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.
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
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
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