On the Calculation of Simple Hinged Deflectors
Abstract Generated abstract
This paper examines the design calculation of simple hinged deflectors used in directional geological-exploration drilling, distinguishing tools for gradual borehole inclination control from those intended to create local sharp curvature or initiate sidetracks. It develops geometric relations for deflector arm length, hinge displacement, bit and borehole diameters, and deflection angle, and analyzes the stability conditions needed for reliable self-orientation at the start of cutting. The study shows that, with a flat bottomhole, the sidetracking bit diameter must generally be less than half the borehole diameter for small deflection angles, limiting practical use. It proposes preparing a conical bottomhole shape to increase hinge displacement and system stability, thereby permitting larger sidetracking tools, while noting that some force effects require experimental clarification.
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On the Calculation of Simple Hinged Deflectors
B. I. Spiridonov
(Presented by the scientific seminar of the Department of Exploration Technology)
In the practice of directional drilling of geological-exploration boreholes, simple hinged deflectors are used to change the magnitude of the zenith angle in the apsidal plane. Deflectors of this type are among the simplest and most reliable tools by means of which it is possible to control the curvature of boreholes.
A simple single hinged deflector (Fig. 1, a) consists of a drilling assembly 1, equipped with a shot or hard-alloy bit 2 and connected by means of a hinged adapter 3 to a string of weighted drill pipes 4. With this arrangement the deflector works to increase the zenith angle, i.e., to “flatten” the borehole. When two hinged connections 3 and 5 (Fig. 1, b), separated by an intermediate link 6, are included in the deflector arrangement, the assembly is used to decrease the zenith angle, i.e., for “straightening.” In this case we are dealing with a double simple hinged deflector.
Simple hinged deflectors are self-orienting deflectors and can be used only in inclined boreholes. Moreover, the greater the zenith angle of the borehole, the more reliable and effective their operation.
According to their purpose and conditions of application, the deflectors under consideration may be divided into two types:
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Simple hinged deflectors intended to change the direction of a borehole during the process of drilling it.
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Simple hinged deflectors used for local curvature of boreholes, involving either their periodic use during directional drilling of the borehole or a single use for cutting an additional borehole in cluster drilling by the wedge-less method.
The principle of operation of simple hinged deflectors of the first type is as follows. Under the action of the horizontal component of the self-weight \(P_{\mathrm{g}}\), the string of weighted drill pipes and the hinged connection rigidly attached to it are positioned on the lower wall of the borehole. The action of the axial force \(P_{0}\), under conditions of eccentric positioning of the axes of the borehole and hinge 3, causes the drilling assembly to skew at a certain angle \(\alpha\) and to work toward “flattening” (Fig. 1, a) or toward “straightening” (Fig. 1, b). The effect of the operation is achieved through preferential drilling of the lower part
the bottomhole in the case of a single and an upper position in the case of a double hinged deflector. It is obvious that the forces of resistance of the rock to drilling, centrifugal forces, oscillatory motions of the drill-pipe string, and other factors tend to change the position of the hinges and of the drilling assembly. However, the continuously acting force \(P_{1}\) ensures, during penetration, the most frequent position of the hinge and of the weighted-drill-pipe string at the lower wall of the borehole and, as a consequence, curvature of the borehole in the required direction. In hinged deflectors of this type the drilling assembly has a diameter corresponding to the design diameter of the borehole.
Theoretical calculations of simple hinged deflectors of the first type, carried out, in particular, by the thematic group of the West Siberian Geological Administration, and a number of examples of their application with positive results, make it possible to regard this type of deflector as an effective means of directional drilling. The intensity of artificial borehole curvature when they are used reaches \(3\)—\(4^\circ\) per \(10\ \text{m}\). But in a number of cases, when geological factors and the anisotropic properties of rocks do not promote curvature of the borehole in the required direction, the use of hinged deflectors may fail to lead to the desired result.
In this case, and also when carrying out multi-bottomhole drilling without the use of wedges, when it is necessary to create a local interval of sharp curvature, simple hinged deflectors of the second type are used. The scheme of their device and the arrangement of individual parts do not differ from deflectors of the first type, but the principle of operation has distinctive features.
Fig. 1. Operating diagrams of simple hinged deflectors of the first type:
\(a\)—single-hinged; \(b\)—double-hinged.
A local sharp curvature in the desired direction can be obtained only when, at the beginning of drilling, the drilling assembly in the borehole occupies a quite definite stable position, toward which the system “drilling assembly—hinged joint—weighted-drill-pipe string” tends during its rotation. The stable position of the deflector may be considered to be that in which the reduced center of gravity of the system is displaced downward by a certain distance \(h\) from its initial position. For given geometric parameters of a hinged deflector in a borehole of specified diameter, the maximum deflection angle, as well as the maximum possible displacement \(h\), can be obtained only in the position for “flattening out” or “twisting,” depending on the system of the hinged deflector.
The literature does not sufficiently cover the questions of selecting and calculating the parameters of hinged deflectors, without which their use with reliable results is impossible.
The first task of the calculation is to determine the possibility of trans—
the displacement of the center of the hinge and of the system’s center of gravity, reduced to it, downward, and the value of \(h\) as functions of the geometric parameters of the hinged deflector. The geometric parameters include:
\(d_k\)—the diameter of the core bit;
\(d_{\text{sh}}\)—the diameter of the hinge body,
\(H\)—the length of the deflector arm, which is determined by the distance along the axis of the bottom-hole assembly from the end face of the bit to the center of the lower hinge;
\(H_1\)—the length of the intermediate link (when a two-hinge deflector is used).
For a borehole diameter \(D\) and a specified deflection angle \(\alpha\), the arm length \(H\) can be calculated from the formula
\[ H=\frac{D-\frac{d_{\text{sh}}}{2}-\frac{d_k}{2}}{\sin \alpha}. \tag{1} \]
The arm length \(H\) can also be determined from the graph (Fig. 2, \(a\)), constructed under the condition that \(d_{\text{sh}}=d_k\).
Let us consider the possibility of displacing the center of the hinge downward by a certain amount \(h\) in the case of a flat borehole bottom. It is obvious that
Fig. 2. \(a\)—graph of the dependence of the deflector arm length on the borehole diameter and the deflection angle.
\(b\)—graph of the dependence of the downward displacement of the hinge center on the deflection angle.
\[ d_k=d_{\text{sh}}=76\ \text{mm} \]
\[ d_k=d_{\text{sh}}=91\ \text{mm} \]
\[ d_k=d_{\text{sh}}=110\ \text{mm} \]
the center of the hinge can move downward (Fig. 3, \(a\)) only when the following inequality is satisfied:
\[ D>\frac{d_{\text{sh}}}{2}+\frac{d_k}{2}+d_k\cos\alpha \tag{2} \]
or
\[ d_k < \frac{D}{1+\cos\alpha} \quad \text{when } d_k = d_{\mathrm{sh}}. \]
As is evident from the inequalities given, for deflection-angle values \(\alpha\) up to \(4—5^\circ\), the diameter of the side-tracking bit must be less than half the borehole diameter.
The magnitude of the possible maximum displacement \(h\) is determined from the expression
\[ h = H - H\cos\alpha - \frac{d_k}{2}\sin\alpha . \tag{3} \]
Thus, the diameter of the pilot borehole, and correspondingly the diameter of the side-tracking bit when cutting a new direction in a flat bottomhole, cannot exceed 76 mm for the existing diameters of geological-exploration boreholes. Therefore, with a flat bottomhole, a simple hinged deflector can be used either for drilling a pilot borehole for auxiliary purposes (setting a wedge, caliper logging, etc.), or for actual directional drilling, but with subsequent reaming of the pilot borehole to the required diameter.
To eliminate this drawback and broaden the field of application of simple hinged deflectors of the second type, a special bottomhole shape may be proposed, for example, in the form of part of a sphere of a certain radius, or in the form of a truncated cone. In this case, downward displacement of the hinge center will be ensured for any ratio of the diameters of the side-tracking bit and the borehole. The height \(b\) of the truncated cone (Fig. 3, b), to which the bottomhole must be machined, at deflection angle \(\alpha\) and side-tracking bit diameter \(d_k\), will be
\[ b = d_k \sin\alpha . \tag{4} \]
The diameter of the lower base of the cone, for borehole diameter \(D\), can be calculated by the formula
\[ d_0 = 2d_k\cos\alpha - D . \tag{4a} \]
With such a bottomhole shape, the displacement of the hinge center downward—and in this case it will have the maximum value for the given combination of borehole and bit diameters—is calculated by the formula
\[ h' = H - H\cos\alpha + \frac{d_k}{2}\sin\alpha . \tag{5} \]
The value \(h'\) can also be determined with sufficient accuracy from the graph (Fig. 2, b).
From comparison of formulas (3) and (5), it is evident that, with the special conical bottomhole shape, the value \(h'\) will exceed the corresponding value of the hinge-center displacement with a flat bottomhole by
\[ h' - h = d_k \sin\alpha , \tag{5a} \]
i.e., at a small deflection angle, by almost a factor of two.
Consequently, with special preparation of the bottomhole it is possible to side-track a borehole in a new direction using simple hinged deflectors of considerably larger diameter than under the same side-tracking conditions in a flat bottomhole. At the same time, the stability of the system is increased owing to the substantially greater downward displacement of the hinge.
The required bottomhole shape can be prepared by a special conical bit equipped with hard-alloy cutters, whose strength is quite sufficient to give the bottomhole the required shape in a short time even in very hard rocks.
At the very beginning of cutting, before the deflecting tool is held by the pilot hole, the system is acted upon by various forces that may bring it out of the stable position that ensures deflection in the required direction. Determining the nature and magnitude of these forces is the second problem in calculating simple hinged deflectors of the second type, whose ultimate purpose is to determine the maximum possible
Fig. 3. Operating diagrams of a simple single hinged deflector of the second type:
a — with a flat face; b — with a face machined as a truncated cone.
diameter of the deflecting bit. In general form, the necessary stability condition for the system (in the case of a single hinged deflector) may be expressed by the inequality
\[ P > \frac{F}{\operatorname{tg} \alpha}, \tag{6} \]
where \(P\) is the magnitude of the axial load, with its point of application at the center of the hinge;
\(F\) is the force acting on the deflecting tool in the plane of deflection and arising from the forces of resistance of the rock to breaking; under the action of these forces the deflecting bit, at the beginning of cutting, tends to move along the face;
\(\alpha\) is the angle of deflection.
Analytical determination of the force \(F\) is difficult to a certain degree, since its magnitude depends on a large number of factors; therefore [[unclear: continuation begins with “vy-”]]
...clarification of the possibility of sidetracking with hinged deflectors of large diameter can subsequently be carried out experimentally.
Analysis of the geometric parameters of simple single hinged deflectors of the second type permits the following conclusions to be drawn.
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Simple hinged deflectors of the second type must possess a definite combination of geometric parameters in order to ensure reliable operation.
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Reliability of operation increases with an increase in the zenith angle of the borehole, the weight of the heavy bottom assembly, and the angle of deflection.
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The diameter of the sidetracking bit must be less than half the borehole diameter when sidetracking in a flat bottomhole.
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A special bottomhole shape makes it possible to increase the diameter of the sidetracking tool with an increase in the degree of stability of the system.