Petroleum Engineering - 406

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Petroleum Engineering - 406

• LESSON 19
• Survey Calculation Methods

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LESSON 11Survey Calculation Methods

• Radius of Curvature
• Balanced Tangential
• Minimum Curvature
• Kicking Off from Vertical
• Controlling Hole Angle (Inclination)

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Homework

• READ
• Chapter 8 Applied Drilling Engineering, (?
  first 20 pages)

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Radius of Curvature Method

• Assumption The wellbore follows a smooth,
  spherical arc between survey points and passes
  through the measured angles at both ends.
  (tangent to I and A at both points 1 and 2).
• Known Location of point 1, ?MD12 and angles
  I1, A1, I2 and A2

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Radius of Curvature Method
Length of arc of circle, L R?rad

? MD R1 (I2-I1) (rad)
A1
I2 -I1
1
North
R1
I1
A1
?North
I2
2
East
?East
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Radius of Curvature - Vertical Section

• In the vertical section, ?MD R1(I2-I1)rad
• ?MD R1 ( ) (I2-I1)deg
  I1 I2-I1
• ?R1 ( ) ( )
• DMD

R1
? Vert
I2
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Radius of CurvatureVertical Section

I1
I2
R1
R1
?MD
I2
? Horiz
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Radius of Curvature Horizontal Section
N
A2
L2 R2 (A2 - A1)RAD

2
A1
so,
L2
?North
DEG
R2
?East
1
DEast R2 cos A1 - R2 cos
A2 R2 (cos A1 - cos A2)
A2
A2-A1
O
A1
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Radius of Curvature Method
DEast R2 (cos A1 - cos A2)

L2
DEast
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Radius of Curvature Method
DNorth R2 (sin A2 - sin A1)

L2
DNorth
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Radius of Curvature - Equations

With all angles in radians!
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Angles in Radians

• If I1 I2, then
• ?North ?MD sin I1
• ?East ?MD sin I1
• ?Vert ?MD cos I1

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Angles in Radians

• If A1 A2, then
• ?North ?MD cos A1
• ?East ?MD sin A1
• ?Vert ?MD

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Radius of Curvature - Special Case

• If I1 I2 and A1 A2
• ?North ?MD sin I1 cos A1,
• ?East ?MD sin I1 sin A1
• ?Vert ?MD cos I1

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Balanced Tangential Method

1
I1
?MD 2
?MD 2
I2
I2
Vertical Projection
0
I2
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Balanced Tangential Method

?Horiz. 2
A2
?N
A1
?Horiz.1
Horizontal Projection
?E
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Balanced Tangential Method - Equations

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Minimum Curvature Method

• This method assumes that the wellbore follows the
  smoothest possible circular arc from Point 1 to
  Point 2.
• This is essentially the Balanced Tangential
  Method, with each result multiplied by a ratio
  factor (RF) as follows

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Minimum Curvature Method - Equations
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Minimum Curvature Method
DL b

O
r
DL 2
P
r
Q
S
R
DL
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Fig 8.22 A curve representing a wellbore
between Survey Stations A1 and A2.
b
b b(A, I)
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Tangential Method

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Balanced Tangential Method

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Average Angle Method

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Radius of Curvature Method

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Minimum Curvature Method
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Mercury Method