Changes

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_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_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_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.

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.

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* ''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'' ([[: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.

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., and B. V. Randall, 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'' ([[: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.

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.

:<math>\mbox{TST}  = (\mbox{TVD}_{b} - \mbox{TVD}_{t}) \times (\cos \delta') - [(\mbox{NSD}_{b} - \mbox{NSD}_{t})^{2} + \, (\mbox{EWD}_{b} - \mbox{EWD}_{t})^{2}]^{1/2} \times \sin \delta')</math>

:<math>\mbox{TST}  = (\mbox{TVD}_{b} - \mbox{TVD}_{t}) \times (\cos \delta') - [(\mbox{NSD}_{b} - \mbox{NSD}_{t})^{2} + \, (\mbox{EWD}_{b} - \mbox{EWD}_{t})^{2}]^{1/2} \times \sin \delta')</math>

In this equation, δ′ indicates the apparent dip of the bed in the direction of the horizontal displacement ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig6.png|Figure 6]]), which is written as

In this equation, δ′ indicates the apparent [[dip]] of the bed in the direction of the horizontal displacement ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig6.png|Figure 6]]), which is written as

:<math>\delta' = \tan^{-1} [\tan \delta \cos (\beta - \varepsilon)]</math>

:<math>\delta' = \tan^{-1} [\tan \delta \cos (\beta - \varepsilon)]</math>

An assumption made here is that the dip of the top and bottom surfaces is essentially the same. The more closely the wellbore direction approximates the dip direction, the more sensitive the thickness calculation will be to stratigraphic thickness changes (see [[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig7.png|Figure 7a]]). The assumption is also violated if the well traverses a zone of strong curvature in the rock such that dip changes rapidly ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig7.png|Figure 7b]]). Such changes can be corrected for if sufficient data are available, but are commonly too small to be of significance.

An assumption made here is that the dip of the top and bottom surfaces is essentially the same. The more closely the wellbore direction approximates the dip direction, the more sensitive the thickness calculation will be to stratigraphic thickness changes (see [[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig7.png|Figure 7a]]). The assumption is also violated if the well traverses a zone of strong curvature in the rock such that dip changes rapidly ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig7.png|Figure 7b]]). Such changes can be corrected for if sufficient data are available, but are commonly too small to be of significance.

To calculate a TST requires survey information as well as some measure of the dip of the beds. Dip can be derived from dipmeter logs (with some caution) (see [[Dipmeters]]) or from maps of geological structure. In some instances, TST maps reveal anomalies in well correlation, resulting in iterative refinement of structural and stratigraphic models. It must be recognized that, where folding occurs, stratigraphic thickness trends on maps of true stratigraphic thickness will be distorted by compression.

To calculate a TST requires survey information as well as some measure of the dip of the beds. Dip can be derived from [[dipmeter]] logs (with some caution) or from maps of geological structure. In some instances, TST maps reveal anomalies in well correlation, resulting in iterative refinement of structural and stratigraphic models. It must be recognized that, where folding occurs, stratigraphic thickness trends on maps of true stratigraphic thickness will be distorted by compression.

==True vertical thickness==

==True vertical thickness==

''True vertical thickness'' (TVT) is the thickness of a geological unit in a well measured in the vertical direction ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig2.png|Figure 2]]). It is a valuable measure for volumetric calculations because it is unaffected by variations in the dip of the unit and can be derived by subtracting computer-gridded structural horizons. In a deviated well with a nonhorizontal unit, the TVT is difficult to calculate because, as the well steps out horizontally, it no longer cuts the bottom of the unit vertically below the point where it penetrated the top of the unit ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig5.png|Figure 5]]). If the dip is in the same direction as the deviation, the unit will appear thicker than it actually is, whereas if the dip is in the opposite direction, the unit will be shortened. The TVT is calculated according to the following formula:

''True vertical thickness'' (TVT) is the thickness of a geological unit in a well measured in the vertical direction ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig2.png|Figure 2]]). It is a valuable measure for volumetric calculations because it is unaffected by variations in the [[dip]] of the unit and can be derived by subtracting computer-gridded structural horizons. In a deviated well with a nonhorizontal unit, the TVT is difficult to calculate because, as the well steps out horizontally, it no longer cuts the bottom of the unit vertically below the point where it penetrated the top of the unit ([[:file:conversion-of-well-log-data-to-subsurface-stratigraphic-and-structural-information_fig5.png|Figure 5]]). If the dip is in the same direction as the deviation, the unit will appear thicker than it actually is, whereas if the dip is in the opposite direction, the unit will be shortened. The TVT is calculated according to the following formula:

:<math>\mbox{TVT}  = (\mbox{TVD}_{b} - \mbox{TVD}_{t}) - [(\mbox{NSD}_{b} - \mbox{NSD}_{t})^{2} + \, (\mbox{EWD}_{b} - \mbox{EWD}_{t})^{2}]^{1/2} \times \tan \delta'</math>

:<math>\mbox{TVT}  = (\mbox{TVD}_{b} - \mbox{TVD}_{t}) - [(\mbox{NSD}_{b} - \mbox{NSD}_{t})^{2} + \, (\mbox{EWD}_{b} - \mbox{EWD}_{t})^{2}]^{1/2} \times \tan \delta'</math>

[[Category:Geological methods]]

[[Category:Geological methods]]