or more methods, operations or portions thereof described herein.

A computer-readable storage medium (e.g.,804, one or more internal, external or remote memories, or one or more registers) comprising instructions stored therein, the instructions comprising code for performing one or more methods or operations described herein.

A computer-readable storage medium (e.g.,804, one or more internal, external or remote memories, or one or more registers) storing instructions that, when executed by one or more processors, cause one or more processors to perform one or more methods, operations or portions thereof described herein.