5. borehole trajectory control - drilling-engineering.com
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5. Borehole Trajectory Control
5.1 Survey Tools
5.2 Borehole Trajectory Calculation Methods
5.3 Assessment of Current Bottom Hole Position
5.4 Borehole Trajectory Correction Methods
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
Survey Tools are used for measurement of wellbore course
(inclination and azimuth)
Types of Survey Tools:
• Magnetic Survey Instruments
• Gyroscopic Survey Instruments
Magnetic and Gyroscopic Survey Tools :
• Single-shot instruments record only one point at a given depth
• Multi-shot instruments record several points along the well depth
Survey Tools can be:
• Dropped
• Lowered on wireline
• Used as a part of MWD
5.1 Survey Tools
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
Mechanical Magnetic Survey Instruments
• Based on the compass principle
• Use Earth’s horizontal magnetic component to reference
magnetic north
• Cannot be used in MWD tools
Electronic Magnetic Survey Instruments
• Use magnetometers to measure the Earth’s magnetic field and
accelerometers to measure Earth’s gravitational field
• Can be used to measure inclination, azimuth and tool face
orientation (TFO)
• Are used in MWD tools
5.1 Magnetic Survey Instruments
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
Used when the accuracy of magnetic survey instruments could
be affected by the presence of magnetic objects (e.g., casing)
Types of gyro instruments:
• Free gyro. Consists of motor-driven spinning mass (rotor)
mounted in a set of gimbals.
• Rate gyro. Has very accurate drift rate of 0.01º/h. Can detect
the Earth’s rotation and geographic north
• Inertial navigation system. Uses a group of gyros to orient the
system to the north and accelerometers to detect movements in
x, y and z planes
5.1 Gyroscopic Survey Instruments
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.2 Borehole Trajectory Calculation
Y (East)
Х (North)
ΔX
Survey Data:
S – Measured Depth (MD)
α – Inclination
φ – Azimuth
Coordinates of actual
trajectory:
X2 = X1 + ΔX
Y2 = Y1 + ΔY
Z2 = Z1 + ΔZ
Z
Survey Data 2
(X2, Y2, Z2)
Survey Data 1
(X1, Y1, Z1)
ΔY
ΔZ
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
1. Minimum Curvature Method
2. Radius of Curvature Method
3. Angle Averaging Method
4. Tangential Method
5. Balanced Tangential Method
5.2 Borehole Trajectory Calculation Methods
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.2 Minimum Curvature Method
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.2 Radius of Curvature Method
Note: α and φ in degrees
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.2 Angle Averaging Method
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.2 Tangential Method
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.2 Balanced Tangential Method
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.2 Borehole Trajectory Calculations
Angle Averaging Method
Y (East)
Х (North)
φ
α
O
B C
D
A
E
Z
(S2, α2, φ2)
(X2, Y2, Z2)
(S1, α1, φ1)
(X1, Y1, Z1)
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
Survey Data:
S – Measured Depth (MD)
α – Inclination
φ – Azimuth
OA = ΔS = ΔMD
OB = ΔS ∙ sin α
OC = ΔX = ΔS sinα cosφ
OD = ΔY = ΔS sinα sinφ
OE = ΔZ = ΔS cosα = ΔTVD
ΔX
ΔY
ΔZ
5.2 Borehole Trajectory Calculation
i1ii
i1ii
;i1ii
ZZZ
YYY
XXX
Absolute Coordinate System
X – direction to North
Y – direction to East
Z – direction downward
Xо = Yо = Zо = 0 coordinate of wellhead
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
Relative Coordinate System
X – direction along projected azimuth
X – direction perpendicular Y
Z – direction downward
5.2 Borehole Trajectory Calculation in Absolute Coordinate System
(Angle Averaging Method)
2cosSZ
2sin
2sinSY
2cos
2sinSX
i1iii
i1ii1iii
i1ii1iii
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.2 Borehole Trajectory Calculation in Relative Coordinate System
(Angle Averaging Method)
]2
cos[2
sinSX прi1ii1i
ii
2cosSX
]2
sin[2
sinSY
i1iii
прi1ii1i
ii
ΔZi
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
φpr
φpr
5.3 Assessment of Current Bottom Hole Position Relative to the Target
φwc
Xc
Yc
Current Bottom Hole
Target
HDct
HD
X
Y
Rt
φe
φt φpr ●
● Wellhead
● Аct
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.3 Assessment of Current Bottom Hole Position Relative to the Target
●
●
Target
Z
X
Act
● Wellhead
TVD
Zc
Rt
αr
Current Bottom Hole
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.3 Assessment of Current Bottom Hole Position Relative to the Target
1. Borehole trajectory calculation
2. Calculation of azimuth of direction from wellhead to current
bottom hole
Yc φwb = arctan ---------- Xc
Xc, Yc – coordinates of current bottom hole
3. Calculation of horizontal displacement from actual bottom
hole to target
HDct = HD – Xc
HD – horizontal displacement
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.3 Assessment of Current Bottom Hole Position Relative to the Target
4. Calculation of azimuth of direction required to hit the target
(right-left edge of the target)
φr = φpr + φt _ φe
where
φpr – projected well azimuth
Rt – radius of target
φt = arctan (Yc / HDct)
φe = arctan (Rt / Аct)
Аct = HDct / cos φt
+
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.3 Assessment of Current Bottom Hole Position Relative to the Target
5. Calculation of inclination angle of direction required to hit the
target (far-near edge of the target)
Act _ Rt αr = arctan --------------------- TVD – Zc
where
TVD – True Vertical Depth
Zc – TVD of actual bottom hole
+
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.3 Calculation of Required Azimuth and Inclination Angle Changes
6. Calculation of required azimuth change
Δφ = φr – φc where
φc – azimuth at current bottom hole
7. Calculation of required inclination angle change
Δα = αr – αc where
αc – inclination angle at current bottom hole
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.4 Tool Face Orientation (TFO)
TFO
Bit
Downhole Motor with ABH
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
TFO is measured from the high side of
the borehole in a plane perpendicular to
the axis of the hole.
5.4 Tool Face Orientation (TFO)
Δα +
Δφ –
Δα –
Δφ –
Δα –
Δφ +
Δα +
Δφ + 270º
180º
90º
0º
TFO
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
Maximum
Right Turn Maximum
Left Turn
Maximum Drop
Maximum Build
Build &
Right Turn
Drop &
Left Turn
Build &
Left Turn
Drop &
Right Turn
5.4 Tool Face Orientation (TFO)
TFO 0º 0º-
90º 90º
90º-
180º 180º
180º-
270º 270º
270º-
360º 360º
Δα + + 0 – – – 0 + +
Δφ 0 + + + 0 – – – 0
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.4 Analytical Method of TFO Calculation
sin αr ∙ sin Δφ TFO = arctan --------------------------------------------------------------------------- sin αr ∙ cos αc ∙ cos Δφ – sin αc ∙ cos αr cos β = cos αc ∙ cos αr + sin αc + sin αr ∙ cos Δφ Lcor = 100 ∙ β / i100
TFO – tool face orientation
αc и φc – inclination angle and azimuth at current bottom hole
αr и φr – required inclination angle and azimuth
Δ φ = φr – φc
Lcor – length of correction run, ft
i100 – dogleg severity (DLS), deg/100ft
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.
5.4 Graphical Method of TFO Calculation
Given: Determine:
αc = 14º φc = 90º Δφ = φr – φc = 110º – 90º = 20º
αr = 20º φr = 110º TFO = 65º
i100 = 6º/100ft Lcor = 100 ∙ β / i100 = 8.4 ∙ 100 / 6 =
= 140ft
Δφ = 20º
αc = 14º
αr = 20º
TFO = 65º
β = 8.4º
Oktay Mamedbekov. Directional Drilling. Borehole Trajectory Control.