Abstract:
A tool for evaluating the internal surfaces of tubular is provided, wherein one or more arms extend outwardly from the tool into contact with an inner wall of the tubular, and changes in the dimensions or condition of the inner wall result in changes in the position of the ends of the arms relative to the tool. This motion is converted, through an electromagnetic transducer, into an electrical signal, the amplitude of which falls is maintained as the temperature of the tool changes. In one aspect, the transducer includes a coil and a moveable metal or magnetic element. The coil is powered by a constant current source, and variations in the resistance of the electrical components of the transducer resultingly do not cause fall off of the output signal amplitude.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    Field of the Invention 
         [0002]    The present disclosure relates to the field of property measurement under conditions where the temperatures to which the measurement device is exposed otherwise cause falloff in the signal indicative of the measured property. More particularly, the present disclosure relates to physical measurement in remote environments, in which a measuring tool is passed through an item to be measured, and the temperatures to which the measuring tool is exposed vary. In one aspect, the measurement device is configured to determine the condition of the inner surfaces of tubulars, for example piping carrying fluids, including well bore tubulars, wherein the condition of the tubular is determined by passing a multi-arm caliper device through the tubular, and the condition of the tubular is inferred from the measurement data received from the multi arm caliper. 
         [0003]    Description of the Related Art 
         [0004]    Multi-arm caliper tools are widely used to evaluate the interior condition of tubular, such as piping, as well as in the field of cased hole wireline logging in order to determine the geometrical properties of the inner surface of tubulars such as casing, liners or tubings. Multi-arm calipers are provided with a plurality of caliper arms extending around a longitudinal centerline or axis of the tool, such that radii extending from the centerline of the tool to the adjacent tubular inner surface may be measured at a plurality of angular locations around the tool longitudinal axis at a relatively high frequency using caliper arms extending from the body of the tool, and these measurements are recorded in the tool and/or transmitted along a wireline to a remote location for recording or analysis. The data is used to assess the integrity of interior surface or wall the tubular, and can be used to locate areas of wall erosion, kinks, abnormal bending, or other geometrical physical indicia of impending loss of the fluid sealing integrity of the tubular. If the tool data indicates an issue with the integrity of the wall or inner surface of the tubular, the owner or operator of the equipment or well in which the tubular is used can take remedial steps, such as locating a liner over the location of the tubular in which there is an integrity issue, replacing the tubular (such as where a secondary tubing was extended into, but not cemented into place, in a well bore, or the tubular is in process equipment and can be accesses for replacement) or sealing off the location in the tubular where the integrity issue is present. Where the tubular is a casing or liner permanently fixed in a well bore, and the well is still producing, the owner or operator of the well will need to determine whether the cost of drilling an additional well to the producing formation location is economically profitable if the well is closed off. 
         [0005]    In one multi-arm caliper tool where the tool is pulled or pushed within the tubular, the tool includes mechanical probe arms that contact the inner surface of the tubular and mechanically transfer the radial geometric variations of the tubular to a transducer individually associated with each arm that in turn translates the mechanical variations of the distance from the tip of the arm in contact with the inner surface of the tubular to the tool housing into electric signals that are fed to a data processing and transmission system, which may be on-board the tool or which may be transmitted, via a wireline, to a remote location such as a surface location where a casing in a well bore is being evaluated. Alternately the signal may be simply recorded within a recorder that is located within or in the vicinity of the caliper tool as part of the downhole tool. 
         [0006]    To translate the mechanical movement of the probe into an electrical signal, the probe is interconnected to a transducer such as a linear variable differential transformer, otherwise known as an LVDT, a differential variable reluctance transducer, otherwise known as a DVRT, or a single ended variable reluctance transducer, otherwise known as a SVRT, wherein movement of the mechanical probe at the end of the probe in contact with the inner surface of the tubular causes movement of a core relative to a winding of the transducer. The winding is powered by a power source, and as the core moves relative to the magnetic field induced by the winding, it causes perturbations thereof. These perturbations and the resulting changes in the electric field are converted to electric signals representative of the distance the core has moved with respect to the winding, and, thus changes in the relative position of the end of the probe arm in contact with the inner surface of the tubular are converted into an electric signal. As the tool traverses a tubular in a well bore, it encounters different ambient temperatures, which, because of the mechanical nature of the tool cause changes in length of the various physical components thereof, as well drift and falloff in the output signal of the electrical components. This includes the fall off of the output signal of the transducer as a result of an increase in wiring resistance of the copper coils of the transducer due to an increase in the temperature to which the transducer is exposed. Inductive sensors such as transducer experience a shift in calibration with variations in temperature due to a change in resistance of the transformer windings thereof, i.e., the windings which, as a result of the movement of a metal or magnetic piece with respect thereto, cause a change in the output of a signal from the windings. The windings are usually made of copper, which exhibits a change in resistance of approximately 3900 parts per million per degree centigrade, i.e., 0.0039% change in resistance per degree Celsius temperature change. The winding resistance is electrically in series with the inductive reactance of the winding at the frequency of excitation, resulting in a fall-off of the signal with an increase in temperature, given a constant amplitude and frequency excitation signal. 
         [0007]    Where the erroneous readings indicate an impending loss of integrity of the tubular such as casing, expensive retrofitting of a sealing sleeve or coating over the indicated location, or plugging of the tubular at and below the location and closing off of the producing well, will occur when it is unnecessary to do so, resulting in significant unnecessary expenditure. Where an erroneous reading fails to detect an integrity issue, the tubular can fail leading to the leakage of the fluids therein into the adjacent environment. Where the temperature to which the tool is exposed undergoes a large temperature change, the falloff of the signal output may be so significant that meaningful data cannot be recovered, with the risk that impending tubular failure may not be detected. Likewise, the operator may need to run the evaluation over again, with resulting increased operation cost. 
         [0008]    Thus, there is a need for a multi-arm caliper tool which provides a reliable signal indicative of physical measurement over a broad range of temperatures. 
       SUMMARY OF THE INVENTION 
       [0009]    There is provided herein a measurement apparatus in which the windings of the transformer are driven with a constant current signal which results in a constant amplitude output signal independent of the temperature to which the tool is exposed during measurement. In one aspect, the measurement apparatus is incorporated into a tubular wall evaluation tool including a tool body, wherein the measurement apparatus is used to determine the condition of an internal surface of a tubular, and outputs a signal representative of that condition, wherein the effect of temperature change on the tool is ameliorated by providing the same current signal to the windings during the measurement period. 
         [0010]    In one aspect, the tool is a multi-arm caliper tool, wherein a plurality of probe arms are extendable therefrom and into contact with the internal surface of the tubular, and each probe arm is individually coupled to a transducer which is configured to output a signal indicative of movement of the probe arm as the tool transits the tubular, the movement of the probe arm induced by changes in the surface geometry of the tubular inner wall. 
         [0011]    In another aspect, the transducer is an LVDT, DVRT or SVRT, and a pulse generator is provided to provide a series of pulses of constant current over the period of the pulse to the winding(s) of the LVDT, DVRT or SVRT, wherein the resultant signal output of the LVDT, DVRT or SVRT does not experience falloff. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0012]    So that the manner in which the above recited features of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only typical embodiments of this invention and are therefore not to be considered limiting of its scope, for the invention may admit to other equally effective embodiments. 
           [0013]      FIG. 1  is a sectional view of a cased wellbore, showing a multi-arm caliper tool suspended therein by a wireline; 
           [0014]      FIG. 2  is a view of the multi-arm caliper tool showing the deployment of the probe arms thereof against the interior wall of the casing; 
           [0015]      FIG. 3  is a partial sectional view of the housing of the multi-arm caliper tool, showing the deployment of a probe arm thereof against the inner wall of well casing, and the interconnection of the probe arm and an LVDT; 
           [0016]      FIG. 4  a partial sectional view of the housing of the multi-arm caliper tool showing the location and arrangement of a reference transducer therein; 
           [0017]      FIG. 5  a partial sectional view of the housing of the multi-arm caliper tool showing the location and arrangement of a reference transducer therein; 
           [0018]      FIG. 6  is a schematic representation of the structure of an LVDT; 
           [0019]      FIG. 7  is a graph representing the output of the LVDT at different temperatures over a range of probe arm movement; 
           [0020]      FIG. 8  is a graph representing the output of the LVDT at different temperatures at a single probe arm position; 
           [0021]      FIG. 9  is a graph representing the output of the reference LVDTs at different temperatures; 
           [0022]      FIG. 10  is a graph representing the voltage output of an LVDT at affixed temperature; 
           [0023]      FIG. 11  is a graphical representation of a corrected LVDT output over an expected in use temperature range; 
           [0024]      FIG. 12  is a flowchart demonstrating the steps of determining a correction value for the LVDT; 
           [0025]      FIG. 13  is a flowchart demonstrating a methodology of using the multi-arm caliper tool and temperature adjustment algorithm to obtain corrected results for the geometric condition of the inner wall of the casing; 
           [0026]      FIG. 14  is a flowchart demonstrating an alternative methodology of using the multi-arm caliper tool and temperature adjustment algorithm to obtain corrected results for the geometric condition of the inner wall of the casing; 
           [0027]      FIG. 15  is an electrical schematic of an LVDT incorporating a constant current driver; 
           [0028]      FIG. 16  is an electrical schematic of an DVRT incorporating a constant current driver; and 
           [0029]      FIG. 17  is an electrical schematic of an SVRT incorporating a constant current driver. 
       
    
    
     DETAILED DESCRIPTION 
       [0030]    Provided herein are apparatus and methods for more accurately assessing the geometric condition, i.e., the actual inner wall profile and condition of a tubular, including the extend in height or depth of areas of erosion, inward bending, outward bending, weldments, seams, fissures and the like, over a broad range of operating temperatures without falloff in the signal of the measuring device. 
         [0031]    Applicants have discovered that the integrity of a measurement tool output signal used for the assessment of the geometric condition, i.e., the actual inner wall profile and condition of a tubular may be enhanced by incorporating a constant current driver as the driver for the winding of the measuring transducer winding and thereby ameliorate the effect of temperature change on the output signal of the measurement tool. For purposes of illustration, the apparatus and methods for providing this improved assessment will be described herein with respect to a multi-arm caliper tool, useful to assess the condition of the inner wall of casing cemented into place in a wellbore. 
         [0032]    Referring to  FIG. 1 , an evaluation tool  10  configured for evaluation of the interior surface of a tubular  14  described herein includes a caliper subassembly configured herein as a multi arm caliper tool  20 , which is supported between a pair of centering stabilizers  30   a,    30   b,  and a data acquisition subassembly  40  which is physically connected to the stabilizer  30   a  and is in communication via a link such as an electrical or optical link, with the multi-arm caliper tool  20 . A line  50  is physically secured to an end  42  of the data acquisition subassembly  40  and extends to a remote location (not shown) and is used to position the tool  10  in the tubular  14 . In the configuration of the tool  10  shown in  FIG. 1 , the tubular is a casing  16  which is held in a well bore  19  by cement disposed intermediate the exterior of the casing  16  and the wall of the well bore  19 . The line  50  may be a wireline, in which data signals generated in the data acquisition subassembly  40  which are indicative of the geometric condition of the inner wall  15  of the casing  16  may be transmitted to a remote surface location. The tool  10  is lowered into the casing  16  with the centering stabilizers  30   a,    30   b  in a retracted state (not shown), and when a desired depth is reached, the arms  32  are extended to the position shown in  FIG. 1 , whereby rollers  34  engage the inner wall  15  of the casing  16 . Although each centering stabilizers  30   a,    30   b  are shown having two arms, at least three, and preferably more, arms  32  extend from the centering stabilizers  30   a,    30   b  to center the multi-arm caliper tool  12  located therebetween within the casing  16 . 
         [0033]    As will be described further herein, the multi-arm caliper tool  12  includes a plurality of probe arms  60 , and in  FIG. 1 , five such probe arms  60   a  to  60   e  are shown. Each probe arm  60  is retractable into a position extending generally along the length of the tool to protect them as the tool  10  is lowered into the casing  16 , and is also positionable in an extended position as shown in  FIG. 1  where the tips of the probe arms engage the inner wall  15  of the casing  16 . Once the multi-arm caliper tool  12  is centered, the probe arms  60  are freed from the retracted position, and the tips thereof engage the inner wall  15  of the casing  16 . As shown in  FIG. 2 , wherein the casing  16  is undisturbed, i.e., is round, and does not include loss of integrity regions such as kinks, out of roundness, or wall erosion, the multi-arm caliper tool  12  is supported by above by wireline  50 , and a plurality, in this example for purposes of ease of understanding, eight probe arms  60   a - h,  extend outwardly from the body of the multi-arm caliper tool  12  and engage the inner wall  15  of casing  16 .  FIG. 2  shows a view of the multi-arm caliper tool  12 , showing a plurality of probe arms  60 , for ease of understanding and to correspond to the structure shown in  FIG. 1 , eight probe arms  60 . However, it is to be understood that a multi-arm caliper tool may have a greater or lesser number of probe arms  60 , typically 4forty or more such probe arms  60 , and eight probe arms  60  are depicted herein for purposes of illustrating the multi-arm caliper tool  12 , and not for purposes of limitation. The greater the number of arms, the better is the circumferential coverage, i.e., the greater the percentage of the wall contacted by an arm, and thus evaluable by the multi-arm caliper tool  20 , for a given nominal tubular diameter. 
         [0034]    Once the probe arms  60  of the multi-arm caliper tool  12  are deployed as shown in  FIG. 1 , the wireline  50  is pulled upwardly, toward the surface (not shown) at a consistent rate of 10 to 60 feet per second (f/s). As the tool  10  moves upwardly in the direction of arrow U in  FIG. 1 , the rollers  34  on the centering stabilizers  30   a,    30   b  allow the tool  10  to move upwardly with minimal friction, and the multi-arm caliper tool  12  remains generally centered in the casing  16 . As the multi-arm caliper tool  12  moves upwardly in the casing  16 , the probe arm  60  tips are spring loaded to engage against the inner wall  15  of the casing  16 , and variations in the distance from the interior of the multi-arm caliper tool  12  with respect to the adjacent inner wall along a radius over which any probe arm  60  extends results in motion of the probe arm  60  tip towards or away from the body of the multi-arm caliper tool  12 . 
         [0035]    Referring now to  FIG. 3 , a partial sectional view of the multi-arm caliper tool  12 , showing the details of the contact of a single probe arm  60  with the inner wall  15  of the casing  16  is provided. Multi-arm caliper tool  12  comprises a housing  62  within which a plurality if probe arm pockets  63  (only one shown in  FIG. 3 ) extend inwardly of the sidewall  66  thereof, such that a probe arm  62  is received in, and extends from, each probe arm pocket  63 . A slot  64  is provided for each probe arm  60  such that a portion of the probe arm  60  extends outwardly from the slot  64 , and an additional portion of the probe arm extends inwardly from the slot  64 . The sidewall  66  of the multi-arm tool  12  extends as a right cylindrical surface, generally centered around the centerline  65  of the tool. The inner end of the probe arm  60  is connected to a distance sensor  120 , such as an LDVT, such that motion of the probe arm  60  in response to changes in the adjacent inner wall  15  surface of the casing  16  as the multi-arm caliper tool  12  moves in the casing may be converted to representative electrical signals. 
         [0036]    Each probe arm  60  is configured having a generally dog-leg shape, wherein a first arm portion  70  is positioned to extend in a first direction outwardly of the slot  64  and a second arm portion  72  extends in a second direction inwardly of the housing  66  from the slot  64  into a secondary opening  80  in the housing  66 . The extending directions of the first and second arm portions  70 ,  72  form substantially right angle  80  centered at a mounting pivot aperture  74  by which the probe arm is secured over a pivot pin  82  extending across the slot  64  in the general direction of the circumference of the housing  66 . Thus, the probe arm  60  is secured within the slot  64  but is free to rotate about the pivot pin  82 . 
         [0037]    First arm portion  70  extends from pivot aperture  74  outwardly of slot  64  and includes an outer wall  90  disposed in a position generally facing the exterior of the tool  12 , and includes a recessed contoured portion  92  terminating at tip  94 . Inner wall  97  thereof extends adjacent a recess wall  68  of the housing  64  extending below the position of slot  64 , and includes an inwardly double canted face adjacent the end thereof terminating at tip  94 . On contoured portion  92  of outer wall  90  adjacent tip  94  is disposed an extending tip  96 . First arm  70  is configured such the extending tip  96 , which extends outwardly from the outer wall  90 , engages the inner surface  15  of the casing  16 . Extending tip is manufactured from a high wear resistant material, such as a carbide or diamond, which has higher wear resistance than the material of probe arm  60 , which may comprise steel such as stainless steel. 
         [0038]    Second arm portion  72  extends from pivot aperture  74  inwardly of slot  64  and terminates within secondary opening  80  of housing  66 . The upper and lower side walls  100 ,  102  of the second arm extend to a gable shaped end  104 , and a secondary aperture  106  extends through the second arm  72  inwardly of the gabled end  104 . A transducer pin  108  extends through the secondary opening  106 , to secure the second arm  72  to the transducer actuating arm  122  of the distance sensor  120  as will be further discussed herein. 
         [0039]    Referring still to  FIG. 3 , housing  62  includes passage  110  extending upwardly from secondary opening  80  and into a transducer pocket  112 . Distance sensor  120 , includes an LVDT  130  positioned in transducer pocket  112  about the opening of actuating arm passage  110  thereinto, a spring loaded pin  134  extending through the passage  110  and extending inwardly of the transducer pocket  112  within the LVDT  130 , with the ferromagnetic core  132  of the LVDT  130  disposed on the end thereof extending inwardly of the LVDT  130 , and the transducer actuating arm  122  pivotally connected to the portion of the spring loaded pin  134  closest to the secondary opening  80 . 
         [0040]    As the multi arm caliper tool  12  traverses upwardly in the casing  16  and encounters a disturbance in the wall  15  of the casing  16 , the extending tip  96  thereof will move toward or away from the housing  66  of the multi arm caliper tool  12 . Because the arm  60  pivots about pivot pin  82  and second arm  72  extends at an oblique angle  80  from first arm  70  and inwardly of the housing  66 , motion of the extending tip  96  toward and away from the housing  66  translates into movement of the center of the transducer pin  108  along the arc  136 , which moves the transducer actuating arm  122  generally inwardly or outwardly of the passage  110 . Movement of the transducer actuating arm  122  causes movement of the spring loaded pin in the passage  110 , resulting in movement of the ferromagnetic core  132  of the LVDT  130  within the body thereof. This movement of the ferromagnetic core  132  in the body of the LVDT generates a disturbance in the electric field of the LVDT, which is measured and converted to a signal which is indicative of the motion of the probe arm tip  96  caused by changes in the geometry of the wall  15  of the casing  16 . 
         [0041]    Referring still to  FIG. 3 , spring loaded pin  134  includes a first portion  136  having a flange  138  thereon from which a pin  140  having the ferromagnetic core  132  on the distal end thereof extends, and a blade portion  136  extending outwardly of the underside of the flange  138  wherein the pinned connection to the actuating arm  122  is pivotally connected thereto. Passage  110  includes a major diameter portion extending from opening  80  in the direction of pocket  112 , and a minor diameter portion  144  communicating therewith and extending into communication with pocket  112 , such that an annular ledge  146  is disposed in passage  110  adjacent to the pocket  112 . A seal, not shown, may be provided in a gland extending inwardly of the circumferential wall of the minor diameter portion  144  to enable reciprocating movement of the pin  134  therethrough, but also seal off the pocket  112  region from fluids in the tubing. A spring  148 , such as a coil spring, is received between flange  138  and annular flange  148 , and around pin  134 , such that the spring tends to urge flange  138 , and thus the pin  108  in the end of second arm  72  of probe arm  60 , in the direction away from the passage (downward in  FIG. 3 ), and hence, urges the probe arm tip  96  against the inner wall  15  of the casing  16 , i.e., outwardly of the housing  66  to maintain the extending tip  96  on the tip  94  of the probe arm in engagement with the inner wall  15  of casing  16 . 
         [0042]    As discussed previously, each of the probe arms  60  pivot at pivot pin  82  extending generally in the circumferential direction of the housing  66 . To help ensure that each probe arm  60  aperture  74  is positioned on the same circumference, and thus each probe arm extending tip  96  will extend equally from the housing  66  if the housing  66  is centered in the tubular and the tubular is perfectly round, each pivot pin  82  is positioned such that the center thereof, i.e., the center of the linear span of the pivot pin  82  across the slot  68  is on the same circumference around the centerline of the housing  66 . 
         [0043]    Referring still to  FIG. 3 , an erosion region  150  is depicted extending inwardly of the wall  15  of casing  16 , and the end of probe arm  94  extends inwardly of the erosion region  150 , such that probe arm extending tip  96  maintains contact with the now eroded wall  15  surface. The original wall surface  152  is shown in phantom, as well as the position of the probe arm  60  and probe arm extending tip  96  if the tip  96  was engaged against the original wall surface  162 . As can be seen in the Figure, the distance the probe arm tip  96  has travelled to the deeper part of the erosion region  150  (furthest inwardly of wall  15 ) is the difference between dimensions p 1  and p 2 . This movement results in movement of the pin  108  in second arms through an arc having an equivalent linear distance in the longitudinal direction of the pin  134  of “S”. The movement of the pin  108  through distance S causes an equal movement of the magnet  132  by the same distance, shown within the LVDT  130  as X 1 . Thus the tool  12  may be calibrated to correlate a difference between p 1  and the actual distance between the tool centerline  65  and the end of the extending probe tip  69 , and a corresponding stroke or movement of the magnet  132  in the LVDT. Likewise, at a single temperature, the difference between p 1  and the actual distance between the tool centerline  65  and the end of the extending probe tip  69  can be correlated to an electrical signal output from the LVDT  130 . 
         [0044]    Referring now to  FIGS. 4 and 5 , the configuration of two locations within housing  82  where reference LVDT&#39;s are located is shown. In the tool  10 , in order to more effectively compensate for temperature based drift in the measured readings of the multiple LVDT&#39;s  130  which are linked to arms  60 , two reference transducers configured as modified LVDT&#39;s  130  configured to provide an electrical signal and enable an assessment of temperature induced drift on the output of the LVDT&#39;s  130  linked to the probe arms  60 , full extension reference transducer  170  and fully retracted reference transducer, are provided in transducer pockets  112  similarly to the LDVT&#39;s  130  used to convert the mechanical motion of arm  60  into electrical signals. The transducer pocket  112  for the reference transducers  170 ,  172  are configured to open into passage  110 , opening  80  and slot  64 . Thus, the ambient conditions experienced at the reference transducers  170 ,  172 , are as closely matched as possible to those of the active LDVT&#39;s interconnected to probe arms  60 . These reference transducers  170 ,  172  may be located in adjacent open slots in the side wall of the housing  82 , or may be disposed so as to be spaced apart by slots  64  having active probe arms  60  therein. 
         [0045]    Referring first to  FIG. 4 , the fully extended reference transducer  170 , i.e., the reference transducer  170  in which the ferromagnetic core thereof is shown in the position where an active transducer would be if connected to a probe arm in a fully extended from the tool state, is configured such that the ferromagnetic core  132  thereof is fixed within the transducer  170  in a position where the magnet in a measuring LVDT, at the maximum outward position of the extending tip  96  of the arm  32  interconnected thereto, would reside. The ferromagnetic core  132  is affixed therein, in this position, by a high temperature adhesive selected to minimize interference with the magnetic field generated by transducer  170 . A thermocouple or other temperature measuring device such as a temperature probe  178  is also provided on the housing adjacent to the slot  64 , for enabling measurement of the in-situ temperature of the reference transducer  170 . 
         [0046]    Referring to  FIG. 5 , the fully retracted reference transducer  172  is configured such that the magnet  132  thereof is fixed within the transducer  170  in a position where, the magnet  132  in an LVDT attached to a probe arm in a fully retracted state, i.e., at the maximum inward position of the tip  96  of the arm  32  interconnected thereto, would reside. The ferromagnetic core  132  is affixed therein, in position, by a high temperature adhesive selected to minimize interference with the magnetic field generated by the magnet  132 . A thermocouple or other temperature measuring device such as a temperature probe  178  is also provided on the housing adjacent to the slot  64 , for enabling measurement of the in-situ temperature of the reference transducer  170 . 
         [0047]    Referring now to  FIGS. 6 through 8 , the operation of an LVDT  130 , and the effect of temperature change thereon, are generally depicted. Referring initially to  FIG. 6 , the LVDT includes a mobile core configured as the magnet  132 , which is moveable within a tubular housing  180 . To one side of the tubular housing  180  is disposed a driving primary coil  182  which is driven by a sinusoidal or other ac drive voltage at a relatively low voltage, and to the opposite side of the tubular housing  180  is disposed a split driven, or secondary, coil  186 , having a center tap  188  positioned approximately mid-way down the length of the secondary coil  186 , and positioned in the center of the stroke of the magnet  132  in the tubular housing  180  between the fully retracted and fully extended positions of an arm  32 . 
         [0048]    A first tap line  194  is connected to the end of the secondary coil  186  adjacent the end of tubular housing  180  where magnet  132  is positioned when arm  32  is fully retracted, and a second tap line  192  extends from the end of secondary coil  186  where the magnet  132  is positioned when arm  32  is in the fully extended position. A center tap line  190  extends from center tap  188 . The arrangement of the primary and secondary coils  180 ,  186 , power supply  184  each LDVT  130 , and taps and tap lines  188 ,  190 ,  192  and  194  are identical for all LDVT&#39;s  130  and the reference transducers  170 ,  172 . 
         [0049]    For ease of understanding, assuming the ferromagnetic core  132  is centered along the length of the tubular housing  180 . As the probe arm  60  ( FIG. 3 ) connected to the LDVT  130  moves inwardly of the housing (the extending tip  96  is travelling on the direction of the housing  82 ) a voltage V 1  and V 2  are measured between center tap line  190  and first and second tap lines  192 ,  194 . Likewise, when extending tip  96  on the probe arm  60  moves in the direction away from the housing  82 , the magnet  132  is moved in a direction outwardly of the tubular housing  180 , causing voltages V 1  and V 2  to appear between the center tap line  190  and the first and second tap lines  192 ,  194 . The location and magnitude of the voltages between the center tap line  190  and the tap lines  192 ,  194  indicate the direction and extent of movement of the tip  94  vis-a-vis the centerline of the housing  82 , indicative of the condition of the wall of the tubular  14  against which extending tip  96  is engaged. Likewise, the reference transducers  170 ,  172  are driven at the same ac voltage as the LDVT&#39;s  130 , and a reference signal corresponding to a fully retracted and a fully extended arm position is generated between center tap line  190  and first and second tap lines  192 ,  194 . It is understandable that other variations of LVDT wiring and respective geometric position of the ferromagnetic core could be similarly used in a way the output signal could vary in the opposite direction such as the output signal would increase as the caliper stroke increases positively. 
         [0050]    Referring now to  FIGS. 7 and 8 , the effect on temperature on the output of the LVDT&#39;s and reference transducers is shown. As is seen in  FIG. 7 , for a given caliper stroke, as the temperature T of the transducer changes from ambient T 0  to a higher temperature T 1 , the voltage detected at the secondary coil  186  drops. As shown in  FIG. 8 , as the temperature of the transducers in the LVDT&#39;s  130  and reference transducers  170 ,  172  increases, the difference in voltage output between a non-extended VO and extended VE tip  94  changes, such that the same extension of the tip  94 , and thus the same movement of the magnet  132  within the tubular housing  180 , results in a greater voltage change as shown by the divergence between the Voltage curves for Vo(t) and VE(t) as the temperature increase from t 0  to T 1 . 
         [0051]    Thus, operating conditions encountered when the tool  10  is operating in a well bore casing, tubing or the like, the downhole measurement at each LVDT  130  and the reference transducers  170 ,  172  produces a raw signal output that is affected by temperature. The ambient temperature encountered by the tool  10  can substantially vary, and the effect on the LVDT  130  and the reference transducers  170 ,  172  can vary based upon on the type of transducer and depending on the way the transducer is actually operated in a given tool. For purposes of the description hereof, the transducers are LVDT type transducers driven with a low voltage sinewave which can operate at a frequency between 5 khz and 40 khz. As discussed previously, the mechanical displacement of the probe arm tip  96  causes movement of the ferromagnetic core  132  (magnetic core) which produces a specific signal amplitude (the output) that can be described by a continuous and linear function over the actual working domain of the transducer, 
         [0052]    1. The voltage output of the transducer is maximum when the magnet  132  is in a retracted position, i.e., the position shown in  FIG. 5  and diminishes, i.e., is reduced, as the ferromagnetic core  132  extends outwardly toward the position thereof in  FIG. 4 , 
         [0053]    2. The overall effect as the temperature is increased, resulting from a combination of factors, is characterized by a gradual decrease of the transducer output for a given probe arm  60  extension from the housing  82 , or tip extension  96  distance from the housing  82 , as the temperature encountered by the tool  10  increases. This effect is substantially linear and homogeneous assuming transducers and use thereof follows precautions that are of the general knowledge in the domain of measurements performed in wells. 
         [0054]    At a given temperature T variation of the output signal of a displacement transducer “i” varies substantially linearly and can be described by the following linear function (1): 
         [0000]    
       
         
           
             
               Vi 
                
               
                 ( 
                 x 
                 ) 
               
             
             = 
             
               
                 Vi 
                  
                 
                   ( 
                   
                     X 
                      
                     
                         
                     
                      
                     0 
                   
                   ) 
                 
               
               + 
               
                 Ki 
                 × 
                 
                   ( 
                   
                     x 
                     - 
                     
                       X 
                        
                       
                           
                       
                        
                       0 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             Where 
              
             
                 
             
              
             
               ( 
               2 
               ) 
             
              
             
               : 
             
           
         
       
       
         
           
             Ki 
             = 
             
               
                 
                   Vi 
                    
                   
                     ( 
                     Xf 
                     ) 
                   
                 
                 - 
                 
                   Vi 
                    
                   
                     ( 
                     
                       X 
                        
                       
                           
                       
                        
                       0 
                     
                     ) 
                   
                 
               
               
                 ( 
                 
                   Xf 
                   - 
                   
                     X 
                      
                     
                         
                     
                      
                     0 
                   
                 
                 ) 
               
             
           
         
       
     
         [0055]    Ki: is the gain of the transducer and is represented by the slope of the response line, 
         [0056]    In  FIGS. 7, 9 and 10 , X 0  marks the minimal position of the mechanical input in the displacement transducer, that coincides with Vi(X 0 ) which is considered the electrical zero of the measurement after calibration and also is the intersect (ordinate) on the LVDT  130  response graph, 
         [0057]    In  FIG. 10 , Xf denotes the maximal position of the mechanical change in the displacement of the ferromagnetic core  132  in the LVDTs  130 . It coincides with the full scale of the measurement Vi(Xf). 
         [0058]    The plurality of LVDT&#39;s  130  and reference transducers  170 ,  170  share a common drive and are calibrated at ambient temperature, i.e., where used to evaluate a well bore tubular at the surface or in a laboratory, so each transducer&#39;s ( 130 ,  170 ,  172 ) output is respectively characterized at least for a minimum mechanical position (retracted) of the arms  32  and for a maximum mechanical position (extended) of the arms  32 . Other intermediate arm  32  positions may also be evaluated during the calibration operation. Ambient temperature is generally the one experienced while preparing for a tool operation at a wellsite. Therefore this reference temperature is somewhat arbitrary. 
         [0059]    Output signals from all transducers, including the active-LVDTs  130  connected to arms and the reference transducers  170 ,  172 , are recorded and maintained in the memory of a logging acquisition system during calibration. 
         [0060]    When the actual measurement commences downhole, the tool has already been submitted to the borehole temperature during its descent into the well and the calibration measurements performed at surface can no longer be used directly because the transducers have now a response that is altered by a certain temperature factor. Prior art systems have used predictive algorithms which attempt to provide calibrations and corrections for changes in the tool temperature, but, these systems may result in errors in measurement of the geometry of the tubular inner surface. 
         [0061]    Referring now to  FIGS. 9 and 10 , the use and operation of the reference sensors  170 ,  170  are graphically shown. At the calibration, i.e., ambient surface temperature where the tool is calibrated, reference sensor  172  having its ferromagnetic core secured in the fully retracted position provides a voltage output of V 1  ref (T 0 ) shown at the “A 0 ” mark on  FIG. 9 . Reference sensor  170 , having the ferromagnetic core  132  thereof fixed in the fully extended position, has a voltage output of V 2  ref (T 0 ) shown at the “B 0 ” location on  FIG. 9 . Thus, assuming a linear change in voltage output from the transducers of the LVDT&#39;s, the linear segment A 0 -B 0  represents a single virtual transducer, operating over a virtual full stroke, where the full stroke of the ferromagnetic core (which corresponds to the full measureable stroke of the extending tip  96 ) is normalized to 1. This linear function has the following form for a pair of reference sensors  170 ,  172 : 
         [0000]        VrefT 0( x )= Vref 1 T 0+ KrefT 0× x  
 
         [0000]      Where: 
         [0000]        KrefT=V ( A 0)− V ( B 0)
 
         [0062]    At any temperature T 1  the pair of reference transducers  170 ,  172  behave in a similar fashion as the plurality of active transducers in the LVDT&#39;s  130 . Each respective output signal is shown as A 1 , B 1  on the graph that determines another linear segment featuring the virtual output of the reference sensors at a temperature T 1 . The function becomes: 
         [0000]        VrefT 1( x )= Vref 1 T 0+ KrefT 0× x  
 
         [0000]      Where: 
         [0000]        KrefT 1= V ( A 1)− V ( B 1)
 
         [0063]    As illustrated in  FIG. 9 , a temperature increase to T 1  from T 0  causes a negative shift of the intersect with the Y axis and also possibly some slight gain change, i.e., the slope of line segment from Tref 1 T 0  to Tref 2 T 0  is less than that from Tref 1 T 1  to Tref 2 T 1 . 
         [0064]    When the plurality of transducers of the LDTV&#39;s  130  and the reference transducers  170 ,  172  are calibrated using mechanical gauges at temperature T 0 , the output of each sensor is recorded for the purpose of normalizing the Y axis intersect and gain of all transducers to a uniform output. This is a general practice, as well as is maintaining the calibration values in a system memory. In the same manner herein, the output of the reference sensors during the calibration is also recorded along with the other data. 
         [0065]    When a measurement is taken by a transducer “i”, at temperature T 1  different than T 0   
         [0066]    (a) The output signal is Vi is read-up along with temperature signal T 1   
         [0067]    (b) The value E of the magnet relative position from a “0” point, representative of the distance that extending tip  96  extends from the centerline  65  of the tool  12 , is approximated as a function of Vi and T 1   
         [0068]    (c) Output reference signals Vref 1  determines α, the correction coefficient at x=0 as: 
         [0000]      α= Vref 1( T 1)/ Vref 1( T 0)
 
         [0069]    (d) Output reference signal Vref 2  determines β, the correction coefficient at x=1 as: 
         [0000]      β= Vref 2( T 1)/ Vref 2( T 0)
 
         [0070]    (e) The determination of the correction coefficient for the transducer “I” is illustrated on the graph of  FIG. 9 . The abscissa E representing the position of the magnet  132  in the cylindrical housing  180  intersects the virtual reference line A 1 -B 1  at C 1  making the temperature correction coefficient “C” the result of a linear proportion of α and β (9): 
         [0000]        C=α ×(1− E )+β× E  
 
         [0071]    (f) The temperature corrected output of the transducer “i” is then calculated as (10): 
         [0000]    
       
         
           
             Vic 
             = 
             
               Vi 
               C 
             
           
         
       
     
         [0072]    (g) Now that Vi is temperature corrected, it is valid to refer to the initial expression of Vi at T 0 , the temperature at which Input and output of Displacement sensors have been calibrated (11) 
         [0000]        ViT ( x )= Vi ( X 0)+ KiT ×( x−X 0)
 
         [0073]    Now extracting “x” the mechanical input of the displacement transducer (12) 
         [0000]    
       
         
           
             x 
             = 
             
               
                 Vic 
                 - 
                 
                   Vi 
                    
                   
                     ( 
                     
                       X 
                        
                       
                           
                       
                        
                       0 
                     
                     ) 
                   
                 
               
               
                 KiT 
                  
                 
                     
                 
                  
                 0 
               
             
           
         
       
     
         [0074]    Where: 
         [0075]    Vi(X 0 ) is the intersect of the caliper arm derived from calibration at T 0   
         [0076]    KiT 0  is the gain of the transducer derived from calibration at T 0 . 
         [0077]    The result is shown graphically on  FIG. 11 , wherein the different effect on the output of the transducers, and thus the LDVT&#39;s over time is shown, and the correlation thereof to result in a corrected output is shown. Thus, as shown in  FIG. 11 , as the temperature increases, the measured voltage output of an LVDT drifts downwardly. By applying a correction factor derived in-situ, the actual position of the extending tip  96  on arm relative to the centerline of the housing may be more accurately established, as shown as the dashed line on  FIG. 11 . 
         [0078]    Referring now to  FIG. 12 , a method of using the tool  10  to obtain accurate information concerning the internal surface of a tubular is shown in chart form. Starting at the calibration step  200 , the caliper arms are calibrated at step  202 , wherein the change in voltage in each LDVT  130  is assessed across at least the fully extended, and fully retracted, position of the tip  94  of each arm  32 . Simultaneously, the ambient temperature, the voltage in reference transducer  170  at the ambient temperature is measured at step  204 , and the voltage in reference transducer  172  at the ambient temperature is measured at step  206 , and recorded in a system memory. At this point, the tool  10  may be used to evaluate the interior surface of a tubular, such as casing  16 . 
         [0079]    Once tool  10  is located in the tubular, such as the casing  16 , and the caliper arms  32  are deployed outwardly as shown in  FIG. 3 , the measuring step  210  may begin. As the tool  10  is pulled toward the surface and traverses the casing, each caliper arm  32  may move inwardly and outwardly of the housing, resulting in a voltage change at the LVDT interconnected therewith. Likewise, the output voltage of the reference transducers  170 ,  172  changes as the temperature thereof changes. As shown at step  210 , logging is undertaken by measuring the voltage output of the LVDT associated with each caliper arm  32  at step  212 , the reference voltage of the reference transducer  170  as is the reference voltage of the reference transducer  172 , and the temperature of the housing is acquired from at least one of temperature probe  178  as the tool  10  is moving in the casing. These measurements are repeated tens or hundreds of times per second, the rate of acquisition of the measured inputs being dependent upon the speed at which the data can be processed and/or transmitted to the surface along the wireline  50 . The measurements may be taken serially, by continuously opening and closing gates to each of the LVDT&#39;s  130 , the two reference transducers  170 ,  172 , and the thermocouple and correlating each set of such readings to a tool depth. 
         [0080]    As the measurements are continuously taken in the measuring step  210 , the measurements are converted to electrical signals and evaluated in the process step  200 . For example, where 8 caliper arms are provided on the tool  10 , data from the eight LVDT&#39;s  130  associated with each of the eight caliper arms  32  are sequentially evaluate, along with a reference voltage for each of reference transducers  170 ,  172 , and at least one temperature probe  178  temperature signal. As seen at step  220 , correction coefficients α and β are generated for use in determining the corrected distance of the tip  94  from the tool centerline. Coefficient α, representing the ratio of the output voltage of reference transducer  170  (fully extended reference) at the measurement temperature divided by the reference voltage thereof measured at ambient is calculated at step  222 , and coefficient β representing the ratio of the output voltage of reference transducer  172  (fully retracted reference) at the measurement temperature divided by the reference voltage thereof measured at ambient as shown at step  224 . These coefficients α and β are then used as correction factors, as discussed herein, to calculate a temperature correction coefficient at step  226 , which is in turn applied to the voltage output of each of the LVDT&#39;s  130  associated with each caliper arm  32  at step  228 , resulting in a corrected caliper arm voltage value  230  which correctly correlates to the distance the tip  94  of each caliper arm  32  extends from the centerline of housing  82 . The resulting caliper arm voltage value  230  for each measured value of each LVDT is either stored in tool memory, or transmitted via wireline  5  to the surface, optionally along with the calibration data. The raw data determined in step  210  may alternatively transmitted along wireline  50 , wherein step  220  is performed at the surface. Combinations of downhole and surface processing of the data may also be undertaken. 
         [0081]    Referring now to  FIGS. 13 and 14 , two different paradigms for data acquisition and processing are shown schematically in flow chart form. In  FIG. 13 , there is shown a methodology for active correction of the caliper arm tip  94  position without the use of reference transducers, wherein the individual LVDT&#39;s  130  associated with each of the caliper arms  32 , or a sampling thereof, have been previously calibrated over an expected temperature range and correction factors representative of coefficients α and β were previously generated and stored in a system memory. In this approach, the voltage signal  240  is sent to the plurality of LVDT&#39;s  242 , and the output thereof is received in the downhole tool electronics  246 . Simultaneously, the temperature of the tool  10  is acquired from a temperature transducer  244 , such as the temperature probe  178 , and the displacement transducer and temperature transducer data is transmitted, via wireline  50 , to a surface data acquisition unit which includes a programmed computer for computing the corrected tip  94  location using the temperature adjustment algorithm  250  and calibration data acquired at different temperatures before the tool was deployed in the well bore. 
         [0082]    In  FIG. 14 , a paradigm for generating correction factors using reference transducers, such as reference transducers  170 ,  172 , is shown. This paradigm, data acquisition and data flow are the same as that shown in  FIG. 13 , except now the reference transducers, shown at box  243  are used, and the coefficients α and β are generated based on the Voltage output, and drift or change in that voltage output, as the tool traverses the tubular being evaluated. 
         [0083]    Referring now to  FIG. 15 , an evaluation circuit for an LVDT  300 , which may be incorporated into a caliper tool in replacement of LDVT  130  of  FIGS. 3 and 6  hereof, is shown. The Linear Variable Differential Transformer (LVDT) consists of a primary winding  302  and a split secondary winding  304  with a first half-winding  304   a  of the secondary winding  304  counter-wound with respect to the other, second half-winding  304   b  of the secondary of the secondary winding  304 , wherein the counterwound first and second half windings  304   a,    304   b  extend from a center tap  306 . The windings are disposed about a bobbin (not shown), over which the wire making up the windings  302 ,  304   a  and  304   b  is wound. Each secondary winding  304   a,    304   b  resides in its own winding space on the bobbin. The primary winding  300  is wound over both secondary half windings  304   a,    304   b  so that when powered it couples magnetically to both secondary half windings  304   a,    304   b.  A ferromagnetic core is reciprocally disposed within a through bore within the bobbin. The center tap  306  is connected to ground, and each of the opposite ends of the first and second half windings  304   a,    304   b  are connected to different ones of the input connections to a differential amplifier  310 . On end of the primary winding  302  is grounded, and the other end thereof connected to the output of a constant current driver. 
         [0084]    The position of the ferromagnetic core within the sensor is inferred by the output of the differential amplifier  310 , as the differential amplifier  310  subtracts the signal of one secondary half winding  304   a  from the signal of the other secondary half winding  304   b,  resulting in an output that is proportional to the position of the magnetic core  308  within the bobbin. 
         [0085]    Referring now to  FIG. 16 , a DVRT sensor circuit using the constant current drive method of winding resistance temperature compensation is shown. The DVRT is connected in bridge fashion to take advantage of the inherent cancellation of drift due to variation in coil resistance. The DVRT includes two counterwound windings  342   a,    342   b  extending from a center tap  344 . The center tap  344  is connected to the input of a buffer amp  348 , and the output of the buffer amp  348  provides a signal from which the position of a permeable magnet core  346  relative to the center tap  344  is inferred. The ends of the windings opposite to the center tap are connected to the outputs of two different constant current drivers  314   a,    314   b.  While this yields noticeable improvement in the accuracy of the measurement versus temperature, an additional improvement is realized due to the fact that each half of the sensor is independently corrected for coil wire resistances introduced by temperature gradients across the coils. In this circuit, there are two constant current drivers  314   a,    314   b.  The two windings  342   a,    342   b  are driven by precision pulses from the constant current drivers  314   a,  which pulses are exactly 180 Degrees out of phase. When the permeable magnetic core  346  is exactly in the middle of the sensor, i.e., the center of the two windings  342   a,    342   b,  the signal, which is received by the Buffer Amp  348 , is essentially zero because the two winding voltages, of exactly opposing magnitude, will cancel each other. Movement of the core  346  toward the winding  342   a  will produce an output that increases from zero to a positive voltage. Movement of the core  346  toward the winding  342   b  will produce an output that changes from zero to a negative voltage. 
         [0086]      FIG. 17  is a block diagram of the SVRT sensor circuit using the constant current drive method of winding resistance temperature compensation. One end of the winding  382  of the SVRT is connected to the output of a constant current driver  314  and to the input connection of a Buffer Amp,  348 . The other end of the single winding  382  is connected to ground. A magnetic target  384  is provided and can be configured as a magnetically permeable core within a mandrel, over which the winding  382  is wound, or a ferromagnetic target in proximity to the end of the winding  382 . The inductance of the winding  382  will increase as the core within the mandrel of the couples with an increasing number of turns of the winding  382  as it is further inserted thereinto. When deployed as a proximity sensor, the inductance will increase as the target moves in closer proximity with the end of the winding  382 . 
         [0087]    In each of the LDVT, DRVT and SRVT circuits described with respect to  FIGS. 15 to 17 , the output of the constant current driver(s)  314  is a pulse instead of a sine wave, to better facilitate high speed multiplexing of a large number of transducers, for example a plurality of transducers on a multi arm caliper tool  10 . The width and amplitude of the drive pulses are very stable with time and temperature. For example, the constant current driver  314  may comprise a precision drive pulse generator which drives a precision voltage to current converter, such as a Howland Current Pump, to output current pulses of the same amplitude. The pulses are conditioned so as to remove higher odd order harmonics to reduce distortion caused by frequency components that might be close to the self-resonant frequency of the transducer windings. The output of the each circuit shown is fed into a Track &amp; Hold Amplifier (not shown) which corrects for phase shift of the signal passing through the transducer by controlling the precise timing of sampling the signal peak. The output of the track and hold amplifier is fed into a high speed Analog to Digital Converter (not shown) which provides a digitized, sampled peak to a main controller (not shown). The entire acquisition cycle is under firmware control in the main controller. The complete circuit, including the main controller and its firmware, comprise an under-sampled, carrier to baseband demodulator. In a casing inspection multi arm caliper having a large number of transducers operating in an extremely hostile environment, a very high degree of aggregate accuracy in measurement can be obtained herewith. 
         [0088]    Preferably, when configured for use in a multi-arm caliper tool, the operation of each sensor (LVDT, DVRT and/or SVRT) is multiplexed, for example using a number of 8-channel multiplexers, such that one out of every eight sensors can be active at any one time. By connecting each sensor into the multiplexer sequentially in relation to the circumferential positions thereof on the multi-arm caliper, cross talk is significantly reduced because active sensors are not physically close to one another around the circumference of the tool. Additionally, because the sensors are dormant, in terms of sensing, until the constant current driver  314  sends a signal thereto, power consumption in the tool is reduced. By providing a constant current output, such as a pulse or pulses of a constant and same current magnitude, temperature induced variation in resistance is irrelevant to the output of the sensor. Thus, a resistance change in the control circuitry and the sensor winding does not affect the sensor output, and fall off does not occur. 
         [0089]    While the foregoing is directed to a specific embodiment of a tubular wall geometry evaluation tool, other and further embodiments may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.