# Latitude, Longitude and Drilling Map Projection

Directional drilling maps are flat, but the Earth is an oblate spheroid. This leads to a challenge to accurately represent the wellbore position on the Earth on a piece of paper. In this section, you will learn about mapping techniques used in directional drilling, limitations and the errors of mapping techniques.

One of the most important concepts of mapping is latitude and longitude.

Latitude is a coordinate used to specify the north-south position of a location on the surface of the Earth. Latitude is an angle which starts from 0° at the equator to 90° at the Earth North-South poles. It is simply defined like this;

• 0 ° at the equator
• +90 ° at the North pole
• -90 ° at the South pole

To define latitude, it is described in degrees, minutes and seconds. Parallel line of latitude is a small circle at particular latitude which is parallel with the Equator.

Figure 1 – Latitude and Longitude Diagram

Longitude is a coordinate used to specify the east-west location on the surface of the Earth by describing as an angular measurement. Longitude is defined in degrees, minutes and seconds. Meridian lines are lines running from the North Pole to the South Pole which connect points with the same longitude. The prime meridian line, passing through the Royal Observatory, Greenwich, England, is defined at 0 degrees. From the prime meridian line to the East, it is identified as 0 to + 180 degrees. From the prime meridian line to the West, it is identified as 0 to – 180 degrees.

Latitude and longitude are used together in order to identify the location on the Earth. For example, the longitude and latitude of London written in degrees, minutes and seconds is 51°30′ 26″ N 0° 7′ 39″ W.

Figure 2 – Latitude and Longitude of London

Earth Shape

The actual Earth’s shape is an oblate spheroid because the Earth’s equatorial diameter is slightly bigger than the Earth’s polar diameter. Even though the flatting of the Earth is one in three hundred, it makes a big difference in scale calculation in maps used in the directional drilling field. For map projections, different regions/countries use different reference ellipsoids and nowadays there are more than 50 ellipsoid models. Approximately, 15 ellipsoids can cover 98% of oil countries in the World. In order to accurately identify locations of the Earth, it is required to identify a Geodetic Datum which consists of ellipsoid, orientation of ellipsoid, unit of length, region of the Earth and office name.

Map Projection

Map projection is a method used to convert the position (latitude-longitude) on the surface of a sphere into another method of positioning that can be drawn on a flat map with known accuracy and a controlled degree of error. X-Y Cartesian coordinate is the most common map positioning method. Two commonly used methods for map projection are Lambert Conformal Conic Projection and Transverse Mercator (TM).

Lambert Conformal Conic Projection

Lambert conformal conic projection (Figure 3), which was introduced by Johann Heinrich Lambert in 1772, is a projection method of the Earth onto a cone. The cone axis coincides with the geographic pole axis of the Earth.

Figure 3 – Lambert Projection

Transverse Mercator

Transverse Mercator is most widely used for map projection and this is the basic principle of the Universal Transverse Mercator system. This method overcomes the scale error at high latitudes which will happen with the Mercator projection. The details in the map are projected into an imaginary cylinder for all latitudes with a narrow area of longitude.

Figure 4 – Transverse Mercator

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.

BBC UK, (2014), Latitude and Longitude Diagram [ONLINE]. Available at:http://www.bbc.co.uk/staticarchive/e344e73982934a546e4c9909087547478672e9ad.png [Accessed 31 August 2016].

Bram.us, (2014), Lambert Projection [ONLINE]. Available at: https://www.bram.us/wordpress/wp-content/uploads/2012/03/conic-projection-560×379.jpg [Accessed 31 August 2016].

Wikipedia, (2014), Transverse Mercator [ONLINE]. Available at:https://upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Transverse_mercator_graticules.svg/400px-Transverse_mercator_graticules.svg.png [Accessed 31 August 2016].

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