# Table Of Dogleg Severities

Station MD

I

A

DLS

# ft

0

0

7100ft

21 6,121

32

14

----

22 6,332

36

8

2.47

23 6,542

34

358

????

1. Consider only inclinational curvature for station number 22.

DLS =100

36-32

6332-6121

2. Consider only directional curvature for station number 22.

### DLS = 100 *

• 8 - 14) * sin 34 (6332 - 6121)
• 1.59 7100 ft

3. Composite curvature between station numbers 21 & 23. Station 21-22:

36-32 9 8-14 . 21 6332 - 612r + (6332 - 6121 sin ö4) J

Station 22-23:

6542-6332

DERIVATION OF WILSON'S DOGLEG SEVERITY EQUATION

There are many dogleg severity formulae and charts and they give almost equal values: Lubinski, Long, and Wilson wrote the more popular ones. The following derivation is Wilson's. He combines the build in a vertical plane with the turn in the horizontal plane to give a three dimensional dogleg severity equation.

More precisely, he projected the drill hole into a vertical plane and set the length of the projection equal to the measured depth of the drill hole. He then projected the drill hole into1 a horizontal plane and set the length of the resulting arc equal to the departure of the drill hole. Finally he used the equation for the curvature of an arc in rectangular coordinates to get his dogleg severity equation.

Observations of the sketch reveal a « dD b ~ dM' « dM a = b sin 0

dx dD

dy dM

dx dM

^ Y

dz dM

= cos 0 further note that d /dz

dM MM

thus, differentiation of the last three equations yields i2„

dM2 r0

dM2 r0

1 r0

dx 1

„ 1.2 - „ o - cos 0 cos 0 - — sinA 0 sm 0 dM2 r0 0

curvature of an arc in rectangular coordinates is dM^ dM dMz

Substitution, squaring and simplification gives l n. r 1 1 • 4 l2

r0 re substitution again yields l

Dogleg severity expressed in °/100 feet is i

DLS = Dogleg severity; °/100 feet

0 = Inclination Angle; 0

0 = Azimuth Angle; 0

M = Drilled Hole (measured depth); feet

0a = Average Inclination Angle; 0

0 0

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### Responses

• Estella
How to combine dog leg with inclination?
9 years ago
• Rose Gammidge
What is dogleg severity in directional drilling jobs?
6 years ago
• marigold
What is a dogleg for vegetation?
10 months ago