Patent Description:
To locate and capture valuable hydrocarbons from subterranean formations, various wellsite tools may be used to perform various tasks, such as drilling a wellbore, performing downhole testing and producing downhole fluids. Downhole drilling tools may be advanced into the earth by a drill string with a bit at an end thereof to form the wellbore. Drilling muds (or other drilling fluids) may be pumped into the wellbore and through the drilling tool as it advances into the earth. The drilling muds may be used, for example, to remove cuttings, to cool the drill bit and/or to provide a coating along the wellbore. The drilling muds may be conductive or non-conductive drilling fluids (e.g., oil based muds (OBM), water based muds (WBM), etc.) During or after drilling, casing may be cemented into place to line a portion of the wellbore, and production tools may be used to draw the downhole fluids to the surface.

During wellsite activities, downhole measurements may be taken to collect information about downhole conditions. The downhole measurements may be taken of various wellsite parameters, such as temperature, pressure, permittivity, impedance, resistivity, gain factor, button standoff, etc. Downhole tools, such as the drilling tool, a testing tool, a production tool, or other tools, may be deployed into the wellbore to take the downhole measurements, such as formation resistivity. In some cases, downhole logs, images or other outputs may be generated from the downhole measurements.

However, the downhole measurement that is taken generally does not only characterize the formation : it is affected by the sensor itself but also by the drilling mud that is situated in the borehole, in particular when the tool is a LWD tool for which the distance between the sensor and the formation (ie standoff) is high. The tool performing the measurements therefore needs to be calibrated in order to have the measurement characterize at best the formation and eliminate influence of the other elements on the measurements.

Generally, the tools are calibrated at the workshop, and the calibration does not take into account the effect of the drilling fluid that is in the wellbore when the measurement is performed. However, when the drilling fluid is a non-conductive fluid such as oil-based mud, it has a very significant impact on the measurement and the accuracy of the measurement is greatly improved when the drilling fluid is taken into account in the calibration.

<CIT> discloses calibrating a tool used for a downhole measurement in-situ in the wellbore casing, before reaching an open hole portion of the borehole for a particular tool. This method is not appropriate for LWD tools. <CIT> discloses a method for correcting a measurement including the use of a test circuit generating a test signal that mimics the downhole environment. <CIT> discloses a method for calibrating an induction tool that takes place above the Earth's surface at different heights. <CIT> discloses a method for calibration of a measurement using a simulated measurement and calculating a calibration coefficient based on a comparison of actual and simulated measurements.

The invention resides in a method for calibrating a resistivity measurement taken by a downhole tool in a borehole as defined in claim <NUM>.

In a further aspect, the invention resides in a system for calibrating a resistivity measurement as defined in claim <NUM>.

<FIG> is a schematic diagram of a drilling system <NUM>, which may be used to drill a well or borehole through a geological formation <NUM>. In the depicted example, a drilling rig <NUM> at the surface <NUM> rotates a drill string <NUM>, which includes a drill bit <NUM> at its lower end to engage the sub-surface formation <NUM>. To cool and/or lubricate the drill bit <NUM>, a drilling fluid pump <NUM> may pump drilling fluid, referred to as "mud" or "drilling mud," downward through the center of the drill string <NUM> in the direction of the arrow <NUM> to the drill bit <NUM>. At the drill bit <NUM>, the drilling fluid may then exit the drill string <NUM> through ports. The drilling fluid may then flow in the direction of the arrows <NUM> through an annulus <NUM> between the drill string <NUM> and the geological formation <NUM> toward the surface <NUM>. In this manner, the drilling fluid may carry drill cuttings away from the bottom of a borehole <NUM>. Drill cuttings or "cuttings" include small pieces of rock or other debris that break away from the geological formation <NUM> as a result of drilling. Once at the surface <NUM>, the returned drilling fluid may be filtered and conveyed back to a mud pit <NUM> for reuse.

Additionally, as depicted, the lower end of the drill string <NUM> includes a bottom-hole assembly <NUM> that includes the drill bit <NUM> along with a downhole tool <NUM>, such as a measuring tool, a logging tool, or any combination thereof. Generally, the downhole tool <NUM> may facilitate determining characteristics of the surrounding formation <NUM>. Thus, in some embodiments, downhole tool <NUM> may include one or more sensors <NUM>. Further references to the sensor <NUM> may refer to one or more sensors <NUM> of the downhole tool <NUM>. In some embodiments, the sensor <NUM> may include an acoustic sensor (for instance, an ultrasonic pulse-echo transducer), which may perform acoustic measurements returned from the surrounding formation <NUM>. In some embodiments, the sensor <NUM> may include an electrical sensor (for instance, an electromagnetic transducer or receiver), which may perform electrical measurements (such as galvanic or inductive electrical measurement) returned from the surrounding formation <NUM>.

As shown on <FIG>, the borehole may be cased in its top portion <NUM>, ie a casing <NUM> has been added to surround the borehole and is attached to formation with cement (not shown) situated between the casing and the formation. The casing insulates the borehole from the formation and consolidates the borehole. In this portion of the borehole, the drilling fluid does not contact the formation. The casing is generally a metallic tubing. On the contrary, in its bottom portion <NUM>, the borehole is open hole, ie the drilling fluid circulating in the borehole directly contacts the formation. The measurements enabling to characterize the formation are generally taken in the open hole portion <NUM> of the borehole.

In some embodiments, a control system <NUM> may control operation of the downhole tool <NUM>. For example, the control system <NUM> may instruct the downhole tool <NUM> to perform measurements using the sensor <NUM> and/or process the measurements to determine characteristics of the surrounding environment (e.g., formation <NUM>). In some embodiments, the control system <NUM> may be included in the downhole tool <NUM>. In other embodiments, the control system <NUM> may be separate from the downhole tool <NUM>, for example, situated in another downhole tool or at the surface <NUM>. In other embodiments, a portion of the control system <NUM> may be included in the downhole tool <NUM> and another portion may be located separate from the downhole tool <NUM>.

When at least a portion is separate from the downhole tool <NUM>, information (e.g., measurements and/or determined characteristics) may be transmitted to and/or within the control system <NUM> for further processing, for example, via mud pulse telemetry system (not shown) and/or a wireless communication system (not shown). Accordingly, in some embodiments, the downhole tool <NUM> and/or the control system <NUM> may include wireless transceivers <NUM> to facilitate communicating information.

To facilitate controlling operation, the control system <NUM> may include one or more processors <NUM> and one or more memory devices <NUM>. Further references to "the processor <NUM>" are intended to include the one or more processors <NUM>. In some embodiments, the processor <NUM> may include one or more microprocessors, one or more application specific processors (ASICs), one or more field programmable logic arrays (FPGAs), or any combination thereof. Additionally, the memory <NUM> may be a tangible, non-transitory, machine-readable medium that stores instructions executable by and data to be processed by the processor <NUM>. Thus, in some embodiments, the memory <NUM> may include random access memory (RAM), read only memory (ROM), rewritable flash memory, hard drives, optical discs, and the like.

The downhole tool may comprise a sensor <NUM> shown in <FIG> used for measuring resistivity of the formation <NUM>. The sensor disclosed in the figure is exemplary. The sensor <NUM> comprises or is otherwise carried with a tool collar <NUM>. The tool collar <NUM> generally comprises a tubular member having interfaces (not shown) at one or both ends for coupling with other components of a tool string. The sensor <NUM> comprises a probe <NUM> having an exterior surface <NUM> that may be substantially flush with an exterior surface <NUM> of the tool collar <NUM>. For example, the probe <NUM> may be received within a recess or other opening <NUM> in the exterior surface <NUM> of the tool collar <NUM>. The probe <NUM> may be extendable away from the tool collar <NUM>, whether via known or future-developed means, for instance a wireline pad.

The probe <NUM> comprises a button electrode <NUM>, an inner or first guard electrode <NUM> surrounding the button electrode <NUM>, and an outer or second guard electrode <NUM> surrounding the inner guard electrode <NUM>. Insulating material <NUM> electrically isolates the button electrode <NUM>, the inner guard electrode <NUM>, and the outer guard electrode <NUM> from each other and from a body <NUM> of the probe <NUM>. The probe <NUM> also comprises one or more return electrodes <NUM>, which are each also isolated from the body <NUM> of the probe <NUM> by insulating material <NUM>. However, the return electrodes <NUM> may be formed by at least portions of the tool collar <NUM> instead of as discrete members carried by the probe <NUM>.

<FIG> also schematically depicts electrical components and connections between the elements described above. For example, one side of an excitation voltage source <NUM> is connected to one of the return electrodes <NUM> and local circuit ground, with the other side of the excitation voltage source <NUM> connected to the outer guard electrode <NUM>. The other one or more return electrodes <NUM> are also connected to local circuit ground. A sampling resistor <NUM> having resistance RBOG (first impedance) connects the button electrode <NUM> to the outer guard electrode <NUM>, and an additional resistor <NUM> having resistance RIGOG (second impedance) connects the inner guard electrode <NUM> to the outer guard electrode <NUM>. The sampling resistor <NUM> and the additional resistor <NUM> may be positioned in a housing <NUM>, such as may be delimited by the outer guard electrode <NUM>.

<FIG> also illustrates an acquisition board <NUM> disposed within the tool <NUM>. The housing <NUM> may contain the acquisition board <NUM>, may be coupled with the acquisition board <NUM>, or may be a distinct component separate from the acquisition board <NUM> but having one or more electronic components coupled with the acquisition board <NUM>, such as the sampling resistor <NUM> and/or the additional resistor <NUM>.

The sensor <NUM> shown in <FIG> may be used for measuring resistivity of the formation <NUM>. During such operations, an alternating current is applied between outer guard electrode <NUM> and a return electrode <NUM> via the voltage source <NUM>. The voltage may be a highfrequency voltage, such as a frequency higher than about <NUM>, or perhaps higher than one MHz, or even ten MHz. Then, the current circulating through the sampling resistor <NUM> is measured. On the basis of the measured current, an measured impedance Zf may be determined and related to the impedance Zform of the formation <NUM>.

The sensor <NUM> disclosed here is a sensor according to an embodiment of the disclosure. A sensor according to such embodiment is disclosed in more details in <CIT>. The tool according to the disclosure may also include other type of resistivity sensors. It is also understood that the downhole tool may also include a plurality of resistivity sensors <NUM>, wherein the sensors are identical or different.

When the measurement with sensor <NUM> is taken is the open hole portion of the borehole, it is considered that the response of the resistivity tool can be modelled by a complex equivalent circuit as illustrated in <FIG>. The complex equivalent circuit is formed as a first mud impedance Zmud1 coupled in series with a measured impedance Zf representative of the formation impedance Zform and coupled in parallel with a second mud impedance Zmud2, as illustrated by the equivalent circuit shown in <FIG>. The formation impedance Zform is determined based on the measured total impedance Zapp.

The circuit model illustrated in <FIG> comprises the impedance Zf, representative of the formation impedance Zform, and a first mud impedance Zmud1 in series, and also a parallel second mud impedance Zmud2. The enhanced circuit model effectively represents a current leakage that occurs as the standoff distance between electrodes of the resistivity tool and the subterranean formation increases - which is the case when the measurement is a LWD measurement taken while drilling. Some of the current paths measured by the resistivity tool are indeed not passing through the subterranean formation. They correspond to the electrical branch comprising the second mud impedance Z mud2. Other currents are passing through the formation and the drilling fluid, which correspond to the electrical branches comprising the measured impedance Zf and the first mud impedance Zmud1. This circuit model thus takes into account the standoff distance between the electrodes of the resistivity tool and the surrounding subterranean formation, which distance may not be accurately known and/or which may corrupt a resistivity estimate of the subterranean formation.

In order to calculate the formation impedance Zform in view of the measured impedance Zf the measurement is taken at a plurality of frequencies that are preferably spanning a large range of frequencies, such as for instance [<NUM>, <NUM>] megahertz ("MHz"). The method for determining the resistivity of the formation with a resistivity tool using such model is disclosed in more details in <CIT>. However, the method for determining the resistivity described herein is an exemplary method. The calibration method according to the disclosure may be applicable to any tool using an electrical model similar to the one disclosed above for determining resistivity of the formation.

As explained hereinabove, such measurement needs to be calibrated to eliminate the effect of the sensor on the measurement. Furthermore, the tool must be calibrated to be able to characterize the formation no matter what the type of drilling fluid (ie mud) circulating in the formation is. An in-situ calibration in the casing enables to increase the measurement accuracy as the tool may be calibrated in the same mud that will be circulating in the borehole while the measurement of the formation resistivity will be performed. As the method that is used and includes a plurality of frequencies spanning a broad range, the calibration shall as well take the mud dispersion, ie the frequency response of the mud impedance, into account. The mud impedance as a function of the frequency is expressed as follows: <MAT> wherein Zmud is the mud impedance, ω is the radial frequency, αXm is a complex number depending on the standoff and F(ω) is a frequency-dependent dispersion function. The calibration method discloses therein enables to calibrate automatically the measurements at all of the frequencies, taking into account the sensor and mud effects on the measurements.

The calibration method <NUM> not according to the invention will be disclosed in reference to <FIG>. It comprises taking (block <NUM>) a plurality of measurements in the borehole at a plurality of locations while the tool is lowered in the borehole. As indicated, the borehole has a top cased hole section <NUM> and a bottom open hole section <NUM> in which the drilling fluid directly contacts the formation. The circuit model modelling the tool response in the formation has been already explained. In the cased hole portion of the borehole however, the tool does not sense the formation but rather sense the casing that is very conductive due to its metallic composition. Therefore, the equivalent circuit comprises a first mud impedance Zmud1, and also a parallel second mud impedance Zmud2 as represented on the model of <FIG>. Some of the current paths measured by the resistivity tool are indeed not passing through the casing. They correspond to the electrical branch comprising the second mud impedance Z mud2. Other currents are passing through the casing and the drilling fluid, which correspond to the electrical branches comprising the first mud impedance Zmud1. The casing is considered as conductive enough to have no impedance contrary to the formation.

The calibration method then comprises representing all of the measured impedance in the complex plan (block <NUM>). Indeed, in view of the above-mentioned models, when the tool is in the cased hole portion of the borehole, as Zmud1 and Zmud2 are proportional to the mud impedance Zmud, the measured impedance linearly depends on the mud impedance. The measured impedance also depends on the standoff. On the contrary, when the measurements are taken in the formation, they do not anymore linearly depend on the mud impedance. Such representation in the complex plane is shown on <FIG>. The representation <NUM> in the complex plan shows the measurement point Z <NUM> in the complex plan. The real part Re(Z) of the measured impedance Z is shown on the ordinate axis <NUM> and the imaginary part Im(Z) of the impedance in abscissa <NUM>. The complex representation also enables to determine the module and phase of the impedance by tracing a line <NUM> between the measured impedance and the origin of the axis, the module |Z| being the distance between the measurement point and the origin while the phase is the angle θ between ordinate axis and line.

When representing all of the measured impedance in the complex plane, the calibrated measurements taken in the casing (taken first while the tool is lowered in the wellbore) will be approximately on a same line, with a same phase for each of the measured frequencies. The module of the measured impedance will also be dependent on the standoff. When the measurements are taken at several frequencies, the measurements at a first frequency may be represented separately from the measurements at a second frequency. In view of the above, when the measurements are taken at a plurality of frequencies, lines representing measurement at different frequencies may have the same slope.

The calibration method may then include building a statistical linear model representative of the measurement in casing based on a first set of measurements corresponding to the first measurements acquired in the borehole, for each of the frequency (block <NUM>). This may be performed via a classic linear regression. A representation of a plurality of measurements <NUM> taken in casing at one frequency are represented on <FIG>. It can be seen that the measurements perfectly fit the line <NUM>.

The calibration method may then include determining if each new measurement is taken in the casing (block <NUM>). When a new measurement is acquired, a criterion is assessed in order to determine if it can be taken into account to refine to linear model. The criterion may be that its distance from the resulting line is not greater than a threshold, or, taking into account several frequencies, that the difference between slopes of the lines representative of the measured resistivity at least at two different frequencies is not greater than a predetermined threshold. Of course, a combination of several criteria may be assessed. The beginning of the open hole section may also be identified based on the one or more criteria, i.e. when the one or more criteria are not met anymore. As it is well known that the cased hole and open hole portions of the borehole are not intricated and that the open hole section always follows the cased hole section, the open hole section may be detected via determining that a predetermined number of consecutive measurements do not match the one or more criteria relative to the predetermined linear model, as defined above.

The calibration method then includes selecting a calibration set of measurements (block <NUM>) upon determining that the open hole section <NUM> has begun. This is fairly simple as all the measurements before the open hole section may be taken into account as the calibration sample. Of course, in order to have a more robust set of measurement points, a number of measurement points just before the open hole section has been reached may be discarded.

Before performing the calibration, the method may include validating the calibration set (block <NUM>). This operation includes verifying that the set of measurements is representative of all of the conditions that may be found in a borehole, for instance a great diversity of standoffs. As it can be shown that the module of the measured impedance is dependent of the standoff measurement, a measured impedance representative of a minimal standoff (ie having a low module) may be compared to a measured impedance representative of a maximal standoff (ie having a high module). On <FIG>, the measured impedance that will serve as a basis for the validation are represented in <NUM> and <NUM>. They correspond for instance to the measurements having a module in the nth and (<NUM>-n)th quantile (with n being preferably less or equal to <NUM>). The verification includes comparing one or more variable representative of the difference between both impedance (using a difference or a ratio for instance) to one or more corresponding predetermined threshold. Each threshold may be a constant or may depend of one or more features of the line statistically representing the measurements in the complex plane. The comparison may include verifying that the standoffs are different enough and/or if the measurements have a sufficiently wide distribution to be greater than the error fit. Based on the result, the calibration set may be considered as valid for an accurate calibration or not. If the calibration is not validated, default calibration coefficients may be applied to the measurements (block <NUM>) and other calibration set may be looked for in the open hole section of the borehole (block <NUM>), as will be explained later in reference to <FIG>.

Alternatively, the calibration method not according to the invention may detect that the conditions for the standoff diversity of a calibration are met, define the calibration sample on this basis and verify afterwards that all of the measurements (or only the measurement of the set taken last) is still in the casing to validate the calibration sample.

Further, the method <NUM> is disclosed as performed in real-time. However, the method may be performed once the entire set of measurement for the borehole has been obtained, as post-processing, in which case the measurements may not be evaluated one after another.

The method not according to the invention therefore offers a calibration on the basis of a great number of measurements that is robust and without any need to trigger the measurement of well-chosen calibration points from the surface. When validating the measurement with additional criteria such as the standoff diversity, it enables to make sure that the calibration will be representative of all of the conditions that may be found in the borehole and therefore will enable accurate measurement.

Once the calibration sample has been validated, the method includes expressing (block <NUM>) the calibration parameters (also designated as the calibration coefficients). The calibration coefficients may be expressed as part of a linear model. Such coefficients will account for most of the effects due to the tool and the drilling fluid on the measurement. However, other type of model might be used, for instance polynomial models having a greater order than <NUM>. As an example, calibration coefficients may be expressed as follows: <MAT> wherein ZAPPa_CAL_Fb is the calibrated measurement (unknown) for the sensor a and frequency b (for a downhole tool having N sensors operating at M frequencies), ZAPPa_UNC_Fb is the uncalibrated measurement (known) for the sensor a and frequency b, and ga, b and ua, b are complex parameters that the calibration operation seeks to determine. It is important to note that ga,b and ua,b have different values for each of the N sensors and each of the M frequencies.

The method then includes determining (block <NUM>) the calibration coefficients ga, <NUM> and ua,<NUM> for measurements taken at a first reference frequency f1, which is a low frequency, i.e. a frequency under a threshold (about <NUM> for the sensor presented hereinabove but the threshold value may depend on architecture of the sensor). Frequency f1 is for instance the lowest measurement frequency. The details of operation <NUM> are represented on <FIG>. The method takes a first hypothesis, which is the following: the line statistically representing the measurements should, once calibrated, contain the origin of the axis (when there is no standoff, the tool is directly in contact with the casing and does not measure any impedance). A point on the line is therefore chosen as the point that should be the origin of the axis. Here, the selected point is the point <NUM> being at minimal distance i.e. the orthogonal projection from the origin of the axis but other points may be chosen. All the measurements of the sensor at frequencies <NUM>. M are calibrated as a function of the calibration hypothesis at the reference frequency f1. In other words, the method includes determining a first relationship between the calibration coefficients for the measurement at the first reference frequency by correlating a point taken on the statistical linear model with the origin of the complex plan (block <NUM>).

Determining the calibration coefficients ga, <NUM> and ua,<NUM> for measurements taken at the first reference frequency also includes comparing (block <NUM>) theoretical impedance in a non-dispersive reference medium, such as air, to uncalibrated measurement in this medium obtained with the sensor a and determining (block <NUM>) a second relationship between the calibration coefficients for the measurement at the first reference frequency based on such comparison. The uncalibrated measurement may have been taken before the job once and for all and may be re-used at each new calibration and/or may be modelled in view of the tool parameters. For low frequencies, it is indeed considered that the measurement is not significantly affected by the mud dispersion or sensor size and that the calibration coefficients are the same or proportional for the reference medium and mud. Determining the calibration coefficients for a low frequency then includes deriving (block <NUM>) from the first and second relationship both calibration coefficients ga,<NUM> and ua,<NUM>.

The determination <NUM> may be performed for all of the sensors that are situated in the borehole and have to be calibrated. Therefore, the output of the determination <NUM> may be all of the coefficients ga, <NUM> and ua, <NUM> with a= <NUM>.

The method may also include determining (block <NUM>) the calibration coefficients ga, <NUM> and ua, <NUM> for measurements taken at least a second frequency f2 lower than the predetermined threshold. The determination <NUM> may also be performed for all of the frequencies fj under the threshold.

The details of the operation <NUM> are represented on <FIG>. The method first comprises operations <NUM> and <NUM> already disclosed above, which will give a first relationship between the calibration coefficients ga, <NUM> and ua, <NUM>.

However, as all of the measurements must be calibrated as a function of the calibration at the reference frequency f1 in order to have coherent measurements, it is not possible to use the same operation that has been performed at <NUM>. It would indeed lead to a non-coherent calibration. Therefore the calibration coefficients ga, <NUM> and ua, <NUM> are determined using the calibration coefficients ga, <NUM> and ua, <NUM> obtained for the first reference frequency.

The method includes correlating (block <NUM>) uncalibrated measurements taken at the reference frequency f1 and uncalibrated measurement taken at second frequency f2. In view of the linear nature of the response, a relationship may be found between the uncalibrated measurement at both frequency, that is mathematically expressed as follows: <MAT> wherein ZAPPa_UNCAL_F2 Fb is the calibrated measurement (known) for the sensor a and frequency f2, ZAPPa_UNC_F1 is the uncalibrated measurement (known) for the sensor a and frequency f1, and pa21 and qa21 are complex parameters.

The method also includes correlating the calibrated measurements (block <NUM>) by expressing the impedance at the second frequency f2 as a function of the impedance of the first reference frequency f1. As the impedance measured at each frequency are both depending on the mud impedance, for each frequency j, the impedance may be expressed as follows: <MAT>, as indicated above, wherein ωj is the radial frequency (ωj = 2πfj), the impedance at frequency f2 may be expressed as follows: <MAT>.

This relationship includes one additional unknown parameter which is F(ω<NUM>). Indeed, F(ω<NUM>) is known from the previous computation from equation <MAT>. As frequency f1 is taken as the reference frequency, it is considered that |F(ω<NUM>)|=<NUM> and the phase of F(ω1) is related to the phase of ZAPPa_CAL_F1 as the term αXm only has an influence on the module of the impedance (as shown by the linear measurements). When the calibration includes the calibration of several sensors, it may be interesting to determine the dispersion function of the mud as a function of the different sensors. Indeed, the properties of the mud should be the same for all of the measurements. Therefore, the phase of F(ω<NUM>) may be defined as the average of the phases obtained at first frequency f1 for all of the calibrated sensors. This gives more robustness to the calibration.

The method then comprises determining a second and third relationship between the calibration coefficients ga,<NUM> and ua,<NUM> and F(ω2) based on the correlations of uncalibrated measurements performed at <NUM> and of the calibrated measurements performed at <NUM> (block <NUM>). This operation is performed first by determining the complex parameters pa21 and qa21 which is made possible by using a plurality of uncalibrated measurements taken in the casing, and then to determine a relationship between the coefficients ga,<NUM>, ua,<NUM> and F(ω2) based on pa21 and qa21 and ga,<NUM> and na,<NUM> using also the correlations (equations (<NUM>) and (<NUM>)) as well as the relationship for each frequency between calibrated and uncalibrated measurements (see equation (<NUM>) above).

Determining the calibration coefficients then includes deriving (block <NUM>) from the first, second and third relationships both calibration coefficients ga,<NUM> and ua,<NUM>.

The determination <NUM> may be performed for all of the sensors that are situated in the borehole and have to be calibrated. Therefore, the output of the determination <NUM> may be all of the coefficients ga,<NUM> and ua,<NUM> with a= <NUM>.

The method may also include determining (block <NUM>) the calibration coefficients ga,<NUM> and ua,b for measurements taken at least a third frequency f3 higher than the predetermined threshold. The determination <NUM> may also be performed for all of the frequencies fj above the threshold. This determination cannot use the measurement in non-dispersive medium to calibrate the measurement at high frequency as other parameters of the tool or the environment may have a higher influence at such frequencies. The details of such operation are shown on <FIG>.

The determination <NUM> first comprises modelling (block <NUM>) the mud dispersion function. The mud dispersion function may be modelled using any appropriate model.

The determination <NUM> then comprises determining (block <NUM>) the unknown parameters of the mud model using the pre-determined values of F(ω1) and F(ω<NUM>) and mud dispersion value for any other frequency below the predetermined frequency threshold defined above. As explained above for F(ω<NUM>), F(ω2) may be determined taking into account the values of the dispersion function obtained for several sensors. The method therefore includes obtaining (block <NUM>) a value of the function F(ω<NUM>) for the frequency f3 (it is reminded that ω<NUM> = <NUM>πf<NUM>). Of course, when the coefficients are sought for several frequencies above the threshold, operation <NUM>, <NUM> may be performed once and taken into account in the determination of the calibration coefficients for each frequency.

The determination also comprises correlating uncalibrated measurements taken at one of the frequencies for which the calibration has already been performed (f1 or f2) and uncalibrated measurement taken at frequency f3, as explained in relationship with operation <NUM>. Based on the measurement taken at frequency f1, the correlation may be expressed as follows: <MAT> wherein ZAPPa_UNCAL_F3 is the uncalibrated measurement (known) for the sensor a and frequency f3, ZAPPa_UNC_F1 is the uncalibrated measurement (known) for the sensor a and frequency f1, and p<NUM> and q<NUM> are complex parameters. It also comprises correlating calibrated measurements at frequency f3 and calibrated measurement taken at one of the frequencies for which the calibration has already been performed (f1 or f2), as explained in relationship with operation <NUM>. Based on the measurement taken at frequency f1, the correlation may be expressed as follows: <MAT> In view of the model previously determined F(ω<NUM>) is not an unknown parameter.

The method then comprises deriving the calibration coefficients ga,<NUM>, ua,b based on the correlations of calibrated measurements performed at <NUM> and of the uncalibrated measurements performed at <NUM> (block <NUM>). This operation is performed first by determining the complex parameters pa31 and qa31, and then by determining the coefficients ga,<NUM>, ua,<NUM> based on pa21 and qa21, F(ω<NUM>) and ga,<NUM> and ua,<NUM> using the correlations as well as the relationship for each frequency between calibrated and uncalibrated measurements (see equation (<NUM>) and (<NUM>) above).

Once the coefficients have been determined for each of the sensors and each of the frequency, the measurements taken in the formation may be corrected (block <NUM>) using the coefficients ga,b and u a,b that have been determined previously during the calibration. If a sensor a obtains a measurement Zmeas at a frequency fb, the measurement will be corrected using the coefficients ga,b and ua,b as follows in order to correct the measurement and then determining the resistivity of the formation based on such measurement : <MAT>.

The method that is presented above enables to calibrate automatically the sensor in the formation, taking into account the parameters of the borehole environment and without any previous operation or control from the operators at the surface.

Alternatively, it is also possible to calibrate the sensors when measurements are taken in a formation where at least two of the operating frequencies are mainly sensitive to the mud. This is possible for instance when a formation has a very low resistivity. Indeed, when the apparent resistivity is less than a threshold the apparent impedance still has a linear behavior, at least at the lowest frequencies. An exemplary method <NUM> for using the open hole section is disclosed in relationship with <FIG>.

The method <NUM> may include, if there is no casing or calibration cannot be performed based on the casing in view of the borehole or job parameters, measuring the resistivity Rt with an additional sensor (block <NUM>). Any known sensor and resistivity determination method may be used.

The formation resistivity Rt is then compared to a predetermined threshold (block <NUM>). The threshold is generally below <NUM> ohm. This operation enables indeed to identify a portion of the wellbore in which the measurement has a linear behavior, at least for frequencies below the threshold as defined above.

If the formation resistivity measured with the additional sensor is below the predetermined threshold, the calibration method may be performed for the whole set of measurements for which the condition is met. In other words, the calibration set is selected (block <NUM>) as per the condition of operation <NUM>. This operation then corresponds to operation <NUM> of method <NUM>. The method <NUM> may then comprise the operations <NUM>-<NUM> of method <NUM>.

Additional verification may be performed before launching the calibration. For instance, the method may also comprise representing in the complex plane the measured impedance over a depth interval corresponding to the interval at which resistivity is under the threshold. If the representation of the impedance measurements is linear over the interval, at least at two frequencies, the calibration method may be launched.

In this case, there are however a few changes. In particular, the method includes expressing the calibration parameters as in operation <NUM> but the expression is different compared to the one of method <NUM>. The expression indeed varies from when the calibration is performed in the casing as the model still has to take into account the formation resistivity. The calibrated measurement is expressed as follows:
<MAT>.

The calibration measurement may also be expressed as follows:
<MAT>.

Therefore, in this case, the measurement corresponding to mud impedance that enables to perform the calibration shall be expressed as:
<MAT>.

Wherein ZAPP_ MUD is the calibrated measurement accounting for the mud impedance (unknown), ZAPP_UNCAL is the uncalibrated measurement, g and u are calibration parameters, Rt is the formation resistivity (determined at operation <NUM>) and kf is a geometrical factor having a known value at low resistivity (its value may for example be determined by simulation or modelling).

More generally a method <NUM> according to the invention (shown on <FIG>) includes taking (block <NUM>) apparent impedance measurements with the sensor at a set of frequencies comprising at least one frequency and at a first plurality of locations in the borehole, wherein the measurement are uncalibrated measurements. The measurements may be taken at several frequencies and the method may be launched in real-time or after the measurements have been acquired for the whole borehole. The method includes identifying a portion of the borehole in which the apparent impedance measurements has a predetermined behavior at least at a first frequency (block <NUM>), wherein the predetermined behavior is that the apparent impedance measurements taken in the portion are substantially fitting a linear model when represented in the complex plane. The portion may be a cased hole portion or an open hole portion penetrating a formation having a resistivity below a predetermined threshold. In the latter case, identifying the portion may include estimating a formation resistivity based on measurements taken with one or more additional sensors and comparing the measured resistivity to the threshold. Alternatively, the method may include representing apparent impedance measurements taken at the at least one frequency in a complex plane, in particular the measurements taken at the second plurality of locations, and fitting a line to the plurality of measurements obtained at a second plurality of locations. Identifying the portion may include verifying that the standard deviation of the measurement points compared to the fitting line is under a threshold. When the set comprises a plurality of frequencies, identifying the portion may also include comparing the slope of a fitting line obtained for measurements taken at the first frequency to a fitting line obtained for measurements taken at a second frequency of the plurality. The measurements taken at the second plurality of locations is a calibration set, and the method includes validating the calibration set, by verifying if one or more criteria relative to the set are met. Such criteria may relate to the standoff, in order to verify that the standoffs are diverse and provide a robust calibration.

The method then includes using a plurality of measurements obtained at a second plurality of location situated in said portion at the first frequency to determine calibration coefficients for the measurements taken at the first frequency (block <NUM>). The second plurality of locations may be a subset of the first plurality of locations. The calibration coefficients may be defined as follows ZAPP_CAL_Fb = gb · ZAPP_UNC_Fb + ub, wherein ZAPP_CAL_Fb is a calibrated measurement at frequency fb, wherein ZAPP_UNC_Fb is the uncalibrated measurement at frequency fb and wherein gb and ub are the calibration coefficients for frequency fb. When the downhole tool comprises a plurality of sensors, the calibration coefficients are determined separately for each sensor.

Operation <NUM> may include selecting a predetermined point on the corresponding fitting line and calculating a first relationship between the calibration coefficients so that this point corresponds to the origin of the complex plane when the measurements are calibrated. It may also include determining a correlation between uncalibrated measurement and theoretical measurement in a non-dispersive medium (such as air) and calculating a second relationship between the calibration coefficients for the first frequency based on the correlation. The calibration coefficients may be determined based on the first and the second relationship. The first frequency is therefore below a first threshold, the threshold may be <NUM>.

When the method includes a plurality of frequencies, it may also include using the calibration coefficients for the measurements at the first frequency to determine the calibration coefficients for the measurements at a second frequency (block <NUM>). This operation may for instance include correlating uncalibrated measurements taken at the first frequency to uncalibrated measurements taken at the second frequency with the following expression: <MAT>.

The operation <NUM> may also include correlating calibrated measurements taken at the first frequency to calibrated measurements taken at the second frequency with the following expression: <MAT>
wherein ZAPP_CAL_F2 is a uncalibrated measurement taken at the second frequency, wherein ZAPP_CAL_F1 is a corresponding uncalibrated measurement taken at the first frequency, wherein ω<NUM> and ω<NUM> are the radial frequencies respectively corresponding to the first and second frequencies and wherein F(ω) is a dispersion function of a drilling fluid filling the borehole.

When the second frequency is below the predetermined threshold, the operation <NUM> may include determining a correlation between uncalibrated measurement and theoretical measurement in a non-dispersive medium and calculating a first relationship between the calibration coefficients based on the correlation, as well as determining a second and a third relationship between the calibration coefficients and the value F(ω2) of the dispersion function at the second frequency based on the correlation between uncalibrated measurements at first and second frequencies and correlation between calibrated measurements at first and second frequency, wherein the method includes determining the calibration coefficients and value F(ω2) of the dispersion function at the second frequency based on the first, second and third relationships.

Alternatively, the method may include, in particular when the second frequency is above the predetermined threshold, modelling the dispersion function F(ω) according to a predetermined model and determining parameters of the model for instance based on values of the dispersion function obtained at least at two reference frequencies (generally below the threshold). When the tool comprises several sensors at least a value of the dispersion function used in the modelling is a combination of the values obtained for each of the plurality of sensors. In this case determining a value of the dispersion function at said reference frequency is based on the uncalibrated measurements at said reference frequency and includes determining a correlation between uncalibrated measurement and theoretical measurement in a non-dispersive medium (as explained above). The calibration coefficients for the second frequency are then calculated based on the correlation of the between uncalibrated measurements at first and second frequency and correlation between calibrated measurements at first and second frequency.

The method may also include (block <NUM>) correcting the (uncalibrated) apparent impedance measurements using the calibration coefficients. The measurements taken at all of the plurality of locations in the borehole may be corrected using the coefficients determined as defined above. The resistivity of the formation is determined based on the corrected or calibrated measurements.

The method according to the disclosure is generally performed in a borehole containing oil-based mud and is particularly appropriate for a LWD tool for which the standoff with the borehole wall is more important. The method according to the disclosure provides an automated on-site calibration that does not require intervention of the operator before or during the measurement acquisition.

The disclosure also relates to an apparatus for calibrating a resistivity measurement, wherein the apparatus includes a downhole tool configured to be conveyed in a borehole, and having at least one sensor situated at a non-zero standoff distance from the borehole configured to estimate the resistivity of an underground formation penetrated by the borehole by taking apparent impedance measurements at a set of frequencies comprising at least one frequency at a first plurality of location in the borehole, wherein the measurement are uncalibrated measurements. The apparatus also includes a set of processors including one or more processors configured to identify a portion of the borehole in which the apparent impedance measurements at least at a first frequency of the set have a predetermined behavior, wherein the predetermined behavior is that the apparent impedance measurements at the at least one first frequency taken in the portion are substantially fitting a linear model when represented in the complex plane, and use a plurality of measurements obtained at a second plurality of location situated in said portion at the first frequency to determine calibration coefficients for the measurements taken at the first frequency.

The downhole tool may be a logging while drilling tools. It may also comprise several sensors. In the latter case, the set of processors is configured to determine calibration coefficients at the first frequency for each of the sensor. The sensor may be configured to take apparent impedance measurements at a plurality of frequencies. In the latter case, the set of processors may be configured to use the calibration coefficients for the measurements at the first frequency to determine the calibration coefficients for the measurements at a second frequency. The set of processors may be situated downhole, at the surface, remotely from the rig or partially downhole, and/or partially at the surface and/or partially remotely. They may be configured to execute one or more operations of the method as disclosed above.

The disclosure also relates to a computer readable storage medium comprising instructions to identify, based uncalibrated apparent impedance measurements at a set of frequencies comprising at least one frequency at a first plurality of location in a borehole by a downhole tool conveyed in the borehole, a portion of the borehole in which the apparent impedance measurements at least at a first frequency of the set have a predetermined behavior, wherein the predetermined behavior is that the apparent impedance measurements at the at least one first frequency taken in the portion are substantially fitting a linear model when represented in the complex plane, and using a plurality of measurements obtained at a second plurality of location situated in said portion at the first frequency to determine calibration coefficients for the measurements taken at the first frequency.

Generally, the computer storage medium comprises instructions for performing one or more operations of the method as mentioned above.

Claim 1:
A method (<NUM>; <NUM>) for calibrating a resistivity measurement taken by a downhole tool (<NUM>) in a borehole, wherein the downhole tool estimates the resistivity of an underground formation (<NUM>) penetrated by the borehole with at least one sensor (<NUM>) situated at a non-zero standoff distance from the borehole, wherein the method includes:
- taking (<NUM>; <NUM>) apparent impedance measurements with the at least one sensor at a set of frequencies comprising at least a first frequency and at a first plurality of locations in the borehole, wherein the measurement are uncalibrated measurements,
the method being characterized in that it further comprises:
- identifying (<NUM>-<NUM>; <NUM>; <NUM>) a portion of the borehole in which the apparent impedance measurements at least at the first frequency have a predetermined behavior, wherein the predetermined behavior is that the apparent impedance measurements taken in the portion are substantially fitting a linear model when represented in the complex plane,
- using (<NUM>; <NUM>) a plurality of measurements obtained at a second plurality of location situated in said portion at the first frequency to determine calibration coefficients for the measurements at said frequency.