5. borehole trajectory control - drilling-engineering.com

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


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


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


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


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


5.2 Minimum Curvature Method


5.2 Radius of Curvature Method

Note: α and φ in degrees


5.2 Angle Averaging Method


5.2 Tangential Method


5.2 Balanced Tangential Method


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)


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


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


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


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



●

●

Target

Z

X

Act

● Wellhead

TVD

Zc

Rt

αr

Current Bottom Hole



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



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

+



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

+


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


5.4 Tool Face Orientation (TFO)

TFO

Bit

Downhole Motor with ABH


TFO is measured from the high side of

the borehole in a plane perpendicular to

the axis of the hole.


Δα +

Δφ –

Δα –

Δφ –

Δα –

Δφ +

Δα +

Δφ + 270º

180º

90º

0º

TFO


Maximum

Right Turn Maximum

Left Turn

Maximum Drop

Maximum Build

Build &

Right Turn

Drop &

Left Turn

Build &

Left Turn

Drop &

Right Turn


TFO 0º 0º-

90º 90º

90º-

180º 180º

180º-

270º 270º

270º-

360º 360º

Δα + + 0 – – – 0 + +

Δφ 0 + + + 0 – – – 0


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


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


5. borehole trajectory control - drilling-engineering.com

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