Technical and economic assessment of directional drilling equipment
Abstract Generated abstract
This paper proposes a technical and economic method for comparing directional drilling deflectors under specific drilling conditions. It argues that assessment by separate changes in inclination and azimuth is insufficient, and instead uses spatial curvature intensity, adjusted for natural borehole curvature, as the technical criterion. The economic component is expressed through additional time per curvature interval and, where relevant, specific capital cost per deflection, combined into an effectiveness indicator. Application to comparative tests of removable wedges in 1969 suggests that the Volkov design was most expedient under the tested conditions, while removable deflectors are rational mainly when natural curvature is weak or aligned with the intended artificial curvature.
Full Text
Technical and Economic Assessment of Directional Drilling Tools
V. I. Ryazanov, B. I. Spiridonov
(Presented by the scientific seminar of the Department of Exploration Technology)
To solve specific problems of directional drilling, a fairly large number of different technical tools have now been developed that make it possible to bring a borehole onto a specified trajectory. The choice and use of one or another of them depend on many factors, the principal ones being the possibility of drilling in the required direction with a specified intensity of curvature of the borehole. For the proper selection of technical tools for directional drilling, it is evidently necessary to carry out a technical and economic assessment of the operation of deflectors, proceeding from the specific conditions of their use; however, at present there is no methodology for calculating an indicator of the effectiveness of bottom-hole assemblies that would make it possible to perform such an assessment.
Comparison of directional drilling tools is usually carried out only by the intensity of curvature obtained after the use of the deflector; at the same time, assessment separately by the magnitude of the change in inclination and azimuth angle cannot be considered correct, since the intensity of azimuthal curvature depends on the inclination angle of the borehole and, all other conditions being equal, may be different. In addition, it is necessary to take into account the direction and intensity of the natural curvature. Artificial curvature in a direction opposite to the natural curvature is, as a rule, considerably more difficult and gives poorer results than in the case where the directions of deflection and natural curvature coincide.
To assess the technical capability of a deflector, it is expedient to use the concept of the spatial angle, which relates the azimuthal and inclination curvature of the borehole. To determine this angle, formulas proposed by A. Lubinski may be applied.
[2], A. E. Kolesnikov [4], and the simpler formula of A. G. Kalinin [3]
\[ \cos\varphi=\cos\Theta_1\cdot\cos\Theta_2+\sin\Theta_1\cdot\sin\Theta_2\cdot\cos\Delta\alpha , \tag{1} \]
where \(\varphi\) is the total spatial angle of curvature;
\(\Theta_1\) and \(\Theta_2\) are, respectively, the initial and final inclination angles of the well in the interval of operation of the deflector;
\(\Delta\alpha\) is the increment of the azimuth angle.
To calculate the magnitude of the angle of spatial curvature, one may also use the simplified formula proposed by M. M. Aleksandrov [1]
\[ \varphi=\sqrt{(\Theta_2-\Theta_1)^2+ \left[\left(\alpha_2-\alpha_1\right)\cdot\sin\frac{\Theta_1+\Theta_2}{2}\right]^2}. \tag{2} \]
The intensity of spatial curvature \(i_\varphi\) can be determined by the formula
\[ i_\varphi=\frac{\varphi}{l}, \tag{3} \]
where \(l\) is the length of the interval of artificial curvature, taken as equal to the length of the borehole from the point of deflection to the depth from which drilling is carried out with a conventional assembly and conventional technology.
By this method it is evidently possible to evaluate both the intensity of artificial spatial curvature \((i_{\varphi\text{и}})\) and that of natural spatial curvature \((i_{\varphi\text{е}})\).
The intensity of the total spatial curvature can be determined from measurements of inclination angle and azimuth at the beginning and end of the curvature interval, while the intensity of spatial natural curvature can be determined from the intervals above and below it, using formulas (2) and (3).
The resulting value of the intensity of spatial curvature \((i_\varphi)\), as a consequence of the influence of artificial and natural curvature, can be determined using methods of vector algebra from the expression
\[ i_\varphi^2=i_{\varphi\text{и}}^2+i_{\varphi\text{е}}^2+2i_{\varphi\text{и}}\,i_{\varphi\text{е}}\cos\gamma , \tag{4} \]
where \(\gamma\) is the angle between the directions of action of the natural and artificial curvature.
For \(\gamma=0^\circ\), \(i_{\varphi\text{и}}=i_\varphi-i_{\varphi\text{е}}\). For \(\gamma=180^\circ\), \(i_{\varphi\text{и}}=i_\varphi+i_{\varphi\text{е}}\),
\[ \tag{5} \]
For intermediate values of \(\gamma\), by solving equation (4), one can determine \(i_{\varphi\text{и}}\). From the magnitude of the intensity of artificial spatial curvature one may judge the technical capabilities of directional-drilling tools.
In addition to the technical assessment of deflectors, their economic assessment is also necessary. Such an assessment is possible in terms of the time required for assembling and setting up the deflector at the surface, running it into the well, orienting it, wedging it off if necessary, and also in terms of the change in labor productivity when drilling an artificially curved interval as compared with conventional drilling. In order to use such a criterion under different conditions, it is evidently necessary to calculate the relative additional time expenditures \(\Delta t\) by the formula
\[ \Delta t=\frac{t_1-t_2}{l}, \tag{6} \]
where \(t_1\) is the actual time expenditure for drilling the curvature interval using directional-drilling tools;
\(t_2\)—the time required to drill the same interval by the conventional method;
\(l\)—the length of the curvature interval.
The time expenditures for drilling the well in the curvature interval by the conventional method may be determined from the average drilling rate in rocks of the given category at the same depth. The length of the curvature interval should be taken as the length of the borehole from the place where the directional-drilling tool is applied to the depth from which drilling continues with a conventional assembly using conventional technology.
In addition to the extra time expenditures, in an economic assessment of deflectors it is also necessary to take into account their cost. Such an assessment is possible according to the following scheme.
Let \(C\) be the cost of the deflector;
\(C_p\)—the cost of repairs, inspections, and preventive maintenance;
\(n\)—the number of curvature cycles after which the deflector is to be written off.
Then the specific capital investments per one deflection are
\[ c=\frac{C+C_p}{n}. \tag{7} \]
For deflectors the value of \(n\), as a rule, is small, and for stationary wedges, in particular, \(n=1\) and \(c=C\).
It is obvious that the greater \(c\) is, the less effective a given directional-drilling tool is. The full indicator of the effectiveness of using a deflector, taking into account its technical capability and economic characteristic, is determined by the formula
\[ k=\frac{t_1-t_2}{l i_{\varphi u}}\,c . \tag{8} \]
As an example, one may cite comparative tests of volumetric wedges carried out by us in 1969 in the Shalymskaya and Rudno-Altai GRE ZSGU. The initial data for the analysis were the data from time studies, drilling logs, inclinometry, and actual geological sections for the wells. The results of comparative tests of removable wedges of the SO-57/36-3 design by G. A. Volkov and A. I. Kovalevsky are given in Table 1. The first two removable wedges
Table 1
Results of comparative tests of removable wedges
| Deflector type | Intensity of spatial artificial curvature, deg/m | Length of curvature cycle, m | Additional time expenditures, h | Deflector effectiveness indicator |
|---|---|---|---|---|
| SO-57/36-3 | 0.4 | 4.7 | 24 | 7.9 |
| Removable wedge designed by G. A. Volkov | 0.31 | 4.1 | 14 | 4.55 |
| Removable wedge designed by A. I. Kovalevsky | 0.34 | 4.1 | 29 | 16.8 |
were used for artificial curvature against the natural curvature, and for the latter, 4 cases of curvature in the direction of the natural curvature were taken. The cost of all the wedges is approximately the same; therefore, the specific capital investments are not taken into account in the comparative analysis.
The comparatively high additional time expenditures for the SO-57/36-3 wedge can be explained by the fact that the expedition lacks diamond reamers for boreholes from \(d = 36\) mm to \(d = 59\) mm; therefore the reaming was carried out twice, first to \(d = 46\) mm and then to \(d = 59\) mm with ordinary bits. The high additional time expenditures for the wedge designed by A. I. Kovalevsky are explained by the above-mentioned design shortcomings.
The comparison shows that, under the existing conditions, the use of the removable wedge designed by G. A. Volkov is the most expedient from a technical and economic point of view. It should be noted, however, that when the SO-57/36-3 wedge is used, the intensity of artificial spatial curvature is the greatest, and the use of special reamers will undoubtedly make it possible to deflect boreholes with maximum effect.
The tests also showed that the use of removable deflectors is rational only under certain conditions: either when the intensity of natural curvature is low, or when the direction of the latter coincides with the direction of artificial curvature.
If this condition is not met, the desired result can be achieved only with large expenditures of money and time, or by using continuous-action deflectors.
REFERENCES
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Aleksandrov M. M. Simplification and acceleration of calculations for determining increments of spatial curvature in individual sections of a borehole.—Scientific and Technical Collection Drilling, No. 10, 1969.
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Vuds G., Lubinsky A. Borehole Deviation During Drilling. Gostoptekhizdat, 1960.
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Kalinin A. G. Deviation of Boreholes. Gostoptekhizdat, 1963.
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Kolesnikov A. E. Analysis of the operation of flexible assemblies in artificial borehole deviation.—Transactions of the North Caucasus Mining Institute, issue 16, 1961.