35 Wellbore Surveying Methods

1PETE 411Well Drilling

Lesson 35

Wellbore Surveying Methods

2Wellbore Surveying Methods

Average Angle Balanced Tangential Minimum Curvature Radius of Curvature Tangential

Other Topics Kicking off from Vertical Controlling Hole Angle

3Read:Applied Drilling Engineering, Ch.8

(~ first 20 pages)

Projects:Due Monday, December 9, 5 p.m.

( See comments on previous years design projects )

4Homework Problem #18

Balanced Cement Plug

Due Friday, December 6

5I, A, MD

6Example - Wellbore Survey Calculations

The table below gives data from a directional survey.

Survey Point Measured Depth Inclination Azimuthalong the wellbore Angle Angle

ft I, deg A, deg

A 3,000 0 20B 3,200 6 6C 3,600 14 20D 4,000 24 80

Based on known coordinates for point C well calculate the coordinates of point D using the above information.

7Example - Wellbore Survey CalculationsPoint C has coordinates:

x = 1,000 (ft) positive towards the easty = 1,000 (ft) positive towards the northz = 3,500 (ft) TVD, positive downwards

z

E (x)

N (y)C

Dz

N

D

C

yx

8Example - Wellbore Survey Calculations

I. Calculate the x, y, and z coordinatesof 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

9The Average Angle Method

Find the coordinates of point D using the Average Angle Method

At point C, x = 1,000 fty = 1,000 ftz = 3,500 ft

80 A 24I 20 A 14I

DD

CC

========

========

ft400MDD, toCfromdepthMeasured ====

10

The Average Angle Method

80 A 24I 20 A 14I

ft 400MD D, to C from depth Measured

DD

CC

========

========

====

z

E (x)

N (y)

C

Dz

N

D

C

yx

11


12


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 (MD) to be tangent to the average angle.

From: API Bulletin D20. Dec. 31, 1985

2III 21AVG

++++====

AVGAVG AsinIsinMDEast ====

AVGIcosMDVert ====

2AAA 21AVG

++++====

AVGAVG AcosIsinMDNorth ====

13

192

24142

III DCAVG ====++++

====

++++====


502

80202

AAA DCAVG ====++++

====

++++====

AVEAVG AsinIsinMDEast ==== 50sinsin19400x ====

ft76.99x ====

14


AVGIcos400Vert ====cos19400z ====

AVGAVG AcosIsinMDNorth ====

ft 71.83y ====

50cossin19400y ====

ft21.378z ====

15


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

16

The Balanced Tangential Method

This method treats half the measured distance (MD/2) as being tangent to I1 and A1 and the remainder of the measured distance (MD/2) as being tangent to I2 and A2.

From: API Bulletin D20. Dec. 31, 1985

[[[[ ]]]]2211 AsinIsinAsinIsin2MDEast ++++====

[[[[ ]]]]2211 AcosIsinAcosIsin2MDNorth ++++====

[[[[ ]]]]12 IcosIcos2MDVert ++++====

17


(((( ))))DDCC AsinIsinAsinIsin2MDEast ++++====

(((( ))))oooo 80sin24sin20sin14sin2

400++++====

ft66.96x ====

18


(((( ))))DDCC AcosIsinAcosIsin2MDNorth ++++====

(((( ))))oooo 80cos24sin20cos14sin2

400++++====

ft59.59y ====

19


(((( ))))CD IcosIcos2MDVert ++++====

(((( ))))oo 14cos24cos2

400++++====

ft77.376z ====

20


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

21

Minimum Curvature Method

22


This method smooths the two straight-line segments of the Balanced Tangential Method using the Ratio Factor RF.

(DL= and must be in radians)2tan2RF ====

[[[[ ]]]] RFAcosIsinAcosIsin2MDNorth 2211 ++++

====

[[[[ ]]]] RFAsinIsinAsinIsin2MDEast 2211 ++++

====

[[[[ ]]]] RFIcosIcos2MDVert 21 ++++

====

23


(((( )))) (((( )))))AAcos(1IsinIsinIIcoscos CDDCCD ====

(((( )))) (((( )))))2080cos(124sin14sin1424cos o00ooo ====cos = 0.9356

= 20.67o = 0.3608 radians

The Dogleg Angle, , is given by:

24


The Ratio Factor,

2tan2RF ====

====

267.20tan

3608.02RF

o

0110.1RF====

25


(((( ))))RFAsinIsinAsinIsin2MDEast DDCC ++++

====

(((( )))) 0110.180sin24sin20sin14sin2

400 oooo ++++====

ft72.97x ====

ft72.97011.1*66.96 ========

26


(((( ))))RFAcosIsinAcosIsin2MDNorth DDCC ++++

====

ft25.60y ====

ft25.60011.1*59.59 ========

(((( )))) 0110.180cos24sin20cos14sin2

400 oooo ++++====

27


(((( ))))RFIcosIcos2MDVert CD ++++

====

(((( )))) 0110.114cos24cos2

400 oo ++++====

ft91.380z ====

ft91.3800110.1*77.376 ========

28


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

29

The Radius of Curvature Method

(((( )))) (((( ))))(((( )))) (((( ))))

2

CDCD

DCDC 180AAII

AcosAcosIcosIcosMDEast

====

(((( )))) (((( ))))(((( )))) (((( ))))

2oooo 18020801424

80cos20cos24cos14cos400

====

ft 14.59 x ====

30


2

CDCD

CDDC 180)AA()II(

)AsinA(sin)IcosI(cosMDNorth

====

2180)2080)(1424(

)20sin80)(sin24cos400(cos14

====

ft 79.83 y ====

31


==== 180

II)IsinI(sinMDVert

CD

CD

ft 73.773 z ====

====

1801424

)14sin24(sin400 oo

32


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

33

The Tangential Method

ft 400MD D, to C from depth Measured ====

80 A 24I 20 A 14I

DD

CC

========

========

80sinsin24400 ====

DD AsinIsinMDEast ====

ft 22.160x ====

34


DIcosMDVert ====24cos400 ====

ft 42.365z ====

DD AcosIsinMDNorth ====

ft 25.28y ====

oo 80cos24sin400====

35


ft 3,865.42365.423,500z

ft 1,028.2528.251,000 y

ft 1,160.22160.221,000x

D,Point At

====++++====

====++++====

====++++====

36

Summary of Results (to the nearest ft)

x y z

Average Angle 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 1,160 1,028 3,865

39

Building Hole Angle

40

Holding Hole Angle

42

CLOSURE

LEAD ANGLE

(HORIZONTAL) DEPARTURE

44

Tool Face Angle

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35 Wellbore Surveying Methods