NEW INCLINOMETER DESIGNS FOR MAGNETIC MEDIA

Yu. L. Boyarko, V. P. Rozhkov, I. G. Leshchenko

(Presented by the scientific seminar of the Department of Exploration Technology)

When drilling exploratory boreholes, present-day technical conditions require that measurements of borehole curvature be made every 25 meters in inclined drilling and every 50 meters in vertical drilling. In the process of drilling boreholes, most often only measurements in the vertical plane are made. Measurement of the azimuthal deviation of a borehole is usually carried out when it is completed and only rarely during drilling.

All this is connected, above all, with the fact that when measuring borehole curvature with modern inclinometers it is necessary to expend a fairly considerable amount of time. Therefore, in order to maintain continuous control of the direction of a borehole during drilling (and this is dictated by direct necessity in directional drilling), one should have inclinometers that require a minimum expenditure of time for their use.

At present, the most advanced inclinometers are in most cases adapted for surveying in an undisturbed medium. These include such widely used instruments as Polyakov’s inclinometer, the ISh-2 and ISh-4 inclinometers, and photoinclinometers of various designs.

In the case, however, of measuring the curvature of boreholes drilled in magnetic rocks or cased with steel casing pipes, one has to use such imperfect instruments as the GBS-Ya, GBS-Ya-2M, MIR, GP-K1, or gyroscopic inclinometers of complex construction. Most of these instruments require much time for surveying boreholes and cannot claim great accuracy or even reliability. Gyroscopic instruments, which do not have these shortcomings and possess survey universality, are still unreliable in operation and have a large outside diameter, which hinders their introduction into the practice of geological exploration work.

In connection with this, several new inclinometer designs are proposed for measurement in a disturbed medium. In developing them, it was taken into account that an inclinometer must permit: a) measurement of borehole curvature in a ferromagnetic medium and in boreholes cased with steel pipes; b) continuous recording of readings as it moves along the borehole shaft.

The proposed schemes are based on the principle of measuring the depth (more precisely, the distance from the wellhead), the azimuthal direction, and the zenith angle of each point of the borehole axis. It is proposed to measure the depth and zenith angle in absolute values, and to replace measurement of the azimuthal direction by measurement of its increment between the corresponding overlying and underlying points of the borehole axis during inclinometer logging while lowering the instrument and, conversely, while raising it.

In this case, with continuous recording of these data, one can obtain a graph of the variation of the increment of the azimuthal direction with borehole depth and a graph of the zenith angle along the entire borehole axis. Having such data for the entire axis, and knowing the azimuthal direction and zenith angle at the wellhead, it is easy to obtain an inclinogram of the entire borehole (Fig. 1).

It is proposed to lower and raise the inclinometer on a cable. The length of the cable being lowered and the magnitude of the zenith angle can be measured by ordinary means; measurement of the increments of the azimuthal angle is achieved by making the inclinometer consist of two cases connected to each other by a hinged device. Each case is oriented in the borehole by a special debalance. When the inclinometer is lowered into an azimuthally curved borehole, the axes of the cases are positioned at a certain angle to one another, corresponding to the intensity of curvature of the axis in the given interval. This angle can be measured with various sensors. The readings can be recorded by self-recording instruments installed at the surface.

In steeply inclined boreholes, it is more effective to measure the azimuthal curvature not directly by the angle between the axes of the cases, but by the angle of rotation between the working plummets. For this purpose, each case, in addition to the plummet for rough orientation of the body, has one working plummet (debalance).

When such an inclinometer (Fig. 2, a) is lowered into an azimuthally curved borehole, rotation of the axes of the 3 working debalances 2 relative to one another will be observed. The resulting angle is recorded by the angle sensor 4.

The relation connecting the mentioned angle with the zenith angle and with the intensity of the borehole’s azimuthal curvature can be found as follows: to simplify the calculations, let us assume that the borehole has azimuthal curvature and lies in a plane inclined to the vertical at an angle \(\Theta\). Figure 2b shows a portion of the borehole axis with an inclinometer located in it. As can be seen from the figure, an angle is formed between the cases, the horizontal projection of which gives the angle \(\alpha\). Let us transfer the upper point of the lower case to the suspension point of the inclinometer \(O\), in such a way that the previous angle between the cases is preserved. Through the axes of the cases let us draw straight rays to their intersection with the horizontal plane. In the horizontal plane we draw the projections of these rays, and from the suspension point we lower a vertical. As a result of the constructions, a triangular pyramid is obtained. If a vertical plane is drawn through the point \(F\) perpendicular to the face \(AOD\), then the angle \(BFC\) will be equal to the angle of divergence of the plummets. Thus, the problem is reduced to finding this angle.

From triangle \(BCF\) we have

\[ \operatorname{tg} \gamma = \frac{BC}{CF}. \tag{1} \]

Using the similarity of triangles \(ACB\) and \(AOD\), we find

Fig. 1. Graphs characterizing borehole curvature:
a — graph of the zenith angle along the entire borehole;
b — graph of the increment of the borehole azimuth;
c — graph of the intensity of azimuthal curvature along the entire borehole.

In-figure labels: \(l\), \(\theta\); \(+\alpha_1\), \(-\alpha_1\), \(0\); \(+\alpha_1\cos\theta\), \(-\alpha_1\cos\theta\), \(0\); “intensity of azimuthal curvature, min/m.”

\[ BC=\frac{AC\cdot OD}{AD}, \]

but from triangle \(FOD\)

\[ OD=\frac{FD}{\operatorname{tg}\Theta}, \]

therefore

\[ BC=\frac{AC\cdot FD}{AD\cdot \operatorname{tg}\Theta}. \tag{2} \]

Solving equations (1) and (2), we obtain

\[ \operatorname{tg}\gamma=\frac{AC\cdot FD}{AD\cdot CF\cdot \operatorname{tg}\Theta}. \tag{3} \]

From triangles \(AFD\) and \(ACF\) we find the unknown sides

\[ AD=\frac{FD}{\cos\alpha}, \]

\[ AC=FC\cdot \operatorname{tg}\alpha \]

Fig. 2. Inclinometer with working plumb bobs.
\(a\) — diagram of the inclinometer; \(b\) — diagram for calculating the angle of divergence of the apsidal planes of the working plumb bobs.
1 — nonworking plumb bobs; 2 — working unbalances; 3 — axes of the working unbalances; 4 — azimuth-angle sensor. \(\Theta\) — zenith angle of the borehole; \(\alpha\) — angle of rotation of the cases relative to one another (or azimuthal increment); \(\gamma\) — angle of divergence of the working plumb bobs.

and, substituting them into equation (3), we finally obtain

\[ \operatorname{tg}\gamma=\frac{\sin\alpha}{\operatorname{tg}\Theta}. \tag{4} \]

Thus, for the borehole zenith angle \(\Theta\) and the angle between the axes of the inclinometer cases \(\alpha\), the divergence of the apsidal planes of the plumb bobs will be equal to

\[ \gamma=\operatorname{Arc\,tg}\left(\frac{\sin\alpha}{\operatorname{tg}\Theta}\right). \tag{5} \]

The angle of rotation of the axes of the inclinometer cases may be found from the formula

\[ \alpha = \Delta \alpha \cdot l, \tag{6} \]

where \(\Delta \alpha\) is the intensity of the azimuthal curvature of the borehole per \(1\) running m;

\(l\) is the distance between the centers of the cases, in meters.

Formula (6) can be represented somewhat differently, namely:

\[ \alpha = \rho_0 \frac{l}{R}, \tag{7} \]

where \(\rho_0\) is the value of a radian expressed in the degree system;

\(R\) is the radius of curvature of the borehole, in meters.

Taking formulas (6) and (7) into account, the angle of divergence of the apsidal planes of the plumb lines may be represented as

\[ \gamma = \operatorname{arc\,tg}\left[\frac{\sin(\Delta \alpha \cdot l)}{\operatorname{tg}\Theta}\right] = \operatorname{arc\,tg}\left[\frac{\sin\left(\rho \cdot \frac{l}{R}\right)}{\operatorname{tg}\Theta}\right]. \tag{8} \]

If the borehole is curved with an intensity of \(1^\circ, 2^\circ, 3^\circ\) per \(20\) running m, then, with a length of the inclinometer cases of \(2.5\) meters, they are positioned in it respectively at angles of \(0^\circ 7.5'\), \(0^\circ 15.0'\), \(0^\circ 22.5'\) to one another. Table 1 gives calculated data for the angle \(\gamma\) at various intensities of azimuthal curvature and various zenith angles of the borehole.

Table 1

Angles of divergence of the apsidal planes
of the working unbalances of the inclinometer with case lengths of 2.5 m

As is evident from the table, at intensities of azimuthal curvature and zenith angles often encountered in the practice of geological-exploration work, the angles of divergence of the apsidal planes of the working plumb lines vary within the range from 10–20 to 20–30°. Such angles can be recorded by angular-displacement sensors of various types.

Let us proceed to consideration of the designs of individual inclinometers.

1. Inclinometer using a strain-gauge sensor (Fig. 3, a).

The inclinometer consists of an upper case 5, balanced by weight 4, and a lower case 10, also balanced by weight 11, which are connected to each other by hinge joint 9. The hinge joint must be sufficiently movable and must not hinder

rotation of the housings relative to one another. In the upper housing there is mounted a zenith-angle sensor 3 and an azimuth-increment plumb line 6, which holds the sensors in the measured plane. A steel measuring beam is rigidly attached to this plumb line; the other end of the beam passes through supports in the lower housing 10. On the measuring beam there are strain-gauge sensors which measure the stresses arising in the beam when it is bent. The stresses correspond strictly to quite definite deflections of the beam and, consequently, to the angles of rotation of the housings relative to one another.

The free end of the beam is made in such a way that the beam is subjected to the bending action of the lower housing, but is not subjected to twisting.

The housings are filled with transformer oil, which equalizes the pressure inside and outside the inclinometer and also helps to damp the moving parts of the instrument. To prevent water from entering the instrument through the hinge joint, the latter must

Fig. 3. Proposed inclinometer layouts.
a — inclinometer using a strain-gauge sensor; б — inclinometer using an inductive sensor; в — inclinometer using an ohmic rheostat sensor of angles of rotation with a liquid contact; г — inclinometer with selsyn coupling

be sufficiently hermetic. The inclinometer is lowered into the borehole on cable 1, which is connected to the inclinometer through candle bridge 2.

The zenith-angle sensor and the azimuth-direction increment sensor are connected to self-recording instruments located at the surface (the circuit is shown in Fig. 3, a). Thanks to this, simultaneously with the lowering (or raising) of the inclinometer, the self-recording instruments trace the curves shown in Fig. 1. From these curves, the azimuths

and the zenith angle of the wellhead, it is easy to obtain an inclinogram of the entire well.

1. Inclinometer using an inductive sensor (Fig. 3, б).

As in the first version, the inclinometer consists of an upper housing 5 and a lower housing 10, balanced by weights 4 and 11. The two housings are connected to one another by hinge 9. In the upper housing there is mounted a zenith-angle sensor 3 and an azimuth plumb 6, on the extension of whose axis there is an inductive sensor 8, located at the center of the hinge. In the lower housing there is mounted an azimuth-increment plumb 12, on the extension of whose axis (also ending in the hinge) there is a driver connected with the movable part of inductive sensor 8.

Unlike the inclinometer of the first version, in this case the sensor measures not the rotation of the axes of the housings relative to one another, but the rotation of the apsidal planes of the upper and lower working plumbs, which increases the accuracy of the inclinometer in steeply inclined wells.

It should be noted that the inductive sensor must be shielded. In the proposed inclinometer circuit, besides inductive sensors, capacitive sensors, radiation sensors, and a number of others may be used.

The electrical circuit of the inclinometer is similar to the circuit given in the first version. The inclinometer is also filled with oil.

1. Inclinometer using an ohmic rheostat sensor of rotation angles with a liquid contact (Fig. 3, в).

In carrying out this version of the inclinometer, either a single-hinge or a multi-hinge design of the instrument may be taken as the basis. A distinctive feature of this version of the inclinometer is that plumb 6 is placed in the upper housing 5, while shaft 7, rigidly connected with it, extends into the very lowest housing, where azimuth sensor 8 is suspended on its cantilevered part. The sensor is made in the form of a hollow torus and is half-filled with mercury, into which is immersed a spiral of wire with high ohmic resistance. In addition, by means of a Cardan suspension the sensor is balanced on the shaft in such a way that the plane of the torus is located at an angle of 45° to the axis of the shaft and, when the inclinometer is straight, is perpendicular to the apsidal plane of the plumb. This position of the torus is preserved both in the vertical and in the inclined position. The torus is fixed against angular displacement relative to shaft 7; therefore even a small azimuthal rotation of the lower part of the inclinometer relative to the upper part will cause a displacement of the mercury level, which, in turn, will be recorded by the recorder.

Calculations show that, with a radius of the resistance spiral located in the torus equal to 20–25 mm (the diameter in this case may be 50–60 mm), rotation of the well in the azimuthal plane with an intensity of 1° per 30 linear m at a zenith angle \(\Theta = 20^\circ\) will cause a change in the length of the wetted resistance wire, wound into a spiral, by 3–4 mm, which in turn will cause a change in the voltage in the circuit and corresponding readings on the instrument even without special amplifiers.

1. Inclinometer with a selsyn link (Fig. 3, г).

Analyzing formula (8), one may conclude that the accuracy of the instrument increases with increasing distance between the inclinometer housings. This property was used in developing the present circuit.

The inclinometer also consists of two housings, but separated from one another by a certain distance. In the upper housing (as in all the other versions) there is located a zenith-angle sensor. The housing body is balanced by weight 4, below which there is located

sensor of azimuthal increment, made in the form of a selsyn. The armature of the selsyn has an unbalanced weight 13, which plays the role of the working plumb bob.

The lower case consists of housing 10, in which the second working plumb bob 12 is placed. Plumb bob 12 and the housing of selsyn 14 are connected to one another by a rigid shaft 7. The inclinometer cases are also filled with oil.

When the inclinometer is lowered into an azimuthally curved borehole, the apsidal planes of working plumb bobs 12 and 13 will diverge; this (in the given inclinometer design) will cause rotation of the armature relative to the housing of the selsyn sensor.

At the surface there is a selsyn receiver, which is electrically connected to the selsyn sensor considered above in such a way that the rotation of the armature in the sensor housing corresponds to rotation of the armature of the selsyn receiver. The latter is connected to a recorder, making it possible to obtain a chart of the azimuthal increment along the entire borehole.

A special feature of this scheme is that the working plumb bobs are separated from one another by a considerable distance (it may be on the order of several meters). In this connection, the angle between the axes of the cases $\alpha$ is considerably larger than can be achieved in the second variant. An increase in the angle $\alpha$ entails an increase in the angle of divergence of the apsidal planes of the working plumb bobs (see formulas (4) and (8)).

Thanks to this feature, the accuracy of the readings of the azimuthal sensor is increased, and it becomes possible to use the given inclinometer in boreholes with weak azimuthal curvature.

The economic effect from the use of such inclinometers may be calculated as follows: for measuring azimuthal curvature with the GBS-Ya instrument to a depth of 500 meters, taking measurements every 100 meters requires 20 crew-hours (according to ENB 1959, Table 36).

When measuring curvature with the proposed instruments, the time expenditures will include only the time for lowering and raising the instrument at the usual speed for geophysical winches, and the time for auxiliary operations, which will amount approximately to 20–25% of the time for lowering and raising the instrument. If, from the same table, one takes the time for measuring curvature to a depth of 500 meters with Polyakov’s instrument, then it will practically be equal to the time for lowering and raising the proposed inclinometers to the same depth. This time will be 1.25 hours.

Thus, for one borehole, taken as average, 18.75 crew-hours are saved; that is, the measurement is carried out 16 times faster.

In addition to the economic aspect, it is also necessary to take into account the qualitative aspect, which should improve in comparison with the quality of measurements by instruments of the GBS-Ya and GP-K1 types.