Petroleum Engineering - 406 LESSON 19 Survey Calculation Methods.
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Transcript of Petroleum Engineering - 406 LESSON 19 Survey Calculation Methods.
![Page 1: Petroleum Engineering - 406 LESSON 19 Survey Calculation Methods.](https://reader031.fdocuments.us/reader031/viewer/2022031813/56649e725503460f94b70889/html5/thumbnails/1.jpg)
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
I2 -I1
1
I1 A1
East
North
North
I2
MD = R1 (I2-I1) (rad)
2 East
Length of arc of circle, L = Rrad
A1
R1
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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= ( ) ( )
MD
180
π
π
180
22 II
MD
1212
1121
I sinI sinII
ΔMD
π
180
I sin RI sin RΔVert
R1
VertI2
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Radius of Curvature:Vertical Section
MD
2111 IcosRIcosRHorizΔ
R1 R1
I1 I2
I2
)IcosI(cosII
ΔMD
π
18021
12
211 IcosIcosRHoriz Δ
Horiz
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Radius of Curvature: Horizontal Section
N
A1
A2
L2
East
2
NorthR2
1
O
A2 A2-A1
A1
L2 = R2 (A2 - A1)RAD
East = R2 cos A1
- R2 cos A2 = R2 (cos A1 - cos A2)
12
22 AA
L180R
πso,
DEG
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Radius of Curvature Method
1212
121
AAII
2AcosAcosIcosIcosMD
East = R2 (cos A1 - cos A2)
12
22 AA
L180R
π
)IcosI(cosII
ΔMD
π
18021
12
L2
2180
π
East =
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Radius of Curvature Method
1212
1221
AAII
AsinAsinIcosIcosMD
North = R2 (sin A2 - sin A1)
12
22 AA
L180R
π
)IcosI(cosII
ΔMD
π
18021
12
L2
2180
π
North =
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Radius of Curvature - Equations
)(
)sin()sin(
)()(
)cos()cos()cos()cos(
)()(
)sin()sin()cos()cos(
12
12
1212
2121
1212
1221
II
IIMDVert
AAII
AAIIMDEast
AAII
AAIIMDNorth
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
12
12
AA
AA sinsin
12
21
AA
AA coscos
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Angles in Radians
If A1 = A2, then:
North = MD cos A1
East = MD sin A1
Vert = MD
12
21
II
II coscos
12
21
II
II coscos
12
12
II
IsinIsin
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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
I2I2
I2
0 Vertical Projection
MD 2
21 Icos2
MDIcos
2
MDVert
21 Isin2
MDIsin
2
MDHoriz
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Balanced Tangential Method
2211
21
2211
21
AIAI2
MDA2HorizA1HorizEast
AIAI2
MDA2HorizA1HorizNorth
sinsin,sinsin
sin.sin.
cossin,cossin
cos.cos.
N
E
A1
A2
Horiz.1
Horiz. 2
Horizontal Projection
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Balanced Tangential Method - Equations
12
2211
2211
IcosIcos2
MDVert
AsinIsinAsinIsin2
MDEast
AcosIsinAcosIsin2
MDNorth
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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
RFIcosIcos2
MDVert
RFAsinIsinAsinIsin2
MDEast
RFAcosIsinAcosIsin2
MDNorth
12
2211
2211
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Minimum Curvature Method
P
r
O
r
RDL
Q
DL 2
2
DLtan
DL
2RF
)AA(cos1IsinIsin)I(Icos(DL) cos
:follows as calculated is DL, angle, egoglD The
122112
DL =
S
PQR Arc
SRPSRF
DLr2
DLtanr
2DL
tanr
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Fig 8.22
A curve representing a
wellbore between Survey Stations A1
and A2.
(A, I)
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Tangential Method
)cos(
)sin()sin(
)cos()sin(
2
22
22
IMDVert
AIMDEast
AIMDNorth
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Balanced Tangential Method
)cos()cos(
)sin()sin()sin()sin(
)cos()sin()cos()sin(
12
2211
2211
II2
MDVert
AIAI2
MDEast
AIAI2
MDNorth
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Average Angle Method
2
IIMDVert
2
AA
2
IIMDEast
2
AA
2
IIMDNorth
21
2121
2121
cos
sinsin
cossin
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Radius of Curvature Method
)(
)sin()sin(
)()(
)cos()cos()cos()cos(
)()(
)sin()sin()cos()cos(
12
12
1212
2121
1212
1221
II
IIMDVert
AAII
AAIIMDEast
AAII
AAIIMDNorth
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Minimum Curvature Method
RFII2
MDVert
RFAIAI2
MDEast
RFAIAI2
MDNorth
21
2211
2211
)cos()cos(
)sin()sin()sin()sin(
)cos()sin()cos()sin(
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Mercury Method
)cos()cos()cos(
)sin()sin()sin()sin()sin()sin(
)cos()sin()cos()sin()cos()sin(
212
222211
222211
ISTLII2
STLMDVert
AISTLAIAI2
STLMDEast
AISTLAIAI2
STLMDNorth