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7. Directional Drilling Survey Calculations

When drilling a directional well, surveys are taken at regular pre-determinedintervals inorder to determine the present downhole location compared to surface location.

In directional survey we note down the inclination and azimuth at the survey point for aparticular survey depth and using these data we calculate the North-South (N-S), ast-West (-W) coordinates and !"# using few mathematical calculations$!here are several methods that can %e used to calculate the survey data, of these someare accurate while are other may produce some error for a given situation$Some of the most common methods used for survey calculation in the industry are&!angential method (Least Accurate)'alanced !angential methodverage ngle methodadius of *urvature method (Most Accurate)+inimum *urvature method (Most Accurate)

!he !angential, 'alanced !angential and verage angle method are %ased on thetrigonometry of a right angle triangle$

TANGENTIAL METHOD

s shown in the figure %elow, II is the actual well%ore course$ !o calculate theinclination at I, we draw a tangent to I$ !he tangential method states that the tangentdrawn at the survey station I is the assumed well%ore course and angle is there.uired inclination which is similar to inclination at I$It usesonly the inclination and direction angles measured at the lower end of the surveycourse length.Now applying trigonometry to the right angle triangle 'I, we have &

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#irectional #rilling & !angential +ethodangle / angle II/ assumed well course / 0+# (change in measured depth for this interval)' / I *os I/ 0!"# (!his will %e e.ual to the !"# for this interval)'I / #eparture0North / 0+# SinI1 *os $0ast / 0+# SinI1 Sin $

It is clear from the a%ove figure that the !angential method gives a noticea%le error in+easured #epth (+#) and #eparture$In !ype I, III and I" holes, the error will %e significant$

With the tangential method, the greater the %uild or drop rate, the greater the error$lso, the distance %etween surveys has an effect on the .uantity of the error$ If surveyintervals were 2 feet or less, the error would %e accepta%le$ !he added e1pense ofsurveying every 2 feet prohi%its using the tangential method for calculating thewell%ore course especially when more accurate methods are availa%le$

"With my study and practice works performed on live well data, I observedthat the calculations based on Tangential Method gives a considerably largevalue of departure and in some cases the well appears to be too shallow. Insome deviated wells, the error in TV was more than !#$ feet."

BALANCED TANGENTIAL METHOD

The balanced tangential method uses the inclination and direction angles at the top andbottom of the course length to tangentially balance the two sets of measured angles.!his method com%ines the trigonometric functions to provide the average inclination anddirection angles which are used in standard computational procedures$

Directional Drilling: Balanced Tangential Method

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3rom 'alanced !angential +ethod, following values are o%tained&0!"# / 0+#4 $ (*osI5 *osI)0North / 0+#4 $ 6(SinI1 *os) 5 (SinI1 *os)70ast / 0+#4 $ 6(SinI1 Sin) 5 (SinI1 Sin)7

This technique provides a smoother curve which shoud more cose!appro"imate the actua we#ore #etween surve!s$ The on%er the distance#etween surve! stations& the %reater the possi#iit! o' error$

A(E)AGE ANGLE METHOD

When using the average angle method, the inclination and azimuth at the lower andupper survey stations are mathematically averaged, and then the well%ore course isassumed to %e tangential to the average inclination and azimuth$

Directional Drilling: Average Angle Method

3rom verage ngle +ethod, following values are o%tained&0!"# / 0+# $ *os(I5I)40North / 0+# $ Sin(I5I)4 $ *os(5)40ast / 0+#4 $ Sin(I5I)4 $ Sin(5)4

*ince the avera%e an%e method is #oth 'air! accurate and eas! to cacuate& itis the method that can #e used in the 'ied i' a pro%ramma#e cacuator or

computer is not avaia#e$ The error wi #e sma and we within the accurac!needed in the 'ied provided the distance #etween surve!s is not too %reat$

)ADI+* O, C+)(AT+)E METHOD

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!he radius of curvature method is currently considered to %e one of the most accuratemethods availa%le$ !he method assumes the well%ore course is a smooth curve %etweenthe upper and lower survey stations$ !he curvature of the arc is determined %y thesurvey inclinations and azimuths at the upper and lower survey stations as shown in3igure %elow$ !he length of the arc %etween I and Iis the measured depth %etweensurveys$

Directional Drilling: Radius of Curvature Method

!he following values are o%tained using radius of curvature method&

0!"# / 6(82) (0+#) (SinI9 SinI)7 4 : (I - I)0North / 6(82)(0+#) (*osI9 *osI) (Sin9 Sin) 7 4 :

(I - I) (- )0ast / 6(82)(0+#) (*osI9 *osI) (*os9 *os) 7 4 :

(I - I) (- )#; / 6(82) (0+#) (*osI9 *osI)7 4 : (I - I)r / 82 4 : (#

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Note& In these e.uations, the inclination and azimuth are in degrees$

Since the calculation using this method %ecomes a tedious Bo%, this method is not usedin field practise unless a programmed software is availa%le %ased on this method$I have hands#on e%perience on few well planning softwares based on thismethod. In the coming blogs, we will discuss on "irectional Well &laning" andfor calculation purpose, I will show you that how these softwares are utili'edto design a directional well.

Here& its worth mentionin% that when the vaue o' incination -I. and a/imuth-A. are same at #oth surve! stations& then the denominator 'or some o' thea#ove equation #ecomes /ero and hence the equation is not de'ined$ This is theE))O) we 'ound usin% 0)adius o' Curvature Method0$

*O HO1 CAN 1E O(E)COME THI* E))O)22

One o' the wa! to overcome this error is to use 0Minimum Curvature Method0

which has #een discussed #eow$

The second method i would suggest is that, we can add any small number (say) % )#! or ) % )#$* to either survey points. The result thus produced will beinsignificant .. +

MINIM+M C+)(AT+)E METHOD

Posted by Deepak Choudhary at :!":## AM

$abels: Average Angle Method%Balanced Tangential Method%Controlled Directional Drilling% Mini&u&

Curvature Method% '()C% Radius of Curvature Method%*urvey Calculations%Tangential Method%

+++.ongcindia.co&

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