Determination of the attitude elements of beds from elevations in a dual-bottomhole well
Abstract Generated abstract
The paper proposes a method for determining the attitude elements of deep strata intersected by a dual-bottomhole well, addressing the cost and operational limitations of oriented coring, inclinometry, and three-bottomhole approaches. The method treats intersections of conformable beds by the two branches as multiple oblique sections of inclined planes, using elevation differences, horizontal projection distances, apparent dip angles, and dip azimuths to construct a graphical and analytical solution. An example calculation shows how plotted apparent dips define lines whose perpendiculars from a common origin yield the true dip direction and dip angle, producing two interpreted attitudes for the studied bed series.
Full Text
DETERMINATION OF THE ATTITUDE ELEMENTS OF STRATA FROM ELEVATIONS IN A DUAL-BOTTOMHOLE WELL
L. A. Pukhlyakov
(Presented by Professor A. V. Aksarin)
Determining the attitude elements of strata that occur at considerable depths plays an exceptionally important role in the search for oil and gas. Various authors have proposed different methods for this purpose. In particular, oriented-core sampling and formation inclinometry are widely used [1, 5]. Methods have been developed for determining the attitude elements of strata from three elevations in three-bottomhole wells [2, 3], and also from two elevations and two unoriented cores from dual-bottomhole wells [4]. These various methods have different shortcomings. In particular, a drawback of the method using three-bottomhole wells is the excessively large amount of additional drilling, owing to which the costs of constructing a single well may increase by 30–40%.
It would seem that the method of two elevations in combination with two unoriented cores should not have this drawback, since very often wellbores become strongly curved, and to correct them the deviated parts are filled with cement. As a result, a certain interval is drilled through a second time. However, taking core from two bores also requires additional expenditures of time and funds, and this worsens the reporting indicators of enterprises (it lowers commercial drilling rates and increases the cost per meter of penetration). Refinement of the structure through the use of these data—that is, in practice, utilization of the rejected parts of the bores—does not improve these indicators (in general it does not affect them). In one way or another, enterprises do not agree to take core from intervals being drilled through again. In this connection, a new method is proposed for determining the attitude elements of strata which, when branches from the main bore are present, does not require any additional operations in the wells—the method of elevations obtained from a dual-bottomhole well.
Let us assume that a certain dual-bottomhole well, the horizontal projection of whose branched part is shown in Fig. 1, has intersected, with each of its branches, a number of strata, the roofs of which were encountered by them at the depths given in Table 1 (cols. 1, 2, and 4). Plotting these points on the horizontal projection of the branched part of the well and connecting them by straight lines (Fig. 1), we obtain several oblique sections of several inclined planes (the surfaces of the strata). However, if these strata lie conformably one upon another, then the given sections will be equivalent to several sections of one and the same inclined plane.
Fig. 1. Horizontal projection of the branched part of a dual-bottomhole well. The numerals indicate the nominal depths (depths measured along the borehole) at the points marked by circles. The short transverse lines show the positions of the points of intersection of the corresponding borehole with the tops of the beds penetrated. The straight lines between them are the lines of oblique sections.
Thus, to solve the problem posed, one can use the same principle that underlies the method for determining the elements of bed attitude from measurements on two walls of a shaft; that is, the principle of oblique sections of an inclined plane. It is best to carry out the solution of such a problem graphically and analytically. Namely:
Fig. 2. Directions of the straight lines of oblique sections with the throws plotted on them (the distance from the center of projection \(O\) to the circles filled in with India ink is according to Table 1. Dotted lines are the averaged straight lines drawn through these circles. The arrows \(OA\) and \(OB\) perpendicular to them. The directions and lengths of these perpendiculars express the directions (azimuths) and throws of the dip angles of the series of beds intersected by the branched part of the well.
- Graphically (in the present case, from Fig. 1) the distances between the horizontal projections of the points at which both branches encounter each of the beds are determined, in meters, \(S\) (col. 7 of Table 1), and analytically the differences in their absolute elevations, also in meters (col. 6 of Table 1), which are substituted into the formula for determining the dip angle of the bed in the oblique section \(\alpha_k\)
\[ \operatorname{tg}\alpha_k=\frac{z_1-z_2}{S}. \tag{1} \]
The results of the calculation are entered in Table 1 (col. 8).
- Using the formula
\[ a=\frac{1}{\operatorname{tg}\alpha_k}, \tag{2} \]
the throws corresponding to the dip angles of the beds in the oblique sections are determined; these are also entered in Table 1 (col. 9).
- The azimuths of dip of the straight lines of the oblique section are determined—the directions expressed in Fig. 1 by straight lines from points with higher absolute elevations to points with lower absolute elevations. In the present case they proved to be equal to \(253^\circ 30'\), \(240^\circ 00'\), etc. (col. 10 of Table 1).
Results of processing data obtained in a two-bottomhole well when determining the elements of occurrence of beds by the method of several oblique sections
(calculation carried out in accordance with Fig. 1)
Table 1
| Name of surface | Data for the first borehole: depths at measurements along the borehole, \(l_1\) | Data for the first borehole: absolute elevations, \(z_1\) | Data for the second borehole: depths at measurements along the borehole, \(l_2\) | Data for the second borehole: absolute elevations, \(z_2\) | Difference of absolute elevations, \(z_1 - z_2\) | Distance between projection points in the plane, \(s\) | Dip angle of the straight section, \(\alpha_k\) | Laying, \(a_k\) | Dip azimuths of the straight section, \(A_k\) |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Top of brown limestone | 1512.5 | −1491.8 | 1511.5 | −1491.1 | 0.7 | 2.6 | 15°05′ | 3.72 | 253°30′ |
| Top of sandstone | 1568.5 | −1547.0 | 1565.0 | −1544.4 | 2.6 | 6.7 | 21°15′ | 2.58 | 240°00′ |
| Top of siltstone | 1595.0 | −1573.2 | 1597.0 | −1569.3 | 3.9 | 8.6 | 24°25′ | 2.21 | 234°30′ |
| Top of brown clay | 1634.5 | −1612.2 | 1627.5 | −1606.6 | 5.6 | 11.8 | 25°30′ | 2.11 | 226°00′ |
| Top of argillite | 1656.0 | −1633.5 | 1643.0 | −1619.0 | 14.5 | 13.2 | 47°45′ | 0.91 | 220°30′ |
| Top of dolomite | 1692.5 | −1669.6 | 1674.0 | −1653.0 | 16.6 | 15.4 | 46°50′ | 0.93 | 213°30′ |
| Top of black clay | 1736.5 | −1713.1 | 1716.5 | −1695.4 | 17.7 | 17.4 | 46°00′ | 0.967 | 205°30′ |
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These directions are plotted from the common center \(O\) on a separate drawing, and the corresponding apparent dips are marked on them. The points obtained are circled (Fig. 2).
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If the beds under study are conformably superposed, then the points circled will give a straight line. A perpendicular to this straight line drawn from the common center \(O\) will give the direction (azimuth) of dip of the bed, and its shortest distance from the center (the length of the perpendicular) is the apparent dip \(a_n\), corresponding to the angle of dip of the series of beds \(\alpha_n\), which is determined by the formula
\[ \operatorname{tg}\alpha_n=\frac{1}{a_n} \]
In the present case we obtained two straight lines, one of which corresponds to a dip angle of \(30^\circ 30'\) and a dip azimuth of \(190^\circ\), and the other to a dip angle of \(48^\circ\) and a dip azimuth of \(231^\circ\).
References
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L. A. Pukhlyakov. Determination of bedding elements of strata from one straight oblique section and two nonoriented cores. Proceedings of TPI, vol. 216, 1971.
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