ELECTROMAGNETIC TOOLS

CROSS REFERENCE

[0001] This application claims the benefit of U.S. Provisional Application No. 62/093,377, entitled "SYSTEMS AND METHODS FOR ACQUIRING MEASUREMENTS USING ELECTROMAGNETIC TOOLS," filed December 17, 2014, the disclosure of which is hereby incorporated herein by reference.

FIELD OF THE DISCLOSURE

[0002] This disclosure generally relates to determining formation properties, and more particularly to systems and methods for acquiring measurements using electromagnetic tools.

BACKGROUND

[0003] Wells are often drilled into the ground to facilitate the extraction of a natural resource from a subsurface reservoir, to facilitate the injection of a fluid into the surface of a subsurface reservoir, or to facilitate the evaluation and monitoring of subsurface formations. The drilling process is sometimes referred to as borehole drilling, and the resulting borehole is often referred to as a "wellbore." Wells can be used to extract (produce) hydrocarbons, such as oil, natural gas, water, or the like.

[0004] Logging may be performed in wellbores to make, for example, formation evaluation measurements to infer properties of the formations (also referred to as "formation properties" or "formation parameters") surrounding the borehole and the fluids in the formations. Typical logging tools may include electromagnetic (resistivity) tools, nuclear tools, acoustic tools, and nuclear magnetic resonance (NMR) tools, though various other types of tools for evaluating formation properties are also available. Some logging tools are run into a wellbore on a wireline cable after the wellbore has been drilled. Although versions of such wireline tools may still be used extensively, as the demand for information while drilling a borehole continues to increase, measurement-while-drilling (MWD) tools and logging-while-drilling (LWD) tools continue to be developed. MWD tools can provide drilling parameter information, such as weight on the bit, torque, temperature, pressure, direction, and inclination. LWD tools can provide formation evaluation measurements, such as resistivity, porosity, NMR distributions, and so forth. MWD and LWD tools can have elements and characteristics common to wireline tools (e.g., transmitting antennas, receiving antennas, sensors, and so forth), but may be designed to endure and operate in a harsh drilling environment.

[0005] The measurements acquired using such tools, such as electromagnetic measurements, can be used to determine various formation properties such as subterranean formation resistivity (including horizontal resistivity (Rh) and vertical resistivity (Rv)), formation dip, azimuth, as well as detection of bed boundaries. Further, sometimes alone or in conjunction with other formation measurements (such as porosity), electromagnetic measurements can be used to indicate the presence of hydrocarbons in the formation. It may be appreciated that propagation measurement is one basic approach to derive formation resistivity from the behavior of an electromagnetic wave passing through rock. In some instances, an electromagnetic signal is generated by a transmitter (e.g., a transmitter antenna system of a tool), the signal passes through the surrounding formation, and the resulting electromagnetic signal is detected by receivers (e.g., receiver antenna systems of the tool). The resistivity of the formation can be determined from the signal's amplitude and phase-shift measured at the different receivers.

[0006] As noted above, tools may employ one or more antennas used for acquiring measurements. These antennas may each have various characteristics, including a quality factor (Q). The Q of an antenna can be a measure of the bandwidth of an antenna relative to the center frequency of the bandwidth. Antennas with a relatively high Q are narrowband, whereas antennas with a relatively low Q are wideband. The higher the value of Q, the more sensitive the input impedance is to small changes in frequency. In some instances, LWD tools have antennas that are operated at specific frequencies with resonant circuits which, when combined with the antenna impedance, operate at a relatively moderate to high Q (e.g., a Q between 20 and 30). During LWD operations, it is often desirable to maintain a relatively high current output to the antenna of the tool. The current output to the antenna is typically at its maximum at the resonant frequencies and, thus, it may be desirable to operate the antenna using a resonant frequency to maintain a high current output to the antenna. Unfortunately, as the environmental changes (e.g., the temperature and pressure in the wellbore changes), the resonant frequency of the antenna can change as well. For example, when the tool is operating in temperatures above 175°C for an extended period of time, insulating materials between a tool's housing and an antenna coil can create a change in the antenna's impedance, shifting the resonant frequency, and potentially reducing the performance of the antenna.

[0007] This background section is intended to introduce various embodiments and associated aspects of the subject matter described and/or claimed below. This discussion is believed to be helpful in providing background information to facilitate a better understanding of the various embodiments and aspects of the present disclosure. Accordingly, it should be understood that these statements are to be read in this light, not as admissions.

SUMMARY

[0008] Embodiments of the disclosure can include systems and methods for acquiring measurements using electromagnetic tools. In particular, in certain embodiments, systems and methods for determining formation properties using electromagnetic logging tools can be provided. In one embodiment, a method can include conducting a frequency sweep of a transmitter antenna system of an electromagnetic measurement tool. The frequency sweep may include operating the transmitter antenna system at different frequencies, and determining current levels corresponding to the different frequencies. The method further includes determining a first current level of the current levels that corresponds to a resonant frequency of the transmitter antenna system, determining a first frequency that corresponds to the first current level, and operating the transmitter antenna system at the first frequency to generate a formation signal that propagates through a formation.

[0009] In another embodiment, a non-transitory computer-readable storage medium may be provided that includes computer-executable instructions that are executable by processors to cause conducting a frequency sweep of a transmitter antenna system of an electromagnetic measurement tool. The frequency sweep may include operating the transmitter antenna system at different frequencies, and determining current levels corresponding to the different frequencies. The computer-executable instructions may be further executable by processors to cause determining a first current level of the current levels that corresponds to a resonant frequency of the transmitter antenna system, determining a first frequency that corresponds to the first current level, and operating the transmitter antenna system at the first frequency to generate a formation signal that propagates through a formation.

[0010] In yet another embodiment, a system may be provided that includes processors and memories storing computer-executable instructions that are executable by the processors to cause conducting a frequency sweep of a transmitter antenna system of an electromagnetic measurement tool. The frequency sweep may include operating the transmitter antenna system at different frequencies, and determining current levels corresponding to the different frequencies. The computer-executable instructions may be further executable by processors to cause determining a first current level of the current levels that corresponds to a resonant frequency of the transmitter antenna system, determining a first frequency that corresponds to the first current level, and operating the transmitter antenna system at the first frequency to generate a formation signal that propagates through a formation.

[0011] This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] FIG. 1 is a diagram that illustrates an example well site system in accordance with one or more embodiments of the disclosure.

[0013] FIG. 2 is a diagram that illustrates an example electromagnetic measurement logging tool in accordance with one or more embodiments of the disclosure.

[0014] FIG. 3A is a diagram that illustrates example components of an electromagnetic measurement logging tool in accordance with one or more embodiments of the disclosure.

[0015] FIG. 3B is a circuit diagram that illustrates example components of a transmitter antenna system in accordance with one or more embodiments of the disclosure.

[0016] FIG. 4 is a diagram that illustrates example components of a controller in accordance with one or more embodiments of the disclosure. [0017] FIG. 5 is a diagram that illustrates an example distributed circuit model in accordance with one or more embodiments of the disclosure.

[0018] FIGs. 6A-6C are example graphical plot diagrams that illustrate current-to-antenna versus frequency responses in accordance with one or more embodiments of the disclosure.

[0019] FIGs 7 A and 7B are example three-dimensional graphical mesh plots of attenuation and phase shift differences relative to that at a nominal frequency versus resistivity in accordance with one or more embodiments of the disclosure.

[0020] FIGs. 8A-9B are example graphical plots of phase shift and attenuation differences relative to that at a nominal frequency in accordance with one or more embodiments of the disclosure.

[0021] FIGs. 10A and 10B are example graphical plots of attenuation and phase shift differences at different frequencies relative to that at a nominal frequency versus measured depth in accordance with one or more embodiments of the disclosure.

[0022] FIGs. 11A-12B are example graphical plots of attenuation and phase shift differences at different frequencies relative to that at a nominal frequency in accordance with one or more embodiments of the disclosure.

[0023] FIG. 13 is a flowchart that illustrates an example method for determining formation properties using an electromagnetic measurement logging tool in accordance with one or more embodiments of the disclosure.

[0024] While the disclosure is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. The drawings may not be to scale. It should be understood, however, that the drawings and detailed description thereto are not intended to limit the disclosure to the particular form disclosed, but to the contrary, are intended to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present disclosure as defined by the appended claims.

DETAILED DESCRIPTION [0025] The present disclosure relates to systems and methods for acquiring measurements using electromagnetic tools. In one embodiment, a system and/or method for determining formation properties using electromagnetic logging tools can be provided. In some embodiments, one or more optimum frequencies for an antenna system are determined, and the antenna system is operated using one of the optimum frequencies. For example, a transmission tuning circuit (TX circuit) of an antenna system may be tuned to a specific impedance of an antenna coil and, as the impedance of the antenna coil changes (e.g., due to changes in environmental conditions, such as change in temperature and pressure), the frequency of the TX circuit can be shifted to account for impedance mismatch between the TX circuit and the antenna coil. In some embodiments, an optimum frequency (or frequencies) may correspond to a relatively high or maximum current output (e.g., a relatively high or maximum Q for the antenna coil). When the current output for an antenna may be at its maximum at the resonant frequency for the antenna, the one or more optimum frequencies may be at or near a resonant frequency for the antenna.

[0026] In some embodiments, one or more optimum frequencies are determined by a frequency sweep of the antenna system. For example, if a resonant frequency is expected to occur near a current operating frequency of about 1.85 MHz (megahertz), a frequency sweep may be performed across the frequency range of about 1.8-1.9 MHz in an effort to identify where the resonant frequency resides. If, for example, the resonant frequency resides at about 1.8652 MHz under a current set of operating conditions, and the sweep includes making 101 discrete current measurements at equal intervals across the frequency band (e.g., taking measurements at about 1.800 MHz, at about 1.801 MHz, and so forth to about 1.900 MHz), then, during the frequency sweep, the highest current measurement (e.g., corresponding to a relatively high or maximum current output, or Q, for the antenna coil) may be acquired during the operation of the antenna system at about 1.865 MHz. As a result, the frequency of about 1.865 MHz may be identified as an optimum frequency for the antenna coil under the current operating conditions, and the frequency of the TX circuit can be shifted to at or about 1.865 MHz. If the antenna system was previously operating at a different or non-optimal frequency (e.g., about 1.85 MHz), then the shift of the frequency of the TX circuit may increase the current output of the antenna coil, thereby improving the performance of the antenna system. [0027] In some instances, a change in the operating frequency of the antenna system can result in a change in the tool response. For example, similar signals having different frequencies may experience different attenuation and phase shifts despite the fact they pass through the same formation and are generated from the same antenna. In some embodiments, measurement corrections are applied to account for the difference in measurements at the different frequencies. For example, a look-up table may be generated that includes a series of adjusted measurement values across a range of operating frequencies. Upon acquiring a measurement at a given operating frequency, a look-up may be performed (e.g., using the look-up table) to determine the measurement's value for the operating frequency.

[0028] Although certain embodiments are described with regard to a propagation-type tool for the purpose of illustration, it will be appreciated that similar embodiments may be employed with any suitable type of tool, such as an induction-type tool or other types of electromagnetic tools.

[0029] FIG. 1 is a diagram that illustrates an example well site system 10 in accordance with one or more embodiments of the disclosure. Such a well site system 10 can be deployed in either onshore or offshore applications. In this type of system, a borehole (also referred to as a "wellbore") 11 may be formed in subsurface formations by rotary drilling. Some embodiments can also use directional drilling.

[0030] A drill string 12 may be suspended within the borehole 11 and may have a bottom hole assembly (BHA) 100 which includes a drill bit 105 at its lower end. The surface system may include a platform and derrick assembly positioned over the borehole 1 1, with the assembly including a rotary table 16, a kelly 17, a hook 18, and a rotary swivel 19. In a drilling operation, the drill string 12 may be rotated by the rotary table 16, which may engage the kelly 17 at the upper end of the drill string. The drill string 12 may be suspended from a hook 18, attached to a traveling block, through the kelly 17 and the rotary swivel 19 which may permit rotation of the drill string 12 relative to the hook 18. In other embodiments, a top drive system may be used.

[0031] Drilling fluid or mud 26 may be stored in a pit 27 formed at the well site. A pump 29 may deliver the drilling fluid 26 to the interior of the drill string 12 via a port in the rotary swivel 19, which may cause the drilling fluid 26 to flow downwardly through the drill string 12, as indicated by the directional arrow 8 in FIG. 1. The drilling fluid 26 may exit the drill string 12 via ports in the drill bit 105, and may then circulate upwardly through the annulus region between the outside of the drill string 12 and the wall of the borehole 1 1, as indicated by the directional arrows 9. In this manner, the drilling fluid 26 may lubricate the drill bit 105 and carry formation cuttings up to the surface as it is returned to the pit 27 for recirculation.

[0032] The drill string 12 may include a BHA 100. In the illustrated embodiment, the BHA 100 may be shown as having one MWD module 130 and multiple LWD modules 120 depicting a second LWD module 120). As used herein, the term "module" as applied to MWD and LWD devices is understood to mean either a single tool or a suite of multiple tools contained in a single modular device. Additionally, the BHA 100 may include a rotary steerable system (RSS), a motor 150, and the drill bit 105.

[0033] The LWD modules 120 may be housed in a drill collar and may include one or more types of logging tools. The LWD modules 120 may further include capabilities for measuring, processing, and storing information, as well as for communicating with the surface equipment. By way of example, the LWD module 120 may include an electromagnetic logging tool. In accordance with various embodiments, the electromagnetic logging tool may include transmitter and receiver antennas for transmission and/or acquisition of electromagnetic measurements.

[0034] The MWD module 130 may also be housed in a drill collar, and can contain one or more devices for measuring characteristics of the drill string 12 and drill bit 105. The MWD module 130 can include one or more weight-on-bit measuring devices, a torque measuring device, a vibration measuring device, a shock measuring device, a stick/slip measuring device, a direction measuring device, and/or an inclination measuring device (the latter two sometimes being referred to collectively as a D&I package). The MWD module 130 may further include an apparatus for generating electrical power for the downhole system. For instance, power generated by the MWD module 130 may be used to power the MWD module 130 and the LWD module(s) 120. In some embodiments, this apparatus may include a mud turbine generator powered by the flow of the drilling fluid 26. It is understood, however, that other power and/or battery systems may be employed. [0035] The operation of the well site system 10 of FIG. 1 may be controlled using a control system 152 located at the surface. The control system 152 may include one or more processor- based computing systems. In the present context, a processor may include a microprocessor, programmable logic devices (PLDs), field-gate programmable arrays (FGPAs), application- specific integrated circuits (ASICs), system-on-a-chip processors (SoCs), or any other suitable integrated circuit capable of executing encoded instructions stored, for example, on tangible computer-readable media (e.g., read-only memory, random access memory, a hard drive, optical disk, flash memory, etc.). Such instructions may correspond to, for instance, workflows and the like for carrying out a drilling operation, algorithms and routines for processing data received at the surface from the BHA 100 (e.g., as part of an inversion to obtain one or more desired formation parameters), and so forth.

[0036] FIG. 2 is a diagram that illustrates an example electromagnetic measurement logging tool (also referred to as a "tool") 200 in accordance with one or more embodiments. The tool 200 may be part of one of the LWD modules 120 of FIG. 1. The tool 200 may be a multi-spacing non-directional electromagnetic propagation or induction tool. In one embodiment, the tool 200 may be capable of facilitating measurements at multiple frequencies, such as at approximately 400 kHz, and approximately 2 MHz. The tool 200 may include an array of antennas, including multiple transmitter antenna systems (T) 202 (e.g., first, second, third, fourth and fifth transmitter antenna systems Tl, T2, T3, T4, T5, respectively) and multiple receiver antenna systems (R) 204 (e.g., first and second receiver antenna systems Rl and R2, respectively), spaced axially along a tool body 208. The multiple transmitter antenna systems Tl, T2, T3, T4, and T5 may be spaced at distances of LI, L2, L3, L4, and L5, respectively, from a measurement point. Additionally, the multiple receiver antenna systems Rl and R2 may each be spaced at a distance of L6 away from the measurement point. In certain implementations, such as when the toll is exposed to harsh drilling environments and an approximately 6.75" drill collar is used, LI may be approximately 16 inches, L2 may be approximately 22 inches, L3 may be approximately 28 inches, L4 may be approximately 34 inches, L5 may be approximately 40 inches, and L6 may be approximately 3 inches. It will be appreciated, however, that various distances are also possible with respect to LI, L2, L3, L4, L5, and L6. In one example embodiment, the tool 200 may be capable of generating approximately 20 measurement channels, including two measurements (e.g., attenuation and phase shift measurements) for five spacings (e.g., each of L1-L5 of the five transmitters T1-T5) at two frequencies (e.g., at approximately 400 kHz, and approximately 2 MHz).

[0037] In certain implementations, some or all of the transmitter antenna systems 202 (e.g., transmitter antenna systems T1-T5) and receiver antenna systems 204 (e.g., receiver antenna systems Rl and R2) of the tool 200 may include axial antennas. As used herein, an axial antenna may be an antenna associated with a dipole moment substantially parallel with the longitudinal axis of the tool 200. An axial antenna may include an antenna coil wound about the circumference of the tool 200 such that the plane of the antenna is orthogonal to the tool axis. In some embodiments, the antenna coil is embedded in composite material located between an outer shield and a collar recess of the tool 200. An axial antenna may produce a radiation pattern equivalent to a dipole along the axis of the tool 200 (by convention the z-direction). As discussed above, electromagnetic measurements determined by axially oriented antennas may be referred to as "conventional" or "non-directional measurements."

[0038] In some embodiments, the tool 200 may lack tilted or transverse antennas, and thus, may not be designed to provide directional measurements. Accordingly, with respect to electromagnetic resistivity measurements, the tool 200 may be configured to provide non- directional resistivity responses. In some embodiments, the tool 200 may include one or more directional antennas. For instance, the tool 200 may include tilted receiver antennas and a transverse transmitter antenna, as well as several axial transmitter and receiver antennas and, thus, may be capable of acquiring both directional and non-directional resistivity measurements.

[0039] The tool 200 may be a model of a tool from Schlumberger Technology Corporation of Sugar Land, Texas. Examples of tools available from Schlumberger that are capable of making non-directional electromagnetic measurements may include those referred to by the trade names ARCVISION, CDR and ECOSCOPE. An example of a tool available from Schlumberger that is capable of acquiring both directional and non-directional resistivity measurements may include a tool referred to by the name of PERISCOPE (which may include tilted receiver antennas and a transverse transmitter antenna, as well as several axial transmitter and receiver antennas). It will be understood, however, that the embodiments disclosed herein are not limited to any particular electromagnetic logging tool configuration, and that the tool 200 depicted in FIG. 2 is merely one example of a suitable electromagnetic logging tool. Moreover, while the tool 200 is described with reference to FIGs. 1 and 2 as being used in an LWD context, it will be understood that the tool 200 may also be conveyed by other suitable means, such as wireline, slickline, coil tubing, wired drill pipe, and so forth.

[0040] FIG. 3A is a diagram that illustrates example components of an electromagnetic measurement logging tool 200 in accordance with one or more embodiments. As illustrated, the tool 200 may include one or more transmitter antenna systems 202 and/or one or more receiver antenna systems 204 communicatively coupled to a controller 300. Each of the one or more transmitter antenna systems 202 may include a voltage source 304, an amplifier 306, a tuning circuit 308, and/or an antenna coil 310. FIG. 3B is a circuit diagram that illustrates example components of a transmitter antenna system 202 in accordance with one or more embodiments. In the illustrated embodiment, the circuit diagram depicts a voltage source 304, an amplifier 306, a tuning circuit 308, and an antenna coil 310. The antenna coil 310 is represented by a resistive component (Rl), an inductive component (LI), and a capacitive component (CI). Ii and h represent the current being fed to the amplifier 306 and to the antenna coil 310, respectively. Ii or I ₂ may be the current to the antenna, and may be referred to as the "current input," the "current output," or, more generally, the "current" to the antenna coil). As described herein, the currents Ii and/or I ₂ may be monitored during a frequency sweep operation to identify one or more optimum operating frequencies (e.g., at or near the resonant frequency) for the transmitter antenna system 202.

[0041] In some embodiments, the controller 300 can be employed to control the operation of the antenna systems 202 and 204. The controller 300 may provide control commands that cause various components of the tool 200 (e.g., the one or more transmitter antenna systems 202 and/or the one or more receiver antenna systems 204) to perform the various operations described herein. For example, the controller 300 may command the tuning circuit 308 of the transmitter antenna systems 202 to operate at a given frequency to generate electromagnetic signals, and, in turn, the transmitter antenna systems 202 may operate at the given frequency to generate electromagnetic signals of the given frequency. The controller 300 may monitor the corresponding electromagnetic signals sensed by the one or more receiver antenna systems 204, and the controller 300 may monitor the current (e.g., the current to the antenna coil 310, the currents Ii and/or I ₂ ) used to operate the transmitter antenna systems 202 at the given frequency. Upon the controller 300 determining that the current to the antenna coil 310 has fallen by a threshold amount, for example, the controller 300 may conduct a frequency sweep to determine one or more optimum frequencies for the transmitter antenna system 202. The frequency sweep may include the controller 300 commanding the tuning circuit 308 of the transmitter antenna systems 202 to operate at a series of signals across a range of frequencies to generate electromagnetic signals across a range of frequencies, and, in turn, the transmitter antenna systems 202 may operate at the range of frequencies to generate electromagnetic signals across the range of frequencies. The controller 300 may monitor the current (e.g., the current to the antenna coil 310, the currents Ii and/or I ₂ ) used to operate the transmitter antenna systems 202 during the frequency sweep, and may identify a relatively high or maximum current to the antenna coil 310 during the frequency sweep and the corresponding frequency. The controller 300 may then command the transmitter antenna system 202 to use that frequency. The tuning circuit 308 may, in turn, shift the frequency to the transmitter antenna system 202 to that commanded by the controller 300, such that the transmitter antenna system 202 operates using this "optimum" frequency determined for the operational conditions. In some embodiments, the controller 300 may acquire measurements via the one or more receiver antenna systems 204 and determine resistivity measurements based on the acquired measurements.

[0042] In some embodiments, the controller 300 can be a processor-based system. FIG. 4 is a diagram that illustrates example components of a controller 300 in accordance with one or more embodiments. The controller 300 may include at least one processor 400 connected, by a bus 402, to volatile memory 404 (e.g., random-access memory) and/or non-volatile memory 406 (e.g., a flash memory and a read-only memory (ROM)). Coded application instructions 408 (e.g., software that may be executed by the processor 400 to enable the control and analysis functionality described herein) and data 410 (e.g., acquired measurements and/or the results of processing) may be stored in the non-volatile memory 406. For example, the coded application instructions 408 can be stored in a ROM, and the data can be stored in a flash memory. The coded application instructions 408 and the data 410 may also be loaded into the volatile memory 404 or a local memory 412 of the processor 400. The memories 404 and 406 may include one or more non-transitory computer-readable storage mediums having program instructions (e.g., coded application instructions 408) stored thereon that are executable by one or more processors (e.g., the processor 400) to cause various operations, including those described herein (e.g., including some or all of the operations of the method 1300 described in more detail below with regard to FIG. 13).

[0043] An input/output (I/O) interface 420 of the controller 300 may enable communication between the processor 400, the input devices 422, and the output devices 424. The I/O interface 420 can include any suitable device that enables such communication, such as a modem or a serial port. In some embodiments, the input devices 422 can include the one or more receiver antenna systems 204, a keyboard, a mouse, and/or the like. The output devices 424 can include the one or more transmitter antenna systems 202, displays, printers, and storage devices that allow output of data received or generated by the controller 300. The input devices 422 and the output devices 424 may be provided as part of the controller 300, although in other embodiments such devices may be separately provided.

[0044] The controller 300 can be provided as part of the control system 152 outside of the wellbore 11. In such embodiments, data collected by the tool 200 can be transmitted from the tool 200 in the wellbore 11 to the surface for analysis by the controller 300. In some other embodiments, the controller 300 is provided within a downhole tool in the wellbore 11, such as within the tool 200, or in another component of the BHA 100. This can enable operational processes to be performed within the wellbore 11. Further, the controller 300 may be a distributed system with some components located in a downhole tool and others provided elsewhere (e.g., at the surface of the wellsite). Whether provided within or outside the wellbore 11, the controller 300 may provide the operations of acquiring measurements using electromagnetic logging tools as described herein.

[0045] The tuning circuit of a transmitter antenna system may be sensitive to frequency change, while the formation may be much less sensitive to frequency change. To understand the effects of an antenna impedance change to a tuning circuit, it may be helpful to consider a distributed model of an antenna. FIG. 5 is a diagram that illustrates an example distributed circuit model 500 (e.g., of a transmitter antenna system 202) in accordance with one or more embodiments. The model 500 includes parallel resistance, capacitance, and inductance in series with AC (alternating current) resistance across the two ends of an antenna coil. At the two ends of the antenna coil, and the middle of the antenna coil, shunt resistance and capacitance are connected to ground to represent the effect of the material and metal surroundings (e.g., material of the collar and the shield of the tool). The antenna may be connected to a transmitter tuning circuit, which for the two operating frequencies in a tool (e.g., tool 200), may generate two resonant responses (e.g., at or near about 400 kHz and 2 MHz). Frequency dependent L (inductance) and C (capacitance) components are illustrated in the figure as well. In the illustrated embodiment, the circuit model 500 is based on use of the following parameters: parallel resistance Rt=100kQ, parallel capacitance Ct=26Pf, shunt resistance Rl=R2=R3=100kQ, and shunt capacitance Cg=86Pf.

[0046] In accordance with the above, the inductance of the modeled antenna may be represented by the following equation:

L = 4.25e · [f l{2.?>e ⁶ )Y ⁰⁵ +1 Of ⁹ (i), where L is the inductance at the frequency / The constants may correspond to a given configuration of the tool employing the modeled antenna. Further, the resistance of the modeled antenna may be represented by the following equation:

R=(f/(23e ⁶ )† ⁹⁵ +025 (2), where R is the AC resistance of the antenna at the frequency / Again, the constants may correspond to a given configuration of the tool employing the modeled antenna. Accordingly, the inductance (L) of the antenna may decrease slightly with an increase in frequency, and the AC resistance (R) of the antenna may increase with increased frequency.

[0047] As noted above, during LWD operations, it is often desirable to maintain a high current output to the antenna of a tool (e.g., maintain a high current output to the antenna coils 310 of the one or more transmitter antenna systems 202 of the tool 200). The current output to an antenna may be at its maximum at the resonant frequencies and, thus, it may be desirable to operate the antenna using the resonant frequency to maintain a high current output to the antenna. Unfortunately, as the environmental changes (e.g., the temperature and pressure in the wellbore changes), the resonant frequency of the antenna can change as well. For example, when the tool is operating in temperatures above 175°C for an extended period of time, insulating materials between a shield and an antenna coil can create a change in the antenna impedance, shifting the resonant frequency, and reducing the performance of the antenna. For example, when operating the antenna at about 2 MHz, the tuned impedance may double as a result of an increase in environmental temperature and pressure increase, indicating a drop in the current output to the antenna.

[0048] FIGs. 6A-6C are example graphical plot diagrams that illustrate current-to-antenna versus frequency responses in accordance with one or more embodiments. The plots illustrate the effect of changing Rt, Ct, R1-R3 and Cg of the above model antenna circuit in accordance with one or more embodiments. FIG. 6A is a plot diagram that illustrates current-to-antenna ("current") versus frequency responses for different resistances (Rt, where Rt=Rl=R2=R3) in accordance with one or more embodiments. The plot illustrates the effect that changing resistance has on the current to the antenna. In the plot, current curves 600a, 600b, 600c and 600d (solid lines) represent current-to-antenna (e.g., the amplitude of current (I)) versus frequency responses for the resistances (Rt) of lOOkQ, lOkQ, lkQ, and 100Ω, respectively. Phase curves 602a, 602b, 602c and 602d (dotted lines) represent the phase of the current (I) versus frequency responses for the resistances (Rt) of lOOkQ, lOkQ, lkQ, and 100Ω, respectively. As evidenced by the peaks of the curves, a first high Q response is observed at two operating frequencies, 400 kHz and 2 MHz. At 2 MHz, when the resistance (Rt) is decreased, the current (I) drops, and below lkQ, the change can be more than 10 dB. Notably, at 400 kHz, the current (I) is less affected. However, when operating at 2 MHz and a resistance (Rt) of only 100Ω, in some instances, the antenna may malfunction because the tuning circuit may not work with such a low current (I).

[0049] FIGs. 6B and 6C illustrate the effect that changing capacitance has on the current to the antenna. FIG. 6B illustrates the effect that changing parallel capacitance has on the current to the antenna. FIG. 6C illustrates the effect that changing shunt capacitance has on the current to the antenna. FIG. 6B is an example graphical plot diagram that illustrates current-to-antenna ("current") versus frequency responses for different parallel capacitances (Ct) in accordance with one or more embodiments. In the plot, current curves 604a, 604b and 604c (solid lines) represent current-to-antenna (e.g., the amplitude of current (I)) versus frequency responses for the parallel capacitances (Ct) of 250 pf, 100 pf and 26 pf, respectively. Phase curves 606a, 606b and 606c (dotted lines) represent the phase of the current (I) versus frequency responses for the parallel capacitances (Ct) of 250 pf, 100 pf and 26 pf, respectively. As can be seen, a shift of the resonant frequency is observed at higher frequencies, including 2 MHz (as indicated by the peaks of the curves at or around 2 MHz shifting to the right (to a higher frequency) with lower parallel capacitance). A similar shift of the resonant frequency is not observed at lower frequencies, including 400 kHz (as indicated by the peaks of the curves at or around 400 kHz not shifting with different parallel capacitance).

[0050] FIG. 6C is an example graphical plot diagram that illustrates current-to-antenna versus frequency responses for different shunt capacitances (Cg) in accordance with one or more embodiments. In the plot, current curves 608a, 608b and 608c (solid lines) represent current-to- antenna (e.g., the amplitude of current (I)) versus frequency responses for the shunt capacitances (Cg) of 250 pf, 150 pf and 86 pf, respectively. Phase curves 610a, 610b and 610c (dotted lines) represent the phase of the current (I) versus frequency responses for the shunt capacitances (Cg) of 250 pf, 150 pf and 86 pf, respectively. As can be seen, a shift of the resonant frequency and magnitude is observed at higher frequencies, including 2 MHz (as indicated by the peaks of the curves at or around 2 MHz shifting to the right (to a higher frequency) and upward (to a higher amplitude) with lower parallel capacitance). A similar shift of the resonant frequency and magnitude is not observed at lower frequencies, including 400 kHz (as indicated by the peaks of the curves at or around 400 kHz not shifting with different shunt capacitance). Thus, in both cases of changing capacitance, the output current-to-antenna may be decreased to several dB depending on how much the environment changes (e.g., due to temperature changes, pressure changes, fluid invasion, component failure, and/or the like) causing the equivalent capacitance parameter drift in the modeled antenna.

[0051] As demonstrated above, the current-to-antenna versus frequency responses show a moderate Q characteristic at the two operating frequencies, 400 kHz and 2 MHz. The parameter drift from environmental changes (e.g., due to temperature changes, pressure changes, fluid invasion, component failure, and/or the like) in an antenna can cause variations in the magnitude of the current to the antenna. Further, shunt/parallel resistance may have strong effects on current output, and a reduced value below 10 kohm can show a loss of up to several dB, especially at about 2 MHz. Moreover, the capacitance can be changed, potentially reducing the current amplitude response at about 2 MHz by several decibels.

[0052] In some embodiments, the operating frequency of a transmitter antenna system 202 can be adjusted to account for shifts in the resonant frequency that may be caused, for example, by changes in the operating environment. In some embodiments, one or more optimum frequencies are determined by a frequency sweep of the transmitter antenna system 202. For example, if a resonant frequency is expected to occur somewhere around a frequency of about 1.85 MHz for the transmitter antenna system 202, a frequency sweep may be performed across a frequency range of about 1.8-1.9 MHz in an effort to identify where the resonant frequency resides for the transmitter antenna system 202 under the current operating conditions. If for example, the resonant frequency resides at about 1.865 MHz under the current set of operating conditions, and the sweep includes making 101 discrete current measurements (e.g., for Ii and/or I ₂ ) at equal intervals across the 1.8-1.9 MHz range (e.g., taking measurements at about 1.800 MHz, at about 1.801 MHz, and so forth to about 1.900 MHz), then, during the frequency sweep, the highest current measurement (e.g., corresponding to a relatively high or maximum current output (I), or Q, for the antenna coil 310) may be acquired during the operation of the transmitter antenna system 202 at about 1.865 MHz. As a result, the frequency of about 1.865 MHz may be identified as an optimum frequency for antenna coil 310 of the transmitter antenna system 202 under the current operating conditions, and the frequency of the tuning circuit 308 can be shifted to at or about 1.865 MHz. If the transmitter antenna system 202 was previously operated at a different or non-optimal frequency (e.g., 1.85 MHz), then the shift of the frequency of the tuning circuit 308 may increase the current output of the antenna coil 310, thereby improving the performance of the transmitter antenna system 202 and the tool 200 under the operating conditions. Such performance improvement may include improving the signal-to-noise-ratio (S R) for measurements acquired using the tool 200.

[0053] As discussed herein, the tool 200 may be used to acquire electromagnetic measurements that can be used to determine various formation properties, such as formation resistivity. In some embodiments, an electromagnetic signal is generated by firing of a transmitter antenna system 202 of the tool 200. The electromagnetic signal passes through the surrounding formation, and a corresponding electromagnetic signal is sensed by the two receiver antenna systems 204 of the tool 200. As the electromagnetic waves propagate through the formation, they are attenuated and delayed (phase shifted) by an amount dependent on the formation' s electromagnetic properties. The tool 200 may measure the ratio of the two receiver voltages (Vi and V ₂ ), called the attenuation 201og(|V2/Vi|), and the phase shift between Vi and V ₂ . The resistivity of the formation can be determined from the amplitude and phase-shift differences measured by the different receiver antenna systems 204. For example, the formation properties can be determined (e.g., by the controller 300) from a look-up table of formation resistivity (Rt) versus attenuation and phase shift and frequency.

[0054] In some instances, a change in the operating frequency of the transmitter antenna system 202 can result in a change in the response of the tool 200. For example, similar signals having different frequencies (e.g., 150 V signals having frequencies of about 1.85 MHz and about 1.865 MHz, respectively) may experience different attenuation and phase shifts despite the fact they pass through the same formation and are generated from the same antenna coil 310. In many instances, it is expected that the resonant frequency (and thus, an optimum frequency) will not shift a large amount and, thus, the sweep band can be relatively narrow (e.g., within +1-5% of the nominal frequency or the current operating frequency). For example, as described herein, the sweep band for a nominal frequency of about 1.85 MHz may be about 0.1 Mhz (e.g., from about 1.8 MHz to about 1.9 MHz). As described herein, in such a small band, the variation of attenuation and phase shift may be substantially linear such that the values can be determined to follow a line that extends between the values at each end of the sweep band. For example, the attenuation may be determined to vary linearly from a first attenuation value at about 1.8 MHz to a second attenuation value at about 1.9 MHz, across the frequency range of about 1.8 MHz to about 1.9 MHz. Similarly, the phase shift may be determined to vary linearly from a first phase shift value at about 1.8 MHz to a second phase shift value at about 1.9 MHz, across the range of about 1.8 MHz to about 1.9 MHz.

[0055] A simple dipole model for the voltage at a receiver loop antenna from a loop transmitter at a distance r is represented by the following:

V = ^ M _t M _r - (l - i - kr) - ^ (3), where k = wave number, and M _t and M _r are the magnetic moments from

the transmitter and receiver loop antennas. This may be true for zz coupling (e.g., where the antennas are oriented in the same direction). For a three antenna sonde with one transmitter and two receivers, pursuant to Equation (3), the attenuation and phase shift from the ratio of the two receiver voltages (V2/V1) can be obtained. The attenuation may be determined as follows:

Attenuation = 20 * log^ ^/V^ (4), where attenuation is in dB, and the phase shift is the angle between the two complex voltages in degrees.

[0056] In an example embodiment, assuming an operating frequency of about 1.865 MHz, to tune the circuit to achieve the maximum current output, the sweeping frequency range may be chosen from about 1.8 MHz to about 1.9 MHz. The measured attenuation and phase shift from different frequencies may be compared to the ones computed at the nominal frequency of about 1.85 MHz. Formation resistivity may vary from about 0.05 S/m to about 100 S/m, for a spacing of about 16" (e.g., for T3 with L3 of 16" as discussed with regard to FIG. 2). FIGs 7 A and 7B are example three-dimensional graphical mesh plots of attenuation and phase shift differences relative to that at a nominal frequency versus resistivity in accordance with one or more embodiments. FIG. 7 A illustrates phase correction spacing versus frequency and resistivity, and FIG. 7B illustrates attenuation correction spacing versus the same ranges of frequency and resistivity. As can be seen, at the nominal frequency (e.g., 1.85 MHz), the difference may be about 0, and for low resistivity formation, the phase shift may vary from about -4 to about 2 degrees, and the attenuation may vary from about -0.6 to about 0.3 dB. At higher formation resistivity, the difference may not be obvious. Notably, the attenuation appears to vary substantially linearly from a first attenuation value at about 1.8 MHz to a second attenuation value at about 1.9 MHz. Similarly, the phase shift appears to vary linearly from a first phase shift value at about 1.8 MHz to a second phase shift value at about 1.9 MHz.

[0057] Similar relationships can be found when considering additional factors, such as the borehole, mud, dielectric effect, anisotropic formations, and so forth. FIGs. 8A and 8B are example graphical plots of phase shift and attenuation differences relative to that at a nominal frequency (that considers the borehole and mud) in accordance with one or more embodiments. The plots correspond to a tool dimension (e.g., diameter) of about 6.75." a formation resistivity (Rt) of about 50 ohm.m, a mud resistivity (Rm) of about 0.2 ohm.m (conducting 5 S/m) and a borehole radius of about 7.5." As can be seen, the difference of attenuation and phase shift from that at the nominal frequency appears to be linear from about 1.8 MHz to about 1.9 MHz for the five different spacings of about 16," 22," 28," 34," and 40" (e.g., for transmitters Tl, T2, T3, T4 and T5, respectively).

[0058] FIGs. 9 A and 9B are example graphical plots of phase shift and attenuation differences relative to that at a nominal frequency (that considers a dielectric effect) in accordance with one or more embodiments. The plots correspond to a formation resistivity (Rt) of about 50 ohm.m, a mud resistivity (Rm) of about 0.2 ohm.m, a borehole radius of about 7.5," a dielectric constant or relative permittivity of about 400 for the formation only, and a dielectric constant or relative permittivity of about 195.6 for the mud. As can be seen, for high dielectric constant formation, the difference of attenuation and phase shift from nominal frequency still appears to be linear from about 1.8 MHz to about 1.9 MHz for the five different spacings of about 16," 22," 28," 34" and 40" (e.g., for transmitters Tl, T2, T3, T4 and T5, respectively).

[0059] FIGs. 10A and 10B are example graphical plots of the attenuation and phase shift differences at different frequencies relative to that at a nominal frequency versus the measured depth (feet) in accordance with one or more embodiments. The plots correspond to a layered medium with anisotropy, in which the conductivities for each layer are (in ohm/m)

From -∞ to -2.5 1 (Ch) 1 (Cv)

-2.5 to -1 le-3 le-3

-1 to 2.5 1 1

2.5 to 6 10 5

6 to co 1 1

[0060] From Taylor's expansion (as indicated in equation (5) below) it is known that f(x)-f(a) will be a linear function for x-a with the rate of f (a), when x is close to a. Further, the frequency range picked from about 1.8M Hz- 1.9 MHz can be compared to a larger range of about 1.3 MHz-2.3 MHz to see if the linearity is kept. FIGs 1 1 A, 1 IB, 12A and 12B are plots of phase shift and attenuation differences from relative to that at a nominal frequency (that considers a dielectric effect) in accordance with one or more embodiments. The solid lines are the computed values, and the dashed line is a straight line connecting the points at two end frequencies. For the smaller range of about 1.8-1.9 MHz (e.g., of FIGs. 11A and 11B), it is observed that the solid and dashed lines overlap each other indicating linearity in the computation of the difference. For the larger frequency range of about 1.3-2.3 MHz (e.g., of FIGs. 12A and 12B), the deviation of the solid line from the dashed line indicates non-linearity in the difference versus frequency.

[0061] In accordance with the present disclosure, an electromagnetic measurement logging tool 200 can be operated in a manner that helps to optimize the performance of the transmitter antenna systems 202, and the performance of the tool 200 overall, to obtain formation measurements that can be used to determine formation properties, such as formation resistivity. For example, with a tool 200 disposed in the borehole 11 during a drilling operation, a measurement cycle can be undertaken that incudes firing each of the transmitter antenna systems 202 individually, (e.g., firing transmitters Tl, T2, T3, T4, T5 in sequence, one after the other) to generate respective electromagnetic signals that propagate into the formation. The propagated signals that result from the firings of the transmitter antenna systems 202 may be sensed by the two receiver antenna systems 204, and the sensed signals can be used to determine various properties of the formation. For example, the measured attenuation and phase shift of the sensed signals can be used to determine the resistivity of the formation at or near the location of the tool 200 during the measurement cycle. This type of measurement cycle can be repeated with the tool 200 disposed in different locations within the borehole 11 (e.g., as the tool 200 is lowered down the borehole 11 during drilling operations) to collect measurements at various depths that can be used to determine various formation properties at the various depths, such as the formation resistivity at the various depths.

[0062] Firing a transmitter antenna system 202 can include driving (or "energizing") the antenna coil 310 the transmitter antenna system 202 with a signal (e.g., an electrical pulse) of a given voltage amplitude (e.g., 150 V) and frequency (e.g., about 1.85 MHz), also referred to as the "operating voltage" and the "operating frequency" of the transmitter antenna system 202. As described above, the current of the signal (also referred to as the "current-to-antenna") at a given operational voltage (VOP) and frequency (fop) may change based on the impedance of the transmitter antenna system 202, including the antenna coil 3 10. And, the impedance of the transmitter antenna system 202 may change as a result of changes in the environmental conditions, such as changes in temperature and pressure. Thus, the current of the signal used to drive an antenna coil 3 10 may change as a result of changes in the environmental conditions, such as changes in temperature and pressure. As discussed above, a change in the impedance of the transmitter antenna system 202 may result in a shift of the resonant frequency of the transmitter antenna system 202. Thus, if the operating frequency was set to an optimum frequency for the impedance of the transmitter antenna system 202 under a first set of operating conditions, but the operating conditions change such that the impedance of the transmitter antenna system 202 changes, then the resonant frequency of the transmitter antenna system 202 may shift such that the operating frequency is no longer an optimum frequency for the transmitter antenna system 202. Such a shift in the resonant frequency can be evidenced, for example, by a drop in the level of the current during subsequent firings of the transmitter antenna system 202.

[0063] In some embodiments, the level of the current of the signal used to drive an antenna coil 3 10 during firing operations is monitored to determine whether the current is changing in a manner that indicates a change in the impedance of the transmitter antenna system 202 and, thus, a shift of resonant frequency of the transmitter antenna system 202. For example, if the current drops a significant amount (e.g., there is a decrease in the current by at least a threshold amount between firings), it may be determined that the impedance of the transmitter antenna system 202 has changed and/or the resonant frequency of the transmitter antenna system 202 has shifted. In some embodiments, a decrease in the current value by at least a threshold amount can trigger an operating frequency adjustment process that includes, for example, identifying an "updated" optimum operating frequency for the transmitter antenna system 202 under the current conditions. The transmitter antenna system 202 may, then, be operated using that "updated" frequency. For example, in subsequent firing operations, the transmitter antenna system 202 may drive the antenna coil 3 10 with a signal having the "updated" optimum operating frequency. In some embodiments, the operating frequency adjustment process can be conducted in response to other triggers in place of, or in combination with, triggering based on a drop in the current. For example, a well operator may manually initiate the operating frequency adjustment process, the operating frequency adjustment process may be set to occur at regular time intervals (e.g., every minute, every ten minutes, hourly, every two hours, daily, and/or the like), the operating frequency adjustment process may be set to occur at regular distance intervals (e.g., every foot of drilling advancement, and/or the like), and/or the operating frequency adjustment process may be set to occur in response to a change in environmental conditions (e.g., in response to a change in temperature by a threshold amount, a change in pressure by a threshold amount, and/or the like).

[0064] In some embodiments, an operating frequency adjustment process for a transmitter antenna system 202 can include conducting a frequency sweep across a band of frequencies that is expected to include the resonant frequency for the transmitter antenna system 202 under the current operating conditions, determining an "updated" optimum operating frequency for the transmitter antenna system 202 under the current conditions, and subsequently operating the transmitter antenna system 202 using that frequency. In some embodiments, a frequency sweep may include identifying a frequency band that is, for example, about +1-5% of a nominal operating frequency, or the current operating frequency. The frequency sweep can also include operating the transmitter antenna system 202 at discrete test frequencies across the band (e.g., at 100 discrete frequencies equally spaced across the frequency band), and measuring the current of the signal used to drive an antenna coil 310 during the operation of the transmitter antenna system 202 at each of the respective test frequencies. Thus, for example, a set of current values may be collected, including a current value measured for each of the respective test frequencies (e.g., 100 current measurements, corresponding to each of the 100 discrete frequencies equally spaced across the frequency band).

[0065] In some embodiments, an operating frequency adjustment process for a transmitter antenna system 202 can include identifying the maximum current to the antenna coil 310 measured during the frequency sweep and/or identifying the corresponding frequency. For example, the maximum current value of the set of current values may be identified, and the frequency (e.g., about 1.865 MHz) corresponding to that current may be identified as well. This frequency may be identified as the optimum frequency for the frequency band, because the high current value may indicate that the frequency is at or near the resonant frequency of the transmitter antenna system 202 under the current conditions. The operating frequency adjustment process may further include setting this "updated" optimum frequency as the operating frequency for the transmitter antenna system 202, and subsequently operating the transmitter antenna system 202 using the frequency. For example, in the next measurement cycle, firing of the transmitter antenna system 202 may include driving the antenna coil 310 of the transmitter antenna system 202 with a signal (e.g., an electrical pulse) having a frequency (e.g., of about 1.865 MHz, the determined "updated" optimum frequency for the transmitter antenna system 202). The other characteristics of the signal, such as the voltage amplitude, may be the same or similar to that used in the prior measurement cycle(s) (e.g., the signal may have a voltage amplitude of 150 V and a frequency of about 1.865 MHz.

[0066] FIG. 13 is a flowchart that illustrates an example method 1300 for determining formation properties using an electromagnetic measurement logging tool in accordance with one or more embodiments. The method 1300 may generally include operating a tool using a first operating frequency (block 1302), determining that one or more operating frequency adjustment conditions exists (block 1304), conducting a frequency sweep (block 1306), determining a second operating frequency (block 1308), operating the tool using the second operating frequency to acquire measurements (block 1310), and determining one or more formation properties using the acquired measurements (block 1312). In some embodiments, some or all of the aspects of the method 1300 can be performed, or otherwise be controlled by, the controller 300 and/or the control system 152.

[0067] In some embodiments, operating the tool using a first operating frequency (block 1302) can include operating at least one of the transmitter antenna systems 202 of the tool 200 using a first operating frequency. For example, operating the tool using a first operating frequency may include firing a first transmitter antenna system 202 (Tl) at a frequency of about 1.850 MHz to generate an electromagnetic signal that propagates into the surrounding formation. The generated signal that propagates into the formation may be referred to as the "formation signal" for the firing of transmitter antenna system 202. Corresponding signals (e.g., attenuated and phase shifted as a result of propagation through the formation) may be sensed by the receiver antenna systems 204 (Rl and R2) and can be used (e.g., by the controller 300) to determine one or more formation measurements and/or one or more formation properties. [0068] Firing the first transmitter antenna system 202 (Tl) may include, for example, the voltage source 304 and amplifier 306 driving the antenna coil 310 of the first transmitter antenna system 202 (Tl) with a signal having a voltage amplitude of about 150V and a frequency of about 1.850 MHz. That is, firing the first transmitter antenna system 202 (Tl) may include operating the first transmitter antenna system 202 (Tl) using an operating voltage of about 150 V and an operating frequency of about 1.85 MHz. Such a firing operation may be performed for one or more measurement cycles. For example, the first transmitter antenna system 202 (Tl) can be fired during each measurement cycle of a set of consecutive measurement cycles. This type of measurement cycle can be repeated with the tool 200 disposed in different locations within the borehole 11 (e.g., as the tool 200 is lowered down the borehole 11 during drilling operations) to collect measurements at various depths that can be used to determine various formation properties at the various depths, such as the formation resistivity at the various depths.

[0069] In some embodiments, determining that an operating frequency adjustment condition exists (block 1304) can include determining that a resonant frequency for one or more transmitter antenna systems 202 has or may have changed, or that there may otherwise be a reason to check whether it would be desirable to operate one or more transmitter antenna systems 202 at a frequency that is different than their current operating frequencies. In some embodiments, determining that an operating frequency adjustment condition exists can include determining that a current-to-antenna for an antenna coil 310 has changed (e.g., dropped) by at least a threshold amount. For example, the current to the antenna coil 310 of the first transmitter antenna system 202 (Tl) may be monitored (e.g., by the controller 300) as the transmitter antenna system 202 is fired during measurement cycles, and if the amplifier current (figure 3B- 12 going into 306) drops by at least a threshold amount (e.g., from nominal operating of 40mA to a 30mA), then it may be determined that an operating frequency adjustment condition exists. That is, for example, if the current drops a significant amount (e.g., the current has dropped at least a threshold amount), it may be determined that the impedance of the transmitter antenna system 202 has changed and/or the resonant frequency of the transmitter antenna system 202 has shifted and, thus, it may be desirable to initiate an operating frequency adjustment process that can be used to determine an updated operating frequency that corresponds to the resonant frequency of the transmitter antenna system 202 under the current operating conditions. If, for example, a predetermined current threshold is about 10 mA (milliamp), and monitoring of the current to the antenna coil 310 of the first transmitter antenna system 202 (Tl) measures currents of about 50 mA, 49.5 mA, and 48.5 mA for first, second and third firings, respectively, of the transmitter antenna system 202, then it may be determined that an operating frequency adjustment condition does not exist after the second firing of the transmitter antenna system 202 (e.g., based on the current dropping only about 0.5 mA from the highest current value of 50 mA), but it may be determined that an operating frequency adjustment condition does exist after the third firing of the transmitter antenna system 202 (e.g., based on the current dropping approximately 1.5 mA from the highest current value of 50 mA).

[0070] In some embodiments, determining that an operating frequency adjustment condition exists can be based on manual user input, and/or one or more other triggering events. For example, it may be determined that an operating frequency adjustment condition does exist if a well operator selects to conduct an operating frequency adjustment process from an application running on the control system 152. Further, if, for example, the operating frequency adjustment process is set to occur at regular time intervals (e.g., every minute, every ten minutes, hourly, every two hours, daily, and/or the like), it may be determined that an operating frequency adjustment condition exists upon the passage of that period of time. That is, for example, if the operating frequency adjustment process is set to occur every ten minutes, then it may be determined that an operating frequency adjustment condition exists if more than ten minutes has elapsed since the last operating frequency adjustment operation. Further, if, for example, the operating frequency adjustment process is set to occur at regular distance intervals (e.g., every foot of drilling advancement, and/or the like), it may be determined that an operating frequency adjustment condition exists upon drilling a corresponding distance. That is, for example, if the operating frequency adjustment process is set to occur every one foot of drilling, then it may be determined that an operating frequency adjustment condition exists if drilling has advanced more than one foot since the last operating frequency adjustment operation. Further, if, for example, the operating frequency adjustment process is set to occur in response to a change in environmental conditions (e.g., in response to a change in temperature by a threshold amount, a change in pressure by a threshold amount, and/or the like), it may be determined that an operating frequency adjustment condition exists upon a corresponding change in the environmental conditions. That is, for example, if the operating frequency adjustment process is set to occur for every 10°C of temperature change, then it may be determined that an operating frequency adjustment condition exists if the temperature at or near the antenna coil 310 has changed more than 10°C since the last operating frequency adjustment operation.

[0071] In some embodiments, conducting a frequency sweep (block 1306) can include conducting a frequency sweep in response to determining that one or more operating frequency adjustment conditions exist. In some embodiments, a frequency sweep can include conducting a frequency sweep across a frequency band that is expected to include a resonant frequency for the transmitter antenna system 202 under the current operating conditions, and acquiring measurements of the current to the antenna coil 310 at each of the frequencies. In some embodiments, a frequency sweep may include identifying a frequency band that is, for example, about +1-5% of a nominal operating frequency, or the current operating frequency. The frequency sweep may include operating the transmitter antenna system 202 at discrete test frequencies across the identified frequency band (e.g., at 100 discrete frequencies equally spaced across the frequency band), and measuring the current of the signal used to drive an antenna coil 310 during the operation of the transmitter antenna system 202 at each of the respective test frequencies. Thus, for example, a set of current values may be collected, including a current value measured for each of the respective test frequencies (e.g., 100 current measurements, corresponding to each of the 100 discrete frequencies equally spaced across the frequency band).

[0072] If, for example, the current operational frequency of the first transmitter antenna system 202 (Tl) is about 1.85 MHz and a resonant frequency is expected to occur at or near the frequency of about 1.85 MHz, a frequency sweep may be conducted across the frequency range of about 1.8-1.9 MHz in an effort to identify the resonant frequency of the first transmitter antenna system 202 (Tl). Such a frequency sweep may include, for example, driving the antenna coil 310 of the first transmitter antenna system 202 (Tl) with signals of about 150 V amplitude, and having frequencies of about 1.800 MHz, at about 1.80 lMHz, and so forth to about 1.900 MHz in sequence. For example, the controller 300 may command or otherwise cause the TX tuning circuit 308 to drive the antenna coil 310 of the first transmitter antenna system 202 (Tl) with signals of about 150 V amplitude, and having frequencies of about 1.800 MHz, about 1.801 MHz, and so forth to about 1.900 MHz in sequence. Measurements may be taken (e.g., by the controller 300) of the current to the antenna coil 3 10 while the antenna coil 310 is being driven at each of the respective frequencies. Thus, for example, the frequency sweep may result in a total of 101 current measurements, one for each of about 1.800 MHz, about 1.801 MHz, and so forth to about 1.900 MHz. Each current measurement for a frequency may include, for example, a measurement of the current to the antenna coil 310 of the first transmitter antenna system 202 (Tl) resulting from driving the antenna coil 310 at the frequency and the operating voltage of about 150 V.

[0073] In some embodiments, determining a second operating frequency (block 1308) can include determining a frequency that corresponds to (e.g., is the same or similar to) the resonant frequency of the transmitter antenna system 202 under the current operating conditions. In some embodiments, determining a second operating frequency can include determining the frequency that corresponds to the highest current measured during the frequency sweep of the transmitter antenna system 202. If, for example, during the frequency sweep of the first transmitter antenna system 202 (Tl) performed across the frequency range of about 1.8-1.9 MHz, the highest current is measured for the approximate 1.865 MHz signal used to drive the antenna coil 310, then the frequency of about 1.865 MHz may be identified as the second operating frequency. The second operating frequency may be an optimum frequency for the antenna coil 310 under the current operating conditions. An optimum frequency may include a frequency of the frequency sweep that is closest to a resonant frequency in the range of the frequency sweep. If, for example, the antenna coil 310 includes actual resonant frequencies at about 400 kHz and 1.8652 MHz and the sweep of 101 equally spaced frequencies is performed across the frequency range of about 1.8- 1.9 MHz (e.g., having about 0.001 MHz frequency resolution), then the highest current of the frequency sweep may be measured at the frequency of about 1.865 MHz, and the frequency of about 1.865 MHz may be selected or otherwise referred to as the optimum frequency under the current operating conditions, despite the fact that it is not the same as the actual resonant frequency.

[0074] In some embodiments, operating the tool using the second operating frequency to acquire measurements (block 1310) can include operating the transmitter antenna system 202 of the tool 200 using the second operating frequency. If for example, the second operating frequency is determined to be about 1.865 MHz, then operating the tool using the second operating frequency may include driving the antenna coil 310 of the first transmitter antenna system 202 (Tl) with a signal having an amplitude of about 150 V and a frequency of about 1.865 MHz. For example, the controller 300 may command or otherwise cause the TX tuning circuit 308 to drive the antenna coil 310 of the first transmitter antenna system 202 (Tl) with a signal having an amplitude of about 150 V and a frequency of about 1.865 MHz. Such an operation may be performed for one or more measurement cycles. For example, the first transmitter antenna system 202 (Tl) can be fired using the second operating frequency of about 1.865 MHz during each measurement cycle of a set of consecutive measurement cycles. This may be performed as the tool 200 is moved in (e.g., lowered down) the borehole 11 to collect measurements (e.g., attenuation measurements and phase shift measurements) at various depths that can be used to determine various formation properties, such as the formation resistivity at the various depths. When the first transmitter antenna system 202 (Tl) is operated to generate a formation signal that propagates into the formation, the first receiver antenna system 204 (Rl) may sense a corresponding signal (e.g., one or more signals resulting from the formation signal propagating through the formation) that can be used (e.g., by the controller 300) to determine a first voltage amplitude (Vi) and a phase (θι) of the formation signal after it propagates through the formation and back to the first receiver antenna system 204 (Rl). The second receiver antenna system 204 (R2) may sense a corresponding signal (e.g., one or more signals resulting from the formation signal propagating through the formation) that can be used (e.g., by the controller 300) to determine a second voltage amplitude (V ₂ ) and a second phase (θ ₂ ) of the formation signal after it propagates through the formation and back to the second receiver antenna system 204 (R2).

[0075] In some embodiments, determining one or more formation properties using the acquired measurements (block 1312) can include determining formation resistivity using the measurements acquired during operation of the tool 200 at the second operating frequency. If, for example, the first transmitter antenna system 202 (Tl) is operated at the frequency of about 1.865 MHz to generate a formation signal that propagates into the formation, and the first receiver antenna system 204 (Rl) senses a first corresponding signal having a first voltage amplitude (Vi) and a first phase (θι), and the second receiver antenna system 204 (R2) senses a second corresponding signal having a second voltage amplitude (V ₂ ) that is different from the first voltage amplitude (Vi) and a second phase (θ ₂ ) that is different from the first phase (θι), then a corresponding attenuation measurement and a corresponding phase shift measurement can be determined (e.g., by the controller 300) based on the voltage amplitudes and phases of the sensed signals. These values can be used (e.g., by the controller 300) to determine the formation resistivity at the location of the tool 200 in the borehole 11. If, for example, the attenuation between the first and second voltages (Vi and V ₂ ) is determined (e.g., by the controller 300) to be about -0.1 dB, then a look-up table (such as that illustrated by the mesh plot of FIG. 7B) that provides values for resistivity versus frequency and attenuation can be used (e.g., by the controller 300) to determine a resistivity of 50 ohms for an attenuation of about -0.1 dB and a frequency of about 1.865 MHz. If, for example, the phase shift between the first and second phases (θι and θ ₂ ) is determined (e.g., by the controller 300) to be about -0.04 degrees, then a look-up table (such as that illustrated by the mesh plot of FIG. 7A) that provides values for resistivity versus frequency and phase shift can be used (e.g., by the controller 300) to determine a resistivity of about 50 ohms for a phase shift of about -0.04 degrees and a frequency of about 1.865 MHz. Thus, for example, if the tool 200 is at a depth of 100 feet when the measurements are acquired via operating the first transmitter antenna system 202 (Tl) using the second operating frequency of about 1.865 MHz, then it can be determined (e.g., by the controller 300) that the formation has a resistivity of about 50 ohms at the depth of about 100 feet based on the determined attenuation of about -0.1 dB and/or the determined phase shift of about -0.04 degrees.

[0076] It will be appreciated that the method 1300 is an example embodiment of a method that may be employed in accordance with the techniques described herein. The method 1300 may be modified to facilitate variations of its implementation and use. The order of the method 1300 and the operations provided therein may be changed, and various elements may be added, reordered, combined, omitted, modified, etc. Portions of the method 1300 may be implemented in software, hardware, or a combination thereof. Some or all of the portions of the method 1300 may be implemented by one or more of the processors/modules/applications.

[0077] Although a single measurement sequence for a single transmitter antenna system 202 (Tl) is discussed for the purpose of illustration, similar techniques may be employed for one or more other transmitters of the tool 200. For example, some or all of the other transmitter antenna systems 202 used for acquiring measurements may be subjected to similar monitoring and operating frequency adjustment operations. Although the formation property of resistivity is discussed as being determined based on a single set of measurements of signals resulting from firing of a single transmitter antenna system 202 for the purpose of illustration, formation properties can be determined using any number of signals from one or more transmitter antenna systems. In some embodiments, the measurements acquired as result of multiple signals generated by one or more transmitters and/or multiple measurement cycles can be used to determine a formation property, such as resistivity. For example, the resistivity measurements acquired via multiple transmitter antenna systems 202 and/or multiple measurement cycles conducted with the tool 200 at a given depth in a wellbore 11 in a formation can be averaged to determine the resistivity of the formation at the depth.

[0078] Although the preceding description has been described herein with reference to particular means, materials and embodiments, it is not intended to be limited to the particulars disclosed herein; rather, it extends to all functionally equivalent structures, methods and uses, such as are within the scope of the appended claims. Further modifications and alternative embodiments of various aspects of the disclosure will be apparent to those skilled in the art in view of this description. Accordingly, this description is to be construed as illustrative only and is for the purpose of teaching those skilled in the art the general manner of carrying out the disclosure. It is to be understood that the forms of the disclosure shown and described herein are to be taken as examples of embodiments. Elements and materials may be substituted for those illustrated and described herein, parts and processes may be reversed or omitted, and certain features of the disclosure may be utilized independently, all as would be apparent to one skilled in the art after having the benefit of this description of the disclosure. Changes may be made in the elements described herein without departing from the spirit and scope of the disclosure as described in the following claims. Headings used herein are for organizational purposes only and are not meant to be used to limit the scope of the description.

[0079] As used throughout this application, the word "may" is used in a permissive sense (i.e., meaning having the potential to), rather than the mandatory sense (i.e., meaning must). The words "include," "including," and "includes" mean including, but not limited to. As used throughout this application, the singular forms "a", "an," and "the" include plural referents unless the content clearly indicates otherwise. Thus, for example, reference to "an element" may include a combination of two or more elements. As used throughout this application, the phrase "based on" does not limit the associated operation to being solely based on a particular item. Thus, for example, processing "based on" data A may include processing based at least in part on data A and based at least in part on data B unless the content clearly indicates otherwise. As used throughout this application, the term "from" does not limit the associated operation to being directly from. Thus, for example, receiving an item "from" an entity may include receiving an item directly from the entity or indirectly from the entity (e.g., via an intermediary entity). Unless specifically stated otherwise, as apparent from the discussion, it is appreciated that throughout this specification discussions utilizing terms such as "processing," "computing," "calculating," "determining," or the like refer to actions or processes of a specific apparatus, such as a special purpose computer or a similar special purpose electronic processing/computing device. In the context of this specification, a special purpose computer or a similar special purpose electronic processing/computing device is capable of manipulating or transforming signals, typically represented as physical electronic or magnetic quantities within memories, registers, or other information storage devices, transmission devices, or display devices of the special purpose computer or similar special purpose electronic processing/computing device.