PETE 411
Well Drilling
Lesson 35
Wellbore Surveying Methods
1
Wellbore Surveying Methods
 Average Angle
 Balanced Tangential
 Minimum Curvature
 Radius of Curvature
 Tangential
Other Topics
 Kicking off from Vertical
 Controlling Hole Angle
2
Read:
Applied Drilling Engineering, Ch.8
(~ first 20 pages)
Projects:
Due Monday, December 9, 5 p.m.
( See comments on previous years’ design
projects )
3
Homework Problem #18
Balanced Cement Plug
Due Friday, December 6
4
I, A, DMD
5
Example - Wellbore Survey Calculations
The table below gives data from a directional survey.
Survey Point
A
B
C
D
Measured Depth
along the wellbore
ft
3,000
Inclination
Angle
I, deg
0
3,200
3,600
4,000
Azimuth
Angle
A, deg
20
6
14
24
6
20
80
Based on known coordinates for point C we’ll calculate
the coordinates of point D using the above information.
6
Example - Wellbore Survey Calculations
Point C has coordinates:
x = 1,000 (ft) positive towards the east
y = 1,000 (ft) positive towards the north
z = 3,500 (ft) TVD, positive downwards
C
Dz
C
N (y)
N
Dz
D
E (x)
D
Dy
Dx
7
Example - Wellbore Survey Calculations
I. Calculate the x, y, and z coordinates
of points D using:
(i) The Average Angle method
(ii) The Balanced Tangential method
(iii) The Minimum Curvature method
(iv) The Radius of Curvature method
(v) The Tangential method
8
The Average Angle Method
Find the coordinates of point D using
the Average Angle Method
At point C,
x = 1,000 ft
y = 1,000 ft
z = 3,500 ft
Measured depth from C to D, DMD  400 ft
IC  14
A C  20
ID  24
A D  80
9
The Average Angle Method
Measured depth from C to D, DMD  400 ft
IC  14
A C  20

ID  24 

A D  80
C
N (y)
Dz
C
D
N
Dz
Dy D
E (x)
Dx
10
The Average Angle Method
11
The Average Angle Method
This method utilizes the average
of I1 and I2 as an inclination, the
average of A1 and A2 as a
direction, and assumes the entire
survey interval (DMD) to be
tangent to the average angle.
IAVG
A AVG
I1  I2

2
A1  A 2

2
DEast  DMD sin IAVG sin A AVG
DNorth  DMD sin IAVG cos A AVG
DVert  DMD cos IAVG
From: API Bulletin D20. Dec. 31, 1985
12
The Average Angle Method
IAVG
A AVG
IC  ID 14  24


 19
2
2
A C  AD 20  80


 50
2
2
DEast  DMD sin IAVG sin A AVE
Dx  400 sin19 sin 50


Dx  99.76 ft
13
The Average Angle Method
DNorth  DMD sin IAVG cos A AVG
Dy  400 sin19 cos 50
Dy  83.71 ft
DVert  400 cos IAVG
Dz  400 cos19
Dz  378.21 ft
14
The Average Angle Method
At Point D,
x = 1,000 + 99.76 = 1,099.76 ft
y = 1,000 + 83.71 = 1,083.71 ft
z = 3,500 + 378.21 = 3,878.21 ft
15
The Balanced Tangential Method
This method treats half the measured distance
(DMD/2) as being tangent to I1 and A1 and the
remainder of the measured distance (DMD/2) as
being tangent to I2 and A2.
DEast 
DMD
 sin I1  sin A1  sin I2  sin A 2
2

DNorth 
DMD
 sin I1  cos A1  sin I2  cos A 2
2

DMD
 cos I2  cos I1
DVert 
2

From: API Bulletin D20. Dec. 31, 1985
16
The Balanced Tangential Method
DMD
sin IC sin AC  sin ID sin AD 
DEast 
2

400

sin 14 o sin 20o  sin 24 o sin 80o
2

Dx  96.66 ft
17
The Balanced Tangential Method
DMD
sin IC cos AC  sin ID cos AD 
DNorth 
2

400

sin 14 o cos 20o  sin 24 o cos 80o
2

Dy  59.59 ft
18
The Balanced Tangential Method
DMD
DVert 
2
 cos ID  cos IC 

400

cos 24 o  cos 14 o
2

Dz  376.77 ft
19
The Balanced Tangential Method
At Point D,
x = 1,000 + 96.66 = 1,096.66 ft
y = 1,000 + 59.59 = 1,059.59 ft
z = 3,500 + 376.77 = 3,876.77 ft
20
Minimum Curvature Method
b
21
Minimum Curvature Method
This method smooths the two straight-line segments
of the Balanced Tangential Method using the Ratio
Factor RF.
2
b
RF  tan
b
2
(DL= b and must be in radians)
DMD
 sin I1  sin A1  sin I2  sin A 2   RF
DEast 
2
DMD
 sin I1  cos A1  sin I2  cos A 2   RF
DNorth 
2
DMD
 cos I1  cos I2   RF
DVert 
2
22
Minimum Curvature Method
The Dogleg Angle, b, is given by:
cos b  cos ID  IC   sin IC sin ID 1  cos(AD  AC )



 cos 24o  14o  sin 14o sin 240 1  cos(800  20o )

cos b = 0.9356
b = 20.67 = 0.3608 radians
o
23
Minimum Curvature Method
The Ratio Factor,
2
b
RF  tan
b
2
 20.67o 
2

RF 
tan 
0.3608
 2 
RF  1.0110
24
Minimum Curvature Method
DMD
sin IC sin AC  sin ID sin AD  RF
DEast 
2


400

sin 14 o sin 20o  sin 24 o sin 80o 1.0110
2
 96.66 * 1.011  97.72 ft
Dx  97.72 ft
25
Minimum Curvature Method
DMD
sin IC cos AC  sin ID cos AD  RF
DNorth 
2


400

sin 14 o cos 20o  sin 24 o cos 80o 1.0110
2
 59.59 * 1.011  60.25 ft
Dy  60.25 ft
26
Minimum Curvature Method
DMD
DVert 
2
 cos ID  cos IC  RF


400

cos 24 o  cos 14 o 1.0110
2
 376.77 * 1.0110  380.91 ft
Dz  380.91 ft
27
Minimum Curvature Method
 At Point D,
x = 1,000 + 97.72 = 1,097.72 ft
y = 1,000 + 60.25 = 1,060.25 ft
z = 3,500 + 380.91 = 3,880.91 ft
28
The Radius of Curvature Method
DMD cos IC  cos ID  cos A C  cos AD   180 
DEast 


ID  IC  AD  AC 
  



2
400 cos 14  cos 24 cos 20  cos 80  180 



24  14 80  20
  
o
o
o
o
2
Dx  95.14 ft
29
The Radius of Curvature Method
DMD (cos IC  cos ID ) (sin AD  sin A C )  180 
DNorth 


(ID  IC ) ( AD  A C )
  
400(cos14  cos 24 )(sin 80  sin 20

(24  14)(80  20)




2
)  180 


  
2
Dy  79.83 ft
30
The Radius of Curvature Method
DMD (sin ID  sin IC )  180 
DVert 


ID  IC
  
400 (sin 24o  sin 14o )  180 



24  14
  
Dz  377.73 ft
31
The Radius of Curvature Method
At Point D,
x = 1,000 + 95.14 = 1,095.14 ft
y = 1,000 + 79.83 = 1,079.83 ft
z = 3,500 + 377.73 = 3,877.73 ft
32
The Tangential Method
Measured depth from C to D, DMD  400 ft
IC  14
A C  20
ID  24
A D  80
DEast  DMD sin ID sin AD
 400 sin24  sin 80
Dx  160.22 ft
33
The Tangential Method
DNorth  DMD sin ID cos AD
 400 sin 24o cos 80o
Dy  28.25 ft
DVert  DMD cos ID

 400 cos 24
Dz  365.42 ft
34
The Tangential Method
 At Point D,
x  1,000  160.22  1,160.22 ft
y  1,000  28.25  1,028.25 ft
z  3,500  365.42  3,865.42 ft
35
Summary of Results (to the nearest ft)
x
Average Angle
y
z
1,100
1,084
3,878
Balanced Tangential 1,097
1,060
3,877
Minimum Curvature 1,098
1,060
3,881
Radius of Curvature 1,095
1,080
3,878
Tangential Method
1,028
3,865
1,160
36
37
38
Building
Hole Angle
39
Holding
Hole Angle
40
41
CLOSURE
(HORIZONTAL)
DEPARTURE
LEAD ANGLE
42
b
43
Tool Face Angle
44