Mud angle determination for electromagnetic imager tools

Aspects of the subject technology relate to systems and methods for identifying a mud angle associated with an electromagnetic imager tool based on tool measurements made during operation of the electromagnetic imager tool. Tool measurements made by an electromagnetic imager tool operating to log a wellbore in a formation can be gathered. The tool measurements can be decomposed into two quantities along a plurality of candidate mud angles for the electromagnetic imager tool. As follows, a mud angle associated with the electromagnetic imager tool can be identified from the plurality of candidate mud angles based on an amount of correlation between the two quantities for each of the plurality of candidate mud angles.

TECHNICAL FIELD

The present technology pertains to identifying a mud angle associated with an electromagnetic imager tool, and more particularly, to identifying a mud angle associated with an electromagnetic imager tool based on tool measurements made during operation of the electromagnetic imager tool.

BACKGROUND

Electromagnetic imager tools have been developed for generating images downhole in wellbores. Specifically, electromagnetic imager tools have been developed to operate in drilling mud to image formations surrounding a wellbore. Electromagnetic imager tools are subject to the mud effect. The mud effect refers to the contribution of the mud to measured impedance. This effect is particularly severe if a formation exhibits low resistivity and/or the distance between the pad's outer surface and the borehole wall, e.g. the formation, is high. Techniques have been developed in order to remove or otherwise minimize the mud effect in an electromagnetic imager tool operating to log a wellbore, e.g. as part of generating images of a surround formation of the wellbore. For example, the Z90 technique has been developed to remove the mud effect for electromagnetic imager tools.

Many of these techniques utilize mud angle in minimizing or otherwise removing the mud effect for electromagnetic imager tools. Mud angle, as used herein is the phase angle of a complex-valued mud impedance of an electromagnetic imager tool. The effectiveness of these techniques in removing the mud effect is strongly dependent on accuracy of an identified mud angle associated with an electromagnetic imager tool. In turn, this can ultimately affect quality and accuracy in images that are processed through these techniques to account for the mud effect. However, often times these techniques rely on inaccurate mud angle estimates to remove the mud effect thereby leading to errors in the application of these techniques. For example, inaccurate mud angle usage can lead to poor image quality and contrast in areas of an image affected by the mud effect. There therefore exist needs for systems and methods for accurately identifying a mud angle for an electromagnetic imager tool.

Actually measuring mud to identify properties of the mud is one way to identify mud angle. Specifically, an electromagnetic imager tool can be operated to just gather measurements of the mud, which can subsequently be used to identify a mud angle. However, this is an inefficient usage of the electromagnetic imager tool. Specifically, operating the electromagnetic imager tool to just take measurements of the mud wastes time during which the electromagnetic imager tool can be operated to actually log a wellbore. Further, the formation still makes contributions to the direct mud measurements, thereby leading to inaccurate mud angle estimates. Tools have been developed with a mud cell for directly measuring mud properties. However, such tools can require additional parts that may increase the cost of the tool while further complicating the tool design process.

DETAILED DESCRIPTION

The disclosed technology addresses the foregoing by identifying a mud angle associated with an electromagnetic imager tool based on tool measurements made during operation of the electromagnetic imager tool. Specifically, a mud angle can be identified from a plurality of candidate mud angles based on correlation between two quantities decomposed from tool measurements made by an electromagnetic imager tool across the plurality of candidate mud angles.

In various embodiments, tool measurements made by an electromagnetic imager tool operating to log a wellbore in a formation can be gathered. The tool measurements can be decomposed into two quantities along a plurality of candidate mud angles for the electromagnetic imager tool. As follows, a mud angle associated with the electromagnetic imager tool can be identified from the plurality of candidate mud angles based on an amount of correlation between the two quantities for each of the plurality of candidate mud angles. Specifically, the identified mud angle can have a smallest amount of correlation between the two quantities across the plurality of candidate mud angles.

In various embodiments, a system can include one or more processors and at least one computer-readable storage medium storing instructions which, when executed by the one or more processors, cause the one or more processors to gather tool measurements made by an electromagnetic imager tool operating to log a wellbore in a formation. The instructions can also cause the one or more processors to decompose the tool measurements into two quantities along a plurality of candidate mud angles for the electromagnetic imager tool. Further, the instructions can cause the one or more processors to identify a mud angle associated with the electromagnetic imager tool from the plurality of candidate mud angles based on an amount of correlation between the two quantities for each of the plurality of candidate mud angles. Specifically, the identified mud angle can have a smallest amount of correlation between the two quantities across the plurality of candidate mud angles.

In various embodiments, a system can include a non-transitory computer-readable storage medium having stored therein instructions which, when executed by a processor, cause the processor to gather tool measurements made by an electromagnetic imager tool operating to log a wellbore in a formation. The instructions can also cause the processor to decompose the tool measurements into two quantities along a plurality of candidate mud angles for the electromagnetic imager tool. Further, the instructions can cause the processor to identify a mud angle associated with the electromagnetic imager tool from the plurality of candidate mud angles based on an amount of correlation between the two quantities for each of the plurality of candidate mud angles. Specifically, the identified mud angle can have a smallest amount of correlation between the two quantities across the plurality of candidate mud angles.

Turning now toFIG. 1A, a drilling arrangement is shown that exemplifies a Logging While Drilling (commonly abbreviated as LWD) configuration in a wellbore drilling scenario100. Logging-While-Drilling typically incorporates sensors that acquire formation data. Specifically, the drilling arrangement shown inFIG. 1Acan be used to gather formation data through an electromagnetic imager tool as part of logging the wellbore using the electromagnetic imager tool. The drilling arrangement ofFIG. 1Aalso exemplifies what is referred to as Measurement While Drilling (commonly abbreviated as MWD) which utilizes sensors to acquire data from which the wellbore's path and position in three-dimensional space can be determined.FIG. 1Ashows a drilling platform102equipped with a derrick104that supports a hoist106for raising and lowering a drill string108. The hoist106suspends a top drive110suitable for rotating and lowering the drill string108through a well head112. A drill bit114can be connected to the lower end of the drill string108. As the drill bit114rotates, it creates a wellbore116that passes through various subterranean formations118. A pump120circulates drilling fluid through a supply pipe122to top drive110, down through the interior of drill string108and out orifices in drill bit114into the wellbore. The drilling fluid returns to the surface via the annulus around drill string108, and into a retention pit124. The drilling fluid transports cuttings from the wellbore116into the retention pit124and the drilling fluid's presence in the annulus aids in maintaining the integrity of the wellbore116. Various materials can be used for drilling fluid, including oil-based fluids and water-based fluids.

Logging tools126can be integrated into the bottom-hole assembly125near the drill bit114. As the both drill bit114extends into the wellbore116through the formations118and as the drill string108is pulled out of the wellbore116, logging tools126collect measurements relating to various formation properties as well as the orientation of the tool and various other drilling conditions. The logging tool126can be applicable tools for collecting measurements in a drilling scenario, such as the electromagnetic imager tools described herein. Each of the logging tools126may include one or more tool components spaced apart from each other and communicatively coupled by one or more wires and/or other communication arrangement. The logging tools126may also include one or more computing devices communicatively coupled with one or more of the tool components. The one or more computing devices may be configured to control or monitor a performance of the tool, process logging data, and/or carry out one or more aspects of the methods and processes of the present disclosure.

The bottom-hole assembly125may also include a telemetry sub128to transfer measurement data to a surface receiver132and to receive commands from the surface. In at least some cases, the telemetry sub128communicates with a surface receiver132by wireless signal transmission. e.g, using mud pulse telemetry, EM telemetry, or acoustic telemetry. In other cases, one or more of the logging tools126may communicate with a surface receiver132by a wire, such as wired drill pipe. In some instances, the telemetry sub128does not communicate with the surface, but rather stores logging data for later retrieval at the surface when the logging assembly is recovered. In at least some cases, one or more of the logging tools126may receive electrical power from a wire that extends to the surface, including wires extending through a wired drill pipe. In other cases, power is provided from one or more batteries or via power generated downhole.

Collar134is a frequent component of a drill string108and generally resembles a very thick-walled cylindrical pipe, typically with threaded ends and a hollow core for the conveyance of drilling fluid. Multiple collars134can be included in the drill string108and are constructed and intended to be heavy to apply weight on the drill bit114to assist the drilling process. Because of the thickness of the collar's wall, pocket-type cutouts or other type recesses can be provided into the collar's wall without negatively impacting the integrity (strength, rigidity and the like) of the collar as a component of the drill string108.

Referring toFIG. 1B, an example system140is depicted for conducting downhole measurements after at least a portion of a wellbore has been drilled and the drill string removed from the well. An electromagnetic imager tool can be operated in the example system140shown inFIG. 1Bto log the wellbore. A downhole tool is shown having a tool body146in order to carry out logging and/or other operations. For example, instead of using the drill string108ofFIG. 1Ato lower the downhole tool, which can contain sensors and/or other instrumentation for detecting and logging nearby characteristics and conditions of the wellbore116and surrounding formations, a wireline conveyance144can be used. The tool body146can be lowered into the wellbore116by wireline conveyance144. The wireline conveyance144can be anchored in the drill rig142or by a portable means such as a truck145. The wireline conveyance144can include one or more wires, slicklines, cables, and/or the like, as well as tubular conveyances such as coiled tubing, joint tubing, or other tubulars. The downhole tool can include an applicable tool for collecting measurements in a drilling scenario, such as the electromagnetic imager tools described herein.

The illustrated wireline conveyance144provides power and support for the tool, as well as enabling communication between data processors148A-N on the surface. In some examples, the wireline conveyance144can include electrical and/or fiber optic cabling for carrying out communications. The wireline conveyance144is sufficiently strong and flexible to tether the tool body146through the wellbore116, while also permitting communication through the wireline conveyance144to one or more of the processors148A-N, which can include local and/or remote processors. The processors148A-N can be integrated as part of an applicable computing system, such as the computing device architectures described herein. Moreover, power can be supplied via the wireline conveyance144to meet power requirements of the tool. For slickline or coiled tubing configurations, power can be supplied downhole with a battery or via a downhole generator.

FIG. 2Aillustrates a perspective view of a LWD electromagnetic imager tool200.FIG. 2Billustrates another perspective view of the LWD electromagnetic imager tool200.FIG. 2Cillustrates yet another perspective view of the LWD electromagnetic imager tool200. The LWD electromagnetic imager tool200/mud imager tool can be integrated as part of an applicable LWD drilling system, such as the logging tools126in the LWD scenario100shown inFIG. 1A.

The LWD electromagnetic imager tool200includes an electromagnetic sensor202disposed along a collar of the LWD electromagnetic imager tool200. The LWD electromagnetic200imager tool shown inFIGS. 2A-2Calso includes first and second ultrasonic transducers204and206, however and in various embodiments, a LWD electromagnetic imager tool200does not have ultrasonic transducers disposed along the collar. Specifically, the LWD electromagnetic imager tool200shown inFIGS. 2A-2Cis merely an example of a LWD electromagnetic imager tool200, and in various embodiments, a LWD electromagnetic imager tool200can have a different design. Specifically, a water-based LWD mud imager tool may have similar designs, and can provide less design and interpretation complications than oil-based LWD mud imager tools, e.g. due to the conductive nature of water-based mud.

LWD electromagnetic mud imager tools can provide a high resolution image of a borehole, e.g. when compared to other borehole imager tools. As a result, LWD electromagnetic mud imager tools can be used to identify damaged borehole sections, provide a better knowledge on the thin beds, and also provide images that can be used to determine the dip angle of formation bed.

The sensor topology of LWD electromagnetic mud imager tools operating in a LWD environment should have minimum complexity, and more importantly, it should not rely on borehole contact. With respect to the LWD electromagnetic imager tool200shown inFIGS. 2A-C, the electromagnetic sensor202can include a single measurement (also called probe, button or current) electrode mounted on the side of the collar. The electromagnetic sensor202can be disposed on the collar such that it is located at a certain distance (standoff) from a borehole wall during operation of the LWD electromagnetic imager tool. Further, the electromagnetic sensor202can include a guard electrode that surrounds, at least a portion of the button electrode. This electrode may be excited by an alternating current, sine-wave generator, and it may be coupled to the formation through a mud, e.g. an oil-based mud. This mud is non-conductive for oil-based muds. As a result, the coupling to the formation is accomplished through displacement currents in the mud. This arrangement provides a low sensitivity to standoff changes in resultant microresistivity image.

In operation of the LWD electromagnetic imager tool200, a measurement current enters the formation, which may have a much lower resistivity than the mud. In the formation, the current flows by conduction and penetrates the formation. The current then returns back toward the borehole where it returns to the body of the LWD electromagnetic imager tool200surrounding the electromagnetic sensor202, e.g. the tool body serves as the return electrode for the LWD electromagnetic imager tool200. The tool body can remain at ground potential because of its large surface area.

Imaging through the LWD electromagnetic imager tool200can be achieved by dividing gathered data/measurements into azimuthal bins as the LWD electromagnetic imager tool200rotates in the borehole during drilling. The LWD electromagnetic imager tool can also include an additional mud resistivity sensor, e.g. a mud cell. In imaging through the LWD electromagnetic imager tool200, real components of the measurements made by the electromagnetic sensor202can be used to determine formation resistivity. Further, mud resistivity measurements made by the mud resistivity sensor can be used to improve the determined formation resistivity measurements. For the purposes of this disclosure, it is assumed that mud sensor is not available or not accurate.

The LWD electromagnetic imager tool200can be a multi-frequency tool. Specifically, the LWD electromagnetic imager tool200can operate at multiple frequencies in gathering measurements. For example, a higher frequency in the MHz range may be used to overcome the nonconductive nature of oil-based muds in generating measurements while a lower frequency in the 100 kHz range may be more sensitive to standoff and thus may be used in standoff determination. Further, gathered standoff information may be used to identify features in the formation. For example, a thin band of increased resistivity can be due to an opening in the rock. In turn, this can be reflected as a jump in apparent standoff.

FIG. 3shows an example current density300generated by the electromagnetic sensor202of the LWD electromagnetic imager tool200operating to measure a formation. A power source drives a voltage between the return electrode, whose voltage with respect to the ground is represented through Vreturnand the probe electrode, whose voltage with respect to a ground is represented by Vprobe. Further, a circuitry is implemented to keep Vprobeequal, or roughly equal, to Vfocusfor focusing of the measurement current. The current transmitted from the electromagnetic sensor is measured, for example through the use of a toroid. The ratio of the voltage difference between probe and return to the transmitted current is used to calculate a measured impedance. A basic circuit theory based model that relates the measured impedance to formation and mud parameters that is applicable to both LWD and wireline tools will be provided after a discussion on wireline electromagnetic tools.

The discussion now continues with a discussion of wireline electromagnetic imager tools.FIG. 4illustrates a schematic diagram of an example pad400of a wireline electromagnetic imager tool, as described above inFIG. 1B. Specifically, the wireless electromagnetic imager tool can be integrated with the tool body146of the downhole tool inFIG. 1B. More specifically, the pad400can be disposed on an outer surface of the tool body146to make measurements as the downhole tool is operated within the wellbore. The electromagnetic imager tool functions to gather measurements while logging a wellbore, e.g. for purposes of imaging a formation surrounding the wellbore. Specifically, the electromagnetic imager tool can operate in a drilling mud to gather measurements for imaging the formation surrounding the wellbore. The electromagnetic imager tool can operate in an applicable type of drilling mud, such as an oil-based mud or a water-based mud, to log the wellbore. Oil-based muds have much higher resistivities than water-based muds. Therefore, the mud effect is much stronger for measurements made in oil-based muds. In operating to log the wellbore, the electromagnetic imager tool can gather applicable measurements that are capable of being measured by the electromagnetic imager tool. For example, measurements made by the electromagnetic imager tool can include apparent impedivity and impedance measurements at the electromagnetic imager tool, complex impedance measurements at the electromagnetic imager tool, voltage measurements at the electromagnetic imager tool, current measurements at the electromagnetic imager tool, phase measurements at the electromagnetic imager tool, and absolute values of impedance measurements at the electromagnetic imager tool.

The measurements gathered by the electromagnetic imager tool can be used to identify values of mud and formation parameters associated with the electromagnetic imager tool, e.g. parameters inside of and outside of the wellbore. Mud and formation parameters include applicable parameters that can be identified from measurements taken by the electromagnetic imager tool for purposes of imaging, e.g. through the wellbore. For example, mud and formation parameters can include mud permittivity, mud resistivity, standoff, formation permittivity of a formation of the wellbore, and formation resistivity of the formation of the wellbore. The values of the mud and formation parameters can be identified using the techniques described herein on a per-button basis for wireline imagers. For example, formation resistivity, formation permittivity, mud resistivity, mud permittivity and standoff values can be identified for each button included as part of a button array402of a pad400. For LWD imagers, measurements are generally obtained using a single button electrode. In that case, azimuthal coverage is obtained by dividing the measurements into azimuthal bins as the tool rotates. Thus, these azimuthal bins in an LWD tool serves the same purpose with the measurements made by multiple button electrodes spaced circumferentially around the tool in a wireline tool. Although the origin of the measurements are different in LWD and wireline tools, the processing methods described herein equally applies to both type of tools.

In operating the wireline electromagnetic imager tool to gather measurements for imaging, a voltage difference can be applied across the button array402and first and second return electrodes404-1and404-2(return electrodes404) of the pad400. This voltage difference can generate currents that pass from the button array402into the mud and a surrounding formation. The pad400also includes a guard electrode406around the button array402. The same potential that is applied to the button array402can be applied to the guard electrode406to focus all or a substantial portion of the current emitted into the mud and the surrounding formation. Specifically, the current can be emitted substantially radially into the surrounding formation by applying the same potential on the guard electrode406and the button array402. An applicable electrical and/or thermal insulating material, such as a ceramic, can fill the remaining portions of the pad400. For example, a ceramic material can be disposed between the return electrodes404and the guard electrode406. The pad400is covered, at least in part, with a housing408. The housing408, and accordingly the pad400through the housing408, can be connected through a securing mechanism to a mandrel. The securing mechanism can be a movable mechanism that moves the housing408and the contained pad400to substantially maintain contact with the formation. For example, the securing mechanism can include an arm that opens and/or swivels to move the housing408and the contained pad400. By moving the housing408and the contained pad to maintain a good contact with the formation, the mud effect can be minimized for wireline imager tools.

Turning back to a discussion of the mud effect and its impact on electromagnetic imager tools, the mud effect, as described previously, refers to the contribution of the mud to the measured impedance. Further and as discussed previously, this effect is particularly severe if a formation exhibits low resistivity and the distance between the button electrode's outer surface and the borehole wall, e.g. the formation, is high. In those instances, measured impedance may have very low sensitivity to the formation features. Maintaining good contact between the pad400and the formation can help wireline imager tools to ensure that the electromagnetic imager tool actually measures the formation and not just the mud when the formation has low resistivity. Since mud effect is a function of standoff, the term standoff effect may be used interchangeably with mud effect in what follows. As will be discussed in greater detail later, the mud effect can be minimized or removed using an applicable technique, such as the techniques described herein. Further, the mud effect can be minimized or removed based on a mud angle determined using an applicable technique, such as the techniques described herein.

FIG. 5illustrates a circuit model of the example pad400illustrated inFIG. 4. Although the exact design of the tool is different for LWD tools, as described with respect toFIGS. 2A-3, the equations derived for the circuit model shown inFIG. 5are applicable for LWD tools. In the model, H denotes the housing (including the mandrel), F denotes the formation, either B or G denotes the button and guard assembly, and R denotes the return signal from the formation and/or the mud. While most of the transmitted current can be returned to the return electrodes, some portions of the transmitted current can return through the housing and/or the mandrel. An impedance value for each button can be calculated by measuring the voltage between the buttons and the return electrodes and dividing the measured voltage by the current transmitted through each button of the button array. Specifically, this technique is represented in Equation 1 shown below. In Equation 1, Z is the button impedance of one of the buttons in the button array, VBRis the button to return voltage, and IBis the button current. With respect to the LWD tools described inFIGS. 2A-CandFIG. 3, VBRcan be replaced with the probe to return voltage, and IBcan be replaced with the current of the probe.

A calculated button impedance, e.g. calculated by Equation 1, can be equal to the impedances of the button and guard assembly and the formation ZBFand the impedances of the return and the formation ZRF, as shown in the circuit model inFIG. 5. While ZBFand ZRFare denoted with respect to the formation F, ZBFand ZRFcan have contributions from both the mud and the formation. Thus, ZBFcan equivalently be represented by Equation 2 shown below.
Z≈ZBF=ZmudZFEquation 2

Accordingly, a measured button impedance, as shown in Equation 2, can have contributions from both the mud and the formation. If the imaginary parts of ZFand Zmudare mainly capacitive, and assuming this capacitance is in parallel with the resistive portion, ZBFcan also be written as shown in Equation 3 below.

In Equation 3, R and C denote the resistance and capacitance and w is the angular frequency (e.g. ω=2πf where f is the frequency in Hz). In Equation 3, subscript M denotes the mud while F denotes the formation. Both the mud resistance and mud capacitance can increase with standoff and decrease with the effective areas of the buttons.

Equation 3 can provide just a basic approximation to the impedance measured by the electromagnetic imager tool. However, Equation 3 can be useful in illustrating the effects of mud and formation parameters on the measured impedance. Specifically, from Equation 3, it can be deduced that high frequencies are needed to reduce the mud contribution to the measured impedance.

FIG. 6is a plot of real parts of the impedances measured by the electromagnetic imager tool versus formation resistivity Rt. In the plot shown inFIG. 6, it is assumed that formation permittivity (εF) is 15, mud permittivity (εM) is 6, and mud resistivity (ρM) is 8000 Ω-m. Results for three different frequencies (1 MHz, 7 MHz and 49 MHz) at two different standoffs (1 mm and 3 mm) are shown. Standoff, as used herein, is the distance of the button electrode's outer surface from the borehole wall. It can be seen fromFIG. 6that there is a separation between different standoffs at lower formation resistivities. This effect can be more pronounced if the frequency is lower. At higher formation resistivities, the dielectric effect in the formation becomes more important and causes a roll-off in measured impedance.

With respect to the mud effect, it can be desirable to operate in a linear region of the curves shown inFIG. 6. Specifically, operating in a linear region can lead to a more accurate correspondence between the real parts of impedance and the true formation resistivity. Further, the mud effect at low formation resistivities can cause an ambiguity in the interpretation of impedance, e.g. through impedance images.

The description now turns to a discussion of the Z90 processing technique for reducing the mud effect.FIG. 7is a plot700of impedances in the complex plane and corresponding Z90 processing of the impedances. While the Z90 processing technique is discussed throughout this paper, the techniques for identifying mud angle described herein, can be implemented in an applicable processing technique that utilizes a mud angle associated with the electromagnetic imager tool.

Z90 processing is applied to reduce the mud effect and make the response of the mud imager tool, e.g. the impedance response, more linear. In the plot700shown inFIG. 7, measured impedance Z, mud impedance ZM, and formation impedance ZFare shown as vectors in the complex plane. Although the approximate direction of the mud impedance vector ZMcan be known, the strength of the vector depends on a number of factors including standoff. However, an orthogonal projection of Z on ZMcan be calculated accurately by measuring the phase angle of the measured impedance, ϕZ, and the phase angle of the mud impedance, ϕM, also referred to as the mud angle. This is applicable to Z90 processing because Z90 processing functions by removing the orthogonal projection of the measured impedance Z on the mud impedance vector Zmfrom the measured impedance Z. In turn, this can reduce or remove the mud effect. The resultant impedance created through Z90 processing, Z90, can be represented as shown below in Equation 4.
Z90=|Z|sin(φZ−φM)  Equation 4

FIG. 8is a plot of real parts of simulated impedances measured by the electromagnetic imager tool versus simulated formation resistivities Rtafter Z90 processing is applied. Specifically,FIG. 8is a plot of the impedances shown inFIG. 6after Z90 processing is performed. As shown in the plot inFIG. 8, the impedance response is more linear across a wider range of formation resistivities after Z90 processing, corresponding to removal of the mud effect from the impedance measurements.

As shown in Equation 4, Z90 processing is dependent on the mud angle, ϕM, associated with the electromagnetic imager tool. In an ideal scenario, the mud angle is assumed to be known, e.g. mud cell measurements or measurements in a cased section of a wellbore. If the mud angle is perfectly known, then Z90 will not have any mud contribution and thus, will be equal to a weighted sum of the real part of formation impedance and the imaginary part of the formation impedance. This is indicated in Equation 5 shown below.
Z90≈w1Re{ZF}+w2Im{ZF}  Equation 5

If it is further assumed that the imaginary part of the formation impedance can be neglected, then Z90 will indeed be a very good approximation to the real formation impedance, as shown in Equation 5.

The plot shown inFIG. 8was made by applying the Z90 processing technique with correct mud angles identified through simulation. Specifically, the mud angles were identified for a circuit representation of an applicable wireline or LWD electromagnetic imager tool, such as the circuit model for the pad400shown inFIG. 4. The correct mud angles identified for the different frequencies are shown in Table 1 below.

TABLE 11 MHz7 MHz49 MHz−69.47°−86.9377°89.5621°
Although the term “mud angle” is used in its singular form throughout this discussion, this is done for simplicity and it is appreciated that mud angle actually varies with frequency.

While the plot shown inFIG. 8was made using accurate mud angles, as discussed previously, the correct mud angle is not actually known in most scenarios and an inaccurate candidate of the mud angle is often used. This can ultimately impact processes, e.g. the Z90 technique, that utilize the mud angle associated with the electromagnetic imager tools.

As discussed previously, one solution to using incorrect mud angle candidates is to directly measure the mud through the electromagnetic imager tool. This measurement can be made by closing the arms of a wireline tool such that contributions from formation resistivity in the tool response are minimized. However and as discussed previously, this is an inefficient usage of the electromagnetic imager tool. Furthermore, this technique is not applicable to LWD tools. Even for wireline tools, the direct measurements made by the tool will still include some formation contributions as well as measurement noise which can negatively impact Z90 processing results. Furthermore, tool calibration may not have been optimized for a case where the pad is close to the tool body causing further inaccuracies. Alternatively, a dedicated mud cell may be included in the tool but this brings forth additional design complexities in addition to the costs associated with incorporating this extra part to the tool. To illustrate the formation contribution and measured noise, the identified mud angle values are shifted 0.5° from their exact values, as shown in Table 2 below.

FIG. 9, is a plot of real parts of simulated impedances measured by the electromagnetic imager tool versus simulated formation resistivities Rtafter Z90 processing is performed on the shifted mud angles. Specifically, the plot shown inFIG. 9is meant to illustrate the effects of direct mud measurements and associated noise on Z90 processing. As shown inFIG. 9, even a deviation as small as 0.5° from the correct value of the mud angle can cause large errors in the processed results. Specifically, this plot shows that an incorrect mud angle, be it as a result of direct mud measurements, noise, and or an incorrect assumption of the mud angle, leads to large errors in the processed results.

FIG. 10illustrates a flowchart for an example method of identifying a mud angle for an electromagnetic imager tool based measurements made by the electromagnetic imager tool. The method shown inFIG. 10is provided by way of example, as there are a variety of ways to carry out the method. Additionally, while the example method is illustrated with a particular order of steps, those of ordinary skill in the art will appreciate thatFIG. 10and the modules shown therein can be executed in any order and can include fewer or more modules than illustrated. Each module shown inFIG. 10represents one or more steps, processes, methods or routines in the method.

The example method shown in the flowchart ofFIG. 10can be used to overcome the previously described deficiencies in identifying mud angle for processing technique, e.g. the Z90 processing technique. Specifically and as will be discussed in greater detail later, an accurate estimation of mud angle associated with the electromagnetic imager tool can be identified from measurements made by the mud imager tool operating to log a wellbore, e.g. as part of imaging a formation. This is in contrast to current techniques that inaccurately identify mud angle of the electromagnetic imager tool. Further, the example method shown inFIG. 10can be implemented without directly measuring the mud and instead can rely on measurements made in actually imaging the formation to identify the mud angle. This can solve for the previously described inaccuracies in mud angle estimation through direct mud measurements and corresponding noise.

At step1000, tool measurements made by the electromagnetic imager tool operating to log a wellbore are gathered. Specifically, the tool measurements gathered at step1000can be made as the electromagnetic imager tool operates to image a surrounding formation of the wellbore. Tool measurements made by the electromagnetic imager tool can include applicable measurements made by the electromagnetic imager tool operating to log the wellbore.

The tool measurements made by the electromagnetic imager tool can be gathered from one or more images of the formation that are created based on measurements gathered by the electromagnetic imager tool. Specifically, the tool measurements can be gathered from one or more images of the formation that are generated by an electromagnetic imaging system associated with the electromagnetic imager tool. For example, impedance measurements made by the electromagnetic imager tool can be gathered from one or more images of the formation generated based on the impedance measurements.

At step1002, the tool measurements are decomposed into two quantities along a plurality of mud angle candidates for the electromagnetic imager tool. Decomposition, as used herein, can include applying an applicable technique to change the measurements made by the electromagnetic imager tool into quantities in a measurable space. Specifically, decomposition can include projecting the measurements or components derived from the measurements, transforming the measurements or the components derived from the measurements, or applying one or more functions to the measurements or the components derived from the measurements to create two quantities in a measurable space. Quantities, as used herein, can include applicable quantities that are capable of being decomposed from the measurements into a measurable space. For example and as will be discussed in greater detail later, decomposing the measurements into two quantities can include generating magnitudes of two orthogonal components of measured impedance at the electromagnetic imager tool. Further in the example, one of the quantities can be in a direction normal to a mud angle candidate of a plurality of mud angle candidates for the electromagnetic imager tool. Additionally, another of the quantities can be in a direction parallel to a mud angle candidate of a plurality of mud angle candidates for the electromagnetic imager tool.

In decomposing the tool measurements into two quantities along a plurality of mud angle candidates for the electromagnetic imager tool, the tool measurements can be decomposed into the two quantities for each of the mud angle candidates. Specifically, the tool measurements can be decomposed into the same two quantities for each of the mud angle candidates. For example, magnitudes of two orthogonal components of measured impedance can be identified for each mud angle candidate for the electromagnetic imager tool. Values of the two quantities can vary between the different mud angle candidates. For example, a magnitude of an orthogonal component of measured impedance for a first mud angle candidate can be greater than a magnitude of the orthogonal component of the measured impedance for a second mud angle candidate. In another example, a projection of a measurement in a direction of a first mud angle candidate can differ from a projection of the measurement in a direction of a second mud angle candidate.

At step1004, a mud angle associated with the electromagnetic imager tool is identified from the plurality of mud angle candidates based on an amount of correlation between the two quantities for the plurality of mud angle candidates. Specifically, a mud angle associated with the electromagnetic imager tool can be identified from the plurality of mud angle candidates based on an amount of correlation between the two quantities for each of the plurality of mud angle candidates. Correlation, as used herein, can be defined according to one or more applicable characteristics of the quantities that relate or otherwise associate the quantities with each other. For example, correlation can include comparing defined characteristics of projected impedance vectors that relate the projected impedance vectors in the complex space. An applicable technique for correlating quantities in a measurable space can be applied to measure an amount of correlation between the two quantities for the mud angle candidates. For example, the Pearson product-moment correlation coefficient can be used to measure an amount of correlation between the two quantities for each of the mud angle candidates. In another example, Spearman's rank correlation coefficient and distance correlation can be used to measure an amount of correlation between the two quantities for each of the mud angle candidates.

The amount of correlation between the two quantities along the plurality of mud angle candidates can be identified along a specific depth interval of the gathered tool measurements. For example, the amount of correlation between impedance vectors decomposed from gathered impedance measurements can be identified for the mud angle candidates along a specific depth interval of the corresponding impedance measurements. The depth interval used in determining correlation between the two quantities can have a length suitable to account for variations in either or both a resistivity profile of the formation and rugosity in one or more walls of the wellbore. For example, impedance measurements gathered over varying resistivity levels of the formation can be decomposed into the two quantities along the mud angle candidates. In turn, the amount of correlation between the two quantities along the mud angle candidates can be determined to ultimately identify one or more mud angles associated with the electromagnetic imager tool.

The mud angle can be identified from the plurality of mud angle candidates based on the mud angle having the smallest amount of correlation between the two quantities amongst each of the plurality of mud angle candidates. In a simplified example, a first mud angle candidate can have less correlation between impedance projections than a second mud angle candidate. In turn, the first mud angle candidate can be selected for the electromagnetic imager tool based on the amount of correlation between the two quantities.

In various embodiments, a plurality of mud angles can be identified from the plurality of mud angle candidates based on an amount of correlation between the two quantities for each of the plurality of mud angle candidates. In turn, the mud angle amongst the identified plurality of mud angles that that minimizes the correlation between the two quantities can ultimately be selected. In various embodiments, multiple candidate mud angles can minimize the correlation between the two quantities, e.g. depending on the mud angle candidates and/or the correlated quantities. In turn, multiple mud angles from the candidate mud angles can be identified and one or more of the identified mud angles can be chosen based on a rule. For example, a mud angle that is closest to −90° can be selected from a plurality of candidate mud angles that minimize the correlation between the two quantities. The plurality of mud angles identified from the plurality of mud angle candidates based on an amount of correlation between the two quantities can form a range of mud angles. Further the plurality of mud angles can include a subset of mud angle candidates that are physically reasonable, e.g. actually capable of being achieved in the mud. For example, the plurality of mud angles can be located in the fourth quadrant of the complex plane, e.g. −90° to 0°.

One or more mud angles identified from the plurality of mud angle candidates based on an amount of correlation between the two quantities can be processed using an applicable technique that utilizes mud angles associated with the electromagnetic imager tool. For example, a mud effect removal process, e.g. Z90 processing, can be applied to one or more images based on the identified mud angle to remove the mud effect from the one or more images. This can improve both quality and contrast in the images, particularly in areas of the image affected by the mud effect. Additionally, the one or more mud angles identified from the plurality of mud angle candidates can be returned to a user, e.g. along with one or more processed images. The user can use the returned mud angle(s) in applying further processing, such as application of an advanced inversion for other mud and formation parameters/properties. In turn, this can reduce amounts of time and computational resources used in applying the advanced inversion.

The description now turns to a discussion of the different quantities that can be decomposed from the tool measurements to identify the mud angle. For example, the tool measurements can be decomposed into magnitudes of two orthogonal components of measured impedance at the electromagnetic imager tool. As measurements gathered by the electromagnetic imager tool are gathered over a large amount of measurement points, e.g. in both the azimuthal direction and the depth direction, the measurements can be flattened into vectors as part of decomposing the tool measurements into the two quantities.

In various embodiments, the tool measurements can be decomposed into two quantities including magnitudes of the orthogonal components of measured impedance at the electromagnetic imager tool. In particular, one or more angles that minimize the correlation of the Z90 measurement with the projection of the measured impedance along a candidate mud angle direction, Z∥, can be identified. Z∥ is shown in Equation 6 below.
Z=|Z|cos φZ−φMEquation 6

FIG. 11is a plot1100of Z90 and Z∥ vectors in the complex plane for identifying the mud angle based on correlation of Z90 and Z∥ quantities. Projections of the measured impedance on the real and imaginary axes, where ZREdenotes the real part of the measured impedance and ZIMdenotes the imaginary part of the measured impedance, are also shown in the plot1100. If the candidate mud angle is denoted as {tilde over (ϕ)}M, where the tilde denotes that the value is an estimate, then {tilde over (Z)}90 and {tilde over (Z)}∥ denote the projections corresponding to this candidate mud angle. As follows the mud angle can be selected according to Equation 7 shown below.
arg{tilde over (φ)}M=└|corr({tilde over (Z)}90,{tilde over (Z)}∥)|┘  Equation 7

In Equation 7, con( ) denotes the correlation of quantities Z90 and Z∥. The quantities can be correlated through an applicable correlation technique, such as using the Pearson product-moment correlation coefficient, as shown in Equation 8 below.

In Equation 8, Cov ( ) denotes the covariance of the two vectors while a denotes the standard deviation of {tilde over (Z)}90 and {tilde over (Z)}∥. Through application of the Pearson product-moment correlation coefficient, correlation can become negative. This can indicate a dependence of two vectors that behave in opposite ways, e.g. one decreases while the other increases. Since the techniques describe herein can use a minimized correlation dependence, an absolute value sign was included in Equation 7 to account for negative correlation.

In various embodiments, the tool measurements can be decomposed into a first quantity including a magnitude of a component of measured impedance at the electromagnetic imager tool normal to a candidate mud angle of the plurality of candidate mud angles. Further, the tool measurements can be decomposed into a second quantity including an imaginary component of the measured impedance. In turn, the magnitude of the component of the measured impedance normal to the candidate mud angles can be correlated with the imaginary component of the measured impedance to ultimately identify the mud angle for the electromagnetic imager tool. Specifically, correlation of the Z90 with ZIMcan be used instead of Z∥ to identify the mud angle. Since Z90 is a measure of the formation resistivity, Equation 9 can be used to obtain the mud angle that minimizes Z90 and ZIMamong a range of possible candidate mud angles.
min └|corr({tilde over (Z)}90,ZIM|)|┘  Equation 9

In various embodiments, the tool measurements can be decomposed into a first quantity including a magnitude of a Zα projection of measured impedance at the electromagnetic imager tool generated based on candidate mud angles. The Zα projection of measured impedance can be a vector projection of Zα processing in a complex plane. Specifically, the Zα projection can be the projection of the vector starting from a measured impedance and ending on a vector parallel to a mud impedance. Further, the tool measurements can be decomposed into a second quantity including an imaginary component of the measured impedance. In turn, the magnitude of the Zα projection for the candidate mud angles can be correlated with the imaginary component of the measured impedance to ultimately identify the mud angle for the electromagnetic imager tool. The mud angle candidate can be identified based on Equation 10. In Equation 10, the tilde over Zα represents that the Zα is calculated using the corresponding mud angle estimate.
min └|corr({tilde over (Z)}α,ZIM|)|┘  Equation 10

In various embodiments, the tool can be decomposed into a first quantity including a magnitude of a component of measured impedance at the electromagnetic imager tool normal to a candidate mud angle\ of the plurality of candidate mud angles. Further, the tool measurements can be decomposed into a second quantity including the component of the measured impedance normal to the candidate mud angle removed from a real component of the measured impedance. In turn, the magnitude of the component of the measured impedance at the electromagnetic imager tool normal to the candidate mud angles can be correlated with the component of the measured impedance normal to the candidate mud angle removed from the real component of the measured impedance to ultimately identify the mud angle for the electromagnetic imager tool. The candidate mud angle can be identified based on Equation 11.
min └|corr({tilde over (Z)}90,(ZRE−{tilde over (Z)}90)|)|┘  Equation 11

In various embodiments, the tool can be decomposed into a first quantity including a magnitude of a Zα projection of measured impedance at the electromagnetic imager tool generated based on a candidate mud angle of the plurality of candidate mud angles. Further, the tool measurements can be decomposed into a second quantity including the Zα projection of the measured impedance generated based on the candidate mud angle removed from a real component of the measured impedance. In turn, the magnitude of the Zα projection of the measured impedance at the electromagnetic imager tool generated based on the candidate mud angle can be correlated with the Zα projection of the measured impedance generated based on the candidate mud angle removed from the real component of the measured impedance to ultimately identify the mud angle for the electromagnetic imager tool. The candidate mud angle can be made based on Equation 12.
min └|corr({tilde over (Z)}α,(ZRE−{tilde over (Z)}α)|)|┘  Equation 12

Tool measurements that are decomposed and used to identify the one or more mud angles can be a subset of the total number of tool measurements made by the electromagnetic imager tool. In particular, specific tool measurements or groups of tool measurements can be selected from the total number of tool measurements made by the electromagnetic imager tool, e.g. in generating one or more images. In turn, the identified tool measurements can be used in identifying the mud angle of the electromagnetic imager tool.

Tool measurements can be selected from a plurality of tool measurements based on absolute values of the tool measurements. Further, the tool measurements can be selected from the plurality of tool measurements using a histogram. Specifically, the tool measurements can be selected based on a histogram of absolute values of the tool measurements. In turn, the measurements selected based on the histogram of absolute values can further be filtered to select measurements with relatively lower absolute impedance values. If exact cutoffs are irrelevant, e.g. where calibration is believed to be inadequate, a percentage based threshold may be applied rather than a predefined threshold for measurement selection. For example, the impedance measurements in the lowest 25% of impedances can be filtered out from the measurements selected using the histogram of absolute values. In order to further simplify calculations, these filtered measurements can be reduced even more by randomly/pseudo-randomly selecting measurements from these filtered measurements. In various embodiments, lowest impedances can be undesirable due to noise or other applicable effects, such as the tool body effect. Accordingly, the measurements can have very low sensitivities to the formation. As a result, a lower threshold of absolute impedances can be applied, e.g. a threshold between 5% and 25% may be used.

Further, tool measurements can be selected from a plurality of tool measurements based on either or both real values and imaginary values of the tool measurements. Real parts of the measurements can be scaled by a tool constant to give apparent resistivity values. However, using absolute value to select the tool measurements can be more beneficial than using the real part of the tool measurements since real part of the measurements does not monotonically increase with formation resistivity. Absolute value measurements may also be preferable to imaginary value measurements since they are more sensitive to formation resistivity if the formation resistivity is low.

Tool measurements can also be selected from a plurality of tool measurements manually by an operator. Specifically, an operator can manually select the tool measurements from the plurality of tool measurements by visually inspecting the plurality of tool measurements and/or one or more images generated from the plurality of tool measurements. For example, an operator can select regions in an image log that have low resistivities and show the mud effect. An operator can also use data from other applicable tools to select the tool measurements from the plurality of tool measurements. In particular, an operator can use data from other tools that logged the formation to select the tool measurements from the plurality of tool measurements. For example, an operator can use formation resistivity results created through a multi-component induction tool or an array laterolog tool to select the tool measurements from the plurality of tool measurements. Alternatively, an operator does not actually select the tool measurements using other tools, but instead the process of selecting the tool measurements based on measurements made by other tools is automated. For example, tool measurements can automatically be selected for formation regions that have low resistivities, as measured by other tools.

Thresholds for selecting tool measurements from a plurality of tool measurements, e.g. the previously described impedance thresholds, can change based on operating frequency of the electromagnetic imager tool. In turn, the tool measurements can be selected based on an operating frequency of the electromagnetic imager tool in making the tool measurements. Further, thresholds can be specific to different formation types. In turn, the thresholds can be selected and applied based on the type of formation that is imaged. Thresholds for selecting tool measurements can be determined and modified by an operator. Specifically, an operator can set thresholds based on a visualization of data. For example, a plot of the real parts of data against the absolute values of the data can be used by an operator to identify thresholds.

Additionally, tool measurements can be selected based on assigned quality indicators to the tool measurements or regions including the tool measurements. For example, a formation region can have high expected resistivities, e.g. as identified by other tools. As a result, the region can be assigned a low quality indicator and tool measurements in these regions can be excluded from the selected tool measurements, e.g. based on the low quality indicator. Further, tool measurements can be selected based on noise levels in the tool measurements. Specifically, the tool measurements can be assigned a quality indicator based on the noise levels in the tool measurements. Subsequently, the tool measurements can be selected if the noise levels are low in the measurements, e.g. as indicated by the quality indicator assigned to the measurements. Noise levels in the measurements can be determined using an applicable technique. For example, changes in a signal for measurements in proximity to each other can be used to determine noise levels in the measurements.

Additionally, tool measurements can be selected from a plurality of tool measurements made by the electromagnetic imager tool based on resistivity measurements made by a different tool from the electromagnetic imager tool, e.g. another tool configured to image a formation. For example, tool measurements can be selected from a plurality of tool measurements made by the electromagnetic imager tool based on resistivity measurements made by an induction type logging tool separate from the electromagnetic imager tool. In another example, tool measurements can be selected from a plurality of tool measurements made by the electromagnetic imager tool based on resistivity measurements made by a laterolog type logging tool separate from the electromagnetic imager tool.

The description now turns to a discussion of an example simulation of identifying mud angles of the electromagnetic imager tool according to the techniques described herein.

In Table 3 shows mud angle values generated using the techniques described herein.

The mud angle values shown in Table 3 were generated used the same mud properties and formation permittivity used to generate the plots shown inFIGS. 8 and 9. To obtain a realistic simulation, a Monte Carlo type simulation was performed where the standoff and formation resistivities were chosen as random/pseudo-random variables with a uniform distribution. Standoff was varied between 1 mm and 5 mm, and formation resistivity was changed between 0.1 Ω-m and 20 Ω-m for 1 MHz, 0.1 Ω-m and 6 Ω-m for 7 MHz, and 0.1 Ω-m and 1 Ω-m for 49 Mhz. These resistivity value ranges for different frequencies is in line with the aforementioned variation of thresholds in selecting resistivity ranges for different frequencies.

Then, using the impedances obtained from the Monte Carlo simulation and Equations 7 and 8, the mud angle that minimizes the correlation among the mud angle values in the fourth quadrant of the complex plane, e.g. between −90° and 0°, was found. A brute force search with a spacing of 0.01° was used in this calculation. Therefore, the results shown in Table 3 can be varied to an accuracy of 0.005°. More complicated techniques can be employed to calculate the mud angle that minimizes Equation 7, such as interpolating the results, fine tuning the results around the final result, or performing an inversion. The computed mud angles shown in Table 3 are very close to true values. The simulation was based on the approximate circuit model of the tool, as shown inFIG. 5, which does not contain noise. However, standoff and formation resistivity were varied.

FIG. 12is a plot of real parts of impedances versus simulated formation resistivities Rtafter Z90 processing is applied based on mud angles identified using the techniques described herein. These results are very close to the case shown in the plot inFIG. 8. The largest discrepancies between the two plots occur for the lowest frequency and at very low resistivities. However, the error in mud angle is just 0.01° for this frequency. In practice, most electromagnetic imager tools employ multiple frequencies so for low resistivity range a higher frequency can be used to image.

FIGS. 13A-Care resistivity images, in the logarithmic scale, of another simulation. The resistivity images shown inFIGS. 13A-Care obtained synthetically, e.g. without any processing using a mud angle identified by the techniques described herein. True resistivity values in this scenario correspond to layers with 30° dip and low resistivities up to a depth of 15.3 inches and then higher resistivity layers above 15.3 inches, e.g. for the button with an azimuth angle of 180° as a reference. It is assumed that formation permittivity (εF) is 15, mud permittivity (εM) is 6, and mud resistivity (ρM) is 8000 Ω-m, which is the same as described previously with respect to the plot shown inFIG. 6. However, simulated frequencies in this case are 1, 10 and 50 MHz. Theoretical mud angles obtained for these frequencies using the circuit model are listed in Table 4.

TABLE 4Resistivities of layers in the formation are listed in Table 5.1 MHz10 MHz50 MHz−69.47°−87.855°−89.571°

Image gray scale is based on the apparent resistivity obtained by dividing the impedances measured at the buttons by an appropriate tool constant. Pixels where there is no data is shown as solid vertical lines in these images.

As shown inFIGS. 13A-C, the low frequency case is especially insensitive to the low resistivity layers due to the mud effect. This is problematic and is correctable by processing corresponding measurements using a mud angle identified through the techniques described herein. Specifically,FIG. 14is a plot of the variation of the absolute value of correlation as a function of candidate mud angles, identified using the techniques described herein, for the corresponding three different frequencies of the simulations represented inFIGS. 13A-C. A range of candidate mud angles between −90° and 0° was selected. Correlation shows a single minimum in the chosen range. Mud angles corresponding to this minimum decreases, e.g. gets closer to −90°, as the frequency increases. Table 6 lists the candidate mud angles that minimized the correlation curves shown inFIG. 14. It can be seen that the results, although imperfect for this multilayer case, e.g. due to shoulder bed and other higher order effects, are very close to the true values, e.g. the greatest error is less than 3° for 10 MHz.

FIG. 15illustrates an example computing device architecture1500which can be employed to perform various steps, methods, and techniques disclosed herein. Specifically, the computing device architecture can be integrated with the electromagnetic imager tools described herein. Further, the computing device can be configured to implement the techniques of controlling borehole image blending through machine learning described herein.

As noted above,FIG. 15illustrates an example computing device architecture1500of a computing device which can implement the various technologies and techniques described herein. The components of the computing device architecture1500are shown in electrical communication with each other using a connection1505, such as a bus. The example computing device architecture1500includes a processing unit (CPU or processor)1510and a computing device connection1505that couples various computing device components including the computing device memory1515, such as read only memory (ROM)1520and random access memory (RAM)1525, to the processor1510.

The computing device architecture1500can include a cache of high-speed memory connected directly with, in close proximity to, or integrated as part of the processor1510. The computing device architecture1500can copy data from the memory1515and/or the storage device1530to the cache1512for quick access by the processor1510. In this way, the cache can provide a performance boost that avoids processor1510delays while waiting for data. These and other modules can control or be configured to control the processor1510to perform various actions. Other computing device memory1515may be available for use as well. The memory1515can include multiple different types of memory with different performance characteristics. The processor1510can include any general purpose processor and a hardware or software service, such as service11532, service21534, and service31536stored in storage device1530, configured to control the processor1510as well as a special-purpose processor where software instructions are incorporated into the processor design. The processor1510may be a self-contained system, containing multiple cores or processors, a bus, memory controller, cache, etc. A multi-core processor may be symmetric or asymmetric.

To enable user interaction with the computing device architecture1500, an input device1545can represent any number of input mechanisms, such as a microphone for speech, a touch-sensitive screen for gesture or graphical input, keyboard, mouse, motion input, speech and so forth. An output device1535can also be one or more of a number of output mechanisms known to those of skill in the art, such as a display, projector, television, speaker device, etc. In some instances, multimodal computing devices can enable a user to provide multiple types of input to communicate with the computing device architecture1500. The communications interface1540can generally govern and manage the user input and computing device output. There is no restriction on operating on any particular hardware arrangement and therefore the basic features here may easily be substituted for improved hardware or firmware arrangements as they are developed.

Storage device1530is a non-volatile memory and can be a hard disk or other types of computer readable media which can store data that are accessible by a computer, such as magnetic cassettes, flash memory cards, solid state memory devices, digital versatile disks, cartridges, random access memories (RAMs)1525, read only memory (ROM)1520, and hybrids thereof. The storage device1530can include services1532,1534,1536for controlling the processor1510. Other hardware or software modules are contemplated. The storage device1530can be connected to the computing device connection1505. In one aspect, a hardware module that performs a particular function can include the software component stored in a computer-readable medium in connection with the necessary hardware components, such as the processor1510, connection1505, output device1535, and so forth, to carry out the function.

The techniques described herein may also be implemented in electronic hardware, computer software, firmware, or any combination thereof. Such techniques may be implemented in any of a variety of devices such as general purposes computers, wireless communication device handsets, or integrated circuit devices having multiple uses including application in wireless communication device handsets and other devices. Any features described as modules or components may be implemented together in an integrated logic device or separately as discrete but interoperable logic devices. If implemented in software, the techniques may be realized at least in part by a computer-readable data storage medium comprising program code including instructions that, when executed, performs one or more of the method, algorithms, and/or operations described above. The computer-readable data storage medium may form part of a computer program product, which may include packaging materials.

The computer-readable medium may include memory or data storage media, such as random access memory (RAM) such as synchronous dynamic random access memory (SDRAM), read-only memory (ROM), non-volatile random access memory (NVRAM), electrically erasable programmable read-only memory (EEPROM), FLASH memory, magnetic or optical data storage media, and the like. The techniques additionally, or alternatively, may be realized at least in part by a computer-readable communication medium that carries or communicates program code in the form of instructions or data structures and that can be accessed, read, and/or executed by a computer, such as propagated signals or waves.

In the above description, terms such as “upper,” “upward,” “lower,” “downward,” “above,” “below,” “downhole,” “uphole,” “longitudinal,” “lateral,” and the like, as used herein, shall mean in relation to the bottom or furthest extent of the surrounding wellbore even though the wellbore or portions of it may be deviated or horizontal. Correspondingly, the transverse, axial, lateral, longitudinal, radial, etc., orientations shall mean orientations relative to the orientation of the wellbore or tool. Additionally, the illustrate embodiments are illustrated such that the orientation is such that the right-hand side is downhole compared to the left-hand side.

The term “radially” means substantially in a direction along a radius of the object, or having a directional component in a direction along a radius of the object, even if the object is not exactly circular or cylindrical. The term “axially” means substantially along a direction of the axis of the object. If not specified, the term axially is such that it refers to the longer axis of the object.

Although a variety of information was used to explain aspects within the scope of the appended claims, no limitation of the claims should be implied based on particular features or arrangements, as one of ordinary skill would be able to derive a wide variety of implementations. Further and although some subject matter may have been described in language specific to structural features and/or method steps, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to these described features or acts. Such functionality can be distributed differently or performed in components other than those identified herein. The described features and steps are disclosed as possible components of systems and methods within the scope of the appended claims.

Statements of the disclosure include:

A method comprising gathering tool measurements made by an electromagnetic imager tool operating to log a wellbore in a formation. The method can also include decomposing the tool measurements into two quantities along a plurality of candidate mud angles for the electromagnetic imager tool. Further, the method can include identifying a mud angle associated with the electromagnetic imager tool from the plurality of candidate mud angles based on an amount of correlation between the two quantities for each of the plurality of candidate mud angles.

A system comprising one or more processors and at least one computer-readable storage medium having stored therein instructions. The instructions which, when executed by the one or more processors, cause the one or more processors to perform operations comprising gathering tool measurements made by an electromagnetic imager tool operating to log a wellbore in a formation. Further, the instructions can cause the one or more processors to decompose the tool measurements into two quantities along a plurality of candidate mud angles for the electromagnetic imager tool. Additionally, the instructions can cause the one or more processors to identify a mud angle associated with the electromagnetic imager tool from the plurality of candidate mud angles based on an amount of correlation between the two quantities for each of the plurality of candidate mud angles.

A non-transitory computer-readable storage medium having stored therein instructions which, when executed by a processor, cause the processor to perform operations comprising gathering tool measurements made by an electromagnetic imager tool operating to log a wellbore in a formation. The instructions can cause the processor to decompose the tool measurements into two quantities along a plurality of candidate mud angles for the electromagnetic imager tool. Further, the instructions can cause the processor to identify a mud angle associated with the electromagnetic imager tool from the plurality of candidate mud angles based on an amount of correlation between the two quantities for each of the plurality of candidate mud angles.

The one or more images generated from the tool measurements can be processed by applying a mud effect removal process to the tool measurements based on the identified mud angle. The identified mud angle can have a smallest amount of correlation between the two quantities across the plurality of candidate mud angles. Further, values of the two quantities vary along the plurality of candidate mud angles. The two quantities can include magnitudes of two orthogonal components of measured impedance at the electromagnetic imager tool where one quantity of the two quantities is in a direction normal to a candidate mud angle of the plurality of candidate mud angles and a second quantity of the two quantities is in the direction parallel to a candidate mud angle of the plurality of candidate mud angles. Further, a first quantity of the two quantities can include a magnitude of a component of measured impedance at the electromagnetic imager tool normal to a candidate mud angle of the plurality of candidate mud angles and a second quantity of the two quantities can include an imaginary component of the measured impedance. Additionally, a first quantity of the two quantities can include a magnitude of a Zα projection of measured impedance at the electromagnetic imager tool generated based on a candidate mud angle of the plurality of candidate mud angles and a second quantity of the two quantities can include an imaginary component of the measured impedance. A first quantity of the two quantities can include a magnitude of a component of measured impedance at the electromagnetic imager tool normal to a candidate mud angle of the plurality of candidate mud angles and a second quantity of the two quantities can include the component of the measured impedance normal to the candidate mud angle removed from a real component of the measured impedance. Also, a first quantity of the two quantities can include a magnitude of a Zα projection of measured impedance at the electromagnetic imager tool generated based on a candidate mud angle of the plurality of candidate mud angles and a second quantity of the two quantities can include the Zα projection of the measured impedance generated based on the candidate mud angle removed from a real component of the measured impedance.

The amount of correlation between the two quantities along the plurality of candidate mud angles can be identified along a depth interval of the tool measurements made by the electromagnetic imager tool. A length of the depth interval of the tool measurements can account for variations in either or both a resistivity profile of the formation and rugosity in one or more walls of the wellbore. The tool measurements decomposed into the two quantities can be a subset of a total number of tool measurements made by the electromagnetic imager tool operating to log the wellbore. The tool measurements can be selected from the total number of tool measurements made by the electromagnetic imager tool based on one or a combination of real values, imaginary values, and absolute values of the tool measurements. Further, the tool measurements can be selected from the total number of tool measurements made by the electromagnetic imager tool based on one or more operating frequencies of the electromagnetic imager tool in making the tool measurements. Additionally, the tool measurements can be selected from the total number of tool measurements made by the electromagnetic imager tool based on a histogram of absolute values of at least a portion of the total number of tool measurements. The tool measurements can also be selected from the total number of tool measurements made by the electromagnetic imager tool based on noise levels in the tool measurements.

The tool measurements can be selected from the total number of tool measurements made by the electromagnetic imager tool based on one or a combination of visual inspection of at least a portion of the total number of tool measurements, visual inspection of one or more images of the formation generated from the at least a portion of the total number of tool measurements, and the resistivity measurements made by a different tool from the electromagnetic imager tool.

The electromagnetic imager tool can be disposed in the wellbore. In turn, the electromagnetic imager tool can be operated in the wellbore to gather the tool measurements by logging the wellbore.