02 Survey Calculations

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SURVEY CALCULATIONS

Survey calculations are used to

predict the position of the

wellbore relative to the surface

location



© 2009 PetroSkills LLC, All Rights Reserved2

Survey Calculations

Based on the properties of aright triangle or the arc of a

circleRIGHT TRIANGLE

90o

Hypotenuse




Survey Calculations

Properties of a right triangle

RIGHT TRIANGLE

Opposite Side

Angle A

HypotenuseAdjacent

Side

hypotenuse

sideopposite A

sin =

hypotenuse

sideadjacent

A

cos =

sideadjacent

sideopposite A

tan =




Survey Calculations

Terminology used in this bookØ MD = Measured depth – Length of the

wellbore measured by the drill string

Ø TVD = True vertical depth – Vertical

component of the measured depth

Ø North = North component of the

horizontal departure




Survey Calculations

Ø East = East component of thehorizontal displacement

Ø = Delta meaning the difference in

Ø Subscript 1 = The upper survey of twosurvey points

Ø Subscript 2 = The lower survey of the

two survey points

Ø I = Inclination from vertical




Survey Calculations

Ø A = Azimuth of the survey (0 to 360degrees)

Ø r = Radius of curvature

Ø VS = Vertical section

Ø DLS = Dogleg severity

Ø DEP = The departure in the horizontal

plane


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Survey Calculations

Commonterminology for

a directional

profile

Vertical Section, ft

Tangent or Hold

DropSection

EOB or EOC

KOP

Build Section

KB, RT, DF

T V D ,

f t



POSITIONING

The earth is an oblate spheroid(a squashed sphere) and maps

are flat, which makes it difficult

to map the earth



Positioning

The earth isdivided intolatitude andlongitude

Ø The equator is 0degrees latitudeand poles are 90degrees

Ø The length of adegree of latitudeis always thesame



Positioning

Ø Meridians or linesof longitude run

from pole to pole

Ø The equator is

divided up into 360

degrees

Ø The distance

between meridianschanges depending

upon the latitude



Positioning

Calculating the longitude and

latitude of a well on a map can

be complicated

Rectangular grids have beendeveloped for use in surveying

and mapping

A geodetic datum is a definitionof a model for the surface of the

earth which uses a grid



Positioning

The NAD27 or North American

Datum 1927 is the most

commonly used datum for North

America (NAD83 is also used)

ED50 or European Datum 1950 is

the most commonly used datum

in the North Sea



Positioning

A map projection is a

mathematical formula which has

been designed to convert the

latitude/longitude method of

positioning to a flat map

With a flat map, wellbores can be

spotted with an X Y coordinatesystem (North, East)



Positioning

The most commonly used map

projection is the Universal

Transverse Mercator (UTM)

The Lambert map projection isalso common throughout the

world and is the most common

in the USA



UTM System

On most maps, the lines of

latitude and longitude are curved

The quadrangles formed by the

intersections of these lines areof different sizes and shapes,

which complicates the locations

of points and the measurementof directions



UTM System

The UTM system tries to solve

this problem

The world is divided up into 60

equal zones, each 6 degreeswide

The zones are from 84.5 degrees

North to 80.5 degrees southPolar regions are covered by

other, special projections



UTM System

Each zone hasits own origin atthe intersectionof its centralmeridian and theequator

The zone is

flattened and asquare gridimposed on it



UTM System

The outer edges

for the ellipsoidare curved

The convergence

is the differencebetween grid north

and true north

At the centralmeridian, grid

north = true north



UTM System

Each of the 60 zones are

numbered starting with one at

the 180th meridian

The areas east and west of theGreenwich Meridian are covered

by zones 30 and 31, respectively

Zones increase to the east anddecrease to the west



UTM System

Points on the earth may be

identified by its zone number, its

distance in meters from the

equator (northing) and its

distance in meters from a north-

south reference line (easting)



UTM System

To avoid negative values of

eastings, the central meridian inany zone is assigned thearbitrary eastings value of

500,000 m Along the equator a zone isabout 600,000 m wide, tapering

towards the polar regionsEastings range in values fromapproximately 200,000 to 800,000





UTM System

For points north of the equator,

northings are measured directly

in meters, with a value of zero at

the equator and increasing

toward the north




UTM System

To avoid negative numbers in

the Southern Hemisphere, the

equator is assigned a value of

10,000,000 m and displacements

in the south are measured with

decreasing, but positive, values




UTM System




Mapping

The surface location of a well is

positioned on a mapThe surface location of the North andEast Coordinates may use the map

coordinates or they may be set aszero North and zero East

When mapping directional wells, it isimportant to know if the wells were

plotted based on true north or gridnorth and what map reference wasused




Mapping



S C l l ti




Survey Calculations

Most common survey methodsØ Tangential

Ø Balanced Tangential

Ø Average AngleØ Radius of Curvature

Ø Minimum Curvature

All of the survey equations arepresented in Table 2-1 (page 2-7)for easy reference

S C l l ti




Survey Calculations

Tangential method uses only thelower survey point and is the least

accurate survey method

I2

S C l l ti




Survey Calculations

The tangential method assumesthe wellbore course is a straight

line tangent to the lower

inclination or azimuth

Tangential method equations

2cos

IMDTVD ´D=D

22 cossin AIMDNorth ´´D=D

22 sinsin AIMDEast ´´D=D

S C l l ti




Survey Calculations

The balanced tangential survey

method assumes the wellbore courseis two straight lines with half thewellbore course tangent to the uppersurvey point and the other half to thelower survey point



S C l l ti




Survey Calculations

The average angle methodassumes the wellbore course is

a straight line tangent to the

average angleI1

÷ø

öçè

æ +

2

21 II

S C l l ti




Survey Calculations

The average angle method is

accurate as long as the surveys arenot too far apart and there is no large

change in azimuth at low inclinations

Average angle equations

÷ø

öçè

æ +´D=D

2cos 21 II

MDTVD

÷øöç

èæ +´÷

øöç

èæ +´D=D

2cos

2sin 2121 A AIIMDNorth

÷ø

öçè

æ +´÷ø

öçè

æ +´D=D

2sin

2sin 2121 A AII

MDEast

S C l l ti




Survey Calculations

Radius of curvature assumesthat the wellbore course is an arcof a circle

Used for planning but not forfinal survey

S C l l ti




Survey Calculations

Radius of curvature hasproblems when inclinations and

azimuths are equal because the

radius of curvature is infinite

Radius of curvature also has

problems when the well walks

past north

S C l l ti




Survey Calculations

Radius of curvature equations

( )12

12 sinsin180

II

IIMDTVD

-

-D=D

p

( ) ( )( )( )

( )( )1212

2

1221

2sinsincoscos180

A AII

A AIIMDNorth

--

--D=D

p

( )( )( )( )( )1212

2

2121

2coscoscoscos180

A AII

A AIIMDEast

--

--D=D

p

( )12

21 coscos180

II

IIMD

DEP -

-D=D

p

( )( )DLSr

p

180=

r B

IIMD 12 -

=D

Survey Calculations




Survey Calculations

Minimum Curvature is thebalanced tangential method but

the straight lines are smoothed

into an arc by a correction factor

Survey Calculations




Survey Calculations

Minimum curvature is suitablefor a computer or programmable

calculator

The inclinations and azimuthsmust be changed to radians

before entering them in the

equationsIt is the most common survey

method used today

Survey Methods




Survey Methods

Minimum curvature equations

- Note: inclination and azimuth must be

entered in radians

( )( )FCIIMDTVD 21 coscos2

+÷øöç

èæ

D=D

( ) ( )[ ]( )FC AI AIMD

North 1122 cossincossin2

´+´÷ø

öçè

æD=D

( ) ( )[ ]( )FC AI AIMD

East 1122 sinsinsinsin

2

´+´÷

ø

öç

è

æD=D

121212 cos1sinsincos1 A AIIIID --´´--=

11

1tan2

2

1 -÷ø

öçè

æ= -

DD

÷ø

öçè

æ´=

2

2tan

2

2 D

DFC

Survey Calculations




Survey Calculations

Every survey calculation muststart somewhere

The beginning is the tie-in point

Ø The surface location and the KB or

RT elevation may be the tie-in point

Ø Maybe a gyro was run in the surface

hole prior to starting the directional

drilling, then the tie-in will be the last

survey of the gyro

Survey Calculations




Survey Calculations

The coordinates of the surface

location must also be determined

Ø For many land wells, the depth will be

zero at the KB, RT or DF

Ø The North and East Coordinates may

be zero and zero

Ø The North and East Coordinates may

also be the map coordinates especially

when drilling from a pad or platform

Survey Calculations




Survey Calculations

Example 2Tangential Method

Ø At 0 and 1,000 feet the inclination is

0°, therefore, the wellbore position is0 North and 0 East.

Ø A survey at 1,100 feet shows theinclination to be 3° in the N21.7Edirection (Azimuth = 21.7). Calculatethe position of the wellbore at 1,100feet.

Survey Calculations




Survey Calculations

Ø Using the tangential method,

calculate ΔTVD

12 MDMDMD -=D

10001100 -=DMD

'100=DMD

2cos IMDTVD D=D

3cos100=DTVD

'86.99=DTVD

Survey Calculations




Survey Calculations

Ø Calculate the true vertical depth

Ø Calculate ΔNorth

12 TVDTVDTVD +D=

100086.992 +=TVD

'86.10992 =TVD

22 cossin AIMDNorth D=D

7.21cos3sin100=DNorth

'86.4=DNorth

Survey Calculations




Survey Calculations

Ø Calculate the North coordinate

Ø Calculate the ΔEast

12 NorthNorthNorth +D=

'0'86.42 +=North

'86.42 =North

22 sinsin AIMDEast D=D

7.21sin3sin100=DEast

'94.1=DEast

Survey Calculations




Survey Calculations

Ø Calculate the East coordinate

The process is repeated until allthe surveys are calculated

12 EastEastEast +D=

'0'94.12

+=East

'94.12 =East

Survey Calculations




Survey Calculations

Average Angle MethodØ Calculate the position of the wellbore

at 1,400 feet using the average angle

method and the survey data at 1,300feet in Table 2-6

12 MDMDMD -=D

'100'300,1'400,1 =-=DMD

Survey Calculations




Survey Calculations

Ø The azimuth at 1,400 feet is 20.30º

÷ø

öçè

æ +´D=D

2cos 21 II

MDTVD

'33.982

129cos100 =÷

ø

öçè

æ +´=DTVD

12 TVDTVDTVD +D=

'13.1397'80.298,1'33.982 =+=TVD



Survey Calculations




Survey Calculations

Radius of Curvature Method

Ø Calculate the position of the wellbore

at 1,500 feet using the radius of

curvature method and the survey data

at 1,400 feet in Table 2-7

12 EastEastEast +D=

'96.15'19.9'77.62 =+=East

Survey Calculations




Ø The azimuth at 1,500 feet is 23.30°

Survey Calculations

12 MDMDMD -=D

'100'400,1'500,1 =-=DMD

( )12

12 sinsin180

II

IIMD

TVD -

-D=D

p

( ) '23.97

1215

12sin15sin100180=

-

-=D

p TVD

12 TVDTVDTVD +D=

'31.1494'08.397,1'23.972 =+=TVD

Survey Calculations




Survey Calculations

( ) ( )( )( )( )( )1212

2

1221

2sinsincoscos180

A AII

A AIIMDNorth --

--D

=D p

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

'67.213.203.231215

3.20sin3.23sin15cos12cos1001802

2

=--

°-°°-°=D

p North

12 NorthNorthNorth +D=

'14.60'47.38'67.212 =+=North

Survey Calculations




Survey Calculations

( ) ( )( )( )( )( )1212

22121

2

coscoscoscos180 A AII

A AIIMDEast--

--D=Dp

( ) ( )( )( )

( )( )

'67.8

3.203.231215

3.23cos3.20cos15cos12cos1001802

2

=

--

--=D

p

East

12 EastEastEast +D=

'62.24'95.15'67.82 =+=East



Survey Calculations




Survey Calculations

Results of the survey

calculations in Example 2-2

Method TVD North East

Tangential 4364.40 1565.23 648.40Balanced Tangential 4370.46 1542.98 639.77

Average Angle 4370.80 1543.28 639.32

Radius of Curvature 4370.69 1543.22 639.30

Minimum Curvature 4370.70 1543.05 639.80

Survey Calculations




Survey Calculations

Relative difference between

survey calculation methods

Method TVD North East

Tangential -6.30 +22.18 +8.60Balanced Tangential -0.24 -0.07 -0.03

Average Angle +0.10 +0.23 -0.48

Radius of Curvature -0.01 +0.17 -0.50

Minimum Curvature +0.00 +0.00 +0.00

Survey Methods




Survey Methods

Class Problem - Problem #3 on

page 2-31Ø MD1 = 100’ MD2 = 200’

Ø I1 = 1o I2 = 1o

Ø A1 = 0o A2 = 180o

Ø Calculate the ΔTVD, ΔNorth and ΔEast

coordinate using the average angle

method and the radius of curvature

method (not minimum curvature)

Survey Methods




Survey Methods

RESULTS

Method ΔTVD ΔN ΔE

Average Angle 99.98 0.00 1.75

Radius of Curv. 99.98 0.00 1.11

Minimum Curv. 100.00 0.00 0.00

Survey Calculations




Survey Calculations

Average Angle Method

÷ø

öçè

æ +´D=D

2cos 21 II

MDTVD

÷ø

öçè

æ +´÷

ø

öçè

æ +´D=D

2cos

2sin 2121 A AII

MDNorth

( ) 98.992

11cos100200 =÷ø

öçè

æ +´-=DTVD

( ) 00.02

1800cos

2

11sin100200 =÷

ø

öçè

æ +´÷

ø

öçè

æ +´-=DNorth

Survey Calculations




Survey Calculations

Average Angle Method

÷ø

öçè

æ +´÷ø

öçè

æ +´D=D

2sin

2sin 2121 A AII

MDEast

( ) 75.12

1800sin

2

11sin100200 =÷

ø

öçè

æ +´÷ø

öçè

æ +´-=DEast

Survey Calculations




Survey Calculations

RADIUS OF CURVATURE METHOD

( )12

12 sinsin180

II

IIMDTVD

--D=D

p

( ) ( )( )( )( )( )1212

2

1221

2sinsincoscos180

A AII

A AIIMDNorth

--

--D=D

p

( )

98.991001.1

1sin001.1sin100200180=

-

--=D

p

TVD

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

00.001801001.1

0sin180sin001.1cos1cos1002001802

2

=--

---=D

p North

Survey Calculations




Survey Calculations

RADIUS OF CURVATURE METHOD

( )( )( )( )( )1212

2

2121

2coscoscoscos180

A AII

A AIIMDEast

--

--D=D

p

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

11.101801001.1

180cos0cos001.1cos1cos1002001802

2

-----=D

p East



Survey Methods




Survey Methods

MINIMUM CURVATURE METHOD

( )( )FCIIMD

TVD 21 coscos2

+÷ø

öçè

æD=D

÷ø

öçè

æ´=

2

2tan

2

2 D

DFC

000102.12

034907.0tan

034907.0

2=÷

ø

öç

è

æ´=FC

( ) ( )( )( )

00.100

000102.10175.0cos0175.0cos2

100200

=D

+÷ø

öçè

æ -=D

TVD

TVD

Survey Methods




Survey Methods

MINIMUM CURVATURE METHOD

( ) ( )[ ]( )FC AI AIMD

North 1122 cossincossin2

´+´÷ø

öçè

æD=D

( ) ( )[ ]( )FC AI AIMD

East 1122 sinsinsinsin2

´+´÷ø

öçè

æD=D

( ) ( )( ) ( ) ( )( )[ ]( )

00.0

000127.1000.0cos0175.0sin1416.3cos0175.0sin2

100200

=D

´+´÷ø

öçè

æ -=D

North

North

( ) ( )( ) ( ) ( )( )[ ]( )

00.0

000127.1000.0sin0175.0sin1416.3sin0175.0sin2100200

=D

´+´÷øöç

èæ -=D

East

East

Survey Methods




Su ey et ods

RESULTS

Method ΔTVD ΔN ΔE

Average Angle 99.98 0.00 1.75

Radius of Curv. 99.98 0.00 1.11

Minimum Curv. 100.00 0.00 0.00



Survey Calculations




y

Closure distance and direction isthe North and East coordinate

expressed as polar coordinates

rather than rectangularcoordinates

Closure distance is a2 + b2 = c2

Survey Calculations




y

Closure distance and directionequations

Must subtract the surfacelocation from the North and East

÷ø

öçè

æ= -

North

EastTanDirectionClosure 1

( ) ( )22EastNorthDistanceClosure +=



Survey Calculations




y

Vertical section equations( ) ( )cos vs clVS Az Az Closure Distance= - ´

Survey Calculations




y

Vertical sectionprojected into

the North –

South and East – West planes

0

2000

4000

6000

8000

10,000

12,000

-1000-3000

-5000-7000

-5000

-3000

-1000

N E

SW

Survey Calculations




y

Survey Calculations




y



© 2009 PetroSkills LLC, All Rights Reserved

“Designer”

Well0

250

500

750

1000

1500

1250

17502000

2250

T r u e V e r t i c a l D e p t h ( m )

Final

Wellbore

Pi lot Hole

Much

more

difficult todo a

vertical

section forthis well



Dogleg Severity




g g y

If I1 = 2o

, I2 = 4o

and ΔMD = 100’,then the dogleg severity would

be

If I1 = 2o, I2 = 4o and ΔMD = 50’,

then the dogleg severity would

be

'100/2100

24 °=

-

=DLS

'100/42

2

50

24°=

-= xDLS

Dogleg Severity




If I1 = 10o

, I2 = 10o

, A1 = 10o

, A2 =20o and ΔMD = 100’, what would

the dogleg severity be?

1.74o/100’

Dogleg Severity




Curvature at 90 degrees

Curvature at 10 degrees

Dogleg Severity




For a change in azimuth, thedogleg severity is a function of

the sine of the inclination (Δ A x

sin I)

Dogleg Severity




Dogleg severity equations(English Units)

In the metric system, replace the100 with 30

( )( ) ( )[ ] ( ){ }21212121

1100 I Cos I Cos ACos ACos ASin ASin I Sin I SinCos

MD DLS ´+´+´´÷

ø

öçè

æ

D= -

( )( )( )( )

2

12

2

12

21

1

22

1002

úû

ùêë

é÷ø

öçè

æ -+ú

û

ùêë

é÷ø

öçè

æ -

D= - I I

Sin A A

Sin I Sin I SinSin MD

DLS

Dogleg Severity




To make it a little easier to

understand, the dogleg severity isapproximately equal to the vectorial

sum of the change in inclination and

the change in azimuth

The equation does not work well at

low inclinations

( ) ( )2

12122

122

sin100

úû

ùêë

é-÷

ø

öçè

æ ++-

D= A A

IIII

MDDLS

Dogleg Severity




DLS

( )1212

2sin A A

II-÷

ø

öçè

æ +

12 II - 222 cba =+

The dogleg severity can be estimated by

the above means

( ) ( )2

12122

122

sin100úûùê

ëé -÷

øöç

èæ ++-

D= A AIIII

MDDLS



Dogleg Severity




DLS equations( )( ) ( )[ ] ( ){ }21212121

1coscoscoscossinsinsinsincos

100II A A A AII

MDDLS ´+´+´´÷

ø

öçè

æ

D= -

( ) ( )( ) ( ) ( )( ) ( ) ( )( )[ ] ( ) ( )( ){ }1cos1cos180cos0cos180sin0sin1sin1sincos100200

100 1 ´+´+´´÷ø

öçè

æ

-= -DLS

'100/00.2 °=DLS

( )( ) ( )( )2

12

2

1221

1

2sin

2sinsinsinsin

1002úû

ùêë

é÷ø

öçè

æ -+ú

û

ùêë

é÷ø

öçè

æ -

D= - II A A

IIMD

DLS

( )( )( )

( )( ) ( )( )22

1

2

11sin

2

0180sin1sin1sinsin

100200

1002úû

ùêë

é÷ø

öçè

æ -+ú

û

ùêë

é÷ø

öçè

æ -

-= -DLS

'100/00.2 °=DLS



Dogleg Severity




Problems caused by doglegsØ Torque and drag

Ø Keyseats and casing wear

Ø Fatigue

Dogleg Severity




Torque and dragare caused bythe frictionbetween the dril l

string and thewall of the hole

Higher tension

and doglegsresult in highertorque and drag

Dogleg Severity




Keyseats andcasing wear are

caused by the

drill string being

rotated in a

dogleg with

higher tension

Dogleg Severity




Fatigue iscaused by

rotating the drill

string in a bend

The cyclic

stresses cause

fatigue

Dogleg Severity




The endurancelimit is the

amount of

bending stress

that can be

tolerated

without causing

fatigue with notension

Dogleg Severity




As the amount of tensionincreases in a dogleg, the

amount of bending that can be

tolerated before causing fatiguedecreases





Dogleg Severity




The bending stress can beestimated from Equation 3-4

In Example 3-5, calculate the

maximum dogleg severity withno tension

DLSDpb 218±=s

Dogleg Severity



DLSDpb

218±=s

( )( )( )p

b

DDLS

218±=

s

( )( )( )

feetDLS 100/3.185.4218

18000 o==

Documents

02 Survey Calculations