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Line 33: − − [[file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig1.png|thumb|{{figure number|1}}Surface projection of well course for a nominally vertical well. © Don Clarke, Dept. of OH Properties, City of Long Beach, CA).]] − − [[file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig2.png|thumb|{{figure number|2}}Well course of two types of deviated wells. True stratigraphic thickness and true vertical thickness of a dipping stratigraphic unit are shown in relation to the measured interval in a well penetrating the unit.]] Line 38:
Line 41: − − [[file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig3.png|thumb|{{figure number|3}}Segment of a curved well path showing angular and dimensional relationships between the top and bottom of the interval.]] Line 50:
Line 51: − − [[file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig4.png|thumb|{{figure number|4}}Linear approximations of a curved well course by the (a) tangential method,<ref name=pt06r20 /><ref name=pt06r23>Dailey, P. 1977, A guide to accurate wellbore survey calculations: Drilling-DCW, May, p. 52–59 and 118–119.</ref> (b) angle averaging method,<ref name=pt06r20 /> and (c) balanced tangential method.<ref name=pt06r20 />]] Line 63:
Line 62: − − [[file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig5.png|thumb|{{figure number|5}}Circular approximations of a curved well course showing angles used for the approximations. (a) Radius of curvature method showing chords of horizontal and vertical circles. This method assumes a constant radius of curvature (constant increase or decrease in deviation between survey points). (b) Minimum curvature method showing chord of single circle and the angle ϕ, which describes the chord.]]
Depth and thickness conversion (view source)
Revision as of 22:50, 3 February 2014
, 22:50, 3 February 2014no edit summary
==True vertical depth==
==True vertical depth==
<gallery>
file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig1.png|{{figure number|1}}Surface projection of well course for a nominally vertical well. © Don Clarke, Dept. of OH Properties, City of Long Beach, CA).
file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig2.png|{{figure number|2}}Well course of two types of deviated wells. True stratigraphic thickness and true vertical thickness of a dipping stratigraphic unit are shown in relation to the measured interval in a well penetrating the unit.
file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig3.png|{{figure number|3}}Segment of a curved well path showing angular and dimensional relationships between the top and bottom of the interval.
file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig4.png|{{figure number|4}}Linear approximations of a curved well course by the (a) tangential method,<ref name=pt06r20 /><ref name=pt06r23>Dailey, P. 1977, A guide to accurate wellbore survey calculations: Drilling-DCW, May, p. 52–59 and 118–119.</ref> (b) angle averaging method,<ref name=pt06r20 /> and (c) balanced tangential method.<ref name=pt06r20 />
file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig5.png|{{figure number|5}}Circular approximations of a curved well course showing angles used for the approximations. (a) Radius of curvature method showing chords of horizontal and vertical circles. This method assumes a constant radius of curvature (constant increase or decrease in deviation between survey points). (b) Minimum curvature method showing chord of single circle and the angle ϕ, which describes the chord.
</gallery>
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 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 (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.
:<math>\mbox{NSD} = \sum (\mbox{MD}_{i} - \mbox{MD}_{i-1}) \times \sin \alpha_{i}\cos \beta_{i}</math>
:<math>\mbox{NSD} = \sum (\mbox{MD}_{i} - \mbox{MD}_{i-1}) \times \sin \alpha_{i}\cos \beta_{i}</math>
:<math>\mbox{EWD} = \sum (\mbox{MD}_{i} - \mbox{MD}_{i-1}) \times \sin \alpha_{i} \sin \beta_{i}</math>
:<math>\mbox{EWD} = \sum (\mbox{MD}_{i} - \mbox{MD}_{i-1}) \times \sin \alpha_{i} \sin \beta_{i}</math>
where
where
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<sub>''i''</sub>, MD<sub>''i''–1</sub>) 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'' (Figure 4a) assumes a constant deviation for the entire interval from one survey point to the next. Thus, the measured depths (MD<sub>''i''</sub>, MD<sub>''i''–1</sub>) 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.
A better approximation, the ''balanced tangential method'' (Figure 4c), is derived by placing the interval depths (MD<sub>i</sub>, MD<sub>''i''–1</sub>) 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'' (Figure 4c), is derived by placing the interval depths (MD<sub>i</sub>, MD<sub>''i''–1</sub>) half way between the individual survey points, thus assuming that the deviation is constant in an interval around the measured point.
* ''m'' = marker depth of interest
* ''m'' = marker depth 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 (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: