Scale Factor in UTM Mapping System and its Application in Directional Drilling

Scale factor represents distortion from a mapping system since the Earth is mapped into a flat surface, but the actual surface is in curvature. Figure 1 illustrates a scale factor with a reference location of the Earth’s surface. If the location is above the map projection plan, the scale factor will be less than 1.0. However, if the location is below the mapping projection, the scale factor will be more than 1.0. A scale factor less than 1 means that the actual distance on the Earth’s surface is longer than the actual distance on the map. Whereas, the scale factor of more than 1 demonstrates that the actual distance on the Earth is shorter than the map distance.

Figure 1 - Scale Factor

Figure 1 – Scale Factor

For UTM, the central meridian (CM) has a scale factor of 0.9996. The locations where the scale factor is one are 320,000m E and 680,000 E (Figure 2).

Figure 2 - Scale Factor Depending on Location for each UTM zone

Figure 2 – Scale Factor Depending on Location for each UTM zone

Example:

This example demonstrates how to use the scale factor to calculate the distance projected in the map.

The surface location is located in UTM 30N. The location coordination is 400,000 E and 6,900,000 N. and the target is located at 401,000 E and 6,899,500N and the UTM zone is 30N. The scale factor at the location is 0.999685. The surface and the target for this  can be illustrated in Figure 3.

Figure 3- Surface and Target Location

Figure 3- Surface and Target Location

Distance from Surface Location to Target

ΔN = 6,899,500 – 6,900,000 = – 500 m

ΔE = 401,000 – 400,000 = 1,000 m

map-distance

Map Distance = 1118.034 m

Figure 4 - Distance from surface to the target illustration

Figure 4 – Distance from surface to the target illustration

True Distance

This distance must be applied to the scale factor in order to get the true distance.

True Distance (m) = Map Distance ÷ scale factor

True Distance (m) = 1118.034 ÷ 0.999685 = 1118.3863 m

The true distance is the horizontal displacement referencing from the surface location to the target.

Target Azimuth

The target in reference to the surface location is located in 2nd quadrant; therefore the target azimuth is calculated by the following relationship;

Target AZI = 90 + tan-1(ΔN÷ΔE)

Target AZI = 90 + tan-1((500) ÷ (1000))

Target AZI = 116.565 degree

References

Adam Bourgoyne, 2014. Directional Drilling and Deviation Control: Definitions and Reasons for Directional Drilling. 1st Edition.

French Oil & Gas Industry Association, 1990. Directional Drilling and Deviation Control. Edition. Technip Editions.

Tom Inglis, 1988. Directional Drilling (Petroleum Engineering and Development Studies) (v. 2). 1987 Edition. Springer.

Related Post

Drilling Formula Excel Sheet Version 1.2 Free Down... This is the second up date of drilling formula spread sheet, Drilling Formula Excel Sheet Version 1.2. Drillingformulas.com distributed the first v...
Ouija Board Directional Drilling Excel Spreadsheet Ouija Board is a method that directional drillers use to calculate inclination and azimuth at the bottom or distance and tool face to drill at require...
Universal Transverse Mercator Application in Direc... Universal Transverse Mercator (UTM) is one of the commonly used map projection methods in directional drilling. In UTM, the world is divided up into 6...
Directional Well Planning and Well Profile The well planning process starts from geologists and reservoir engineers who decide the best place for the wellbore. They may only need to determine a...
Share the joy
  • 514
  •  
  •  
  •  
  •  
  •  
  •  
  •  
  •  
    514
    Shares
Tagged , , , . Bookmark the permalink.

About DrillingFormulas.Com

Working in the oil field and loving to share knowledge.

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.