Proceedings of the Tomsk Polytechnic Institute named after S. M. Kirov, holder of the Order of the October Revolution and the Order of the Red Banner of Labor

Vol. 264　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1976

On the Problem of Correcting a Well Deviating from a Given Point

L. A. Pukhlyakov

(Presented by Professor S. S. Sulakshin)

Before correcting a well that deviates from a given point, it is necessary to determine its deviation. This can be done in the following way. First, the above-bottomhole (“zenith”) angle of the given point \(\Theta_t\) is determined. The calculation is carried out by the formula

\[ \tan \Theta_t = \frac{s}{z_{\text{bot}} - z_t}, \tag{1} \]

where

\(z_{\text{bot}}\) is the absolute elevation of the last measurement point of the well (the bottomhole), \(z_t\) is the absolute elevation of the given point, and \(s\) is the distance between the projections of these points onto the horizontal plane (Fig. 1, left).

Fig. 1. Vertical (left) and horizontal (right) projections of the well and the point to which it must be brought. The solid contour line shows the completed wellbore, the dot-dash line its continuation, and the ordinary dashed line the direction to the given point.

Suppose that in a certain case these quantities turned out to be as follows: \(z_{\text{bot}} = -1550\ \text{m}\), \(z_t = -2250\ \text{m}\), and \(s = 520\ \text{m}\). Substituting them into expression (1), we obtain

\[ \tan \Theta_t = \frac{520}{-1550 - (-2250)} = \frac{520}{700} = 0.743. \]

\[ \Theta_t = 36^\circ 30'. \]

The solution of this problem can also be carried out graphically. To do this, the distance between the projections of the points under consideration onto the horizontal plane \((s)\) is laid off along the horizontal axis, and along the vertical axis—the difference of the absolute elevations. The value of the sought angle is determined with a protractor.

Secondly, the zenith (nadir) angle of the well at the bottomhole \((\Theta_{\text{skv}})\) is determined. It is taken directly from the inclinometer. Let us suppose that in the case under consideration it has turned out to be equal to \(18^\circ\).

Thirdly, the azimuths of the specified point \(A_t\) and of the well inclination \(A_{\text{sk}}\) are determined. In doing so, the azimuth of the well inclination should likewise be taken directly from the inclinometer, introducing into it a correction for magnetic declination. To determine the azimuth of the specified point, one should draw the horizontal projection of the well and plot the specified point on it as well. Let us suppose that the azimuth of the specified point has turned out to be \(290^\circ\), and the azimuth of the well inclination at the moment of calculation \(323^\circ\) (Fig. 1, right).

Next it is necessary to find such a position of the bent sub relative to which it can be turned through a definite angle. In this connection the following is recommended.

1. As drill pipes, use pipes employed in electric drilling, that is, such pipes inside which there are sections of three-core cable, connected to one another when the pipes are screwed together.

2. Equip the bent sub with an angle-measuring instrument whose readings would be the greater, the more the front part of the sub is raised.

3. Lower the drilling tool to the bottomhole, supply current to the angle-measuring instrument, and slowly rotate the string of drill pipes, seeking the greatest reading of the angle meter. Obviously, with such a position of the bent sub, which may be called the initial one, the zenith angle of the well will begin to increase intensively, while the azimuth will remain unchanged. In order for the well to begin gaining curvature in the direction of the specified point, it is necessary to turn the string of drill pipes through a certain angle, which may be called the angle of rotation. To determine it, one may use a Wulff net. For this purpose the Wulff net is arranged so that its equator occupies a vertical position, and its upper end is taken as the origin (Fig. 2). Then tracing paper is superposed on the Wulff net, and on it, in accordance with the limb, radii are drawn expressing the azimuths of the well inclination \((A_{\text{sk}})\) and of the specified point \((A_t)\). The first of these is drawn with a dotted dashed line, the second with a simple dashed line (Fig. 2, upper).

After this a compass is taken, and one leg of it is set at the center of the Wulff net, while the other is moved upward along its vertical diameter to such a distance as corresponds to the value of the nadir angle of the specified point \((\Theta_t)\). In the present case this is \(36^\circ 30'\). It is borne in mind that the measurement is made in the system of meridians of the net. With the obtained opening an intersection is made on the line of the simple dashed line, which expresses the azimuth of the specified point \((A_t)\). The obtained point is circled (Fig. 2).

Then the radius that expresses the radius of the well inclination (the dotted dashed line) is brought into coincidence with the vertical diameter (equator) of the net. The circled point will thereby move and will occupy the position shown in Fig. 2, lower. From its new position, from top to bottom along the parallel on which it has found itself, a curve is drawn of such length as corresponds to the value of the zenith angle near the well bottomhole (in the present case \(18^\circ\)), if the measurement is made in the system of meridians. The very lowest point of the obtained curve is circled

triangle; through it a solid straight line is drawn from the center of the grid. On the limb of the grid it gives us the angle of turn \(\psi\), in this case (Fig. 2, lower) \(310^\circ\). The same principle underlies the operation of the instrument of Yu. S. Vasiliev [1, p. 44].

If it is impossible to orient the deflecting tool relative to the plane of inclination of the well at the last measurement point—for example, if it is lowered on oriented rods (pipes)—then its azimuth can be determined by the formula

\[ A_{\mathrm{defl}} = A_{\mathrm{sk}} + \psi, \tag{2} \]

in this case

\[ A_{\mathrm{defl}} = 323^\circ + 310^\circ = 633^\circ = 273^\circ. \]

As is evident from the last expression, the azimuth of the deflector differs greatly from the azimuth of the assigned point, which in this case is \(290^\circ\).

At the same time as the azimuth of the deflector is determined on the Wulff net, the total deviation of the well from the assigned point \(j\) is also determined. To do this, the compass is again taken and one of its legs is set at the center of the grid, while the other is moved to the triangle point. With the resulting opening, an arc is drawn to the vertical diameter of the grid (Fig. 2, lower). As a result, we obtain a segment of this diameter. Its length will correspond to the magnitude of the total deviation of the well from the assigned point \(j\). In this case it turned out to be \(22^\circ\).

Fig. 2. Determination of the angle of turn on the Wulff net. The direction (azimuth) of the assigned point is shown by a simple dashed line; the direction (azimuth) of the well in the near-bottom zone is shown by a dotted dashed line. Through the triangle point passes a radius expressing the angle of turn.

The time of work using the deflector depends on the magnitude of the total deviation. Suppose that, in the case under consideration, the intensity of curvature of the well over the interval where deflector \(i\) is used reaches \(2^\circ\) per 10 meters. Then, with its use, we must drill 110 m.

After drilling this interval, the well is again surveyed and its conformity to the assigned direction is checked, as described above.

References

1. Yu. S. Vasiliev, N. B. Sivokhina, A. S. Bronzov, Permissible Deviations of Wellbores from the Design. Gostoptekhizdat, 1963.