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Directional Survey Calculations

More than 20 methods have been developed to calculate the directional survey, which provides the 3D location of a directional wellbore anywhere along its entire length. The more common methods include (1) tangential, which is the least accurate and is no longer used; (2) trapezoidal, also called balanced tangential; (3) average angle; (4) radius of curvature; and (5) minimum curvature. Many companies have their own methods, and new algorithms are occasionally published. The accuracy of any method varies with the configuration of the wellbore. The radius of curvature and minimum curvature methods are the most widely used today, and the latter is considered slightly more accurate for most wells. The method of calculation is typically noted on the survey. If you work in an area with deviated wells and surveys of different vintages, you can reduce the wellbore position uncertainty due to calculation method by using the same algorithm, such as minimum curvature, to recalculate all surveys. Computer software for this is readily available. The TVD calculated for a survey can vary by tens of feet between an older method, such as the tangential method, and a more modern method, such as the minimum curvature method.

If you are working an area with surveys of different vintages and using a computer workstation, all of the directional survey data for the wells should be entered as the basic survey measurements, that is, MD, deviation angle, and direction of deviation. Allow the computer software to calculate the directional survey results using the radius of curvature or minimum curvature method. Some computer software allows you to enter calculated data from directional surveys, such as TVD and rectangular coordinates, rather than MD. If you enter these calculated data from old surveys rather than the MD, you are introducing unnecessary positioning errors associated with older calculation methods into your database.

Three measurements go into the directional survey: (1) measured depth, (2) deviation angle, and (3) direction of deviation. These measurements, taken at specific depth intervals, are used to calculate the directional survey of a well. Figure 3-17 shows a portion of the directional survey from a deviated well. The tabular printout for this directional survey has nine columns of data for each survey point in the well (Table 3-3).


Figure 3-17 Part of the directional survey for a deviated well. (Published by permission of Gardes Directional Drilling.)

Table 3-3 Explanation of data shown in Figure 3-17




Subsea depth of wellbore in feet


Measured depth of wellbore in feet


True vertical depth of wellbore in feet


Angle of wellbore deviation (inclination angle)


Planned direction of wellbore (true bearing)


Distance in feet from the surface location along the proposed directional path


True bearing and distance of each survey point from the surface location in rectangular coordinates


True bearing and distance from surface location directly to each survey point


Maximum change in hole angle in degrees per 100 ft

If the cased or surface section of the hole was surveyed with a nonmagnetic survey tool such as a drift indicator, the angle of the cased portion of the hole will be displayed on the survey along with an estimate of the maximum possible deviation of this portion of the hole, as shown in Figure 3-18. The 146.75-ft maximum deviation, prominently shown on the survey, indicates that if the wellbore drift in the cased portion of the hole were all in the same direction, the well at a depth of 3513 ft could be as much as 146.75 ft from the surface location. Notice at the end of the survey that it indicates that the bottom of the hole lies within a circle of radius 146.75 ft with its center located 203.94 ft south 63°27' west of the surface location. Such information may be important in fault, structure, and isochore mapping.


Figure 3-18 A directional survey from a well in which the surface casing was surveyed with a Totco tool providing deviation angle but not direction. Notice, at 3513 ft, that the maximum possible deviation of the cased hole is 146.75 ft. This assumes that the wellbore deviation in this portion of the hole was in one direction.

Directional surveys are used to plot wellbores on base maps. The applications of these plots are discussed later in this chapter.

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