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## Petroleum Engineering 406

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### Chapter 8 'Applied Drilling Engineering', ( first 20 pages) Radius of Curvature Method ... Vert. I2. Radius of Curvature: Vertical Section. R1. R1. I1. I2. I2. Horiz ... – PowerPoint PPT presentation

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Title: Petroleum Engineering 406

1
Petroleum Engineering - 406
• LESSON 19
• Survey Calculation Methods

2
LESSON 11 Survey Calculation Methods
• Balanced Tangential
• Minimum Curvature
• Kicking Off from Vertical
• Controlling Hole Angle (Inclination)

3
Homework
• Chapter 8 Applied Drilling Engineering, (?
first 20 pages)

4
• 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

5
Length of arc of circle, L R?rad

A1
I2 -I1
1
North
R1
I1
A1
?North
I2
2
East
?East
6
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
7

I1
I2
R1
R1
?MD
I2
? Horiz
8
N
A2

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
9
DEast R2 (cos A1 - cos A2)

L2
DEast
10
DNorth R2 (sin A2 - sin A1)

L2
DNorth
11

12
• If I1 I2, then
• ?North ?MD sin I1
• ?East ?MD sin I1
• ?Vert ?MD cos I1

13
• If A1 A2, then
• ?North ?MD cos A1
• ?East ?MD sin A1
• ?Vert ?MD

14
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

15
Balanced Tangential Method

1
I1
?MD 2
?MD 2
I2
I2
Vertical Projection
0
I2
16
Balanced Tangential Method

?Horiz. 2
A2
?N
A1
?Horiz.1
Horizontal Projection
?E
17
Balanced Tangential Method - Equations

18
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

19
Minimum Curvature Method - Equations
20
Minimum Curvature Method
DL b

O
r
DL 2
P
r
Q
S
R
DL
21
Fig 8.22 A curve representing a wellbore
between Survey Stations A1 and A2.
b
b b(A, I)
22
Tangential Method

23
Balanced Tangential Method

24
Average Angle Method

25