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Petroleum Engineering - 406
LESSON 19
Survey Calculation Methods
LESSON 11Survey Calculation Methods
Radius of Curvature Balanced Tangential Minimum Curvature
– Kicking Off from Vertical
– Controlling Hole Angle (Inclination)
Homework
READ:Chapter 8 “Applied Drilling Engineering”,
( first 20 pages)
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
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
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
Radius of Curvature:Vertical Section
MD
2111 IcosRIcosRHorizΔ
R1 R1
I1 I2
I2
)IcosI(cosII
ΔMD
π
18021
12
211 IcosIcosRHoriz Δ
Horiz
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
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 =
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 =
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!
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
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
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
Balanced Tangential Method
1 I1
MD 2
I2I2
I2
0 Vertical Projection
MD 2
21 Icos2
MDIcos
2
MDVert
21 Isin2
MDIsin
2
MDHoriz
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
Balanced Tangential Method - Equations
12
2211
2211
IcosIcos2
MDVert
AsinIsinAsinIsin2
MDEast
AcosIsinAcosIsin2
MDNorth
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:
Minimum Curvature Method - Equations
RFIcosIcos2
MDVert
RFAsinIsinAsinIsin2
MDEast
RFAcosIsinAcosIsin2
MDNorth
12
2211
2211
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
Fig 8.22
A curve representing a
wellbore between Survey Stations A1
and A2.
(A, I)
Tangential Method
)cos(
)sin()sin(
)cos()sin(
2
22
22
IMDVert
AIMDEast
AIMDNorth
Balanced Tangential Method
)cos()cos(
)sin()sin()sin()sin(
)cos()sin()cos()sin(
12
2211
2211
II2
MDVert
AIAI2
MDEast
AIAI2
MDNorth
Average Angle Method
2
IIMDVert
2
AA
2
IIMDEast
2
AA
2
IIMDNorth
21
2121
2121
cos
sinsin
cossin
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
Minimum Curvature Method
RFII2
MDVert
RFAIAI2
MDEast
RFAIAI2
MDNorth
21
2211
2211
)cos()cos(
)sin()sin()sin()sin(
)cos()sin()cos()sin(
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
