Use of the Curvature Method To Determine True Vertical Reservoir Thickness
Authors: Rivero R.T. 
Published: December 2007

A generalized curvature method of directional survey interpretation can be shown to converge into the Tangential method for curvatures close to zero. True vertical thickness corrections may be made based on directional surveys, taking into account the slant of the hole and the dip of the formation.

Introduction
Net pay is one of the most important factors in determining equity participation formulas. In the past, it was picked directly from the logs of reasonably vertical holes with relatively negligible error. In directionally drilled wells, net pay must be selected by correcting data observed log thickness of a zone to the value that would have been logged if the well had penetrated the zone vertically through the point it pierced the top of the bed. These corrections must take into account the borehole inclination as well as the dip and strike of the formation. They may be made using the true coordinates of the points at which the top and bottom of the pay zone are penetrated by the well. These coordinates can be obtained by the Tangential (straight line) method of directional survey interpretation, which in certain cases has doubtful accuracy. In those instances when the segments between survey stations are curved, the Tangential method will cause errors that, because of their cumulative effects, may become substantial.
To correct for the effects of these errors, Wilson presented an improved method of directional survey presented an improved method of directional survey computation, which he called the "Radius of Curvature". He derived the necessary equations for those cases in which the curvature of the wellbore was either on a vertical or on a horizontal plane, pointing out that the Tangential method was materially a different interpretive technique.
Wilson's solutions may be generalized. A general set of equations of the Curvature method of directional survey interpretation can be shown to converge into the equations of the Tangential method when the borehole curvature either is zero or approaches zero. The purpose of this paper is to derive an analytical expression for true vertical formation thickness when a bed of known dip and strike is pierced by a slanted well. Since the accuracy of these calculations is dependent upon the true location of points on the wellbore, the Curvature method affords at this time a computational technique that is superior to those existing heretofore. The wide availability of computers makes the application of the equations an easy task.

Directional Survey Interpretation
For every survey station, three items of information are recorded by companies engaged in running directional surveys:
the depth at which the instrument was stopped; the drift of its axis off the vertical; and (3) the drift direction on a horizontal plane. plane.
Two sources of possible error are immediately apparent. First, the tool may not have been centralized; that is, its axis may not have coincided with that of the wellbore. Second, the measured depth may have been in error because of cable stretch or because the cable was not centered in the wellbore. Other sources of error inherent in particular recording instruments may also become apparent. However, even if these sources of error axe ignored, it is possible to introduce a computational error during the interpretation of the survey, if it is assumed that survey points are connected by straight lines.
JPT
P. 491