MULTILATERAL WELLS AS A MEANS OF IDENTIFYING DEEP STRUCTURES

L. A. Pukhlyakov

(Submitted by the Department of Geology and Exploration of Oil and Gas Fields)

The importance of knowledge of tectonics in prospecting for oil and gas, and the need to improve methods for studying it

Oil deposits are, as a rule, confined to the upper parts of anticlines, monoclines, and domes; therefore, in order to justify the placement of prospecting wells, the deep structure of a given area is always studied to some extent—the structure favorable for the accumulation of oil or gas is identified. For this purpose, as a rule, geological surveys are first carried out, then structural drilling and seismic exploration. However, all these methods are not always effective, and in the course of prospecting drilling the structures must always be refined.

The point is that structural drilling is usually carried out at depths of 400–500 meters, whereas the search for oil and gas deposits in horizons remote from the surface is carried out at 2000–2500 meters and more. In this case it is assumed that structures in the lower horizons should correspond to structures in the overlying ones. In fact, this correspondence almost always proves to be very, very relative. These structures, as a rule, are displaced relative to one another. Moreover, in areas with a more or less complex tectonic structure it is still possible to establish certain regularities of such displacement. As for plain regions, where the dips of the limbs of structures do not exceed one or two degrees—for example, in the Volga region—it is very difficult, and even impossible, to establish any regularities whatever in the displacements of structures. As a result, for a final conclusion on one or another area it is necessary to drill no fewer than five wells there, for only with five wells can one form some idea of the deep structure of the area.

In connection with the foregoing, in order to refine ideas about the deep structure of one or another area, oil workers widely employ the method of convergences [2, 3]. However, this method also requires the drilling of a considerable number of prospecting wells. Attempts are known to use oriented core for the same purpose [4]. However, the difficulties in processing it, and especially the insufficient accuracy of this method, do not allow oil workers to introduce it widely into production.

In the present article, for constructing structural maps of deeply occurring horizons it is proposed to use multilateral wells, which have already found wide application in the exploration of solid mineral deposits.

Essence of the Method

If the geologist has at his disposal two ordinary wells, then, in constructing a profile, he can draw as many anticlines and synclines as he likes, none of which, however, will be reliable (Fig. 1, a). Thus his ideas about the deep structure of the given area will be very approximate.

Each multilateral well represents, as it were, a series of three wells, only slightly separated from one another, drilled to the given horizon. On the basis of the data from each of them it is already possible to determine not only absolute elevations, but also the elements of occurrence of the bed (surface) of interest to the geologist. Hence the construction of this bed will be more unambiguous, and therefore more reliable (Fig. 1, b, c, d, e). Working with a map, the geologist will be able, from the same data, to determine also the direction (azimuth) of dip of the bed and, if the first two wells are favorably located (Fig. 1, b; 2, a), to determine from them the probable position of the dome of the structure, so that even the third (ordinary) well will make it possible to draw a final conclusion about the productivity of the area.

If the first two wells are “unfavorably” located (Fig. 1, c; 2, b), it will be necessary to add one more multilateral well and one ordinary well to each of them—only after this will it be possible to make a final conclusion about the prospects or lack of prospects of the given area and about the possibility or impossibility of continuing exploration work on it. Here, however, it should be added that the “unfavorable” placing of the first two wells will mean only that, on the area under study, the flanks of two structures favorable for the accumulation of oil and gas (anticlines or domes) have been discovered, and therefore subsequently the number of wells for the exploration of each of these structures will again be reduced to three. In complex structures the number of wells will, of course, be somewhat larger.

Effectiveness of the New Method

To determine the elements of occurrence of a bed with an accuracy of up to \(1^\circ\), the points at which the various branches of the given well encounter the given bed must be separated by up to 10 m; therefore the length of the branches from the main borehole must reach 200–300 m. Thus the total amount of drilling for each well must increase by 500–600 m, which, at a main-borehole depth of 2 km, will amount to 25–30%. Calculations show that, compared with an ordinary well, the drilling time of a multilateral well should increase by 40%, and the construction cost by 50%. Thus, the drilling of two multilateral wells and one ordinary well (sufficient for a conclusion about the prospects of a structure) will be equivalent to drilling four ordinary wells. Four ordinary wells, however, even when a structural map for the overlying horizon is available, are insufficient for reaching a conclusion about the prospects of one area or another.

This, however, does not exhaust the importance of multilateral wells. When an area is drilled exclusively with single-bore wells, the tectonics of the basement always remains completely unexplored (and sometimes it is of exceptional interest), whereas just one multilateral well will already make it possible to say something about it. But even this is not all: on the basis of ordinary wells we can say nothing about disjunctive disturbances even in the bed under study, although at times there is an acute need for this. Two wells drilled on different sides of a possible disjunctive …

Fig. 1. Interpretation of data from ordinary and multilateral drilling on profiles.

Fig. 2. Examples of interpretation of data from two multilateral wells on a map.

multilateral wells will give a completely precise answer to this question (Fig. 1, d).

Drilling multilateral wells

Drilling multilateral wells does not require any special equipment and therefore can be carried out by any organization engaged in oil and gas exploration. It is recommended that it be performed in the following order. After the main borehole has been drilled, it is investigated by all available methods that do not require setting it with casing. Special attention is paid to the depths at which the surfaces separating different horizons are encountered, and to measurements of the elements of the well curvature. Then a cement plug is set in this borehole at a height of 150–200 m from the bottom, and a second borehole is drilled.

The second borehole is drilled to a depth of 150–200 m and is investigated by the same methods as the first, after which a cement plug is likewise set in it. In doing so, the plug must be set with such calculation that the beginning of the third borehole will be above the beginning of the second.

The third borehole is drilled to the same depth and is first investigated by the same methods as the first two, but then it is set with casing and tested for inflow of fluid.

When drilling directionally inclined wells, orienting the tool usually takes a great deal of time. In the present case there is no need for this, since the elements of the attitude of the bed can be determined for any direction of the three boreholes. The exception is the case in which all three boreholes lie in one plane. However, the probability of such a coincidence is small, and, if necessary, a fourth branch can be drilled.

Processing data on well curvature

The proposed procedure provides for processing data on well curvature in rectangular coordinates. The calculation is reduced to a table (Appendix 1).

As the calculation points in this table, the points taken are not the measuring points, as is very often done in some drilling offices, but, as A. L. Vychegzhanin [1] recommends, points located between them. Because of this, the measuring points turn out to be at the midpoints of the calculation intervals, and there is no need to find average values of the zenith angles and azimuths of well inclination. Thus, the calculation begins with determining the calculation points—the lower boundaries of the calculation interval (col. 1). Column 2 (the upper boundary and the calculation interval) contains the same figures as column 1, only shifted down by one line. The values in columns 3, 4, and 5 are simply copied from the table of measurements of the elements of well curvature. The topographic azimuth is determined from the magnetic one by adding to it the value of the magnetic declination. The length of the calculation interval is established so that the measuring points correspond to its midpoint.

The calculation itself begins with determining the horizontal projection of the given calculation interval (col. 8). The values of this column are calculated by the formula

\[ r = \Delta L \cdot \sin \Theta, \tag{1} \]

where

\(r\) is the length of the calculation interval (taken from the corresponding row of column 7);

\(\Theta\) is the zenith angle at the given point (taken from column 4). The values of the coordinate increments \(\Delta X\) and \(\Delta Y\) for the given calculation intervals (columns

Table of coordinates of calculation points of well 114

Appendix 1
Absolute elevation of wellhead \(H=-159.1\) m; borehole inclination \(x=-1^\circ\)

9 and 11) are calculated by the formulas

\[ \Delta X = r \cdot \cos A_{\mathrm{sk}}, \tag{2} \]

\[ \Delta Y = r \cdot \sin A_{\mathrm{sk}}, \tag{3} \]

and the corresponding coordinates of particular calculation points are obtained by summing all coordinate increments of the corresponding intervals,

\[ \sum \Delta X = \Delta X_1 + \Delta X_2 + \ldots + \Delta X_n, \tag{4-a} \]

\[ \sum \Delta Y = \Delta Y_1 + \Delta Y_2 + \ldots + \Delta Y_n. \tag{4-b} \]

As for the vertical components of the corresponding calculation intervals, the proposed method does not provide for calculating them by the usual formula

\[ \Delta Z = \Delta L \cdot \cos \Theta. \tag{5} \]

This is because, in the calculations, greater difficulty is caused by finding the sum of these increments. The method provides for calculating the shortfalls of these increments relative to the full lengths of the calculation intervals, or the increments of the depth corrections for curvature. The calculation is carried out by the formula

\[ \Delta Z' = \Delta L (1 - \cos \Theta), \tag{6-a} \]

which is reduced to the form

\[ \Delta Z' = 2 \Delta L \cdot \sin^2 \left(\frac{\Theta}{2}\right). \tag{6-b} \]

Since formula (6-b) contains one half of the zenith angle \(\frac{\Theta}{2}\), this value is determined and entered in column 13. The value itself of the increment of the depth correction for curvature \((\Delta Z')\), determined by formula (6-b), is entered in column 14. The total shortfall of all increments of the vertical component, or the total magnitude of the depth correction for curvature, for the various calculation points is determined by a formula analogous to formula (4-a),

\[ \sum \Delta Z'_n = \Delta Z'_1 + \Delta Z'_2 + \ldots + \Delta Z'_n, \tag{4-c} \]

or, more precisely, by the formula

\[ \sum \Delta Z'_n = \sum \Delta Z'_{n-1} + \Delta Z'_n. \tag{7} \]

In this case, for calculating these quantities for the first intervals of the second and third boreholes, the value to be taken as the initial \(\sum \Delta Z'_{n-1}\) is \(\sum \Delta Z'\) of the lowermost calculation point of the unbranched part of the borehole. This value is entered in column 15.

Finally, the absolute elevations of the calculation points (column 16) are determined by the formula

\[ Z = H - (L_p - \sum \Delta Z'), \tag{8} \]

where \(H\) is the absolute elevation of the wellhead, and \(L_p\) is the nominal depth of the given calculation point (the measured depth along the borehole), taken from column 1 of the table under consideration.

Use of a Logarithmic Slide Rule in Calculations by Formulas (1, 2, 3, and 6-b)

In calculations by formulas (1, 2, 3, and 6-b), it is recommended to use a logarithmic slide rule, specifically: in calculations by the first

... three of them should proceed as follows. The end (or beginning) of the sine scale is aligned with the division of the main scale of the ruler that corresponds to the length of the calculation interval when calculating by formula (1), or to the value of the horizontal displacement \((r)\) when calculating by formulas (2 and 3). Then the hairline of the runner of the ruler is aligned with the division of the sine scale that corresponds to the value of the zenith angle \((\Theta)\) when calculating by formula (1), to the value of the azimuth of the well inclination \((A_{\mathrm{T}})\) when calculating by formula (3), or to the value of the difference between this azimuth and a right angle \((90^\circ - A_{\mathrm{T}})\) when calculating by formula (2). The answer is read on the main scale of the ruler opposite the hairline of the runner.

When calculating by formula (6-6), the end (beginning) of the sine scale is aligned with the division of the square scale of the ruler that corresponds to twice the length of the calculation interval \((2\Delta L)\). Then the hairline of the runner is aligned with the division of the sine scale that corresponds to half the zenith angle \((\Theta/2)\). The answer is read on the square scale of the ruler opposite the hairline of the runner.

When determining the position of the decimal point in the result obtained, it is convenient to use the following rule: if half the zenith angle is close to \(40'\), then the result obtained will be approximately 10,000 times smaller than twice the length of the calculation interval; if half the zenith angle is close to \(2^\circ\), the quantity of interest will already be 1000 times smaller than twice the length of the calculation interval; if it is close to \(5^\circ 30'\), then the quantity of interest will be 100 times smaller than twice the length of the calculation interval, etc. In other cases this result will have an intermediate value.

Determination of the Elements of Bed Occurrence from Individual Wells

Before determining the elements of bed occurrence from a given well, it is necessary to construct, on a large scale—for example \(1:100\), \(1:200\), \(1:500\), or, in the extreme case, \(1:1000\)—the horizontal projection of the branched part of this well. Then on this projection it is necessary to plot the points at which the various laterals of this well meet the given bed. They must be located between the corresponding calculated points, according to which the construction of the individual laterals was carried out, at distances corresponding to their elevations one above another (Fig. 3).

Then the absolute elevations of these points are written beside them. They must be carefully computed, and therefore their calculation is entered in a table (Appendix 2). In the first column of this table are given the well number (Arabic numeral), the lateral number (Roman numeral), and the name of the horizon (surface) being mapped. Column 2 gives the nominal depth (the measured depth along the lateral) of the point where this lateral meets the given horizon \((L_{\mathrm{vst}})\); column 3 gives the nominal depth of the nearest calculated point above it \((L_{\mathrm{r}})\); column 4 gives the excess of the nominal depth of this point of intersection over the nominal depth of the nearest calculated point above it \((\Delta L'')\); column 5 gives the total correction for curvature of the nearest calculated point above \((\Sigma \Delta Z')\)—taken from the corresponding row of column 15 of the table of coordinates of calculated points (Appendix 1); column 6 gives the increment of the correction for curvature due to the interval containing the point of intersection \((\Delta Z')\)—taken from the corresponding row of column 14 of the table of coordinates of calculated points (Appendix 1).

The calculation proper begins with determining the increment of the correction to depth for curvature due to the excess of the depth of the point of intersection over

by the depth of the calculation point \((\Delta Z'')\), which is calculated by the formula

\[ \Delta Z''=\Delta Z'\cdot \frac{\Delta L''}{\Delta L}. \tag{9} \]

In the case we are considering (Appendix 2), this calculation takes the form

\[ \Delta Z''=0.85\frac{13.1}{20}=0.56. \tag{9-a} \]

After this, the total magnitude of the depth correction for curvature is determined for the given point of intersection, for which a formula analogous to formula (7) is used:

Fig. 3. Horizontal projection of the branched part of a multilateral well and determination from it of the elements of bed occurrence.

\[ \sum \Delta Z''=\sum \Delta Z' + \Delta Z''. \tag{7-a} \]

In the case we are considering (Appendix 2), this calculation takes the form

\[ \sum \Delta Z''=16.74+0.56=17.30. \]

Finally, by a formula analogous to formula (8),

\[ Z_{\mathrm{int}}=H-\left(L_{\mathrm{int}}-\sum \Delta Z''\right) \tag{8-a} \]

the absolute elevation of the point of intersection is determined. In the case considered (Appendix 2), this calculation takes the form

\[ Z_{\mathrm{int}}=159.4-(2493.1-17.3)=-2316.4. \]

Thus, on the projection made there will be three points precisely tied to one another in space. Determination of the bedding elements from them can be carried out in the usual way, namely: connect these points by straight lines, divide the lines into segments corresponding to elevations by a definite number of meters, and through the ends of the segments obtained draw the structure contours of the given bed (Fig. 3). A perpendicular to the structure contours obtained will indicate to us the direction (azimuth) of dip of the bed—in the case under consideration (Fig. 3) it is approximately \(201^\circ\). As for the dip angle, it can be determined by the usual formula

Appendix 2

Table for calculating absolute elevations of the points of intersection of individual wellbores with individual horizons

\[ \tg \alpha = \frac{h}{a}, \tag{10} \]

where \(h\) is the contour interval between structure contours (in this case 1 m);
\(a\) is the distance between structure contours (in this case \(\sim 5\) m), whence the dip angle should be approximately \(11^\circ\).

Determination of the probable position of the dome of the deep structure in the given area

The bedding elements of the bed obtained from individual wells are plotted on a working map (at a scale of 1 : 500000 or 1 : 100000) together with the absolute elevations of the given bed. From them several structure contours are constructed in the area of each of the wells (Fig. 2), by connecting which with one another we obtain the outlines of the subsurface structures in the given area.

References

1. A. L. Vychegzhanin. Tables for rationalizing office geological work and calculating reserves of useful minerals. Geotekhizdat, 1957.
2. K. A. Moshkovich. Discovery of an oil pool from a convergence map. Oil Industry, No. 1, 1956.
3. N. N. Forsh. On the methodology of structural analysis of platform tectonic structures. Gostoptekhizdat, 1953.
4. N. F. Frolov, E. F. Frolov. Geological observations and constructions when drilling deviated wells. Gostoptekhizdat, 1957.