Borehole logging sensor and related methods

Abstract

A method of optimizing the cross-sectional shape of a logging tool sensor includes the step of, for a given major axis dimension, selecting the minor axis dimension such that for a circular borehole geometry the cross-sectional area of the space between the sensor and a said circular borehole with which the sensor is pressed into contact is minimized. Logging tools optimized according to this technique exhibit beneficial sensor stand-off characteristics.

Claims

1. A rigid logging tool sensor comprising a cross-section being generally borehole geometry-consistent over a range of borehole diameters and comprising a transverse cross-sectional shape being an ellipse.

2. The rigid logging tool sensor according to claim 1, wherein for a given major axis dimension of the ellipse, a minor axis dimension is optimized for a circular borehole geometry such that an area of a cross-sectional space between the sensor and the circular borehole geometry with which the sensor is pressed into contact is minimized.

3. The rigid logging tool sensor according to claim 1, wherein the major and minor axis dimensions of the transverse cross-sectional shape are optimized for a range of the circular borehole geometries.

4. A method of optimizing the cross-sectional shape of the rigid logging tool sensor according to claim 1, the method including the step of, for a given major axis dimension of the ellipse, selecting a minor axis dimension such that for a circular borehole geometry a cross-sectional area of a space between the sensor and the circular borehole geometry with which the sensor is pressed into contact is minimized.

5. The method of optimizing the cross-sectional shape of the rigid logging tool sensor according to claim 4, including the step of, for the given major axis dimension of the ellipse, selecting the minor axis dimension corresponding to half an elliptical width such that for the circular borehole geometry the cross-sectional area of the space between the sensor and the circular borehole geometry with which the sensor is pressed into contact is minimized.

6. The method according to claim 4, comprising repeating the step of selecting in respect of a plurality of axis dimensions of the ellipse in order to provide a plurality of optimized cross-sectional shapes.

7. The method according to claim 6, including the further step of selecting from the plurality of optimized cross-sectional shapes one or more of the cross-sectional shapes that minimize stand-off in a chosen range of the circular borehole geometries.

8. A logging tool including the rigid logging tool sensor according to claim 1 disposed thereon.

9. A method of using a logging tool including the rigid logging tool sensor according to claim 1, the method including the steps of (a) deploying the logging tool in a borehole; (b) causing the rigid logging tool sensor to be pressed against a wall of the borehole so as to minimize a cross-sectional area of a space between the sensor and the borehole wall; and (c) drawing the logging tool along the borehole while operating the logging tool to acquire log data.

10. The method according to claim 9, the method further including the step of storing, displaying, transmitting, processing or printing the log data or a log derived therefrom.

11. A rigid logging tool sensor comprising a cross-section being generally borehole geometry-consistent over a range of borehole diameters and comprising a cross-sectional shape including a convexly curved partial ellipse being less than a whole of an ellipse.

12. The rigid logging tool sensor according to claim 11, wherein the cross-sectional shape is truncated along a line that is parallel to a major axis of the ellipse.

13. The rigid logging tool sensor according to claim 11, wherein the cross-sectional shape is truncated along a line that is parallel to a major axis of the ellipse, and wherein the line coincides with the major axis of the ellipse.

14. The rigid logging tool sensor according to claim 11, wherein for a given major axis dimension of the partial ellipse a minor axis dimension corresponding to half an elliptical width is optimized for a circular borehole geometry such that a cross-sectional area of a space between the sensor and the circular borehole geometry with which the sensor is pressed into contact is minimized.

15. The rigid logging tool sensor according claim 11, wherein major and minor axis dimensions of the partial ellipse comprises a transverse cross-sectional shape optimized for a range of circular borehole geometries.

16. The rigid logging tool sensor according to claim 11, wherein the sensor comprises an acoustic logging sensor, a nuclear logging sensor, a resistivity logging sensor, a permittivity sensor, a conductivity logging sensor, or a nuclear magnetic resonance sensor.

17. A logging tool including the rigid logging tool sensor according to claim 11 disposed thereon.

18. A method of using a logging tool including the rigid logging tool sensor according to claim 11, the method including the steps of (a) deploying the logging tool in a borehole; (b) causing the rigid logging tool sensor to be pressed against a wall of the borehole so as to minimize a cross-sectional area of a space between the sensor and the borehole wall; and (c) drawing the logging tool along the borehole while operating the logging tool to acquire log data.

19. The method of according to claim 18, the method further including the step of storing, displaying, transmitting, processing or printing the log data or a log derived therefrom.

Description

DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 illustrates in schematic form a circular or part-circular prior art logging tool sensor pad that is pressed into contact with the wall of a circular borehole, and illustrates by way of shading the extent of stand-off of the sensor pad;

(2) FIG. 2 is a view similar to FIG. 1 illustrating an elliptical or truncated elliptical logging tool sensor pad similarly pressed into contact with the circular borehole wall, and again indicating the extent of stand-off by way of shading;

(3) FIG. 3 shows the variance of the extent of stand-off of the elliptical sensor pad of FIG. 2 with variation of ellipse minor axis dimension;

(4) FIG. 4 is a series of plots comparing the extent of stand-off of a series of elliptical or part-elliptical logging tool sensor pads according to the present disclosure with the extent of stand-off of a circular logging tool sensor pad; and

(5) FIGS. 5a-5e illustrate the cross-sections of a number of elliptical, part-elliptical, and/or part-circular sensor pads, according to the present disclosure.

(6) There now follows a description of preferred embodiments of the present disclosure, by way of non-limiting example, with reference being made to the accompanying figures.

DETAILED DESCRIPTION

(7) Referring to the drawings, there is shown in FIG. 1 a prior art sensor pad 10 that in practice would be supported in a cylindrical, elongate logging tool such that the convexly curved outer surface 13 of the sensor pad 10 is presented on the exterior of the logging tool and can be pressed into contact with the wall 11 of a borehole 12.

(8) In FIG. 1, the features of the logging tool are omitted for ease of presentation. The sensor pad and the borehole are shown transversely sectioned. The sensor pad is of essentially a D-shaped cross-section, having a truncated circular profile such that the surface 13 is a circular arc. The features of the sensor pad 10 described below for the most part would also be present in a sensor pad of fully circular cross-section.

(9) The shaded area A.sub.w visible in FIG. 1 is representative of the extent of stand-off of the sensor pad 10. This is the area enclosed by projection of the shape of the surface 13 onto the borehole wall 11.

(10) In FIG. 1, the line 14 is the chord corresponding to truncation of the circle of which the surface 13 forms part. Chord line 14 intersects the borehole wall 11 at two points 16a, 16b as illustrated. The angle subtended at one of these intersection points 16a between the radius r.sub.BH of the borehole 12 and line 17 normal to the surface 13 is designated as .sub.BH. The angle subtended between the radius r.sub.p of the circle defining the surface 13 and the normal line 17 is .sub.p.

(11) The area of the chord of the borehole enclosed by chord line 14 and borehole wall 11 is designated as A.sub.c and the area of the sensor pad 10 enclosed by chord line 14 and surface 13 is A.sub.p. The distance along normal line 17 from the center of the borehole 12 to the chord line 14 is x.sub.0 and the remainder of the distance from the chord line 14 along the normal line 17 to the borehole wall is a. The distance along chord line 14 from normal line 17 to the intersection of chord line 14 with the surface 13 of the sensor pad 10 is b.

(12) If r.sub.BH>r.sub.p as illustrated in FIG. 1, the area A.sub.w is given by:

(13) $\begin{array}{cc}{A}_w=A_{\mathrm{BH}}-A_p-A_c=\frac{r_{\mathrm{BH}}}{2}\left[{}_{\mathrm{BH}}-\sin \left({}_{\mathrm{BH}}\right)\cos \left({}_{\mathrm{BH}}\right)\right]-\frac{r_p}{2}\left[{}_p-\sin \left({}_p\right)\cos \left({}_p\right)\right]-{}_0^{\frac{b}{{}^{{}^{\tan \left[{\sin }^{-1}\left(\frac{b}{r_{\mathrm{BH}}}\right)\right]}}}-x_0}\sqrt{r_{\mathrm{BH}}^2-\left(x-x_0\right)}-\mathrm{bdx}& \left(1\right)\end{array}$
where .sub.p=sin.sup.1(b/r.sub.p), .sub.BH=sin.sup.1(x.sub.0/r.sub.BH) and x.sub.0=(r.sub.BHa).

(14) In the event that r.sub.BHr.sub.p, the integral (A.sub.c) in Equation 1 vanishes and x.sub.0=cos(x.sub.0/r.sub.BH).

(15) If, for the sake of example, the radius r.sub.p is 100 mm (4 inches), the sensor pad 13 will fit snugly into a 200 mm (8 inch) diameter borehole with no stand-off, and the area A.sub.w is zero. Such a sensor pad inserted into other sizes of borehole larger than 200 mm in diameter however exhibits varying amounts of stand-off as illustrated by line 18 of FIG. 4, which line plots the value of A.sub.w against the diameter of the borehole in which the sensor pad is deployed. As illustrated by FIG. 4, the degree of stand-off is significant for most values of borehole diameter other than that corresponding to the value of r.sub.p.

(16) A borehole as employed in e.g. the oil and gas extraction industries usually has a diameter measured in the range 7 to 9 inches, being the diameters of drill heads commonly in use. As is apparent from FIG. 4, the stand-off of a part-circular cross-section sensor pad in which r.sub.p is 100 mm (4 inches) is significant in 7 inch and 9 inch or larger diameter boreholes. As explained above at the least this is a significant inconvenience in log signal processing.

(17) Referring now to FIG. 2, there is shown one form of logging tool sensor pad 20 according to the present disclosure. Sensor pad 20 is made of rigid materials and therefore does not conform fully to the shape of a borehole in which it is deployed. An aim of the present disclosure therefore is to optimize the design of the sensor pad 20 in order to minimize the sensor pad stand-off that derives from the inability of the sensor pad to change shape in order to conform to the borehole shape.

(18) In FIG. 2, the sensor pad 20 is shown in cross-sectional view inserted into a borehole 12 having a circular cross-section wall 11. Thus the borehole 12 in FIG. 2 is the same as the borehole 12 of FIG. 1. In like manner to FIG. 1, FIG. 2 omits for clarity other features of the logging tool that support the sensor pad 20 and cause it to be pressed against the wall 11 of the borehole 12. Although feature 20 is referred to as a sensor pad, this component could be constructed in a form other than that of a pad per se. The principles of the present disclosure in other words apply to sensors of elliptical or part-elliptical cross-section whether constituted as recognizable pads or not.

(19) In FIG. 2, the ellipse representing the cross-section of the sensor pad 20 has a minor radius a and a major radius b. The ellipse may be regarded as having been translated along the normal line 17 by a distance x.sub.0 from the center of the borehole cross-section and in a direction perpendicular to the normal line 17, again measured with respect to the center of the borehole cross-section, by a distance y.sub.0.

(20) As is apparent from FIG. 2, an elliptical sensor pad 20 of the size illustrated contacts the circumferential borehole wall 11 at two points. In FIG. 2 the co-ordinates of the upper such point are denoted as (X, Y). The angle subtended between the radius r.sub.BH of the borehole intersecting point (X, Y) and the normal line 17 is signified by in FIG. 2.

(21) The stand-off of the sensor pad 20 is denoted by the shaded area 19 in FIG. 2. A comparison of this area 19 with area A.sub.w of FIG. 1 can be used to assess whether the stand-off of particular design of elliptical or part-elliptical sensor of the present disclosure is superior to that of the circular cross-section sensor pad 10 of the prior art.

(22) The expressions describing the elliptical sensor pad 20 of FIG. 2 are:
b.sup.2x.sup.2+a.sup.2y.sup.2=1(2)
(xx.sub.0).sup.2+(yy.sub.0).sup.2=r.sub.BH.sup.2(3)

(23) Substituting the co-ordinates X, Y into the equation of a circle gives Y={square root over ((r.sup.2(Xx.sub.0).sup.2))}. Substituting this expression for Y into the equation for an ellipse gives b.sup.2X.sup.2+a.sup.2[r.sub.BH.sup.2(Xx.sub.0).sup.2]a.sup.2b.sup.2=0 which is quadratic in X. This is solved in the usual way to give:

(24) $\begin{array}{cc}X=\frac{-x_0{a}^2\sqrt{x_0^2{a}^4-\left(b^2-a^2\right)\left(a^2{r}_{\mathrm{BH}}^2-x_0^2{a}^2-a^2{b}^2\right)}}{b^2-a^2}& \left(4\right)\end{array}$

(25) The gradient of the tangential line at the point [X, Y] can be found by implicit differentiation of the equation of an ellipse (Equation 3) to give y=b.sup.2X/(a.sup.2Y). The gradient of the radius of the circle at point [X, Y] is then M=a.sup.2Y/(b.sup.2X)=tan =Y/(Xx.sub.0). Rearranging gives X=x.sub.0a.sup.2/(a.sup.2b.sup.2). Equating this to the expression for X in Equation 4 gives the result:

(26) $\begin{array}{cc}{x}_0=\sqrt{\frac{b^2{r}_{\mathrm{BH}}^2-b^4-a^2{r}_{\mathrm{BH}}^2+a^2{b}^2}{b^2}}& \left(5\right)\end{array}$

(27) As the radius of the borehole is increased beyond a certain limit, the contact will change from two point to single point. Two point contact occurs when ab.sup.2/r.sub.BH and single point contact occurs thereafter. Above this limit, the relation x.sub.0=r.sub.BHa holds.

(28) The cross-sectional area between the pad and the borehole wall (the shaded area 19 in FIG. 2) can be found by integration to give the expression:

(29) $\begin{array}{cc}A=2\left[{}_0^{r_{\mathrm{BH}}+x_0}\sqrt{r_{\mathrm{BH}}^2-{\left(x-x_0\right)}^2}\mathrm{dx}-{}_0^{x_0-\sqrt{r_{\mathrm{BH}}^2-b^2}}-b+\sqrt{r_{\mathrm{BH}}^2-\left(x-x_0\right)}\mathrm{dx}-\frac{\mathrm{ab}}{4}\right]& \left(6\right)\end{array}$

(30) For a fixed ellipse major radius b and borehole radius r.sub.BH, it is possible to find the optimal fit by minimising equation 4 with respect to the pad ellipse minor radius a. For an 8 (200 mm) diameter borehole a plot of gap area A as a function of ellipse minor radius a is shown in FIG. 3. For a pad major diameter of 85 mm, the optimum minor diameter for an 8 (203 mm) borehole is 28.28 mm (radius 14.14. mm).

(31) The foregoing optimization technique forming part of the present disclosure may readily be repeated for differing borehole sizes and elliptical cross-section axis combinations. As desired the optimization aspect of the present disclosure can be automated e.g. using a suitably programmed digital computer.

(32) A desired elliptical major/minor axis ratio can then be chosen from the resulting plurality of data so as to provide pad dimensions that offer optimal conformity over a specific range of borehole diameters. The range of borehole diameters may be chosen e.g. as the widest range possible, or may be biased towards certain specific ranges such as the most frequently encountered range of borehole diameter. Other optimization criteria are also possible and within the scope of this present disclosure.

(33) FIG. 4 shows the cross-sectional stand-off area for a prior art circular or D-shaped pad optimized for an 8 (200 mm) diameter borehole compared to elliptical pads optimized for 7 (175 mm), 8 (200 mm) and 9 (230 mm) diameter boreholes. The stand-off values are represented in FIG. 4 by respective plot lines 41, 42 and 43. Although the elliptical pad 20 of the present disclosure is never fully optimal for any particular borehole diameter, it beneficially displays a smaller cross-sectional stand-off area over a wider range of borehole sizes than the traditional D-shaped pad cross-section.

(34) As noted, one design of sensor pad 20 according to the present disclosure exhibits a partially elliptical cross-section. Such sensor pads also can be optimized using the technique described above since it is necessary to optimize the dimensions only of the side of the elliptical profile that contacts the borehole. The opposite face of the sensor pad can from the standpoint of borehole contact optimization be of any shape, including flat planes that therefore define truncated elliptical shapes.

(35) A plot such as FIG. 4 may beneficially be used in the selection of an optimal sensor design from a range of such designs created in accordance with the method of the present disclosure as specified. Thus for example plot line 41 indicates the standoff cross-sectional area as a function of borehole diameter for an ellipse of 3.35 inch (85 mm) major axis dimension the minor axis dimension of which is optimized to provide the least standoff in a 7 inch (approximately 180 mm) diameter borehole. Such a pad would provide superior standoff minimization compared to the other pad designs considered in the FIG. 4 in boreholes diameters that are less than approximately 7.5 inches (approximately 190 mm). Plot line 43 shows the standoff cross-sectional area as a function of borehole diameter for an ellipse of 3.35 inch (85 mm) major axis dimension the minor axis dimension of which is optimized to provide the least standoff in a 9 inch (approximately 230 mm) diameter borehole. This pad would provide superior standoff minimization compared to the other pad designs in FIG. 4 when the borehole diameter is in the range 8.5 inches to 15 inches (approximately 215 mm to 380 mm).

(36) The foregoing represents one way, of several, in which optimization of the sensor design can take place when selecting from a range of individually optimized ellipse cross-section sizes.

(37) The line of truncation of such a sensor pad may be parallel to the major axis of the elliptical shape and indeed in some embodiments of the present disclosure may coincide with the major axis. In other embodiments however this need not be the case.

(38) A number of elliptical, part-elliptical and part-circular cross-section sensor pads is shown in FIGS. 5a to 5e. In each of FIGS. 5a to 5e various exemplary electrodes are schematically represented by the numerals 24, 124, 224, 324, and 424. In each of these figures the electrodes adopt the shapes and positions of the electrodes of a pad of a microlaterolog (resistivity) logging device. This is for illustration purposes only however, and a variety of other electrode arrangements is possible within the scope of the present disclosure.

(39) In such arrangements, it need not necessarily be the case that the electrodes are exposed on the surface of a sensor as illustrated; and on the contrary it is possible for the electrodes to be covered, or embedded in the sensors.

(40) Moreover, some logging tool pad designs may not require the presence of recognizable electrodes at all. All such variants sensor design are within the scope of the present disclosure as broadly defined herein.

(41) The electrodes when present may be connected in various ways known to the person of skill in the art in order to give rise to operational logging tool sensor constructions.

(42) The variant sensor 21 of FIG. 5a includes a substrate 22 of fully elliptical cross-section.

(43) The sensor profile in FIG. 5b includes a substrate 122 of the sensor 121 essentially of D-profile.

(44) In FIG. 5c, a further non-flat sensor variant 221 is shown, in which the substrate 222 is a truncated version of the substrate 121 of FIG. 5b.

(45) The cross-section of sensor 321 illustrated in FIG. 5d includes a convexly curved, part-circular front face of substrate 322 in which the electrodes 324 are secured. The rear face of the substrate 322 is cuboidal as shown.

(46) The sensor 421 of FIG. 5e differs from that of FIG. 5d by reason of the line of truncation defining the rear face of the substrate 422 being a chord of the circle of which the front face supporting the electrodes 424 is part.

(47) The sensor examples of FIGS. 5a to 5e are not intended to be limiting of the scope of the present disclosure, and are merely illustrative of the fact that numerous sensor profiles may be adopted, it being desirable principally that the as illustrated front convexly curved surface of the sensor is capable of conforming to the profile of a section of borehole wall with a minimal air gap or stand-off. The dimensional optimization method of the present disclosure described herein may readily be applied for this purpose to sensors such as those shown in FIGS. 5a to 5e.

(48) As mentioned herein, use of any sensor pad according to the present disclosure may include (a) deploying the logging tool in a borehole (e.g. by supporting a logging tool including such a pad on wireline or on drill pipe); (b) causing the logging tool sensor to be pressed against the wall of the borehole so as to minimize the cross-sectional area of the space between the sensor and the borehole wall (e.g. by activating a caliper arm that presses the entire logging tool, including the sensor pad, into contact with the borehole wall; or by activating an extensible arm or other member on which the sensor pad of the present disclosure is mounted); and (c) drawing the logging tool along a borehole (e.g. by winding in or paying out wireline; or withdrawing or adding stands of drill pipe) while operating the logging tool to acquire log data. Such log data may, depending on the design of the logging tool, be transmitted in real time to a surface location or may be stored or processed within the logging tool. The resulting log data may be further stored, downloaded, uploaded, transmitted, displayed, printed, or otherwise processed as data values, data signals or as recognizable data logs.

(49) Step (c) may include as necessary relieving the force pressing the sensor pad into contact with the borehole wall in order to permit the logging tool to move as described, and subsequently again exerting the force in order to permit logging to re-commence.

(50) The methods of using logging tools described herein include conventional aspects of logging tool operation, such as but not limited to the generation of electrical signals indicative of log data; and the transformation of those signals to further signals that may be presented e.g. in a display or in printed form as one or more logs. Such aspects are known to the person of skill in the art and are not described in detail herein.

(51) Preferences and options for a given aspect, feature or parameter of the present disclosure should, unless the context indicates otherwise, be regarded as having been disclosed in combination with any and all preferences and options for all other aspects, features, and parameters of the present disclosure.

(52) The listing or discussion of an apparently prior-published document in this specification should not necessarily be taken as an acknowledgement that the document is part of the state of the art or is common general knowledge.