# Patent

## Title
Two loop calibrator

## Abstract

Misalignment of the transmitter and receiver coils of an induction logging tool is determined by positioning the logging tool with a coil axially encompassing the transmitter coil and/or the receiver coil, and activating the transmitter at a plurality of rotational angles.

## Background
CROSS REFERENCE TO RELATED APPLICATIONS
The present invention is a continuation-in-part of patent application Ser. No. 10/841,397 filed on May 7, 2004.


BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention is related to the field of apparatus design in the field of oil exploration. In particular, the present invention describes a method for calibrating multicomponent logging devices used for detecting the presence of oil in boreholes penetrating a geological formation.
2. Description of the Related Art
Electromagnetic induction resistivity well logging instruments are well known in the art. Electromagnetic induction resistivity well logging instruments are used to determine the electrical conductivity, and its converse, resistivity, of earth formations penetrated by a borehole. Formation conductivity has been determined based on results of measuring the magnetic field of eddy currents that the instrument induces in the formation adjoining the borehole. The electrical conductivity is used for, among other reasons, inferring the fluid content of the earth formations.
In general, when using a conventional induction logging tool with transmitters and receivers (induction coils) oriented only along the borehole axis, the hydrocarbon-bearing zones are difficult to detect when they occur in multi-layered or laminated reservoirs. These reservoirs usually consist of thin alternating layers of shale and sand and, oftentimes, the layers are so thin that due to the insufficient resolution of the conventional logging tool they cannot be detected individually. In this case the average conductivity of the formation is evaluated.
Conventional induction well logging techniques employ coils wound on an insulating mandrel. One or more transmitter coils are energized by an alternating current. The oscillating magnetic field produced by this arrangement results in the induction of currents in the formations which are nearly proportional to the conductivity of the formations. These currents, in turn, contribute to the voltage induced in one or more receiver coils. By selecting only the voltage component which is in phase with the transmitter current, a signal is obtained that is approximately proportional to the formation conductivity. In conventional induction logging apparatus, the basic transmitter coil and receiver coil has axes which are aligned with the longitudinal axis of the well logging device. This arrangement tends to induce secondary current loops in the formations that are concentric with the vertically oriented transmitting and receiving coils. The resultant conductivity measurements are indicative of the horizontal conductivity (or resistivity) of the surrounding formations. There are, however, various formations encountered in well logging which have a conductivity that is anisotropic. Anisotropy results from the manner in which formation beds were deposited by nature. For example, “uniaxial anisotropy” is characterized by a difference between the horizontal conductivity, in a plane parallel to the bedding plane, and the vertical conductivity, in a direction perpendicular to the bedding plane. When there is no bedding dip, horizontal resistivity can be considered to be in the plane perpendicular to the bore hole, and the vertical resistivity in the direction parallel to the bore hole. Conventional induction logging devices, which tend to be sensitive only to the horizontal conductivity of the formations, do not provide a measure of vertical conductivity or of anisotropy.
In a transverse induction logging tools the response of transversal coil arrays is also determined by an average conductivity, however, the relatively lower conductivity of hydrocarbon-bearing sand layers dominates in this estimation. In general, the volume of shale/sand in the formation can be determined from gamma-ray or nuclear well logging measurements. Then a combination of the conventional induction logging tool with transmitters and receivers oriented along the well axis and the transversal induction logging tool can be used for determining the conductivity of individual shale and sand layers.
One, if not the main, difficulties in interpreting the data acquired by a transversal induction logging tool is associated with vulnerability of its response to borehole conditions. Among these conditions is the presence of a conductive well fluid as well as wellbore fluid invasion effects
In the induction logging instruments the acquired data quality depends on the formation electromagnetic parameter distribution (conductivity) in which the tool induction receivers operate. Thus, in the ideal case, the logging tool measures magnetic signals induced by eddy currents flowing in the formation. Variations in the magnitude and phase of the eddy currents occurring in response to variations in the formation conductivity are reflected as respective variations in the output voltage of receivers. In the conventional induction instruments these receiver induction coil voltages are conditioned and then processed using analog phase sensitive detectors or digitized by digital to analog converters and then processed with signal processing algorithms. The processing allows for determining both receiver voltage amplitude and phase with respect to the induction transmitter current or magnetic field waveform.
There are a few hardware margins and software limitations that impact a conventional transversal induction logging tool performance and result in errors appearing in the acquired data.
The general problems encountered are discussed in U.S. Pat. No. 6,734,675 and U.S. Pat. No. 6,586,939 to Fanini et al., both having the same assignee as the present application and the contents of which are incorporated herein by reference. Fanini '939 discloses a transverse induction logging tool having a transmitter and receiver for downhole sampling of formation properties, the tool having a symmetrical shielded split-coil transmitter coil and a bucking coil interposed between the split transmitter coils to reduce coupling of the transmitter time varying magnetic field into the receiver. The tool provides symmetrical shielding of the coils and grounding at either the transmitter or receiver end only to reduce coupling of induced currents into the received signal. The tool provides an insulator between receiver electronics and the conductive receiver housing having contact with conductive wellbore fluid, to reduce parasitic current flowing in a loop formed by the upper housing, feed through pipe, lower housing and wellbore fluid adjacent the probe housing or mandrel. An internal verification loop is provided to track changes in transmitter current in the real and quadrature component of the received data signal.
Fanini '675 discloses a transverse induction logging tool having a transmitter and receiver for downhole sampling of formation properties, the tool having a symmetrical shielded split-coil transmitter coil and a bucking coil interposed between the split transmitter coils to reduce coupling of the transmitter time varying magnetic field into the receiver. The tool provides symmetrical shielding of the coils and grounding at either the transmitter or receiver end only to reduce coupling of induced currents into the received signal. The tool provides an insulator between receiver electronics and the conductive receiver housing having contact with conductive wellbore fluid, to reduce parasitic current flowing in a loop formed by the upper housing, feed through pipe, lower housing and wellbore fluid adjacent the probe housing or mandrel. An internal verification loop is provided to track changes in transmitter current in the real and quadrature component of the received data signal.
SUMMARY OF THE INVENTION
One embodiment of the invention is an apparatus for evaluating an induction logging tool for use in a borehole. The logging tool includes a current source which activates a transmitter coil on the logging tool and a receiver coil spaced apart axially from the transmitter coil wherein the receiver coil produces a signal in response to the activation of the transmitter coil. The apparatus includes at least one conducting loop which axially encompasses the transmitter coil and/or the receiver coil. The signal produced by the receiver coil is indicative of a misalignment between the transmitter coil and the receiver coil. A single conducting loop may encompass both the transmitter coil and the receiver coil. Two electrically connected conducting loops may be used with one of the loops encompassing the transmitter coil and the other loop encompassing the receiver coil. The transmitter coil may have an axis substantially parallel to or substantially orthogonal to a longitudinal axis of the logging tool. The receiver coil may have an axis substantially parallel to or substantially orthogonal to a longitudinal axis of the logging tool. The apparatus may further include a support which rotates the logging tool through a plurality of angles with the transmitter being activated at each of the angles, and a processor which estimates from the signals at each of the rotational angles the angle of misalignment. The misalignment angle may be estimated based on a rotational angle at which the signal is substantially zero.
Another embodiment of the invention is a method of evaluating an induction logging tool for use in a borehole. A transmitter coil on the tool is activated. A signal is provided using a receiver coil in response to the activation of the transmitter coil. From the signal, a misalignment angle between the transmitter coil and the receiver coil. The method includes using at least one conducting loop for axially encompassing the transmitter coil and/or the receiver coil. The encompassing may be done by using a single conducting loop. The encompassing may be done by using a first loop for encompassing the transmitter coil and a second loop for encompassing the receiver coil. The transmitter coil may have an axis that is substantially parallel to or orthogonal to a longitudinal axis of the tool. The receiver coil may have an axis that is substantially parallel to or orthogonal to a longitudinal axis of the tool. The logging tool may be rotated through a plurality of angles with the transmitter being activated at each of the angles, and the misalignment angle may be estimated from the signals at each of the angles. The misalignment angle may be estimated from an angle at which the signal is substantially zero.



BRIEF DESCRIPTION OF THE DRAWINGS
The present invention is best understood with reference to the accompanying figures in which like numerals refer to like elements and in which:
FIG. 1 (prior art) shows schematically a wellbore extending into a laminated earth formation, into which wellbore an induction logging tool as used according to the invention has been lowered;
FIG. 2A (prior art) illustrates a conventional resistivity measurement in the vertical direction;
FIG. 2B (prior art) illustrates a resistivity measurement in the horizontal direction;
FIG. 3 is an overall flow chart of the procedures of the present invention;
FIG. 4 illustrates a borehole conductivity simulator (BCS) used in the present invention;
FIG. 5 illustrates an assembly for calibrating of transverse arrays in a logging tool;
FIG. 6 illustrates an assembly for calibrating longitudinal arrays in a logging tool;
FIGS. 7-8 illustrate assemblies for calibrating XY cross-component arrays; and
FIGS. 9-10 illustrate assemblies for calibrating XZ cross-component arrays.



DETAILED DESCRIPTION OF THE INVENTION
The instrument structure provided by the present invention enables increased stability and accuracy in an induction wellbore logging tool and its operational capabilities, which, in turn, results in better quality and utility of wellbore data acquired during logging. The features of the present invention are applicable to improve the structure of a majority of known induction tools.
The invention will now be described in more detail and by way of example with reference to the accompanying drawings. FIG. 1 schematically shows a wellbore 1 extending into a laminated earth formation, into which wellbore an induction logging tool as used according to the present invention has been lowered. The wellbore in FIG. 1 extends into an earth formation which includes a hydrocarbon-bearing sand layer 3 located between an upper shale layer 5 and a higher conductivity than the hydrocarbon bearing sand layer 3. An induction logging tool 9 used in the practice of the invention has been lowered into the wellbore 1 via a wire line 11 extending through a blowout preventor 13 (shown schematically) located at the earth surface 15. The surface equipment 22 includes an electric power supply to provide electric power to the set of coils 18 and a signal processor to receive and process electric signals from the receiver coils 19. Alternatively, the power supply and/or signal processors are located in the logging tool.
The relative orientation of the wellbore 1 and the logging tool 9 with respect to the layers 3, 5, 7 is determined by two angles, one of which θ as shown in the FIG. 1. For determination of these angles see, for example, U.S. Pat. No. 5,999,883 to Gupta, et al. The logging tool 9 is provided with a set of transmitter coils 18 and a set of receiver coils 19, each set of coils 18, 19 being connected to surface equipment 22 via suitable conductors (not shown) extending along the wire line 11.
Each set of coils 18 and 19 includes three coils (not shown), which are arranged such that the set has three magnetic dipole moments in mutually orthogonal directions, that is, in x, y and z directions. The three-coil transmitter coil set transmits Tx, Ty and Tz. The receiver coil receives Rx, Ry and Rz plus the cross components, Rxy, Rxz and Rzy. Thus, coil set 18 has magnetic dipole moments 26a, 26b, 26c, and coil set 19 has magnetic dipole moments 28a, 28b, 28c. In one embodiment the transmitter coil set 18 is electrically isolated from the receiver coil set 19. In an alternative embodiment, each coil in transmitter coil set 18 electrically isolated from each other and each coil in receiver coil set 19 electrically isolated from each other. The coils with magnetic dipole moments 26a and 28a are transverse coils, that is they are oriented so that the magnetic dipole moments are oriented perpendicular to the wellbore axis, whereby the direction of magnetic dipole moment 28a is opposite to the direction of magnetic dipole moment 26a. Furthermore the sets of coils 18 and 19 are positioned substantially along the longitudinal axis of the logging tool 9.
As shown in FIG. 2A, conventional induction logging tools provide a single transmitter and receiver coil that measure resistivity in the horizontal direction. In the conventional horizontal mode, as shown in FIG. 2A, the resistivities of adjacent high resistivity sand and low resistivity shale layers appear in parallel, thus the resistivity measurement is dominated by low resistivity shale. As shown in FIGS. 1 and 2B, in the present invention a transverse coil is added to measure resistivity in the vertical direction. In the vertical direction, the resistivity of the highly resistive sand and low resistivity shale are appear in series and thus the vertical series resistivity measurement is dominated by the resistivity of the highly resistive sand.
For ease of reference, normal operation of the tool 9, as shown in FIGS. 1 and 2B, will be described hereinafter only for the coils having dipole moments in the x-direction, i.e. dipole moments 26a and 28a. During normal operation an alternating current of a frequency f1 is supplied by the electric power supply of surface equipment 22 to transmitter coil set 18 so that a magnetic field with magnetic dipole moment 26a is induced in the formation. In an alternative embodiment, the frequency is swept through a range f1 through f2. This magnetic field extends into the sand layer 3 and induces a number of local eddy currents in the sand layer 3. The magnitude of the local eddy currents is dependent upon their location relative to the transmitter coil set 18, the conductivity of the earth formation at each location, and the frequency at which the transmitter coil set 18 is operating. In principle the local eddy currents act as a source inducing new currents, which again induce further new currents, and so on. The currents induced into the sand layer 3 induces a response magnetic field in the formation, which is not in phase with the transmitted magnetic field, but which induces a response current in receiver coil set 19. The magnitude of the current induced in the sand layer 3 depends on the conductivity of the sand layer 3, the magnitude of the response current in receiver coil set 19. The magnitude also depends on the conductivity and thereby provides an indication of the conductivity of the sand layer 3. However, the magnetic field generated by transmitter coil set 18 not only extends into sand layer 3, but also in the wellbore fluid and in the shale layers 5 and 7 so that currents in the wellbore fluid and the shale layers 5 and 7 are induced.
The overall procedures of the present invention used to ensure proper functioning of a deployed multicomponent induction logging tool is summarized in FIG. 3. Calibration the instrument's arrays is done, particularly estimating its transfer coefficient 101. Subsequently, a final verification of the tuning and calibration consistency is performed 103. This is followed by a verification of isolator sufficiency 105 for preventing an axial current flow between the tool's top and bottom housings/electronics through the feed-through pipe and conductors while logging in the boreholes filled with conductive mud.
In further detail, the fully made tool is placed in calibration area which has a small number of external conductive parts that could affect tool readings (machinery, measurement tools, etc.). For example, positioning the tool at approximately 15 ft (4.6 m) above the ground typically reduces the tool reading to a value less than about 10 mS/m. The tool is positioned parallel to the Earth with the array to be adjusted pointing normal to the ground. The instrument's top and bottom housing are interconnected with a borehole conductivity simulator (BCS) and the insulator is shorted.
FIG. 4 illustrates the BCS, comprising an assembly of conductor 401 and resistor 410, which electrically couples top housing 405 and bottom housing 404. A closed circuit is thus created from bottom housing 404 through resistor 410 through top housing 405 through a feed-through pipe running from bottom housing to top housing through mandrel 408. The value of resistor 410 can be configured to be approximately equal to a total conductance value the tool would experience inside a borehole well according to its specifications. A resistance value of approximately 20 Ohms is typically chosen.
In this arrangement the tool becomes very sensitive to the axial current that could be induced by the array transmitter in the following loop: “top housing-shorted feed-through pipe-bottom housing-BCS”. The magnitude of the current will be proportional to the array coils displacement from their longitudinal alignment and simulator resistor value.
To balance the array its transmitter coil may be moved in the plane parallel to the ground. This coil movement is performed until absolute minimum in the array reading is reached. Upon adjustment the transmitter coil frame is fixed inside the mandrel with the sets of non-conductive screws and/or with epoxy. Shorting the isolator between the upper housing and the mandrel is done to significantly increase the magnitude of the axial current in this test procedure and, therefore, increase accuracy of balancing. A similar positioning may be done in the vertical direction. As discussed below, the tool is more sensitive to mispositioning in the vertical direction than in the horizontal direction. Suitable positioning screws may be provided in the logging tool to accomplish this movement.
After the first horizontal array has been tuned the tool is rotated about its axis and similar procedure has been performed with next horizontal array. Generally, the instrument might have a plurality of transverse and tilted arrays so that similar tuning could be developed for each sensor. After balance of all arrays has been completed, the tool isolation short is removed and mandrel is covered with the non-conductive pressure sleeve.
Calibration of transfer coefficient is done after the instrument is positioned in the low conductive calibration environment and inserted inside the calibrator. The calibration principle lies in introducing a certain magnetic load for calibrating array so that its signal readings are identical to the values to be read while logging a homogeneous formation. This is done with use of a calibrator whose electromagnetic parameters and coupling with the tool are precisely known. Using the calibrator, tool loading is achieved by the connecting certain impedance to the terminal of normally-open calibrator loop. Thus, the open loop presents an infinitely resistive formation. Conversely, by shorting, almost infinitely conductive formation is presented. Therefore, any value of the formation conductivity corresponds to its unique value of the calibration loop load.
Acquiring the calibration signal is typically done in the mode “calibration load connected-disconnected”. This difference in the tool reading indicates on how much the tool output voltage swings when the formation conductivity changes from 0 to the calibrated value. To perform calibration the tool array may be oriented normal to the ground as this leads to more consistency in measurements and apparently make its transversal arrays less sensitive to any noise currents that maybe circulating on the Earth surface in place of measurement (machinery, radio-stations, etc.).
After the tool transfer coefficient has been determined, the tool readings while the calibrator loop is not loaded reflect environmental conductivity and, in particular, ground conductivity. This data has to be known and stored for further processing.
The last step in calibration is verification of the tool symmetry and immunity to axial currents. The overall tool symmetry assumes that the same array reads the same values of the “ground” or environmental conductivity while its measurement direction points to ground or from the ground. For these purposes the tool is rotated around its longitudinal axis on 180°. Absence of such a “direction sensitivity” would indicate normal tool functioning and ensure respective symmetry while operating in the well bore.
For verification of the suppressing axial currents—a modified BCS test may be run with the short removed in the feed-through. Thus, connecting and disconnecting the BCS to the tool should result in absolute minimal difference in readings that would indicate for proper operation in the well without formation-dependable offset in the tool data. This modified BCS test could be run as described, or, to reduce calibration time, performed right after the transfer coefficient is determined.
Turning now to FIG. 5, one arrangement of the alignment loop is discussed. Shown therein is an alignment loop 501 surrounding an array characterized by the transmitter coil 504 directed along an X direction (Tx) and the receiver coil 508 directed along the X direction (Rx). Bucking coil Bx 506 is also shown. This array is denoted as XX, using a nomenclature in which the first letter signifies the orientation direction of the transmitter coil and the last letter signifies the orientation direction of the receiver coil. This nomenclature is generally used herein. The XX and YY arrays in the multi-component tool are ideally aligned at 90° from each other. When this alignment is not met, the response of the cross components (XY, YX) are affected by part of the reading of the related main component. The alignment measuring method of the present invention is based on analyzing the output of the cross-component system when the tool is rotated inside of an alignment loop.
The alignment loop 501 is a stationary loop, lying so that the longitudinal axis of the loop and the longitudinal axis of the well-logging tool are substantially aligned. Its dimensions are such as to obtain substantial inductive coupling with the transmitter as well as with the receiver of both XX and YY arrays. An important aspect of the present invention is that no portion of either the transmitter or the receiver coil extend beyond the loop. This is in contrast to prior art devices in which this condition is not satisfied. When this condition is not satisfied, the resulting calibration is sensitive to the position of the calibration loop relative to the transmitter and receiver coils, and is hence suspect. The arrangement shown in FIG. 5 uses a single calibration loop where this condition is satisfied. The single calibration loop axially encompasses the transmitter coil and the receiver coil. A detailed analysis of the signals is given later in this document. The logging tool is supported within the alignment loop by suitable support (not shown) that has the capability of rotating the logging tool about its axis through known angles.
FIG. 6 illustrates a loop alignment assembly usable for aligning ZZ arrays in a testing device. Transmitter TZ 601, bucking coil BZ 603 and receiver RZ 605 are disposed along the feed-through pipe 615 and have a common longitudinal axis. Alignment loop 610 is substantially coaxial with receiver RZ 605 and substantially centered on RZ. As with the arrangement of FIG. 5, the receiver coil is axially encompassed by d the calibration loop 610.
Cross component array calibration is discussed next. FIG. 7 illustrates an embodiment for calibration of an XY array using a calibration box. This functions in the same manner as a calibration loop, and may be considered to be one. Transmitter 701 and bucking coil 703 are disposed along the feed-through pipe oriented to produce a magnetic moment in an X-direction. Receiver 705 is disposed along the same feed-through pipe having an orientation so as to receive components of a magnetic moment in a is disposed along the same feed-through pipe having an orientation so as to receive components of a magnetic moment in Y-direction. The alignment loop 710 is disposed at an angle of 45° so as to be oriented halfway between the X-direction and the Y-direction. To simplify the illustration, the box has been depicted without showing it as extending beyond the transmitter and receiver coils.
Those skilled in the art would recognize that the alignment loop shown in FIGS. 5 and 7 would be bulky and possible difficult to manage under field conditions. An embodiment of the present invention that addreses this problem is discussed next. FIG. 8 illustrated an alternate embodiment for aligning an XY array. Alignment loop 815 is located at the TX 801, and alignment loop 810 is positioned at the RXY cross-component receiver 805. Both alignment loops are oriented along the same direction as their respective transmitter/receiver. A wire 820 electrically couples alignment loop 810 and alignment loop 815. The individual loops 810 and 815 are easier to handle than a single large box, and by use of the electrical connection 820, are functionally equivalent to box 501 of FIG. 5. In the configuration of FIG. 8, the loop 815 axially encompasses the transmitter coil 801 and tge loop 810 axially encompasses the receiver coil.
FIG. 9 illustrates an assembly for orienting of the XZ cross-component array. Transmitter TX 901 and bucking coil BX 903 are disposed along the feed-through pipe oriented so as to produce a magnetic moment along an X-direction. The receiver RZ 905 is disposed along the feed-through pipe and oriented so as to be receptive to Z-components of magnetic moments. The alignment loop 920 can be positioned centrally between main X-transmitter 901 and Z-cross-component receiver 905 and tilted 45° with respect to the tool longitudinal axis 910. The assembly of FIG. 8 displays small signals during XZ array calibration. This signal tends to display a high sensitivity to the angle.
FIG. 10 illustrates an alternate embodiment for aligning the XZ cross-component array. As in the apparatus shown in FIG. 8, two loops are used. Transmitter TX 1001 and bucking coil BX 1003 are disposed along the feed-through pipe oriented so as to produce a magnetic moment along an X-direction. The receiver RZ 1005 is disposed along the feed-through pipe and oriented so as to be receptive to Z-components of magnetic moments. Alignment loop 1010 is centered on transmitter TX 1001, and alignment loop 1015 is coaxial with receiver RZ 1005. A wire 1020 electrically couples alignment loop 1010 and alignment loop 1015. In contrast to the assembly of FIG. 0, calibration using two alignment devices displays a large signal for the XZ array calibration.
We next discuss in detail the use of the alignment loop for establishing the coil orientation. When examining a cross-component array, the XY or YX response obtained by rotating the tool inside of the alignment loop has a zero-crossing each time that either a transmitter or a receiver coil is perpendicular to the plane of the loop. Whichever coil (transmitter or receiver) is substantially aligned with the loop (enclosed in the same plane) experiences a maximum coupling with the alignment loop. When the position of the aligned coil is varied around the point of alignment with the alignment loop, the coupling response between them undergoes a slow change corresponding to the variation. The non-aligned coil experiences a minimum coupling with the alignment loop. When the position of the non-aligned coil is varied around this point of minimal coupling, the coupling experiences an abrupt change. The coupling becomes zero when the non-aligned coil achieves perpendicularity with the alignment loop. A practitioner in the art would recognize that the zero-crossings of the coupling response are significantly affected by the coil that is at right angle to the alignment loop, regardless of whether the perpendicular coil is a receiver or a transmitter. The substantially aligned coil plays little or no role in the production of a zero-crossing. The angle between successive zero crossings thereby represents an alignment angle between the two related coils.
Mathematically, the inductive coupling between two coils resembles a cosine function of the angle between them. Thus, the coupling response system of coils made by an aligned system of cross components and an alignment loop is given by the following expression:




  
    
      
        
          R
          ⁡
          
            (
            φ
            )
          
        
        =
        
          
            K
            ·
            cos
          
          ⁢
          
            
          
          ⁢
          
            
              (
              φ
              )
            
            ·
            cos
          
          ⁢
          
            
          
          ⁢
          
            
              (
              
                φ
                -
                
                  π
                  2
                
              
              )
            
            .
          
        
      
    
    
      
        
          (
          1
          )
        
        .
      
    
  




Applying trigonometric identities, Eq. (1) can be simplified to

R(φ)=K·cos(φ)·sin(φ),  (2).

and since





  
    
      
        
          
            sin
            ⁢
            
              
            
            ⁢
            
              
                (
                φ
                )
              
              ·
              cos
            
            ⁢
            
              
            
            ⁢
            
              (
              φ
              )
            
          
          =
          
            
              1
              2
            
            ⁢
            sin
            ⁢
            
              
            
            ⁢
            
              (
              
                2
                ·
                φ
              
              )
            
          
        
        ,
      
    
    
      
        
          (
          3
          )
        
        ,
      
    
  




it follows that





  
    
      
        
          R
          ⁡
          
            (
            φ
            )
          
        
        =
        
          
            K
            ·
            
              1
              2
            
            ·
            sin
          
          ⁢
          
            
          
          ⁢
          
            
              (
              
                2
                ·
                φ
              
              )
            
            .
          
        
      
    
    
      
        
          (
          4
          )
        
        .
      
    
  




Eqn. (4) illustrates that there are two cycles of variation for each cycle of tool rotation.

By considering a misalignment angle β between transmitter and receiver, the response function can now be expressed as




  
    
      
        
          
            R
            ⁡
            
              (
              
                φ
                ,
                β
              
              )
            
          
          =
          
            
              K
              ·
              cos
            
            ⁢
            
              
            
            ⁢
            
              
                (
                φ
                )
              
              ·
              cos
            
            ⁢
            
              
            
            ⁢
            
              (
              
                φ
                -
                
                  π
                  2
                
                +
                β
              
              )
            
          
        
        ,
      
    
    
      
        
          (
          5
          )
        
        ,
      
    
  




where each cosine function characterizes the response of the individual cross component coils. It is easy to see that

R(φ,β)=0  (6),

when





  
    
      
        
          φ
          =
          
            n
            ·
            
              π
              2
            
          
        
        ⁢
        
          

        
        ⁢
        
          or
          ⁢
          
            
          
          ⁢
          when
        
        ⁢
        
          

        
        ⁢
        
          
            
              φ
              -
              
                π
                2
              
              +
              β
            
            =
            
              
                
                  n
                  ·
                  
                    π
                    2
                  
                
                ⁢
                
                  
                
                ⁢
                with
                ⁢
                
                  
                
                ⁢
                n
              
              =
              
                ±
                1
              
            
          
          ,
          2
          ,
          3
          ,
          ...
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          7
          )
        
      
    
  




According to eqn. (7), the angle between successive zero-crossings represents the alignment angle among the cross component coils. An intuitive graphical approach can therefore be used to measure the misalignment angle between transmitter and receiver.

Alternatively, the misalignment angle can be obtained simply by using a trigonometric regression function to analyze the response of the system. Applying trigonometric identities to Eqn. (5), the response of the misaligned system can be written as




  
    
      
        
          
            R
            ⁡
            
              (
              
                φ
                ,
                β
              
              )
            
          
          =
          
            
              
                K
                ·
                cos
              
              ⁢
              
                
              
              ⁢
              
                
                  (
                  φ
                  )
                
                ·
                sin
              
              ⁢
              
                
              
              ⁢
              
                
                  (
                  φ
                  )
                
                ·
                cos
              
              ⁢
              
                
              
              ⁢
              
                (
                β
                )
              
            
            +
            
              
                K
                ·
                
                  
                    cos
                    2
                  
                  ⁡
                  
                    (
                    φ
                    )
                  
                
                ·
                sin
              
              ⁢
              
                
              
              ⁢
              
                (
                β
                )
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            R
            ⁡
            
              (
              
                φ
                ,
                β
              
              )
            
          
          =
          
            
              
                K
                ·
                
                  1
                  2
                
                ·
                sin
              
              ⁢
              
                
              
              ⁢
              
                
                  (
                  
                    2
                    ·
                    φ
                  
                  )
                
                ·
                cos
              
              ⁢
              
                
              
              ⁢
              
                (
                β
                )
              
            
            +
            
              
                K
                ·
                
                  
                    cos
                    2
                  
                  ⁡
                  
                    (
                    φ
                    )
                  
                
                ·
                sin
              
              ⁢
              
                
              
              ⁢
              
                (
                β
                )
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            R
            ⁡
            
              (
              
                φ
                ,
                β
              
              )
            
          
          =
          
            
              
                
                  K
                  2
                
                ·
                sin
              
              ⁢
              
                
              
              ⁢
              
                (
                
                  
                    2
                    ·
                    φ
                  
                  +
                  β
                
                )
              
            
            +
            
              
                
                  K
                  2
                
                ·
                sin
              
              ⁢
              
                
              
              ⁢
              
                (
                β
                )
              
            
          
        
      
    
    
      
        (
        8
        )
      
    
  




The last expression in eqn. (8) indicates that a graphical representation of the coupling response of the misaligned cross component system resembles a sinusoidal function. The period of this sinusoid equals 180° and has offsets on both the abscissa and the ordinate. The offset on the abscissa is β, and the offset on the ordinate is (K/2)sin(β). Also, the coupling response is of the form A sin(x+B)+C, where A=K/2, B=β and C=(K/2)(sin(β). The coefficient B obtained with such fitting represents the misalignment angle. The cross component response can thus be fit to this curve.

The sensitivity to possible displacement along the tool's longitudinal axis or vertically can be analyzed by changes in the product M=MT-CMC-R, where MT-C is the mutual inductance between the transmitter and the alignment coils, and MR-C is the mutual inductance between the alignment and the receiver coils. Measurements show that typically there is in general a flexibility of 1′′ in horizontal positioning, and about half that amount in vertical positioning without substantially affecting the induction response.
To properly position the arrays, the transmitter coil of one array is moved in the direction normal to the ground. This coil movement is performed until an absolute minimum in the coupling response is determined. Upon adjustment, the transmitter coil frame is fixed inside the mandrel. After the first horizontal array has been tuned, the tool is rotated on its axis and a similar procedure is performed with the other horizontal array. Generally, similar tuning can be developed for an instrument having a plurality of transverse and tilted arrays. After balance of all arrays has been achieved, the tool isolation short is removed and mandrel is covered with the non-conductive pressure sleeve.
A final verification of the coil balancing and calibration consistency is made. Calibration of a transfer coefficient is performed once the instrument is inserted inside the calibrator in the low conductive calibration environment. A magnetic load is introduced suitable for calibrating array, so that its signal readings are identical to the values to be read while logging a homogeneous formation. The magnetic load is introduced using the above-referenced calibrator using known electromagnetic parameters and coupling parameters. The tool loading can be achieved by connecting selected impedance to the terminal of a normally-open calibrator loop. Thus, the open loop represents an infinitely resistive formation. Once shorted, the closed loop represents an almost infinitely conductive formation (limited only by internal impedance of the wires of the calibrator loop). Therefore, a calibration loop load can be chosen effectively representing a given formation conductivity values.
Implicit in the control and processing of the data is the use of a computer program on a suitable machine readable medium that enables the processor to perform the control and processing. The machine readable medium may include ROMs, EPROMs, EEPROMs, Flash Memories and Optical disks.
While the foregoing disclosure is directed to the preferred embodiments of the invention, various modifications will be apparent to those skilled in the art. It is intended that all variations within the scope and spirit of the appended claims be embraced by the foregoing disclosure.
The following definitions are helpful in understanding the scope of the invention:

    alignment: the proper positioning or state of adjustment of parts in relation to each other;
    calibrate: to standardize by determining the deviation from a standard so as to ascertain the proper correction factors;
    coil: one or more turns, possibly circular or cylindrical, of a current-carrying conductor capable of producing a magnetic field;
    EAROM: electrically alterable ROM;
    Encompass: to enclose completely
    EPROM: erasable programmable ROM;
    flash memory: a nonvolatile memory that is rewritable;
    machine readable medium: something on which information may be stored in a form that can be understood by a computer or a processor;
    misalignment: the condition of being out of line or improperly adjusted;
    Optical disk: a disc shaped medium in which optical methods are used for storing and retrieving information;
    Position: an act of placing or arranging; the point or area occupied by a physical object
    Quadrature: 90° out of phase; and
    ROM: Read-only memory.

## Claims

1. An apparatus for evaluating an induction logging tool for use in a borehole, the logging tool comprising:
(a) a current source configured to actuate a transmitter coil on the induction logging tool; and
(b) a receiver coil axially spaced apart from the transmitter coil, the receiver coil configured to produce a signal in response to the activation of the transmitter coil;
the apparatus comprising:
(c) a single conducting loop axially encompassing the transmitter coil, and the receiver coil;
wherein the signal is indicative of a misalignment angle between the transmitter coil and the receiver coil.

2. The apparatus of claim 1 wherein the transmitter coil has an axis that is one of (i) parallel to a longitudinal axis of the logging tool, and (ii) substantially orthogonal to a longitudinal axis of the logging tool.

3. The apparatus of claim 1 wherein the receiver coil has an axis that is one of (i) parallel to a longitudinal axis of the logging tool, and (ii) substantially orthogonal to a longitudinal axis of the logging tool.

4. The apparatus of claim 1 further comprising:
(i) a support configured to rotate the logging tool through a plurality of angles, the transmitter being configured to be activated at each of the plurality of rotational angles, and
(ii) a processor configured to estimate from the signals at each of the plurality of rotational angles the misalignment angle.

5. The apparatus of claim 4 wherein the processor is configured to determine the misalignment angle at least in part by using a relation of the form:




  
    R
    ⁡
    
      (
      
        φ
        ,
        β
      
      )
    
  
  =
  
    
      K
      ·
      cos
    
    ⁢
    
      
    
    ⁢
    
      
        (
        φ
        )
      
      ·
      cos
    
    ⁢
    
      
    
    ⁢
    
      (
      
        φ
        -
        
          π
          2
        
        +
        β
      
      )
    
  



where K is a gain factor, φ is an angle between one of the coils and a plane defined by the at least one conducting loop, and β is the misalignment angle.

6. The apparatus of claim 4 wherein the processor is configured to determine the misalignment angle based on estimating a rotational angle at which the signal is substantially zero.

7. A method of evaluating an induction logging tool for use in a borehole, the method comprising:
(a) activating a transmitter coil on the induction logging tool;
(b) using a receiver coil to receive a signal in response to the activation of the transmitter coil;
(c) positioning the logging tool during the activation of the transmitter coil with a single conducting loop axially encompassing the transmitter coil, and the receiver coil; and
(d) estimating from the received signal a misalignment angle between the transmitter coil and the receiver coil, wherein the misalignment angle indicates a level of accuracy of the induction logging tool.

8. The method of claim 7 wherein the transmitter coil has an axis that is one of (i) parallel to a longitudinal axis of the logging tool, and (ii) substantially orthogonal to a longitudinal axis of the logging tool.

9. The method of claim 7 wherein the receiver coil has an axis that is one of (i) parallel to a longitudinal axis of the logging tool, and (ii) substantially orthogonal to a longitudinal axis of the logging tool.

10. The method of claim 7 further comprising: rotating the logging tool through a plurality of angles, the transmitter being activated at each of the plurality of rotational angles, wherein
estimating the misalignment angle further comprises using signals at each of the plurality of rotational angles.

11. The method of claim 10 wherein determining the misalignment further comprises using a relation of the form:




  
    R
    ⁡
    
      (
      
        φ
        ,
        β
      
      )
    
  
  =
  
    
      K
      ·
      cos
    
    ⁢
    
      
    
    ⁢
    
      
        (
        φ
        )
      
      ·
      cos
    
    ⁢
    
      
    
    ⁢
    
      (
      
        φ
        -
        
          π
          2
        
        +
        β
      
      )
    
  



where K is a gain factor, φ is an angle between one of the coils and a plane defined by the at least one conducting loop, and β is the misalignment angle.

12. The method of claim 10 wherein estimating the misalignment angle further comprises estimating a rotational angle at which the signal is substantially zero.

13. The method of claim 7 further comprising using the induction logging tool on the basis of the estimated misalignment angle and producing a log of a resistivity of an earth formation.