Changes

The ''true vertical depth'' (TVD) of a point within a well is the depth to that point measured on a line connecting the point to the center of the earth. It may be derived from the measured depth by correcting for the deviation of the well. Critically important to an understanding of the three-dimensional path of a well are the following facts:

The ''true vertical depth'' (TVD) of a point within a well is the depth to that point measured on a line connecting the point to the center of the earth. It may be derived from the measured depth by correcting for the deviation of the well. Critically important to an understanding of the three-dimensional path of a well are the following facts:

* Wells are not straight; even nominally vertical holes commonly show substantial horizontal displacement even if the deviation is too small to produce a large change in true vertical depth (Figure 1).

* Wells are not straight; even nominally vertical holes commonly show substantial horizontal displacement even if the deviation is too small to produce a large change in true vertical depth ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig1.png|Figure 1]]).

* Wells are not commonly deviated from the surface, but rather are drilled approximately vertical to a kick-off point, where deviation is built up to a planned degree (see “[[Wellbore trajectory]]”). The rest of the well can be drilled at a constant angle, or the well can be returned toward the vertical to penetrate the horizon of interest (Figure 2).

* Wells are not commonly deviated from the surface, but rather are drilled approximately vertical to a kick-off point, where deviation is built up to a planned degree (see “[[Wellbore trajectory]]”). The rest of the well can be drilled at a constant angle, or the well can be returned toward the vertical to penetrate the horizon of interest ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig2.png|Figure 2]]).

* Deviation is rarely constant in a well, even when that is the objective of drilling.

* Deviation is rarely constant in a well, even when that is the objective of drilling.

As a consequence, location of the position of any point in a well must be calculated using data from well surveys and an additive formula.

As a consequence, location of the position of any point in a well must be calculated using data from well surveys and an additive formula.

For a simple case (Figure 3), in which the well course is approximated as a series of straight line segments parallel to the individual survey measurements, the formula is as follows:

For a simple case ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig3.png|Figure 3]]), in which the well course is approximated as a series of straight line segments parallel to the individual survey measurements, the formula is as follows:

:<math>\mbox{TVD}  = \sum (\mbox{MD}_{i} - \mbox{MD}_{i-1}) \times \cos \alpha_{i}</math>

:<math>\mbox{TVD}  = \sum (\mbox{MD}_{i} - \mbox{MD}_{i-1}) \times \cos \alpha_{i}</math>

* ''i'' = survey point number (i = 0 at surface)

* ''i'' = survey point number (i = 0 at surface)

The intervals can be defined in several ways depending on the accuracy and simplicity of calculation required. The ''tangential'' or ''terminal angle method'' (Figure 4a) assumes a constant deviation for the entire interval from one survey point to the next. Thus, the measured depths (MD_''i'', MD_''i''–1) for each interval coincide with the depth at the survey points, and the angle used would be for the lower survey point. Although easy to calculate, this method is likely to be substantially in error and is generally not recommended.<ref name=pt06r20>Craig, J. T. Jr., Randall, B. V., 1976, Directional survey calculation: Petroleum Engineer, March, p. 38–54.</ref><ref name=pt06r57>Inglis, T. A., 1987, Directional Drilling, Petroleum Engineering and Development Studies, Volume 2: London, Graham and Trorman, chap. 9, p. 155–171.</ref> It is mentioned here for historical reasons, as it has been widely used. Alternatively, the ''angle averaging method'' (Figure 4b) uses the average for the two survey points at either end of the segment.

The intervals can be defined in several ways depending on the accuracy and simplicity of calculation required. The ''tangential'' or ''terminal angle method'' ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig4.png|Figure 4a]]) assumes a constant deviation for the entire interval from one survey point to the next. Thus, the measured depths (MD_''i'', MD_''i''–1) for each interval coincide with the depth at the survey points, and the angle used would be for the lower survey point. Although easy to calculate, this method is likely to be substantially in error and is generally not recommended.<ref name=pt06r20>Craig, J. T. Jr., Randall, B. V., 1976, Directional survey calculation: Petroleum Engineer, March, p. 38–54.</ref><ref name=pt06r57>Inglis, T. A., 1987, Directional Drilling, Petroleum Engineering and Development Studies, Volume 2: London, Graham and Trorman, chap. 9, p. 155–171.</ref> It is mentioned here for historical reasons, as it has been widely used. Alternatively, the ''angle averaging method'' ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig4.png|Figure 4b]]) uses the average for the two survey points at either end of the segment.

A better approximation, the ''balanced tangential method'' (Figure 4c), is derived by placing the interval depths (MD_i, MD_''i''–1) half way between the individual survey points, thus assuming that the deviation is constant in an interval around the measured point.

A better approximation, the ''balanced tangential method'' ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig4.png|Figure 4c]]), is derived by placing the interval depths (MD_i, MD_''i''–1) half way between the individual survey points, thus assuming that the deviation is constant in an interval around the measured point.

These formulas are derived for calculation of well positions from data at specific survey points. Calculation of the location of a stratigraphic top or other depth of interest on the well log may require interpolation of the inclination and bearing angles between survey points. The simplest approach is to interpolate linearly between the survey points above and below the point of interest:

These formulas are derived for calculation of well positions from data at specific survey points. Calculation of the location of a stratigraphic top or other depth of interest on the well log may require interpolation of the inclination and bearing angles between survey points. The simplest approach is to interpolate linearly between the survey points above and below the point of interest:

* ''i'' = next survey point below the marker depth

* ''i'' = next survey point below the marker depth

More sophisticated approaches to well-depth correction are the radius of curvature method (Figure 5a) and the minimum curvature method (Figure 5b). The ''radius of curvature method'' approximates the well path as a circular arc in the vertical plane, which is then wrapped around a vertical cylinder. The equations in the method (from <ref name=pt06r20 />) are as follows:

More sophisticated approaches to well-depth correction are the radius of curvature method ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig5.png|Figure 5a]]) and the minimum curvature method ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig5.png|Figure 5b]]). The ''radius of curvature method'' approximates the well path as a circular arc in the vertical plane, which is then wrapped around a vertical cylinder. The equations in the method (from <ref name=pt06r20 />) are as follows:

:<math>\mbox{TVD}  = (180/\pi)\sum (\mbox{MD}_{i} - \mbox{MD}_{i-1}) \times (\sin \alpha_{i} - \sin \alpha_{i-1}) /(\alpha_{i} - \alpha_{i-1})</math>

:<math>\mbox{TVD}  = (180/\pi)\sum (\mbox{MD}_{i} - \mbox{MD}_{i-1}) \times (\sin \alpha_{i} - \sin \alpha_{i-1}) /(\alpha_{i} - \alpha_{i-1})</math>