Patent Description:
Traditionally, borehole imager tools may be used in obtaining a detailed characterization of reservoirs. These borehole imager tools may provide a resistivity image of the formation immediately surrounding the borehole. Borehole imager tools may be used to determine formation stratigraphy, dips of the formation layers as well as, borehole and formation stress. During drilling operations borehole imager tools may be particularly important in learning about thin beds, fracture locations, and low resistivity formations. To detect thin beds, fracture locations, and low resistivity formations borehole imager may transmit a current through an injector electrode into the formation. A return electrode may record the current after the current has passed through the formation. Measuring this current may allow an operator to determine characteristic and properties of thin beds, fracture locations, and low resistivity formations. During measurement operations current may pass from the injector electrode and "leak" through the formation and into the downhole tool and not the return electrode. This may reduce the sensitivity of the borehole imager tools to the low resistivity formations. A manifestation of the current leakage is the nonlinearity of the phase response of the tool with respect to frequency. Phase response of an ideal mud imager tool is expected to be a slowly changing function of frequency for the range of frequencies the tool is employed. However, in practice, phase response of the tool is observed to be highly nonlinear and to exhibit a resonance type behavior due to the current leakage. Furthermore, frequency response of different pads may vary based on their axial location on the mandrel. <CIT> describes a resistivity logging tool including a plurality of excitation electrodes, at least one return electrode, and a plurality of monitor electrodes. <CIT> describes a formation measurement and processing technique where the resistivity tool utilizes capacitive coupling between the tool and the formation to obtain resistivity data useful to generate a resistivity image of the formation. <CIT> describes a system and method for imaging properties of subterranean formations in a wellbore is provided. The system comprises a formation sensor for collecting currents injected into the subterranean formations, the formation sensor positionable on a downhole tool deployable into the wellbore. <CIT> describes an apparatus and method which may operate to mount an electrode assembly with the exterior of a casing string to be placed in a borehole in a subterranean formation. <CIT> describes an apparatus and method for measuring electrical properties of an underground formation surrounding a borehole.

For a detailed description of the examples of the disclosure, reference will now be made to the accompanying drawings in which:.

The present disclosure discloses a system and method for optimization of downhole tool performance through the measurement of a phase response of the downhole tool with respect to frequency. The proposed method may measure the phase response of the downhole tool to determine the frequencies where the downhole tool is stable (i.e., away from the resonance) for each measurement unit (such as each pad) and select operating frequencies of the downhole tool based on this information. The proposed system and method may increase the ability for the pad to sense and measure a low resistivity formation and reduce noise levels in the measurements through the optimization of the operating frequency.

Additionally, the present disclosure relates methods for electrically isolating a pad from a mandrel of a downhole tool. For example, current emitted by an injector electrode from the pad may travel, or "leak," through the formation, into the downhole tool, and through the pad to a return electrode disposed on the pad. The return electrode may measure the "leakage current," which may be identified as part of a formation. Additionally, the measured "leakage current" may include more amps than current measured from the formation. Therefore the "leakage current" may washout and/or cover the measured current from the formation, which may lead to skewed and/or false measurements. This leakage current is the primary cause of the resonances in the tool response. Reducing the leakage current will make the optimization of the operating frequency easier and more robust. Thus, it may be beneficial to design and build a system that may prevent "leakage current" from being measured by the return electrode. The invention is defined by a method for identifying an operating frequency according to claim <NUM> and a system for downhole imaging according to claim <NUM>.

<FIG> illustrates a cross-sectional view of an example of a well measurement system <NUM>. As illustrated, well measurement system <NUM> may include downhole tool <NUM> attached to a vehicle <NUM>. In examples, it should be noted that downhole tool <NUM> may not be attached to a vehicle <NUM>. Downhole tool <NUM> may be supported by rig <NUM> at surface <NUM>. Downhole tool <NUM> may be tethered to vehicle <NUM> through conveyance <NUM>. Conveyance <NUM> may be disposed around one or more sheave wheels <NUM> to vehicle <NUM>. Conveyance <NUM> may include any suitable means for providing mechanical conveyance for downhole tool <NUM>, including, but not limited to, wireline, slickline, coiled tubing, pipe, drill pipe, drill string, downhole tractor, or the like. In some examples, conveyance <NUM> may provide mechanical suspension, as well as electrical connectivity, for downhole tool <NUM>.

Conveyance <NUM> may include, in some instances, a plurality of electrical conductors extending from vehicle <NUM>. Conveyance <NUM> may include an inner core of seven electrical conductors covered by an insulating wrap. An inner and outer steel armor sheath may be wrapped in a helix in opposite directions around the conductors. The electrical conductors may be used for communicating power and telemetry between vehicle <NUM> and downhole tool <NUM>.

Conveyance <NUM> may lower downhole tool <NUM> in borehole <NUM>. Generally, borehole <NUM> may include horizontal, vertical, slanted, curved, and other types of borehole geometries and orientations. Imaging tools may be used in uncased sections of the borehole. Measurements may be made by downhole tool <NUM> in cased sections for purposes such as calibration.

As illustrated, borehole <NUM> may extend through formation <NUM>. As illustrated in <FIG>, borehole <NUM> may extend generally vertically into the formation <NUM>, however borehole <NUM> may extend at an angle through formation <NUM>, such as horizontal and slanted boreholes. For example, although <FIG> illustrates a vertical or low inclination angle well, high inclination angle or horizontal placement of the well and equipment may be possible. It should further be noted that while <FIG> generally depicts a land-based operation, those skilled in the art may recognize that the principles described herein are equally applicable to subsea operations that employ floating or sea-based platforms and rigs, without departing from the scope of the disclosure.

Information from downhole tool <NUM> may be gathered and/or processed by information handling system <NUM>. For example, signals recorded by downhole tool <NUM> may be stored on memory and then processed by downhole tool <NUM>. The processing may be performed real-time during data acquisition or after recovery of downhole tool <NUM>. Processing may alternatively occur downhole or may occur both downhole and at surface. In some examples, signals recorded by downhole tool <NUM> may be conducted to information handling system <NUM> by way of conveyance <NUM>. Information handling system <NUM> may process the signals, and the information contained therein may be displayed for an operator to observe and stored for future processing and reference. Information handling system <NUM> may also contain an apparatus for supplying control signals and power to downhole tool <NUM>.

Systems and methods of the present disclosure may be implemented, at least in part, with information handling system <NUM>. While shown at surface <NUM>, information handling system <NUM> may also be located at another location, such as remote from borehole <NUM>. Information handling system <NUM> may include any instrumentality or aggregate of instrumentalities operable to compute, estimate, classify, process, transmit, receive, retrieve, originate, switch, store, display, manifest, detect, record, reproduce, handle, or utilize any form of information, intelligence, or data for business, scientific, control, or other purposes. For example, an information handling system <NUM> may be a processing unit <NUM>, a network storage device, or any other suitable device and may vary in size, shape, performance, functionality, and price. Information handling system <NUM> may include random access memory (RAM), one or more processing resources such as a central processing unit (CPU) or hardware or software control logic, ROM, and/or other types of nonvolatile memory. Additional components of the information handling system <NUM> may include one or more disk drives, one or more network ports for communication with external devices as well as an input device <NUM> (e.g., keyboard, mouse, etc.) and video display <NUM>. Information handling system <NUM> may also include one or more buses operable to transmit communications between the various hardware components.

Alternatively, systems and methods of the present disclosure may be implemented, at least in part, with non-transitory computer-readable media <NUM>. Non-transitory computer-readable media <NUM> may include any instrumentality or aggregation of instrumentalities that may retain data and/or instructions for a period of time. Non-transitory computer-readable media <NUM> may include, for example, storage media such as a direct access storage device (e.g., a hard disk drive or floppy disk drive), a sequential access storage device (e.g., a tape disk drive), compact disk, CD-ROM, DVD, RAM, ROM, electrically erasable programmable read-only memory (EEPROM), and/or flash memory; as well as communications media such as wires, optical fibers, microwaves, radio waves, and other electromagnetic and/or optical carriers; and/or any combination of the foregoing.

As discussed below, methods may utilize an information handling system <NUM> to determine and display a high-resolution resistivity image of formation <NUM> immediately surrounding borehole <NUM>. This high-resolution resistivity image may depict boundaries of subsurface structures, such as a plurality of layers disposed in formation <NUM>. These formation images may be used in reservoir characterization. Formation images with high resolution may allow accurate identification of thin beds and other fine features such as fractures, clasts and vugs. These formation images may provide information about the sedimentology, lithology, porosity and permeability of formation <NUM>. The formation images may complement, or in some cases replace, the process of coring.

In examples, rig <NUM> includes a load cell (not shown) which may determine the amount of pull on conveyance <NUM> at the surface of borehole <NUM>. Information handling system <NUM> may include a safety valve which controls the hydraulic pressure that drives drum <NUM> on vehicle <NUM> which may reel up and/or release conveyance <NUM> which may move downhole tool <NUM> up and/or down borehole <NUM>. Conveyance <NUM> may provide a means of disposing downhole tool <NUM> into borehole <NUM>. The safety valve may be adjusted to a pressure such that drum <NUM> may only impart a small amount of tension to conveyance <NUM> over and above the tension necessary to retrieve conveyance <NUM> and/or downhole tool <NUM> from borehole <NUM>. The safety valve is typically set a few hundred pounds above the amount of desired safe pull on conveyance <NUM> such that once that limit is exceeded; further pull on conveyance <NUM> may be prevented.

Downhole tool <NUM> may include a plurality of electrodes, such as button array <NUM>. Downhole tool <NUM> may also include a return electrode <NUM>. It should be noted that the plurality of electrodes disposed on button array <NUM> may be any suitable electrode and is should be further noted that return electrode <NUM> may be any suitable electrode. Button array <NUM> and/or return electrode <NUM> may be disposed on at least one pad <NUM> in any suitable order. For example, a pad <NUM> may include only button arrays <NUM> and/or return electrodes <NUM>. Further, a pad <NUM> may include both button array <NUM> and return electrodes <NUM>. Pads <NUM> may attach to a mandrel <NUM> of downhole tool <NUM> through upper arm <NUM> and lower arm <NUM>. It should be noted that mandrel <NUM> may be defined as the supporting structure of downhole tool <NUM> which may act as a platform for any peripheral (e.g., upper arm <NUM>, lower arm <NUM>, conveyance <NUM>, etc.) to attach to downhole tool <NUM>. Upper arm <NUM> and lower arm <NUM> may extend pad <NUM> away from downhole tool <NUM>. In examples, both upper arm <NUM> and lower arm <NUM> may place pad <NUM> in contact with borehole <NUM>. It should be noted that there may be any suitable number of arms and/or extensions that may be used to move pad <NUM> away from downhole tool <NUM> and in close proximity with borehole <NUM>, or vice versa.

During operations, an operator may energize an individual electrode, or any number of electrodes, of button array <NUM>. A voltage may be applied between the electrode of button array <NUM> and return electrode <NUM>. The level of the voltage may be controlled by information handling system <NUM>. This may cause currents to be transmitted through the electrode of button array <NUM>. It should be noted that there may be any number of currents transmitted into formation <NUM>. These currents may travel through the mud disposed in borehole <NUM> and formation <NUM> and may reach back to return electrode <NUM>. The amount of current emitted by each electrode may be inversely proportional to the impedance seen by the electrode. This impedance may be affected by the properties of formation <NUM> and the mud directly in front of each electrode of button array <NUM>. Therefore, current emitted by each electrode may be measured and recorded in order to obtain a formation image of the resistivity of formation <NUM>.

To produce a resistivity image of formation <NUM>, a current may be emitted from at least one electrode from button array <NUM> and return to return electrode <NUM>. In examples, current may be emitted from any transmission type electrode along downhole tool <NUM>. These two electrodes may be referred to as the current electrodes. Then, the voltage drop across a pair of the electrodes of button array <NUM> may be measured and used to estimate the impedance of formation <NUM>. In these alternative implementations, button electrodes may be referred to as voltage electrodes or monitor electrodes. Proposed method may operate in any of the two designs above or any other similar oil-based mud resistivity imager tool without any limitations.

In examples, downhole tool <NUM> may operate with additional equipment (not illustrated) on surface <NUM> and/or disposed in a separate well measurement system (not illustrated) to record measurements and/or values from formation <NUM> to render a resistivity image of formation <NUM>. Without limitation, downhole tool <NUM> may be connected to and/or controlled by information handling system <NUM>, which may be disposed on surface <NUM>. Without limitation, information handling system <NUM> may be disposed down hole in downhole tool <NUM>. Processing of information recorded may occur down hole and/or on surface <NUM>. In addition to, or in place of processing at surface <NUM>, processing may occur downhole. Processing occurring downhole may be transmitted to surface <NUM> to be recorded, observed, and/or further analyzed. Additionally, information recorded on information handling system <NUM> that may be disposed down hole may be stored until downhole tool <NUM> may be brought to surface <NUM>. In examples, information handling system <NUM> may communicate with downhole tool <NUM> through a fiber optic cable (not illustrated) disposed in (or on) conveyance <NUM>. In examples, wireless communication may be used to transmit information back and forth between information handling system <NUM> and downhole tool <NUM>. Information handling system <NUM> may transmit information to downhole tool <NUM> and may receive as well as process information recorded by downhole tool <NUM>. In examples, a downhole information handling system (not illustrated) may include, without limitation, a microprocessor or other suitable circuitry, for estimating, receiving and processing signals from downhole tool <NUM>. Downhole information handling system (not illustrated) may further include additional components, such as memory, input/output devices, interfaces, and the like. In examples, while not illustrated, downhole tool <NUM> may include one or more additional components, such as analog-to-digital converter, filter and amplifier, among others, that may be used to process the measurements of downhole tool <NUM> before they may be transmitted to surface <NUM>. Alternatively, raw measurements from downhole tool <NUM> may be transmitted to surface <NUM>.

Any suitable technique may be used for transmitting signals from downhole tool <NUM> to surface <NUM>. As illustrated, a communication link (which may be wired or wireless and may be disposed in conveyance <NUM>, for example) may be provided that may transmit data from downhole tool <NUM> to an information handling system <NUM> at surface <NUM>.

<FIG> illustrates an example of pad <NUM>. It should be noted that pad <NUM> may be connected to downhole tool <NUM> (e.g., referring to <FIG> and <FIG>). Pad <NUM> may serve to place button array <NUM> and/or return electrode <NUM> in contact with or in close proximity to borehole <NUM>. Pad <NUM> may include a button array <NUM>, a return electrode <NUM>, a guard <NUM>, and a housing <NUM>. In examples, there may be a plurality of button arrays <NUM>. In examples, return electrode <NUM> and button array <NUM> may be disposed directly on downhole tool <NUM>. Button array <NUM> may include an injector electrode <NUM>, wherein injector electrode <NUM> may be a sensor that senses impedance of formation <NUM>. It should be noted that injector electrode <NUM> may be a button electrode. There may be any suitable number of injector electrodes <NUM> within button array <NUM> that may produce a desired, predetermined current. Without limitation, the range for a suitable number of injector electrodes <NUM> within button array <NUM> may be from about one injector electrode <NUM> to about one hundred injector electrodes <NUM>. For example, the range for a suitable number of injector electrodes <NUM> within button array <NUM> may be from about one injector electrode <NUM> to about twenty-five injector electrodes <NUM>, from about twenty-five injector electrodes <NUM> to about fifty injector electrodes <NUM>, from about fifty injector electrodes <NUM> to about seventy-five injector electrodes <NUM>, or from about seventy-five injector electrodes <NUM> to about one hundred injector electrodes <NUM>.

In examples, there may be a plurality of return electrodes <NUM>. One of the return electrodes <NUM> may be disposed on one side of button array <NUM>, and another one of the return electrodes <NUM> may be disposed on the opposite side of button array <NUM>. These return electrodes <NUM> may be disposed at equal distances away from button array <NUM> or at varying distances from button array <NUM>. Without limitation, the distance from the center of one of the return electrodes to the button array may be from about one inch to about one foot. In examples, a voltage difference between button array <NUM> and return electrodes <NUM> may be applied, which may cause currents to be emitted from button array <NUM> into the mud (not illustrated) and formation <NUM> (referring to <FIG>).

During operations, an operator may energize button array <NUM>. A voltage may be applied between each injector electrode <NUM> and return electrode <NUM>. The level of the voltage may be controlled by information handling system <NUM>. This may cause currents to be transmitted through button array <NUM>. These currents may travel through the mud and formation <NUM> and may reach back to return electrode <NUM>. The amount of current emitted by each injector electrode <NUM> may be inversely proportional to the impedance seen by that injector electrode <NUM>. This impedance may be affected by the properties of formation <NUM> and the mud directly in front of each injector electrode <NUM>. Therefore, current emitted by each injector electrode <NUM> may be measured and recorded in order to obtain an image of the resistivity of formation <NUM>.

In examples, a current may be transmitted from injector electrode <NUM> and return to return electrode <NUM>. These two electrodes may be referred to as the current electrodes. Then, the voltage drops across button array <NUM> may be measured and used to estimate the impedance of formation <NUM>. In these alternative implementations, injector electrodes <NUM> may be referred to as voltage electrodes or monitor electrodes. Proposed method may operate in any of the two designs above or any other similar oil-based mud resistivity imager tool without any limitations. In the rest of the text, the imager tool will be assumed to be of the first design without any loss of generality.

Guard <NUM> may help to focus most of the current produced by button array <NUM> into formation <NUM> radially. Guard <NUM> may be disposed around button array <NUM>. Guard <NUM> may include the same potential as button array <NUM>.

In examples, housing <NUM> may serve to protect button array <NUM> and return electrodes <NUM> from the surrounding mud and formation <NUM>. Housing may be made with any suitable material. Without limitation, suitable material may include metals, nonmetals, plastics, ceramics, composites and/or combinations thereof. In examples, housing <NUM> may be a metal plate. Housing <NUM> may be connected through upper arm <NUM> to downhole tool <NUM> (e.g., referring to <FIG>). An insulating material may be used to fill the remaining portions of pad <NUM>. In examples, ceramics may be used as the insulating material to fill the remaining portions of pad <NUM>.

An impedance value may be calculated through the current transmitting between an injector electrode <NUM> and formation <NUM> for each injector electrode <NUM>. The voltage between button array <NUM> and return electrodes <NUM> may be measured and divided by the transmitted current to produce a value for the impedance seen by each injector electrode <NUM>. Most of the transmitted current may be returned to return electrodes <NUM> although some portions of it may return through housing <NUM> and downhole tool <NUM> (e.g., referring to <FIG>).

During logging operations, measurement data taken by pad <NUM> may include resistivity and permittivity. Measurements of resistivity and permittivity may contain contributions from oil-based mud that is may be disposed between pad <NUM> and the wall of borehole <NUM> as well as the signal coming from the formation. To accurately estimate formation resistivity and formation permittivity, downhole oil-based mud properties may be measured. Currently, there is no mud cell used in downhole tool <NUM>, thus downhole mud properties may be determined from measurements already taken by downhole tool <NUM>. As discussed below, broadband oil-based mud properties may be determined from multi-frequency measurements data as well as physical borehole <NUM> and/or pad <NUM> information.

In general, the measurement medium of pad <NUM> may be modeled as a homogeneous formation with a thin layer of oil-based mud between pad <NUM> and formation <NUM>. When pad <NUM> is placed on formation <NUM> without a mud layer, response measurement may only be from formation <NUM>. However, when there is a mud layer present, the response is influenced by the thickness of the mud layer as well as the mud properties, in addition to the properties of formation <NUM> behind the mud layer. That being said, the response for certain formations <NUM> predominantly consist of the mud signal, which may make this response suitable for determining mud properties.

<FIG> illustrates an example in which downhole tool <NUM> may be disposed in a drilling system <NUM>. As illustrated, borehole <NUM> may extend from a wellhead <NUM> into formation <NUM> from surface <NUM>. As illustrated, a drilling platform <NUM> may support a derrick <NUM> having a traveling block <NUM> for raising and lowering drill string <NUM>. Drill string <NUM> may include, but is not limited to, drill pipe and coiled tubing, as generally known to those skilled in the art. A kelly <NUM> may support drill string <NUM> as it may be lowered through a rotary table <NUM>. A drill bit <NUM> may be attached to the distal end of drill string <NUM> and may be driven either by a downhole motor and/or via rotation of drill string <NUM> from surface <NUM>. Without limitation, drill bit <NUM> may include, roller cone bits, PDC bits, natural diamond bits, any hole openers, reamers, coring bits, and the like. As drill bit <NUM> rotates, it may create and extend borehole <NUM> that penetrates various formations <NUM>. A pump <NUM> may circulate drilling fluid through a feed pipe <NUM> to kelly <NUM>, downhole through interior of drill string <NUM>, through orifices in drill bit <NUM>, back to surface <NUM> via annulus <NUM> surrounding drill string <NUM>, and into a retention pit <NUM>.

With continued reference to <FIG>, drill string <NUM> may begin at wellhead <NUM> and may traverse borehole <NUM>. Drill bit <NUM> may be attached to a distal end of drill string <NUM> and may be driven, for example, either by a downhole motor and/or via rotation of drill string <NUM> from surface <NUM>. Drill bit <NUM> may be a part of bottom hole assembly <NUM> at distal end of drill string <NUM>. Bottom hole assembly <NUM> may further include downhole tool <NUM>. Downhole tool <NUM> may be disposed on the outside and/or within bottom hole assembly <NUM>. Downhole tool <NUM> may include test cell <NUM>. As will be appreciated by those of ordinary skill in the art, bottom hole assembly <NUM> may be a measurement-while drilling (MWD) or logging-while-drilling (LWD) system.

Without limitation, bottom hole assembly <NUM> may be connected to and/or controlled by information handling system <NUM>, which may be disposed on surface <NUM>. Without limitation, information handling system <NUM> may be disposed down hole in bottom hole assembly <NUM>. Processing of information recorded may occur down hole and/or on surface <NUM>. Processing occurring downhole may be transmitted to surface <NUM> to be recorded, observed, and/or further analyzed. Additionally, information recorded on information handling system <NUM> that may be disposed down hole may be stored until bottom hole assembly <NUM> may be brought to surface <NUM>. In examples, information handling system <NUM> may communicate with bottom hole assembly <NUM> through a fiber optic cable (not illustrated) disposed in (or on) drill string <NUM>. In examples, wireless communication may be used to transmit information back and forth between information handling system <NUM> and bottom hole assembly <NUM>. Information handling system <NUM> may transmit information to bottom hole assembly <NUM> and may receive as well as process information recorded by bottom hole assembly <NUM>. In examples, a downhole information handling system (not illustrated) may include, without limitation, a microprocessor or other suitable circuitry, for estimating, receiving and processing signals from bottom hole assembly <NUM>. Downhole information handling system (not illustrated) may further include additional components, such as memory, input/output devices, interfaces, and the like. In examples, while not illustrated, bottom hole assembly <NUM> may include one or more additional components, such as analog-to-digital converter, filter and amplifier, among others, that may be used to process the measurements of bottom hole assembly <NUM> before they may be transmitted to surface <NUM>. Alternatively, raw measurements from bottom hole assembly <NUM> may be transmitted to surface <NUM>.

Any suitable technique may be used for transmitting signals from bottom hole assembly <NUM> to surface <NUM>, including, but not limited to, wired pipe telemetry, mud-pulse telemetry, acoustic telemetry, and electromagnetic telemetry. While not illustrated, bottom hole assembly <NUM> may include a telemetry subassembly that may transmit telemetry data to surface <NUM>. Without limitation, an electromagnetic source in the telemetry subassembly may be operable to generate pressure pulses in the drilling fluid that propagate along the fluid stream to surface <NUM>. At surface <NUM>, pressure transducers (not shown) may convert the pressure signal into electrical signals for a digitizer (not illustrated). The digitizer may supply a digital form of the telemetry signals to information handling system <NUM> via a communication link <NUM>, which may be a wired or wireless link. The telemetry data may be analyzed and processed by information handling system <NUM>.

As illustrated, communication link <NUM> (which may be wired or wireless, for example) may be provided that may transmit data from bottom hole assembly <NUM> to an information handling system <NUM> at surface <NUM>. Information handling system <NUM> may include a processing unit <NUM> (Referring to <FIG>), a video display <NUM> (Referring to <FIG>), an input device <NUM> (e.g., keyboard, mouse, etc.) (Referring to <FIG>), and/or non-transitory computer-readable media <NUM> (e.g., optical disks, magnetic disks) (Referring to <FIG>) that may store code representative of the methods described herein. In addition to, or in place of processing at surface <NUM>, processing may occur downhole.

<FIG> illustrate an example of bottom hole assembly <NUM> that includes another example of pads <NUM>. In examples there may be any number of pads <NUM> disposed on bottom hole assembly <NUM> that may operate and function to perform imaging operations in oil based muds. It should be noted that water based mud imagers may have similar designs, and may generally provide less design and interpretation complications than oil based mud imagers due to the conductive nature of the water based mud. Bottom hole assembly <NUM> may operate in a logging-while-drilling (LWD) and/or measuring-while-drilling (MWD) imaging. As described below, bottom hole assembly <NUM> may provide a high resolution image of borehole <NUM> (e.g., referring to <FIG>) and may be used to identifying damage sections of borehole <NUM>. This may provide knowledge on thin beds in formation <NUM> and also provide images that may be used to determine a dip angle of formation beds.

In this example, pad <NUM> may be attached directly to bottom hole assembly <NUM> and may not utilize one or more arms. Without limitation, pad <NUM> may serve to place pad <NUM> and/or injector electrode <NUM> in contact with or in close proximity to borehole <NUM> (e.g., referring to <FIG>). Pad <NUM> may include an injector electrode <NUM> and guard electrode <NUM>. Guard electrode <NUM> may surround injector electrode <NUM>. In examples, guard electrode <NUM> may be excited by an alternating current, sine-wave generator, and it may be coupled to formation <NUM> (e.g., referring to <FIG>) through the oil based mud. The mud is non-conductive for oil based muds, consequently, the coupling to formation <NUM> by displacement currents in mud <NUM>. This arrangement provides a low sensitivity to standoff changes in the microresistivity image. This may allow injector electrode <NUM> and guard electrode <NUM> may operate and function to sense impedance of formation <NUM> (e.g., referring to <FIG>).

In an LWD environment, the sensor topology can have minimum complexity, and more importantly, may not rely on contact with borehole <NUM> (e.g., referring to <FIG>). During measurement operations, a current enters formation <NUM> from injector electrode <NUM>, which may have a much lower resistivity than the mud. In formation <NUM>, the current density flows by conduction. The current penetrates formation <NUM> and then returns back toward borehole <NUM> where it returns to bottom hole assembly <NUM>. The body of bottom hole assembly <NUM> may remain at ground potential because of its large surface area.

Imaging is accomplished by dividing data into azimuthal bins as bottom hole assembly <NUM> (e.g., referring to <FIG>) rotates in borehole <NUM> (e.g., referring to <FIG>) during drilling operations. As illustrated in <FIG>, bottom hole assembly <NUM> may include an additional mud resistivity sensor <NUM>. The real component of measurements taken by injector electrode <NUM> may be used to determine formation resistivity, whereas mud resistivity measurement from mud resistivity sensor <NUM> is used to validate the formation resistivity measurement. During operations, multiple frequencies may be used by bottom hole assembly <NUM>. In examples, a higher frequency in the MHz range may be used to overcome the nonconductive mud for oil based muds while a lower frequency in the <NUM> range may be more sensitive to standoff and thus may be used in standoff determination. Standoff information may be used to identify features in formation <NUM> (e.g., referring to <FIG>). For example, a thin band of increased resistivity is due to an opening in the rock if it also shows as a jump in apparent standoff, but is more likely a thin bed if little change is recorded in apparent standoff.

<FIG> illustrates an example of a circuit model that may approximate the pad <NUM> illustrated in <FIG>. Effects of the transmitted current may be approximately characterized by a housing-to-formation impedance value 500A, a return electrode-to-housing impedance value 500B, a return electrode-to-formation impedance value 500C, a button-to-housing impedance value 500D, and a button -to-formation impedance value 500E. Impedance may be calculated below, wherein Z is the impedance, VBR is the button-to-return electrode voltage and IB is the button current: <MAT>.

The value calculated in Equation (<NUM>) may be equal to ZBF + ZRF, as shown in <FIG>, wherein ZBF is the impedance from injector electrode <NUM> to formation <NUM> and ZRF is the impedance of return electrode <NUM> to formation <NUM>. Note that for different injector electrodes <NUM> of the button array <NUM>, these impedances may differ based on the variations in borehole <NUM> (e.g., referring to <FIG> and <FIG>) and the environment. These variations in measured impedances in an impedance image may be used to determine geophysical features. Also note that both ZBF and ZRF have contributions from both the surrounding mud and formation <NUM> (e.g., referring to <FIG>). Thus, equivalently it can be written in Equation (<NUM>) as: <MAT>.

As a result, measured impedance may have contributions from both the mud and formation <NUM>, wherein Zmud is the impedance of the mud and ZF is the impedance of formation <NUM>. Imaginary parts of ZF and Zmud may be assumed to be mainly capacitive. Assuming this capacitance may be in parallel with the resistive portion, then ZBF may also be written as: <MAT> wherein RM is the mud resistance, RF is the resistance of formation <NUM>, CM is the mud capacitance, CF is the capacitance of formation <NUM>, j is the unit imaginary number, and ω is the angular frequency. Both the mud resistance and mud capacitance may increase as standoff increases and may decrease with the increase in effective area of injector electrode <NUM>. "Standoff' may be used to denote the distance of the pad <NUM> (e.g., Referring to <FIG>) from a wall of borehole <NUM> (e.g., referring to <FIG>). Standoff of each injector electrode <NUM> in button array <NUM> may vary. In examples, standoffs of return electrode <NUM> may differ from those of injector electrodes <NUM> as well. Standoff variations may significantly affect button-to-formation impedance value 500E. In the simplified circuit model, it may be assumed that the standoff of each component of pad <NUM> may be constant. Standoff may assume that pad <NUM> is movable while downhole tool <NUM> remains immobile. In examples, to achieve large distances from the wall of borehole <NUM>, downhole tool <NUM> may be moved along with pad <NUM>. In examples, the term "eccentricity" may be used instead of "standoff'. The proposed methods (discussed further below) may be equally valid whether pad <NUM> moves or both pad <NUM> and downhole tool <NUM> move.

<FIG> shows a cross-sectional view of pad <NUM> disposed on bottom hole assembly <NUM> (e.g., referring to <FIG>). As illustrated, injector electrode <NUM> and guard electrode <NUM> illustrated electric-current-density lines <NUM>. Electric-current-density lines <NUM> emanate from injector electrode <NUM> and guard electrode <NUM> into formation <NUM> while remaining parallel in the region close to injector electrode <NUM>, which is further identified in area <NUM>. Near the edges of guard electrode <NUM>, electric-current-density lines <NUM> may diverge, as illustrated in area <NUM>. The accuracy of the resistivity measurement and the ability to operate without significant sensitivity to standoff is dependent upon maintaining electric-current-density lines <NUM> that are parallel, as show in area <NUM>. When the standoff distance becomes large enough, electric-current-density lines <NUM> inside of area <NUM> will become non-parallel, and the resistivity measurement will become sensitive to standoff.

With continued reference to <FIG>, a power source drives a voltage between the return electrode <NUM> and the other electrodes and a circuit is designed to keep Vprobee equal to Vfocus for focusing. The current transmitted from the button electrode is measured, for example through the use of a toroid. The apparent formation resistivity Ra may be determined in accordance with ohm's law: <MAT> where k is a calibration constant, V is the magnitude of the power source and I is the in-phase magnitude of the current flow from the measurement electrode. It should be recognized that the apparent formation resistivity given by equation (<NUM>) is only a first order approximation. Information from the mud cell may be used to further improve the accuracy of the measured apparent resistivity.

Mud cell provides measure of mud resistivity rM and capacity cM. When the impedance of the thin mud layer is included in the measurements by the sensing surface, we see that <MAT> where RF is the formation resistivity and RM is resistivity of mud layer. RM is proportional to the standoff(i.e., the thickness of the mud layer) and mud resistance and capacitance from mud cell measurement. <MAT> or <MAT>.

The apparent resistivity is function of frequency, conductivity and dielectric permittivity of the mud and the formation resistivity. It should be noted, for pad <NUM> disposed on bottom hole assembly <NUM> (e.g., referring to <FIG>) the dielectric permittivity of formation <NUM> (e.g., referring to <FIG>) is ignored in this example and may be corrected using higher order processing methods.

<FIG> illustrates a graph of measured impedance versus formation resistivity found using pad <NUM> (e.g., referring to <FIG> and <FIG>). Equation (<NUM>) may be used to obtain basic performance curves for downhole tool <NUM>. These basic performance curves may be fairly accurate in homogeneous formations <NUM> (e.g., referring to <FIG>) in determining the variation of the response of an exemplary injector electrode <NUM> in button array <NUM> with changing environmental parameters. In <FIG>, the real part of the measured impedance versus the formation resistivity may be determined using Equation (<NUM>), which is illustrated on graph <NUM> in <FIG>. The imaginary part of the impedance may be determined by the mud capacitance, therefore it may not be necessary to plot it. In an example, illustrated in <FIG>, it may be assumed that formation permittivity (εF) is <NUM>, mud permittivity (εM) is <NUM>, and mud resistivity (ρM) is <NUM>Ω-m. Results for three different frequencies (<NUM>, <NUM> and <NUM>) at two different standoffs (so=<NUM> and so=<NUM>), where (so) stands for standoff of the tool, may be displayed in <FIG>.

As illustrated in <FIG>, a separation between different standoffs at lower formation resistivities may be viewed. This effect may be more pronounced if the frequency is lower. At higher formation resistivities, the dielectric effect in formation <NUM> (e.g., referring to <FIG>) may cause a roll-off in measured impedance, as illustrated in <FIG>. Operating in a linear region of the curve, displayed in <FIG>, may produce a more accurate correspondence between the impedance image and that of the true formation resistivity. The standoff effect at low formation resistivities may cause an ambiguity in the interpretation of the impedance images. These raw measurements may be used, but the contrast of the resistivity image may be reduced. Furthermore, small errors in standoff measurements may cause a large difference in the impedance reading. It may be observed from <FIG> that measured impedance may begin to decrease as the formation resistivity increases. This "rolloff" may be caused by the dielectric effects in the formation <NUM> (e.g., referring to <FIG>) and may become more pronounced at higher frequencies.

The graph in <FIG> illustrates that lower frequencies may be more suitable for measuring high formation resistivities while higher frequencies are more suitable to measure lower formation resistivities. For this reason, downhole tool <NUM>, which may be a downhole imaging too, such as an oil based mud imager or water based mud imager, may generally be implemented as multi-frequency tools. Multi-frequency measurements may also reduce uncertainty in resolving different mud and formation properties through an inversion process. Operational frequencies of downhole tool <NUM> (e.g., referring to <FIG> and <FIG>) may be adjustable through a central control unit and may be changed based on the specifications of the job.

<FIG> is a graph illustrating variation of the phase angle of the complex impedance of the downhole tool <NUM> (e.g., referring to <FIG>) versus frequency is shown for a frequency range of <NUM> to <NUM>. This model is obtained using the basic circuit model of downhole tool <NUM> outlined above. It may be seen that, in a typical operating range of downhole tool <NUM>, phase response increases monotonically and smoothly. This ideal model is obtained using a formation resistivity of <NUM>Ω-m and a relative permittivity of <NUM> and an oil based mud resistivity of <NUM>Ω-m and permittivity of <NUM>.

<FIG> shows an example of how phase angle measurements taken by downhole tool <NUM> (e.g., referring to <FIG>) may look like in a practical situation. <FIG> illustrates that a practical response deviates from an ideal response in the sense that multiple resonance frequencies are observed in the real measurements similar to what is shown in <FIG>. Furthermore, the response differs between different pads <NUM> (e.g., referring to <FIG>) while injector electrodes <NUM> (e.g., referring to <FIG>) on a single pad show frequency behavior that is essentially same. Thus, measurements were obtained using the average response of each pad <NUM>. Without limitation, described methods may be applicable when applied to individual measurements of each injector electrode <NUM>.

While a pad <NUM>, identified as pad <NUM> in <FIG>, may show a response akin to that of <FIG>, a second pad <NUM>, identified as pad <NUM>, may show a response akin to <FIG>. Comparing <FIG> shows that resonance frequencies are shifted between different pads <NUM>. Such effects are particularly pronounced if pads <NUM> are located on a different axial location on mandrel <NUM> (e.g., referring to <FIG>). This arrangement is common in practice in order to increase the coverage of downhole tool <NUM> (e.g., referring to <FIG>). In examples, downhole tool <NUM> may include two sets of <NUM> or <NUM> pads <NUM> each. Each pad <NUM> may be separated circumferentially while pads <NUM> of a first set and pads <NUM> of a second set are located at a rotated azimuthal angle with respect to the first set such that they provide azimuthal coverage in sections that are not covered by the first set. During measurement operations, it is undesirable to operate close to resonance frequencies, which may lead to measurements taken by downhole tool <NUM> to change sharply. As downhole tool <NUM> is lowered or pulled up in borehole <NUM> (e.g., referring to <FIG>), arms of downhole tool <NUM> continuously adjust to maximize contact between pad <NUM> and the wall of borehole <NUM>. Additionally, the centralization of downhole tool <NUM> also changes constantly. Pressure and temperature changes lead to variations in the response of downhole tool <NUM> as well. If downhole tool <NUM> is operating close to a resonance frequency, these changes lead to a much greater effect on measurements taken by downhole tool <NUM>. As a result, effective noise in the measurements increase and results degrade.

The primary reason for the occurrence of such a resonance may be the interaction between the pads <NUM> (e.g., referring to <FIG>) and mandrel <NUM> of downhole tool <NUM> (e.g., referring to <FIG>). This is confirmed through experimental observations. Large effects on tool performance were measured due to pad location with respect to other pads <NUM> as well as the positioning of pad <NUM> with respect to mandrel <NUM> (e.g., referring to <FIG>). Experiments in isolating pad <NUM> from mandrel <NUM> using mechanical and electronical means further confirmed occurrence of such a resonance is based on an interaction between pad <NUM> and mandrel <NUM> of downhole tool <NUM> because it decreased the resonance behavior of downhole tool <NUM>. Without limitation, mechanical isolation is intended to mean that the isolation is applied using a component that primarily serves a mechanical purpose. The intent of mechanical isolation for this matter is to block electrical coupling as well. As described below, several considerations have been taken to maximize isolation of pads <NUM> from the mandrel <NUM> of downhole tool <NUM>.

One technique for isolation may be to electrically isolate pad <NUM> from mandrel <NUM>(e.g., referring to <FIG>). The connection between pad <NUM> and mandrel <NUM> may be through any arm that connects pad <NUM> to mandrel <NUM>, for example, upper arm <NUM> and lower arm <NUM> (e.g., referring to <FIG>). In examples, upper arm <NUM> and lower arm <NUM> may be made of metal and therefore mandrel <NUM> and pad <NUM> are in electrical contact. To isolate these two parts, a break in the electrical contact may be introduced. An example of isolation is the use of an electrically non-conductive material at the contact point between on or more arms and pad <NUM>. Without limitation, non-conductive material may be disposed anywhere along the arms to interrupt the electrical contact between pad <NUM> and mandrel <NUM>. In examples, each arm that supports pad <NUM> may be made of an electrically non-conductive material as well.

<FIG> illustrates an example of a system for electrically isolating pad <NUM> from mandrel <NUM> with a single arm <NUM>. <FIG> illustrates another example of a system for electrically isolating pad <NUM> from mandrel <NUM> with an upper arm <NUM> and a lower arm <NUM>. As illustrated in <FIG>, a conductive path between pad <NUM> and mandrel <NUM> may traverse through single arm <NUM>, upper arm <NUM>, and lower arm <NUM>. Generally, single arm <NUM>, upper arm <NUM>, and lower arm <NUM> may be made of metal, which may act as a conductive path and may allow mandrel <NUM> and pad <NUM> to be in electrical contact. To electrically isolate mandrel <NUM> and pad <NUM>, a break in the electrical contact, the conductive path, may be introduced. For example, electrical isolation may be obtained utilizing an electrically non-conductive material <NUM> such as a non-conductive ceramic or polyetheretherketone (PEEK). As illustrates electrically non-conductive material <NUM> isolates two points of contact between housing <NUM> and single arm <NUM>, upper arm <NUM>, or lower arm <NUM>. Electrically non-conductive material <NUM> may be a layer of non-conductive ceramic. Any suitable thickness of electrically non-conductive material <NUM> may be used, in examples, <NUM>/<NUM> of an inch (<NUM> millimeter) of electrically non-conductive material <NUM> may be used. Electrically non-conductive material <NUM> prevents metal to metal contact between housing <NUM> and single arm <NUM>, upper arm <NUM>, or lower arm <NUM>. A metal-to-metal contact may form a conductive path between housing <NUM> and mandrel <NUM> through single arm <NUM>, upper arm <NUM>, or lower arm <NUM>. Electrically non-conductive material <NUM> may break the conductive path, electrical contact, between housing <NUM> and mandrel <NUM> by preventing metal on metal contact. In examples, electrically non-conductive material <NUM> may also be disposed at any suitable location on single arm <NUM>, upper arm <NUM>, or lower arm <NUM> to interrupt the electrical contact between pad <NUM> and mandrel <NUM>. Still further, single arm <NUM>, upper arm <NUM>, or lower arm <NUM> may be made of an electrically non-conductive material. In examples with a single arm or more than two arms, any suitable combinations of mounting brackets, sections or arms or the entirety of arms may be made non-conductive to increase isolation.

In examples, to further electrically isolate pad <NUM> from mandrel <NUM>, electronic connections (i.e., wiring) between pad <NUM> and mandrel <NUM> may be isolated. Wiring that may connect button array <NUM> and return electrode <NUM> to downhole tool <NUM> (e.g., referring to <FIG>). In examples, information handling system <NUM> (e.g., referring to <FIG>) may be disposed in and/or about downhole tool <NUM>. Button array <NUM> and return electrode <NUM> may be connected to information handling system <NUM> through wiring. In examples, button array <NUM> and return electrode <NUM> may be connected to an information handling system <NUM> disposed on surface <NUM> (e.g., referring to <FIG>) through downhole tool <NUM> and conveyance <NUM> (e.g., referring to <FIG>). In examples, wiring may be disposed in insulated sheaths that may include ferrite material or isolation transformers may be disposed on the wiring to prevent current from moving between different components. Additionally, electrically isolating wiring disposed on pad <NUM> from mandrel <NUM> may be performed in a number of ways.

For example, connections on pad <NUM> may be identified as +V, having a positive voltage or -V, having a negative voltage. Positive voltage may be connected to individual injector electrodes <NUM> on button array <NUM> (e.g., referring to <FIG>). Negative voltage may be connected to return electrode <NUM> and ground. Ground may be defined as the support structure of housing <NUM>. In examples, to electrically isolate pad <NUM> from mandrel <NUM> none of the connections on pad <NUM> may be connected to mandrel <NUM> directly. Instead, the ground of housing <NUM> may be at least partially connected to main electronics, without limitation, information handling system <NUM>, disposed in downhole tool <NUM>.

In examples, main electronics disposed in downhole tool <NUM> (e.g., referring to <FIG>) may be grounded to a chassis (not illustrated) either in direct contact and/or direct wiring, such as a ground wire. The chassis may be a structure inside downhole tool <NUM> which may act as structural support and/or protective support to electronics disposed in downhole tool <NUM>. The chassis may then be grounded to mandrel <NUM> (e.g., referring to <FIG>). To overcome the non-conducting mud and provide a capacitive coupling to formation <NUM> (e.g., referring to <FIG>), high frequencies may be employed in downhole tool <NUM>. This implies during operations downhole tool <NUM> may maintain a high impedance between the pad ground and the main electronics ground at higher frequencies while the lower frequency signals such as the power coming through mandrel <NUM> to pad <NUM> may be unimpeded. To electrically isolate the ground of pad <NUM> (such as housing <NUM>) and the ground of mandrel <NUM> at a high frequency, an inductance sufficiently high to generate a k-Ohm range impedance at the frequency of operation may be placed in the line that connects the ground of pad <NUM> and the ground of the electronics disposed in downhole tool <NUM>. The values of the inductance to obtain such an impedance value are in the tens of micro henrys. As discussed in more detail below, to facilitate the further tuning of pads <NUM> to ensure common operating frequencies for different pads <NUM>, such inductances may be made variable.

With continued reference to <FIG>, an example to electrically isolate pad <NUM> from mandrel <NUM> (e.g., referring to <FIG>) may include identifying a common mode of the voltage measurement between injector electrode <NUM> and return electrode <NUM> (e.g., referring to <FIG>). Common mode is defined a voltage reference that is common for two measurement points whose differential voltage is calculated. Large variations of common mode voltage may occur in the measurement of the voltage between injector electrode <NUM> and return electrode <NUM>, which may make current measurements inaccurate. For example, magnitude of the common mode voltage may be <NUM> times or higher than the magnitude of the differential voltage being measured. This would mean approximately <NUM> additional bits that needs to be accounted for the dynamic range of the measurement. To avoid large values of common mode voltage one of the two voltages +V and -V may be connected to the ground of pad <NUM>, which may ensure that the common mode is limited. As discussed above, the isolation at high frequency between mandrel <NUM> and pad <NUM> may be obtained by introducing an impedance in the line that connects the grounds of pad <NUM> and the ground of electronics disposed in downhole tool <NUM>.

The purpose of the connections explained in <FIG> above avoid contact between pad <NUM> and mandrel <NUM> (e.g., referring to <FIG>). Variations on the connections explained above that accomplish the isolation may also be used. Even though the above mechanical and electrical steps may have been implemented, downhole tool <NUM> (e.g., referring to <FIG>) may still exhibit resonance issues, as there may be a limit to the isolation that may be achieved in such manner. For example, electrical, mechanical, cost, and design requirements may prevent an ideal response corresponding to the perfectly isolated case as shown in <FIG>.

In those instances, according to the invention it is desired to operate at a frequency or frequencies that are not the resonance frequencies. These frequencies exhibit a more stable performance of downhole tool <NUM> (e.g., referring to <FIG>) as mentioned above. Selection of the frequencies may be performed by, first, analyzing performance of downhole tool <NUM> versus frequency. For this, a frequency sweep is be performed. This frequency sweep may be done in a known, homogeneous formation with controlled standoff to minimize external effects which may create variations or noise in measurements. An ideal testing environment may be a large test tank filled with water, which may use a thin insulating tube that may separate downhole tool <NUM> from the fluid and mimic oil based mud or water based mud. However, performing the frequency sweep in such a controlled environment is not absolutely necessary. Resonance frequencies may also be identified, for example, downhole. In those instances, stationary measurements in a smooth zone such as a cased hole interval may provide the best data. The results of such frequency sweeps would be as shown in <FIG>. Once such plots are obtained for each pad <NUM> (or each injector electrode <NUM>, or any other desired operational group), it may be divided into frequency zones. For example, downhole tool <NUM> may operate at two frequencies, one lower frequency that may be less affected from the dielectric roll-off and one higher frequency that may be less affected by a standoff. Lower frequency zone may cover frequencies between <NUM>-<NUM> as an example while the higher frequency zone may cover between <NUM>-<NUM> as an example.

After determining frequencies for measurement operation, stable (non-resonant) frequencies are found within the desired zones for each pad <NUM> (e.g., referring to <FIG>). This may be performed by a visual inspection of an operator. Operator may select a frequency that is not close to a resonance frequency for every pad <NUM> for each of the predetermined frequency zones. As an example, for the examples shown in <FIG>, analyst may pick <NUM> as a relatively stable frequency for both pad <NUM> (e.g., referring to <FIG>) and pad <NUM> (e.g., referring to <FIG>) for the lower zone while <NUM> may be selected as the frequency for the upper zone. Downhole tool <NUM> may be programmed to perform the logging in these two frequencies and the image of the formation may be obtained.

In examples, frequency selection may be automated. Without limitation, a functional fit to the measurement data away from the resonance zones may be obtained for each pad <NUM> (e.g., referring to <FIG>). Such a function may be based on a predicted ideal response of downhole tool <NUM> (e.g., referring to <FIG>), for example based on a circuit based approach that was described above. Additionally, a polynomial fit may be applied. For example, a polynomial order that may take most actual variations in the tool response into account without overly fitting the data may be selected. Such a polynomial order may be between <NUM> and <NUM>. However, the actual order would be tool dependent and thus different orders may be more appropriate for different downhole tools <NUM>. Once a polynomial fit with the determined order is fitted to data, such as in a least squares method, an error between the fit and the measurement data may be calculated. It is expected that measurements from highly resonant frequencies may deviate more significantly from such a fit. Thus, errors may be sorted and a percentage of the points with a higher error (such as <NUM>%) may be excluded from a second polynomial fit. This second fit may fit the data that correspond to frequencies away from the resonances better. This approach may be repeated iteratively a number of times, such as <NUM> times, to find a better fit. Such a polynomial fit operation is computationally inexpensive so there should be no significant downside to increasing the number of iterations. However, results are expected to converge after a few iterations so the benefit of increasing the number of iterations is limited.

Additional examples may include manual intervention for the above processes. An operator may adjust the thresholds (i.e. percentage of the data excluded from fit at each iteration) and the polynomial order or the operator may manually select the data that should not be included in the fitting process. <FIG> shows an application of the described procedure to the response shown in <FIG>, using a polynomial order of <NUM>. As illustrated in the graph of <FIG>, a polynomial fit that is close to the ideal response is obtained.

Once the fit is obtained in the above manner, the frequency points that deviate significantly from the fit may be excluded from the fit process. For this, an absolute threshold may be used. For example, the frequencies that deviate <NUM> degrees from the fit may be deemed to be unstable. <FIG> shows the frequency points <NUM> obtained using this procedure.

Another example for the determination of the operating frequencies may use the approximate slope of the change of measurement phase with respect to frequency. Absolute value of the approximate slope for the frequency point Fj (Sj) may be calculated in an example implementation by: <MAT>.

Here, ∠Fj denotes the phase angle of the measurement at frequency Fj. For the frequencies at the edges, one sided approximation for slopes may be used based on the difference between the nearest frequency point and the edge frequency. In examples, all the slopes may be calculated using just the forward or backward slopes instead of the average of forward and backward slopes. Then, points with absolute approximate slopes larger than a threshold may be thrown out to get rid of frequencies close to resonance. Threshold may be determined using an average or median of the absolute value of slopes. As an example, when the procedure described here is applied to <FIG>, results shown in <FIG> may be obtained.

As illustrated in <FIG>, a small strip of frequencies around the resonance are illustrated where the response has minima <NUM> for reduced slopes. Such points may easily be eliminated using visual inspection or by discarding frequencies if the width of a frequency band with stable frequencies is too short.

In another example, the previous two methods may be combined; e.g. a frequency point that satisfies both the approximate slope criterion as well as the polynomial fit criterion may be returned. The result of such an approach is shown in <FIG>.

Once the stable frequencies (or frequency bands) are found for each of individual pad <NUM> (e.g., referring to <FIG>), final stable frequencies that are selected for every pad <NUM> may be found. In a district frequency sweep, this is just the frequencies that are selected to be stable for every pad <NUM>. Note that, in general pads' resonance frequencies were seen to be very similar unless they are separated axially. Since most tools in existence use two sets of pads <NUM> that are axially separated, in essence finding the final stable frequencies may be found by finding the intersection of these two separate set of pads <NUM>. Thus, frequency sweeps may be performed for just one pad <NUM> in a set of pads at the same axial location, or the average of the measurements of all the pads <NUM> in a pad set may be taken. This may be applied to all pads <NUM> or even all injector electrodes <NUM> (e.g., referring to <FIG> and <FIG>) of all pads <NUM> (as mentioned before) otherwise in exactly the same manner as described.

After the determination of the stable frequencies, a selection of the final operating frequencies may be made among them. This selection may be made manually or automatically. For example, in the above example with two given frequency bands, the stable frequency that is closest to the center of the band may be selected. In another example, a stable frequency that is the lowest among the possible frequencies may be selected for the lower (<NUM>-<NUM>) frequency band, while for the higher frequency band (<NUM>-<NUM>) the highest stable frequency in the band may be selected. In another example, a chosen frequency may be an input (for example, <NUM> for the lower band and <NUM> for the upper band) and the frequency that is the closest to this target among the stable frequencies may be selected. These approaches may easily be extended to downhole tool <NUM> (e.g., referring to <FIG>) that have more than two operating frequencies.

In examples, a common stable operating frequency may not be obtained between different pads <NUM> (or injector electrodes <NUM>). In examples, pads <NUM> may be modified to adjust their phase response behavior. This may be done, for example, through a variable inductor or capacitor connected to the circuitry that connects the pad electronics ground and the downhole tool electronics ground. Once the resonance behavior is modified for one or more pads <NUM>, the above steps may be repeated to find the stable operating frequencies.

Figure <NUM> shows workflow <NUM> for isolating pad <NUM> from mandrel <NUM> (e.g., referring to <FIG>). Workflow <NUM> may begin with block <NUM>. In block <NUM>, pad <NUM> and mandrel <NUM> are mechanically isolated from each other, as described above. After mechanically isolating pad <NUM> from mandrel <NUM>, there may still be resonance issues. In block <NUM>, a frequency sweep is performed on measurements from downhole tool <NUM> for each selected measurement unit. It should be noted that "measurement unit" is a general term that encompass all possible implementations, such as, measurements of individual injector electrodes <NUM>, average measurement of each injector electrode <NUM> on a pad <NUM> or the average measurement of each pad <NUM> for a set of pads <NUM> at the same axial location. In block <NUM>, non-resonant frequencies are determined for each measurement unit. Next, in block <NUM>, non-resonant frequencies common to every measurement unit are determined. In block <NUM> it is determined if a non-resonant frequency exist in each of the given frequency ranges. In block <NUM>, If a suitable frequency is not found, one or more of the pads <NUM> should be tuned to alter their resonance frequency. In examples, tuning would involve changing the tuning inductor of each pads <NUM> in a set of pads <NUM> in approximately the same amount while leaving other pads <NUM> in a second set of pads <NUM> that is axially displaced from the first set as is in a common two pad set configuration. Then blocks <NUM> to <NUM> are repeated. If a non-resonant frequency exists in each of the given frequency ranges in block <NUM>, then in block <NUM> an operating frequency is elected form among the stable frequencies for each frequency range.

In an alternate embodiment for selecting the common stable frequencies between different pads <NUM> (or another measurement unit), a cost function approach may be used. Cost function may be a weighted combination of a term based on the norm of the distance of a given frequency to the desired operating frequency plus a term quantifying the stability of the given frequency for each pad. This second term may be based on the norm of the error between the measured phase response and an approximation to the ideal phase response using a function fitting process as described above. Frequencies that minimize the cost function in given frequency bands may be selected as the operating frequencies.

In examples, additional mechanical isolation of pad <NUM> from mandrel <NUM> may be performed by utilizing insulation transformers for the connection between the pad electronics and tool electronics to further improve the electrical isolation of the tool. Additionally, ferrite sleeves or ferrite chokes may be wrapped around portions of mandrel <NUM> or the arms of pads <NUM> to further increase the isolation.

As described above, that the phase response of downhole tool <NUM> has been used as the indicator of the resonance throughout the disclosure. In examples, a frequency sweep of signals with similar information may also be used to determine resonance frequencies and apply the described method. For example, a sweep of the absolute value of the signal may be performed instead.

Response of downhole tool <NUM> may exhibit differences based on manufacturing tolerances, mandrel configuration etc. Thus, described technique may be applied to each manufactured tool separately and optimal frequencies unique to each downhole tool <NUM> may be determined. The systems and methods may include any of the various features for electrically isolating a pad from a mandrel using the systems and methods disclosed herein.

Although the present disclosure and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations may be made herein without departing from the spirit and scope of the disclosure as defined by the appended claims. The preceding description provides various examples of the systems and methods of use disclosed herein which may contain different method steps and alternative combinations of components. It should be understood that, although individual examples may be discussed herein, the present disclosure covers all combinations of the disclosed examples, including, without limitation, the different component combinations, method step combinations, and properties of the system. It should be understood that the compositions and methods are described in terms of "comprising," "containing," or "including" various components or steps, the compositions and methods can also "consist essentially of" or "consist of" the various components and steps. Moreover, the indefinite articles "a" or "an," as used in the claims, are defined herein to mean one or more than one of the element that it introduces.

For the sake of brevity, only certain ranges are explicitly disclosed herein. However, ranges from any lower limit may be combined with any upper limit to recite a range not explicitly recited, as well as, ranges from any lower limit may be combined with any other lower limit to recite a range not explicitly recited, in the same way, ranges from any upper limit may be combined with any other upper limit to recite a range not explicitly recited. Additionally, whenever a numerical range with a lower limit and an upper limit is disclosed, any number and any included range falling within the range are specifically disclosed. In particular, every range of values (of the form, "from about a to about b," or, equivalently, "from approximately a to b," or, equivalently, "from approximately a-b") disclosed herein is to be understood to set forth every number and range encompassed within the broader range of values even if not explicitly recited. Thus, every point or individual value may serve as its own lower or upper limit combined with any other point or individual value or any other lower or upper limit, to recite a range not explicitly recited.

Claim 1:
A method for identifying an operating frequency, comprising:
performing a frequency sweep (<NUM>) using one or more injector electrodes (<NUM>) disposed on a pad (<NUM>), wherein the pad is connected to a downhole tool (<NUM>);
recording one or more measurements from the frequency sweep;
characterized in that the method further comprises identifying one or more non-resonant frequencies (<NUM>) from the frequency sweep; and
selecting one or more operating frequencies (<NUM>) of the downhole tool based on the one or more non-resonant frequencies.