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# Calculation methods for directional survey

There are several known methods of computing directional survey. The five most commonly used are: tangential, balanced tangential, average angle, curvature radius, and minimum curvature (most accurate).[1]

## Tangential

This method uses the inclination and hole direction at the lower end of the course length to calculate a straight line representing the wellbore that passes through the lower end of the course length. Because the wellbore is assumed to be a straight line throughout the course length, it is the most inaccurate of the methods discussed and should be abandoned completely.

## Balanced tangential

Modifying the tangential method by taking the direction of the top station for the first half of the course length, then that of the lower station for the second half can substantially reduce the errors in that method. This modification is known as the balanced-tangential method. This method is very simple to program on hand-held calculators and in spreadsheets and gives accuracy comparable to the minimum-curvature method.

## Average angle

The method uses the average of the inclination and hole-direction angles measured at the upper and lower ends of the course length. The average of the two sets of angles is assumed to be the inclination and the direction for the course length. The well path is then calculated with simple trigonometric functions.

With the inclination and hole direction measured at the upper and lower ends of the course length, this method generates a circular arc when viewed in both the vertical and horizontal planes. Curvature radius is one of the most accurate methods available.

## Minimum curvature

Like the curvature-radius method, this method, the most accurate of all listed, uses the inclination and hole direction measured at the upper and lower ends of the course length to generate a smooth arc representing the well path. The difference between the curvature-radius and minimum-curvature methods is that curvature radius uses the inclination change for the course length to calculate displacement in the horizontal plane (the true vertical depth [TVD] is unaffected), whereas the minimum-curvature method uses the Dogleg Severity (DLS) to calculate displacements in both planes. Minimum curvature is considered to be the most accurate method, but it does not lend itself easily to normal, hand-calculation procedures.

The survey results are compared against those from the minimum-curvature method, as shown in Table 1. Large errors are seen in the tangential method for only approximately 1,900 ft of deviation. This demonstrates that the tangential method is inaccurate and should be abandoned completely. The balanced-tangential and average-angle methods are more practical for field calculations and should be used when sophisticated computational equipment or expertise may not be available. These should be noted as “Field Results Only.”

## References

1. API D20, Bulletin on Directional Drilling Survey Calculation Methods and Terminology. 1985. API: Washington, DC.