CHAPTER # 8CHAPTER # 8

Directional Drilling and Directional Drilling and Deviation ControlDeviation Control

DRILLING ENGINEERINGDRILLING ENGINEERING

7.27.2 Build and Hold TrajectoryBuild and Hold Trajectory

• Circumference = Circumference = rr

• S=rS=r n radians max. inclination anglen radians max. inclination angle

• 1 radian = 1801 radian = 180 o o// = 57.29578 = 57.29578 o o

• 11oo = = /180 radians/180 radians

• q = degrees per unit length = q = degrees per unit length = /L/L

= inclination angle build up rate= inclination angle build up rate

• q = 1q = 1oo/100ft /100ft

r = S /r = S /• r = radius of curvaturer = radius of curvature

S =

qlength

rees

S

deg1

rees

length

q deg

1

180

deg

1

rees

length

q

11

1801180qor

q(8.1)(8.1)

= T

• To find angle T look at triangle OBA

13

31tanDD

X

AO

BAT

13

31arctanDD

XT

To find angle consider triangle OBC

BO

COSin

(8.2)(8.2)

(8.3a)(8.3a)

(8.3b)(8.3b)

(8.4)(8.4)

CO = CO =

22 )()( BAOABO

231

213 )()( XDDBO

213

231

1

)()( DDXSin

213

231

1

)()(arcsin

DDX

= T

(8.5)(8.5)

13

31

213

231

1 arctan)()(

arcsinDD

X

DDX

Length of the arc section DC (buildup section)Length of the arc section DC (buildup section)

(8.6)(8.6)

1801

rDC

qDC

qr

1

1801

(8.7)(8.7)

Length of CB (Trajectory Path)Straight at constant inclination angle can be determined from BCO

tan

tan

1

1

rCB

CB

r

CB

CO

Total measured depth DM for TVD of D3 is

tan1

1

r

qDDm

(8.8)(8.8)

Horizontal departure at end of build up

)cos1(cos 1112

2

rrrX

OCDconsiderECX

(8.9)(8.9)

True Vertical depth at end of build up section

sin112 rDD (8.12)(8.12)

Geometry for the build sectionGeometry for the build section

Measure depth and Horizontal departure before reaching maximum angle along any part of build up.

Consider intermediate inclination angle

XN=Horizontal Departure at C

DN=Vertical depth

Consider DOC

)cos1(

cos

sin

11

11

11

rX

rrX

rDD

N

N

N

(8.11)(8.11)

(8.10)(8.10)

New measured depth for any part of the New measured depth for any part of the build upbuild up

qDDMN

1

New measured depth at TVD of (DNew measured depth at TVD of (D**< D< D33)(D)(D22<D<D**< D< D33))

cos

sin111

rDD

qDDMP

(8.13)(8.13)

(8.16)(8.16)

Horizontal Departure XHorizontal Departure X** (X (X22<X<X**< X< X33))

tan)sin()cos1( 11 rDDrX (8.18)(8.18)

For r1 < X3

)(sin

)()(180

13

13

13

1

13

13

rX

DDarcTan

DD

rarcCos

rX

DDarcTan

(8.20)(8.20)

Build-hold-and-drop and hold (modified-S)Build-hold-and-drop and hold (modified-S)

Directional quadrants and compass measurementsDirectional quadrants and compass measurements