Download - CHAPTER # 8
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