02 Survey Calculations.pps

SURVEY CALCULATIONSSURVEY CALCULATIONS
ell!ore relative to the surfaceell!ore relative to the surface
locationlocation
Survey CalculationsSurvey Calculations
"ased on the properties of a"ased on the properties of a
ri#ht trian#le or the arc of ari#ht trian#le or the arc of a
circlecircle RIGHT TRIANGLE
$roperties of a ri#ht trian#le$roperties of a ri#ht trian#le
RIGHT TRIANGLE
Opposite Side
Angle A
Hypotenuse Adjacent
Ter%inolo#y used in this !oo&Ter%inolo#y used in this !oo& MD = Measured depth Length o!
the "ell#ore $easured #% the drill
string
hori)ontal departure
hori)ontal displace$ent
Su#script = &he upper surve% o!
t"o surve% points
t"o surve% points
degrees
plane
Co%%onCo%%on
a directionala directional
Tan#ent or (oldTan#ent or (old
)rop)rop
SectionSection
*O$*O$
$OSITIONIN,$OSITIONIN,
The earth is an o!late spheroidThe earth is an o!late spheroid
-a s.uashed sphere/ and %aps-a s.uashed sphere/ and %aps
are flat' hich %a&es it difficultare flat' hich %a&es it difficult
to %ap the earthto %ap the earth

$ositionin#$ositionin#
The earth isThe earth is divided intodivided into latitude andlatitude and lon#itudelon#itude &he e1uator is 0
degrees latitude and poles are 0 degrees

!ro$ pole to pole
degrees
&he pri$e $eridian runs thru the
o#servator% at 3reen"ich, *ngland
Longitude 0 to 40 degrees east and
"est !ro$ that point
Calculatin# the lon#itude andCalculatin# the lon#itude and
latitude of a ell on a %ap canlatitude of a ell on a %ap can
!e very co%plicated!e very co%plicated
Rectan#ular #rids have !eenRectan#ular #rids have !een
developed for use in surveyin#developed for use in surveyin#
A #eodetic datu% is a definitionA #eodetic datu% is a definition
of a %odel for the surface of theof a %odel for the surface of the
earth hich uses a #ridearth hich uses a #rid

The NA)01 or North A%ericanThe NA)01 or North A%erican
)atu% 2301 is the %ost)atu% 2301 is the %ost
co%%only used datu% for Northco%%only used datu% for North
A%erica -NA)45 is also used/A%erica -NA)45 is also used/
E)67 or European )atu% 2367 isE)67 or European )atu% 2367 is
the %ost co%%only used datu%the %ost co%%only used datu%
in the North Seain the North Sea

A %ap pro8ection is aA %ap pro8ection is a
%athe%atical for%ula hich has%athe%atical for%ula hich has
!een desi#ned to convert the!een desi#ned to convert the
latitude9lon#itude %ethod oflatitude9lon#itude %ethod of
positionin# to a flat %appositionin# to a flat %ap
:ith a flat %ap' ell!ores can !e:ith a flat %ap' ell!ores can !e
spotted ith an ; Y coordinatespotted ith an ; Y coordinate
syste% -North' East/syste% -North' East/

The %ost co%%only used %apThe %ost co%%only used %ap
pro8ection is the Universalpro8ection is the Universal
Transverse <ercator -UT</Transverse <ercator -UT</
The La%!ert %ap pro8ection isThe La%!ert %ap pro8ection is
also co%%on throu#hout thealso co%%on throu#hout the
orld and is the %ost co%%onorld and is the %ost co%%on
in the USAin the USA

UT< Syste%UT< Syste%
On %ost %aps' the lines ofOn %ost %aps' the lines of
latitude and lon#itude are curvedlatitude and lon#itude are curved
The .uadran#les for%ed !y theThe .uadran#les for%ed !y the
intersections of these lines areintersections of these lines are
of different si=es and shapes'of different si=es and shapes'
hich co%plicates the locationshich co%plicates the locations
of points and the %easure%entof points and the %easure%ent
of directionsof directions
The UT< syste% tries to solveThe UT< syste% tries to solve
this pro!le%this pro!le%
The orld is divided up into >7The orld is divided up into >7
e.ual =ones' each > de#reese.ual =ones' each > de#rees
ideide
The =ones are fro% 4?@6 de#reesThe =ones are fro% 4?@6 de#rees
North to 47@6 de#rees southNorth to 47@6 de#rees south
$olar re#ions are covered !y$olar re#ions are covered !y
other' special pro8ectionsother' special pro8ections


The outer ed#esThe outer ed#es for the ellipsoidfor the ellipsoid are curvedare curved
The conver#enceThe conver#ence is the differenceis the difference !eteen #rid north!eteen #rid north and true northand true north

Each of the >7 =ones areEach of the >7 =ones are
nu%!ered startin# ith one atnu%!ered startin# ith one at
the 247the 247thth %eridian%eridian
The areas east and est of theThe areas east and est of the
,reenich <eridian are covered,reenich <eridian are covered

$oints on the earth %ay !e$oints on the earth %ay !e
identified !y its =one nu%!er' itsidentified !y its =one nu%!er' its
distance in %eters fro% thedistance in %eters fro% the
e.uator -northin#/ and itse.uator -northin#/ and its
distance in %eters fro% a northBdistance in %eters fro% a northB
south reference line -eastin#/south reference line -eastin#/

To avoid ne#ative values ofTo avoid ne#ative values of eastin#s' the central %eridian ineastin#s' the central %eridian in any =one is assi#ned theany =one is assi#ned the ar!itrary eastin#s value ofar!itrary eastin#s value of 677'777 %677'777 %
Alon# the e.uator a =one isAlon# the e.uator a =one is a!out >77'777 % ide' taperin#a!out >77'777 % ide' taperin# toards the polar re#ionstoards the polar re#ions

+or points north of the e.uator'+or points north of the e.uator'
northin#s are %easured directlynorthin#s are %easured directly
in %eters' ith a value of =ero atin %eters' ith a value of =ero at
the e.uator and increasin#the e.uator and increasin#
toard the northtoard the north

To avoid ne#ative nu%!ers in theTo avoid ne#ative nu%!ers in the
Southern (e%isphere' theSouthern (e%isphere' the
e.uator is assi#ned a value ofe.uator is assi#ned a value of
27'777'777 % and displace%ents27'777'777 % and displace%ents
in the south are %easured ithin the south are %easured ith
decreasin#' !ut positive' valuesdecreasin#' !ut positive' values

The surface location of a ell isThe surface location of a ell is positioned on a %appositioned on a %ap
The surface location of the North andThe surface location of the North and East Coordinates %ay use the %apEast Coordinates %ay use the %ap coordinates or they %ay !e set ascoordinates or they %ay !e set as =ero North and =ero East=ero North and =ero East

Survey calculations are used toSurvey calculations are used to
deter%ine the position of thedeter%ine the position of the
ell!ore relative to the surfaceell!ore relative to the surface
location or a %ap coordinatelocation or a %ap coordinate

<ost co%%on survey %ethods<ost co%%on survey %ethods &angential 5alanced &angential Average Angle Radius o! Curvature Mini$u$ Curvature

Tan#ential %ethod uses only theTan#ential %ethod uses only the
loer survey point and is the leastloer survey point and is the least
accurate survey %ethodaccurate survey %ethod

The tan#ential %ethod assu%esThe tan#ential %ethod assu%es
the ell!ore course is a strai#htthe ell!ore course is a strai#ht
line tan#ent to the loerline tan#ent to the loer
inclination or a=i%uthinclination or a=i%uth
Tan#ential %ethod e.uationsTan#ential %ethod e.uations
2cos I MDTVD ×=

The !alance tan#ential is anThe !alance tan#ential is an
accurate survey %ethod !utaccurate survey %ethod !ut
seldo% usedseldo% used
( )2 coscos 2
I I MD
The avera#e an#le %ethodThe avera#e an#le %ethod
assu%es the ell!ore course isassu%es the ell!ore course is
a strai#ht line tan#ent to thea strai#ht line tan#ent to the
avera#e an#leavera#e an#le I2

The avera#e an#le %ethod isThe avera#e an#le %ethod is
accurate as lon# as the surveys areaccurate as lon# as the surveys are
not too far apart and there is no lar#enot too far apart and there is no lar#e
chan#e in a=i%uth at lo inclinationschan#e in a=i%uth at lo inclinations
Avera#e an#le e.uationsAvera#e an#le e.uations

+

+
×
+

+
×
+×=
MDEast

pro!le%s hen inclinations andpro!le%s hen inclinations and
a=i%uths are e.ual !ecause thea=i%uths are e.ual !ecause the
radius of curvature is infiniteradius of curvature is infinite
Radius of curvature also hasRadius of curvature also has
pro!le%s hen the ell al&spro!le%s hen the ell al&s
past northpast north
( )2
−− −−
A AI I
−− −−
<ini%u% Curvature is the<ini%u% Curvature is the
!alanced tan#ential %ethod !ut!alanced tan#ential %ethod !ut
the strai#ht lines are s%oothedthe strai#ht lines are s%oothed

<ini%u% curvature is suita!le for<ini%u% curvature is suita!le for a co%puter or pro#ra%%a!lea co%puter or pro#ra%%a!le calculator calculator
The inclinations and a=i%uthsThe inclinations and a=i%uths %ust !e chan#ed to radians%ust !e chan#ed to radians !efore enterin# the% in the!efore enterin# the% in the e.uationse.uations

Survey <ethodsSurvey <ethods
− (ote inclination and a)i$uth $ust #e entered in radians
( )( )FC I I MD
TVD 2 coscos 2
×+×
=

Every survey calculation %ustEvery survey calculation %ust
start so%eherestart so%ehere
The !e#innin# is the tieBin pointThe !e#innin# is the tieBin point &he sur!ace location and the 75 or
R& elevation $a% #e the tie8in point
Ma%#e a g%ro "as run in the sur!ace
hole prior to starting the directional
drilling, then the tie8in "ill #e the last
surve% o! the g%ro

The coordinates of the surfaceThe coordinates of the surface
location %ust also !e deter%inedlocation %ust also !e deter%ined 9or $an% land "ells, the depth "ill #e
)ero at the 75, R& or +9
&he (orth and *ast Coordinates $a%
#e )ero and )ero
"hen drilling !ro$ a pad or plat!or$

Example 2 Example 2
Tangential Method Tangential Method At 0 and ,000 !eet the inclination is
0:, there!ore, the "ell#ore position is 0 (orth and 0 *ast;

Calculate >(orth
2 TVDTVDTVD +=
Calculate the *ast coordinate
The process is repeated until allThe process is repeated until all
the surveys are calculatedthe surveys are calculated
2 East East East +=
Avera#e An#le <ethodAvera#e An#le <ethod Calculate the position o! the "ell#ore
at ,@00 !eet using the average angle
$ethod and the surve% data at ,/00
!eet in &a#le 286
2 MDMDMD −=
?00?/00,?@00, =−=MD

+×=
MDTVD
MDNorth

+
×
+×=
MDEast
Radius of Curvature <ethodRadius of Curvature <ethod Calculate the position o! the "ell#ore
at ,B00 !eet using the radius o!
curvature $ethod and the surve%
data at ,@00 !eet in &a#le 28<
2 East East East +=
&he a)i$uth at ,B00 !eet is 2/;/0:
−− −−
2
−− −−
2

Results of the surveyResults of the survey
calculations in Ea%ple 0B0calculations in Ea%ple 0B0
<ethod<ethod TV)TV) NorthNorth EastEast
Tan#entialTan#ential ?5>?@?7?5>?@?7 26>6@0526>6@05 >?4@?7>?4@?7
"alanced Tan#ential"alanced Tan#ential ?517@?>?517@?> 26?0@3426?0@34 >53@11>53@11
Avera#e An#leAvera#e An#le ?517@47?517@47 26?5@0426?5@04 >53@50>53@50

survey calculation %ethodssurvey calculation %ethods
<ethod<ethod TV)TV) NorthNorth EastEast
Tan#entialTan#ential B>@57B>@57 D00@24D00@24 D4@>7D4@>7
"alanced Tan#ential"alanced Tan#ential B7@0?B7@0? B7@71B7@71 B7@75B7@75
Avera#e An#leAvera#e An#le D7@27D7@27 D7@05D7@05 B7@?4B7@?4
Radius of CurvatureRadius of Curvature B7@72B7@72 D7@21D7@21 B7@67B7@67
<ini%u% Curvature<ini%u% Curvature D7@77D7@77 D7@77D7@77 D7@77D7@77

Class $ro!le% B $ro!le% 5 onClass $ro!le% B $ro!le% 5 on
pa#e 0B52pa#e 0B52
MD = 00 MD2 = 200
A = 0o A2 = 40o
coordinate using the average angle
$ethod and the radius o! curvature
$ethod .not $ini$u$ curvature
Avera#e An#leAvera#e An#le 33@3433@34 7@777@77 2@162@16
Radius of Curv@Radius of Curv@ 33@3433@34 7@777@77 2@222@22
<ini%u% Curv@<ini%u% Curv@ 277@77277@77 7@777@77 7@777@77


+×=
MDTVD
( ) 4; 2
cos00200 =

+
×
+×=
MDEast
( )2
−− −−
2
( )( )( )
A AI I
−− −−
2

= −−××−−=
( ) ( )FC I I MD
TVD 2 coscos 2
00200
( ) ( )[ ]( )FC AI AI MD
North 22 cossincossin 2
00200
00200
Avera#e An#leAvera#e An#le 33@3433@34 7@777@77 2@162@16
Radius of Curv@Radius of Curv@ 33@3433@34 7@777@77 2@222@22
<ini%u% Curv@<ini%u% Curv@ 277@77277@77 7@777@77 7@777@77

rather than rectan#ularrather than rectan#ular
coordinatescoordinates

e.uationse.uations
<ust su!tract the surface<ust su!tract the surface

= −
Vertical section is the hori=ontalVertical section is the hori=ontal
len#th of a pro8ection of thelen#th of a pro8ection of the
!orehole into a specific vertical!orehole into a specific vertical
plane and scaled ith theplane and scaled ith the
vertical depthvertical depth

Vertical sectionVertical section
pro8ected intopro8ected into
G :est planes G :est planes
7
0777
?777
>777
4777
27'777
20'777
067067
677677
167167
27772777
26772677
20672067
21672167
07770777
00670067
l ) e p
l ) e p
2 0 6 7
2 0 6 7
2 7 7 7
2 7 7 7
0 6 7
6 7 7
B B ? 6 7
? 0 6 7
? 7 7 7
5 1 6 7
5 6 7 7
5 0 6 7
5 7 7 7
0 1 6 7
7
0 0 6 7
7
7
2 6 7 7
7
2 7 7 7
1 6 7
6 7 7
0 6 7
)o#le# Severity)o#le# Severity
)o#le# severity is a %easure of)o#le# severity is a %easure of
the a%ount of chan#e in thethe a%ount of chan#e in the
inclination and9or a=i%uth of ainclination and9or a=i%uth of a
!orehole' usually epressed in!orehole' usually epressed in
de#rees per 277 feet or de#reesde#rees per 277 feet or de#rees

IfIf I I 22 0 0oo'' I I 00 ? ?oo andand FFMDMD 277J' 277J'
then the do#le# severity ouldthen the do#le# severity ould
!e!e
IfIf I I 22 0 0oo'' I I 00 ? ?oo andand FFMDMD 67J' 67J'
then the do#le# severity ouldthen the do#le# severity ould
!e!e
( ) ?00D2
00
2@ °=
− =DLS
( ) ?00D@
2
2
B0
2@ °=
− = ! DLS
IfIf I I 22 27 27oo'' I I 00 27 27oo'' A A22 27 27oo'' A A00
0707oo andand FFMDMD 277J' hat ould 277J' hat ould
the do#le# severity !eKthe do#le# severity !eK
2@1?2@1?oo 9277J 9277J
&urvature at 90 degrees
&urvature at 10 degrees
+or a chan#e in a=i%uth' the+or a chan#e in a=i%uth' the
do#le# severity is a function ofdo#le# severity is a function of
the sine of the inclination -the sine of the inclination -FF A A
sinsin I I //
)o#le# severity e.uations)o#le# severity e.uations
-En#lish Units/-En#lish Units/
In the %etric syste%' replace theIn the %etric syste%' replace the
277 ith 57277 ith 57
( ) ( ) ( )[ ] ( ){ } 21212121
1100 I Cos I Cos ACos ACos ASin ASin I Sin I SinCos
MD DLS ×+×+××
DLS
To %a&e it a little easier toTo %a&e it a little easier to
understand' the do#le# severity isunderstand' the do#le# severity is
approi%ately e.ual to the vectorialapproi%ately e.ual to the vectorial
su% of the chan#e in inclination andsu% of the chan#e in inclination and
the chan#e in a=i%uththe chan#e in a=i%uth
The e.uation does not or& ell atThe e.uation does not or& ell at
lo inclinationslo inclinations
DLS
( )2 I I − 222 c "a =+
The dogleg severity can be estimated byThe dogleg severity can be estimated by
the above meansthe above means
( ) ( ) 2
Class $ro!le% B $ro!le% 2Class $ro!le% B $ro!le% 2
pa#e 5B25pa#e 5B25 Calculate the dogleg severit% !or the
!ollo"ing surve%s
I I 22 2 2oo I I 00 2 2oo
A A22 7 7oo A A00 247 247oo

)LS e.uations)LS e.uations ( ) ( ) ( )[ ] ( ){ }2222
coscoscoscossinsinsinsincos
MD DLS ×+×+××
00 ×+×+××
00200
002
$ro!le%s caused !y do#le#s$ro!le%s caused !y do#le#s &or1ue and drag
7e%seats and casing "ear
9atigue
Tor.ue and dra#Tor.ue and dra# are caused !yare caused !y the frictionthe friction !eteen the drill!eteen the drill strin# and thestrin# and the all of the holeall of the hole

*eyseats and*eyseats and
drill strin# !ein#drill strin# !ein#
rotated in arotated in a
do#le# ithdo#le# ith
hi#her tensionhi#her tension

+ati#ue is+ati#ue is
caused !ycaused !y
strin# in a !endstrin# in a !end
The cyclicThe cyclic
stresses causestresses cause
fati#uefati#ue
The enduranceThe endurance
a%ount ofa%ount of
!endin# stress!endin# stress
tolerated ithouttolerated ithout
ith no tensionith no tension

As the a%ount of tensionAs the a%ount of tension
increases in a do#le#' theincreases in a do#le#' the
a%ount of !endin# that can !ea%ount of !endin# that can !e
tolerated !efore causin# fati#uetolerated !efore causin# fati#ue
decreasesdecreases
50
7!3
100
4!9

The !endin# stress can !eThe !endin# stress can !e
esti%ated fro% E.uation 5B?esti%ated fro% E.uation 5B?
In Ea%ple 5B6' calculate theIn Ea%ple 5B6' calculate the
%ai%u% do#le# severity ith%ai%u% do#le# severity ith
no tensionno tension

( )( )( )DLSD p" 24±=σ
( ) ( ) ( ) p
4000 o==

02 Survey Calculations.pps

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