Well co-ordinates

Physical representation of a well on the earth's surface can be done by-

1. Geographical co-ordinates
2. Rectangular co-ordinates
3. Polar co-ordinates

1. Geographical Co-ordinates

Let's discuss representation of well location in Geographical co-ordinates.

Latitude (Parallels) & Longitude (Meridian) represents the geographical co-ordinates of the earth. We can determine any location on the earth with the help of these.

Latitude (φ) & Longitude (λ) is the angle between N/S point & E/W point on the earth's surface respectively and center of the earth.

Equator is the reference point in latitudes and designated as 0°; it divides earth into Northern Hemisphere (0° to 90°N) & Southern Hemisphere (0° to 90°S).

There are two main points in longitude -

1. Prime Meridian (0°)
2. International Date line (180°)

Prime Meridian divides earth into Eastern Hemisphere (0° to 180°E) and Western Hemisphere (0° to 180° W).

Degrees of latitude and longitude can be further sub divided into minutes and seconds.

1 degree (°) = 60 minutes (')

and 1 minute (') = 60 seconds (")

There are three basic ways to display geographical co-ordinates:

1. Degrees, Minutes, Seconds (D M S)

2. Degrees, Minutes as decimal (D M.m)

3. Numerical (in degrees)

Example:

Amsterdam co-ordinates might be written as 52°22'25'' N, 4°53'27" E .

Degrees and decimal minutes: 52°22.416' N, 4°53.45' E 

(lat = 52°, 22' + 25/60'; lat = 4°, 53' + 45/60')

Degrees can also be expressed as decimals: 52.3736° N, 4.890° E

(lat = 52°+ 22/60°+ 25/3600°; lat = 4°+ 53/60° + 45/3600°)

Note: Latitude is written first, followed by longitude.

One degree of latitude is approximately 69 miles;

a minute of latitude is approximately 1.15 miles;

a second of latitude is approximately 0.02 miles.

However, one degree of longitude varies in size. At the equator, it's approximately 69 miles and the size decreases to zero as the meridians meet at the pole.

2. Rectangular Co-ordinates

In 1637 Rene Descartes, a French mathematician and philosopher, developed a method of associating the points on a plane with pairs of numbers. By drawing two number lines or axes, perpendicular at the 0 point or origin, a Rectangular Co-ordinate system is formed.

 

A point on this coordinate plane is associated with a pair of numbers called an Ordered Pair. The first number in the pair corresponds to the projection of the point on the horizontal or x-Axis. The second number corresponds to the projection of the point on the vertical or y-Axis. 

Points P and Q are associated with the ordered pairs (1,2) and (2,-3) respectively. Such ordered pairs are called Rectangular Co-ordinates.

This Rectangular Co-ordinate system has been adopted in directional drilling for several purposes. The easiest being, determining bottom hole location of the well w.r.t well head or rig location

In this case a Rectangular Co-ordinate system is set up by, 

y-axis being replaced by N/S co-ordinates, 

x-axis being replaced by E/W co-ordinates and 

0 or origin being replaced by well head.

Note: N/S co-ordinates are represented first followed by E/W co-ordinates.

North is +ve number that indicates the distance NORTH from the well head/rig location, while a -ve number indicates a distance SOUTH.

East is +ve number that indicates the distance EAST from the well head/rig location, while a -ve number indicates a distance WEST.

Both these form an ordered pair and represents the bottom hole well location with reference to well head/rig location.

N/S & E/W are represented on a Plan View or Horizontal Plot.

N/S & E/W values will be respectively,

• +ve & +ve for well direction from 0° to 90°.
• -ve & +ve for well direction from 90° to 180°
• -ve & -ve for well direction from 180° to 270°
• +ve & -ve for well direction from 270° to 360/0°

Example:

Horizontal Plots of four wells are shown. Locate N/S & E/W coordinates.

(N/S,E/W) Co-ordinates at;

A = (60,60) 

B = (75,-15)

C = (-60,-45)

D = (75,-75)

3. Polar Co-ordinates

In directional drilling, polar co-ordinates are used for representing location of a point as a distance away from the origin and a direction away from the origin.

Origin is taken as well head or rig location;
Closure distance gives the distance away from the origin; and
Closure azimuth gives the direction of the well.

Although points are not plotted on polar graphs, polar co-ordinates are used to locate bottom hole closure. 

Example:

Find bottom hole location of four wells from same well head/rig location from the horizontal plot.

Point A is at 20 m @ 330°
Point B is at 25 m @ 125°
Point C is at 25 m @ 250°
Point D is at 15 m @ 245°
Point E is at 30 m @ 90°

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