Deviation of Wells of the Alexandrovsk Oil Exploration Expedition and the Need to Account for It in Constructing Structural Maps

V. I. Volkov, L. A. Pukhlyakov

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

The object of study of the Alexandrovsk oil exploration expedition is the northern part of Tomsk Oblast, which at present is regarded as the most promising area (several fields here have yielded commercial oil). This was the reason why the authors began to study the materials of this expedition. It should be noted here that geologists give sufficient attention to this question—that is, to the analysis and accounting of data on well deviation—only in those areas where artificial deflection of wellbores is carried out, and also where deviations reach significant magnitudes and do not fall within the permissible limits. The latter, as a rule, are characteristic of areas where the geological section is composed of rocks of increased hardness (silicified limestones, dolomites, etc.) and where, because of this, increased bit pressures are used to increase the mechanical drilling rate.

In the north of Tomsk Oblast the section is composed of relatively less competent rocks, which are satisfactorily destroyed under small axial loads on the bit. As a consequence of this, the deviation of wells from the vertical here does not exceed \(5^\circ\) (i.e., it falls within permissible limits), and due attention is not paid to this question.

The purpose of the present work is to decide whether such an attitude toward well deviations is justified or not. In the course of the work, the horizontal displacement of bottoms relative to wellheads \(r\) and the correction of depth for curvature \(\sum \Delta z'\) were determined. The horizontal displacements of bottoms relative to wellheads were determined by the method of rectangular coordinates in accordance with the formulas

\[ \Delta x = 25 \sin \Theta \cos A, \tag{1} \]

\[ \Delta y = 25 \sin \Theta \sin A, \tag{2} \]

where

\(\Delta x\) — increment of the coordinate directed from south to north;
\(\Delta y\) — increment of the coordinate directed from west to east;
\(\Theta\) — zenith angle of the well at the measurement point;
\(A\) — azimuth of the well inclination at the measurement point;
\(25\) — coefficient expressing the length of the measurement interval in meters.

The calculation was performed with the aid of special tables [1], which provide the third digit after the decimal point. Such accuracy fully satisfies the problem posed.

The values of \(\Delta x\) and \(\Delta y\) obtained in this way were added together, and the final magnitude of the displacement was determined by the formula

\[ r=\sqrt{(\Sigma \Delta x)^2+(\Sigma \Delta y)^2}. \tag{3} \]

The results of the calculation are summarized in Table 1.

Table 1

Horizontal displacements of well bottoms relative to their collars for wells of the Alexandrovsk oil-exploration expedition

As can be seen from this table, the displacement of the bottoms relative to the collars for individual wells, as a rule, does not exceed 50 m and only once (well 5) exceeded 100 m. This means that on maps at a scale of 1:100000 these values may only rarely exceed one millimeter. Hence such deviations will not have a substantial effect on the positions of individual contour lines on a structural map and on the boundaries of deposits. Nevertheless, there is no basis for ignoring them completely. These values should be reflected in reports at least in order to give an idea of their magnitudes.

Usually, in constructing structural maps from drilling data, the vertical components of the wellbores to a given point are first determined. The calculations are carried out by the formula

\[ \Sigma \Delta z=\Delta z_1+\Delta z_2+\ldots+\Delta z_n, \tag{4} \]

where

\[ \Delta z_n=25\cos\Theta_n. \tag{5} \]

Then the absolute elevations of individual points are determined. The calculations are carried out by the formula

\[ z=H-\Sigma \Delta z, \tag{6} \]

where

\(H\) — the absolute elevations of the well collars.

Here, however, it must be noted that determining the vertical components of wellbores, or of their parts, by formulas (4) and (5) is a very laborious matter. Therefore many authors, for example N. F. Frolov and E. F. Frolov [2], recommend determining this value through its deficiency relative to the length of the calculation interval, which has received the name of the depth correction for curvature \(\Delta z'\). The physical meaning of this quan-

is shown in Fig. 1, and its increment over individual intervals is determined by the formula

\[ \Delta z' = 25 \cdot (1-\cos \Theta). \tag{7} \]

The values of this correction obtained over the individual intervals are summed, and their total values \(\Sigma \Delta z'\) are substituted into the formula for determining the absolute elevations of particular points:

\[ z = H - (l - \Sigma \Delta z'), \tag{8} \]

where
\(l\) is the depth of occurrence of the given point when measured along the borehole.

It is especially convenient to use the depth correction for curvature when the zenith angles of the wells are small, when the number of significant figures in it does not exceed three. For comparison, let us compare the calculation of these values for the point 137.5 m in well 3 (see Table 2).

Table 2

Calculation of the vertical component and of the depth correction for curvature for the point 137.5 m in well No. 3 of the Sosninskaya area

In determining increments of the depth correction for curvature for individual wells of the Aleksandrovsk Oil Exploration Expedition, special tables [1] were used. The values of the total magnitudes of these corrections for individual wells are given in Table 3. As can be seen from this table, they have the most varied values: from 0.261 m (well 4) to 3.463 m (well 5), so that the difference between them in individual cases exceeds 3 m. Such magnitudes may be ignored if the dips of individual structural flanks reach several degrees and the excesses of elevations are tens and hundreds of meters. However, under the conditions of the Middle Ob region, the dips of structural flanks are measured in units of degrees, and sometimes in fractions of a degree. Hence ignoring an excess of three meters here may lead to serious distortions of the configurations of structures and to the incorrect placement of new exploratory wells.

Similar inaccuracies may arise when determining the depth of the water-oil contact. For example, suppose that the water-oil contact lies absolutely horizontally; then, allowing for the depth correction for curvature, we shall draw it precisely so. But if we begin

to ignore it, then in one place we shall draw it higher, and in another lower, than it actually lies, and in this way we shall completely distort the conception of the structure of the deposit.

Fig. 1. Diagram of the interrelationships among the various elements of well deviation

Table 3

Depth correction for deviation in wells of the Alexandrovsk Oil Exploration Expedition

Conclusion

The analysis carried out shows that well deviations must be taken into account in all cases, however small these deviations may be.

LITERATURE

1. L. A. Pukhlyakov. Tables for processing deviated and multibottom wells when measuring deviation elements at intervals of 10 and 25 meters. Publishing House of Tomsk University, 1966.

2. N. F. Frolov, E. F. Frolov. Geological observations and constructions during the drilling of deviated wells. Gostoptekhizdat, 1957.