Directional Drilling Survey Calculations

7. Directional Drilling Survey Calculations When drilling a directional well, surveys are taken at regular pre-determined pre-determined intervals  intervals in order 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 a particular survey depth and using these data we calculate the North-South (N-S), astWest (-W) coordinates and !"# using few mathematical calculations$ !here are several methods that can %e used to calculate the survey data, of these some are 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 (Least Accurate) Accurate) 'alanced !angential method verage ngle method adius of *urvature method (Most ( Most Accurate) Accurate) +inimum *urvature method (Most ( Most Accurate) Accurate) !he !angent ngential ial,, 'al 'alanc anced ed !angenti ngential al and ver verage age angle angle method method are %ased %ased on the trigonometry trigonometry of a right angle triangle$ TANGENTIAL METHOD s show shown n in the the figu figure re %elo %elow w, I I is the actual actual well% well%ore ore co cours urse$ e$ !o calcul calculate ate the inclination at I , we draw a tangent to I$ !he tangential method states that the tangent draw drawn n at the survey survey statio station n I  is the assumed well%ore course and angle  is the re.uired inclination which is similar to inclination at I $ It uses only the inclination and direction angles measured at the lower end of the survey  course length. Now applying trigonometry to the right angle triangle 'I , we have &

#irectional #rilling & !angential +ethod angle  / angle I I / 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 / #eparture 0North / 0+# SinI 1 *os  $ 0ast / 0+# SinI 1 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 survey intervals were 2 feet or less, the error would %e accepta%le$ !he added e1pense of  surveying every 2 feet prohi%its using the tangential method for calculating the well%ore course especially when more accurate methods are availa%le$ "With my study and practice works performed on live well data, I observed  that the calculations based on Tangential Method gives a considerably large value of departure and in some cases the well appears to be too shallow. In  some 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 and  bottom 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 and direction angles which are used in standard computational procedures$

3rom 'alanced !angential +ethod, following values are o%tained& 0!"# / 0+#4 $ (*osI 5 *osI ) 0North / 0+#4 $ 6(SinI  1 *os) 5 (SinI 1 *os)7 0ast / 0+#4 $ 6(SinI 1 Sin) 5 (SinI 1 Sin)7 This technique provides a smoother curve which shoud more cose! appro"imate the actua we#ore #etween surve!s$ The on%er the distance #etween surve! stations& the %reater the possi#iit! o' error$ A(E)AGE ANGLE METHOD When using the average angle method, the inclination and azimuth at the lower and upper survey stations are mathematically averaged, and then the well%ore course is assumed 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(I5I)4 0North / 0+# $ Sin(I5I)4 $ *os(5)4 0ast / 0+#4 $ Sin(I5I)4 $ Sin(5)4 *ince the avera%e an%e method is #oth 'air! accurate and eas! to cacuate& it is the method that can #e used in the 'ied i' a pro%ramma#e cacuator or computer is not avaia#e$ The error wi #e sma and we within the accurac! needed in the 'ied provided the distance #etween surve!s is not too %reat$

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

!he radius of curvature method is currently considered to %e one of the most accurate methods availa%le$ !he method assumes the well%ore course is a smooth curve %etween the upper and lower survey stations$ !he curvature of the arc is determined %y the survey inclinations and azimuths at the upper and lower survey stations as shown in 3igure %elow$ !he length of the arc %etween I  and I is the measured depth %etween surveys$

Directional Drilling: Radius of Curvature Method

!he following values are o%tained using radius of curvature method& 0!"# / 6(82) (0+#) (SinI  9 SinI )7 4 : (I  - I) 0North / 6(82) (0+#) (*osI  9 *osI) (Sin 9 Sin) 7 4 : (I - I) ( - ) 0ast / 6(82) (0+#) (*osI  9 *osI) (*os 9 *os) 7 4 : (I - I) ( - ) #; / 6(82) (0+#) (*osI  9 *osI )7 4 : (I - I) r / 82 4 : (#