Survey Calculations Directional and Horizontal Drilling

Chapter 2 SURVEY CALCULATIONS INTRODUCTION

Directional surveys are taken at specified intervals in order to determine the position of the bottom of the hole relative to the surface location. The surveys are converted to a North-South (N-S), East-West (E-W) and true vertical depth coordinates using one of several calculation methods. The coordinates are then plotted in both the horizontal and vertical planes. By plotting the survey data, the rig personnel can watch the progress of the well and make changes when necessary to hit a specified target.

There are several methods that can be used to calculate survey data; however, some are more accurate than others. Some of the most common methods that have been used in the industry are:

1. Tangential,

2. Balanced Tangential,

3. Average Angle,

4. Radius of Curvature and

5. Minimum Curvature

Of these methods, the tangential method is the least accurate, and the radius of curvature and the minimum curvature are the most accurate. The industry uses primarily minimum curvature.

The first three calculation methods are based on the trigonometry of a right triangle; therefore, a review of these trigonometric functions would be in order.

By definition, a right triangle has one angle which is equal to 90. The sum of the other two angles is 90. Therefore, the sum of all three angles is 180. Referring to the triangle in Figure 2-1, the angles are A, B, and C with C being the right angle (90).

C = 90

A + B = 90

A + B + C = 180

In Figure 2-1, the length of the triangle sides are designated a, b, and c. Therefore we can say that for a right triangle: when c is the hypotenuse of the triangle. The hypotenuse is always the side opposite the right angle (90). The length of the hypotenuse can be determined by rearranging the equation to read:

222 cba =+

22 bac +=

Copyright 2004 OGCI/PetroSkills. All rights reserved. 2-1

H o r i z o n t a l a n d D i r e c t i o n a l D r i l l i n g C h a p t e r 2

Figure 2-1. Right Triangle

The following equations also apply to a right triangle.

Sine of angle A

ca

hypotenusesideoppositeASin ==

Cosine of angle A

cb

hypotenusesideadjacentACos ==

Tangent of angle A

ba

sideadjacentsideoppositeATan ==

2-2 Copyright 2004 OGCI/PetroSkills. All rights reserved

H o r i z o n t a l a n d D i r e c t i o n a l D r i l l i n g S u r v e y C a l c u l a t i o n s


Sine of angle B

cb

hypotenusesideoppositeBSin ==

Cosine of angle B

ca

hypotenusesideadjacentBCos ==

Tangent of angle B

ab

sideadjacentsideoppositeBTan ==

The values of sine, cosine and tangent of angles from 0 to 90o are given in the Appendix.

Example 2-1 Given: Well XYZ in Figure 2-2, assume the triangle represents the plan view of a

well. In this well, B is the surface location and A is the position of the bottom of the hole. The length "b" would then be the East coordinate and is equal to 450 feet. The length "a" would be the North coordinate and is equal to 650 feet.

Determine: 1. The closure distance (length c), and

2. The closure direction (angle B).

Solution: To aid in solving the problem, a plan view similar to Figure 2-2 should be constructed and labeled. Then, use the trigonometric functions of a right triangle to solve the problem.

1. Calculate the closure distance:

222 bac += 22 bac +=

( ) ( )22 650450 +=c ftc 57.790=

2. Calculate the closure direction. The direction of a borehole is always given in azimuth from 0 to 360 or from the north or south such as:

WN '1348


EN '4310

ES '042

WS '3224

In this example, angle "B" would be the closure direction. Solving for angle "B":

'57.790'450 ==

hypotenusesideoppositeBSin

5692.0=BSin .

= 70.34B (See Appendix for Sine table and interpolate)

Figure 2-2. Horizontal Plan View of Well XYZ

North: 650, East: 450,

Closure Distance: 790.57, Closure Direction: N34o42E (Azimuth 34.70)




The closure direction can be expressed in azimuth as 34.70 or it can be expressed in the coordinate system. Converting the decimal to minutes:

Minutes = (decimal)(60)

Minutes = (0.70) (60)

Minutes = 42'

Therefore, the closure distance and direction are: 790.57' and N3442' E.

Presented next is a brief explanation of the most commonly used survey calculation methods and the appropriate calculations.

TANGENTIAL

At one time the tangential method was the most widely used because it was the easiest (Table 2-1). The equations are relatively simple, and the calculations can be performed easily in the field. Unfortunately, the tangential method is the least accurate method and results in errors greater than all the other methods. The tangential method should not be used to calculate directional surveys. It is only presented here to prove a point.

The tangential method assumes the wellbore course is tangential to the lower survey station, and the wellbore course is a straight line. Because of the straight line assumption, the tangential method yields a larger value of horizontal departure and a smaller value of vertical displacement when the inclination is increasing. This is graphically represented in Figure 2-3.

Figure 2-3. Illustration of Tangential Calculation Method

In Figure 2-3, Line is the assumed wellbore course. The dashed line AB is the change in true vertical depth and the dashed line is the departure in the horizontal direction. The opposite is true when the inclination is decreasing. In Type I, III and IV holes, the error will be significant. In a Type II hole, the error calculated while increasing angle will be offset by the error calculated while decreasing angle but only when the build and drop rates are comparable.

2AI

2BI


With the tangential method, the greater the build or drop rate, the greater the error. Also, the distance between surveys has an effect on the quantity of the error. If survey intervals were 10 feet or less, the error would be acceptable. The added expense of surveying every 10 feet prohibits using the tangential method for calculating the wellbore course especially when more accurate methods are available.

The North-South, East-West coordinates are determined by assuming the horizontal departure of the course length is in the same direction as the azimuth recorded at the lower survey station, but this assumption is wrong. The actual wellbore course will be a function of the upper and lower survey stations. Therefore, the tangential method results in an additional error because an error already exists due to the method used to calculate the horizontal departure. The error is compounded when the North-South, East-West coordinates are calculated.

Table 2-1. Directional Survey Calculation Formula

Tangential

2ICosMDTVD = Equation 2-122 ACosISinMDNorth = Equation 2-2

22 ASinISinMDEast = Equation 2-3

Balanced Tangential

( )212 ICosICosMDTVD += Equation 2-4

( ) ([ ]22112 ACosISinACosISinMDNorth += ) Equation 2-5

( ) ([ ]22112 ASinISinASinISinMDEast += ) Equation 2-6Average Angle

+=2

21 IICosMDTVD Equation 2-7

+

+=22

2121 AACosIISinMDNorth Equation 2-8

+

+=22

2121 AASinIISinMDEast Equation 2-9




Radius of Curvature

( )( )(( )

)12

12180II

ISinISinMDTVD = Equation 2-10

( ) ( )( )( )( )( )12122

12212180

AAIIASinASinICosICosMDNorth

= Equation 2-11

( )( )( )( )( )12122

21212180

AAIIACosACosICosICosMDEast

= Equation 2-12

( )(( )

)12

21180II

CosICosIMDDEP = Equation 2-13

( )( )DLSr 180= Equation 2-14

rBIIMD 12 = Equation 2-15

Minimum Curvature

( ) FCICosICosMDTVD 212 +

= ( ) Equation 2-16( ) ([ ( )FCACosISinACosISinMDNorth 11222 +

= )] Equation 2-17

( ) ([ ]( )FCASinISinASinISinMDEast 11222 +

= ) Equation 2-18( ) ( )[ ]{ 121212 11 AACosISinISinIICosD }= Equation 2-19

1112 2

1

= D

TanD Equation 2-20

=22

22 DTan

DFC Equation 2-21

Note: Use inclinations and azimuths in radians only

Calculations for Closure

= NorthEastTanDirectionClosure 1 Equation 2-22

( ) ( )22 EastNorthDistanceClosure += Equation 2-23


Vertical Section

( ) ( DistanceClosureAzAzCosVS clvs = ) Equation 2-24Dogleg Severity

( ) ( ) ( )[ ] ({ }212121211100 ICosICosACosACosASinASinISinISinCosMDDLS ++

=

)or

( )( ) 212212211 22200

+

= IISinAASinISinISinSin

MDDLS

Equation 2-25

Equation 2-26

BALANCED TANGENTIAL

The balanced tangential method is similar to the tangential method in that the wellbore course is determined by the tangent to the angle. The difference between the two methods is the balanced tangential uses both the upper and lower survey stations. The top half of the wellbore course is approximated by the upper inclination line in Figure 2-4 and the lower half of the wellbore course is approximated by the lower inclination line . The azimuth is approximated in the same manner. Both the upper and lower portions of the assumed wellbore course are in error, but the errors are opposite and will nearly cancel each other. Therefore, the balanced tangential method is accurate enough for field applications. The balanced tangential equations are more difficult to perform (Table 2-1) and are more likely to result in an error because of mechanical mistakes while making the calculations.

AI12AI

Figure 2-4. Illustration of Balanced Tangential Calculation Method




AVERAGE ANGLE

When using the average angle method, the inclination and azimuth at the lower and upper survey stations are mathematically averaged, and then the wellbore course is assumed to be tangential to the average inclination and azimuth. The calculations are very similar to the tangential method (Table 2-1), and the results are as accurate as the balanced tangential method. Since the average angle method is both fairly accurate and easy to calculate, it is the method that can be used in the field if a programmable calculator or computer is not available. The error will be small and well within the accuracy needed in the field provided the distance between surveys is not too great. The average angle method is graphically illustrated in Figure 2-5. The average angle method does have problems at low inclinations with large changes in azimuth so it should not be used for vertical wells.

221 II +

Figure 2-5. Illustration of Average Angle Calculation Method

RADIUS OF CURVATURE

The radius of curvature method is currently considered to be one of the most accurate methods available. The method assumes the wellbore course is a smooth curve between the upper and lower survey stations. The curvature of the arc is determined by the survey inclinations and azimuths at the upper and lower survey stations as shown in Figure 2-6. The length of the arc between and is the measured depth between surveys. In the previous methods, the wellbore course was assumed to be one or two straight lines between the upper and lower survey points. The curvature of the wellbore course assumed by the radius of curvature method will more closely approximate the actual well; therefore, it is more accurate. Unfortunately, the equations are complicated (Table 2-1) and are not easily calculated in the field without a programmable calculator or computer.

1I 2I

A closer inspection of the radius of curvature equations show that if the inclination or azimuth are equal for both survey points, a division by zero will result in an error. In Figure 2-6 the radius, r, will become infinitely long. In that case, the minimum curvature or average angle


methods can be used to make the calculations. It is also possible to add a small number (such as 1 x 10-4) to either survey point. The resulting error will be insignificant.

Generally, the radius of curvature calculations are used when planning a well. Using one of the three previous methods to plan a well will result in substantial errors when calculating over long intervals. This will be further explained in the section on planning a well.

Figure 2-6. Illustration of Radius of Curvature Calculation Method

MINIMUM CURVATURE

The minimum curvature method is similar to the radius of curvature method in that it assumes that the wellbore is a curved path between the two survey points. The minimum curvature method uses the same equations as the balanced tangential multiplied by a ratio factor which is defined by the curvature of the wellbore. Therefore, the minimum curvature provides a more accurate method of determining the position of the wellbore. Like the radius of curvature, the equations are more complicated and not easily calculated in the field without the aid of a programmable calculator or computer. The equations can be found in Table 2-1.

Figure 2-7 is a graphic representation of the minimum curvature calculations. The balanced tangential calculations assume the wellbore course is along the line 21 AIAI + . The calculation of the ratio factor changes the wellbore course to 21 BIBI + which is the arc of the angle . This is mathematically equivalent to the radius of curvature for a change in inclination only.

B

So long as there are no changes in the wellbore azimuth, the radius of curvature and minimum curvature equations will yield the same results. If there is a change in the azimuth, there can be a difference in the calculations. The minimum curvature calculations assume a curvature that is the shortest path for the wellbore to incorporate both surveys. At low inclinations with large changes in azimuth, the shortest path may also involve dropping inclination as well as turning. The minimum curvature equations do not treat the change in inclination and azimuth separately as do the radius of curvature calculations.




Figure 2-7. Illustration of Minimum Curvature Calculation Method

Table 2-2. Surveys for a Near Vertical Well

MEASURED DEPTH (feet)

DRIFT ANGLE (degrees)

DRIFT AZIMUTH (degrees)

0.00 0.00 0.00

100.00 1.00 94.80

200.00 1.50 140.00

300.00 1.75 186.00

400.00 1.50 120.00

500.00 2.00 240.00

600.00 2.00 350.00

700.00 1.50 260.00

800.00 1.25 200.00

900.00 1.75 180.00

1,000.00 1.50 340.00 The tangential and average angle methods treat the inclination and azimuth separately. Therefore, larger horizontal displacements will be calculated. The radius of curvature method assumes the well must stay within the survey inclinations and will also yield a larger horizontal displacement though not as large as the tangential and average angle. The minimum curvature equations are more complex than the radius of curvature equations but are more tolerant. Minimum curvature has no problem with the change in azimuth or inclination being equal to zero. When the wellbore changes from the northeast quadrant to the northwest quadrant, no adjustments have to be made. The radius of curvature method requires adjustments. If the previous survey azimuth is 10 and the next survey is 355, the well walked left 15. The radius of curvature equations assume the well walked right 345 which is not true. One of the two


survey azimuths must be changed. The lower survey can be changed from 355 to -5, and then the radius of curvature will calculate the correct coordinates.

Table 2-2 shows survey data for a near vertical well to 1,000 feet. The survey data exhibits large changes in azimuth which is common in near vertical wells. Figure 2-8 shows a plot of that survey data. Note that the minimum curvature calculations always yield the least amount of departure. There will also be a slight difference in TVD. The minimum curvature calculations are recommended for near vertical wells and for the vertical portions of a directional well.

The minimum curvature equations are more complex than the radius of curvature equations but are more tolerant. Minimum curvature has no problem with the change in azimuth or inclination being equal to zero. When the wellbore changes from the northeast quadrant to the northwest quadrant, no adjustments have to be made. The radius of curvature method requires adjustments. If the previous survey azimuth is 10 and the next survey is 355, the well walked left 15. The radius of curvature equations assume the well walked right 345 which is not true. One of the two survey azimuths must be changed. The lower survey can be changed from 355 to -5, and then the radius of curvature will calculate the correct coordinates.

Figure 2-8. Plan View




Example 2-2 Given: The survey data for Directional Well No. 1 are shown in Table 2-3.

Determine: The wellbore position at each survey point using the tangential, balanced tangential, average angle, radius of curvature, and minimum curvature method.

Table 2-3. Survey for Example 2-2

MEASURED DEPTH (feet)

DRIFT ANGLE (degrees)

DRIFT AZIMUTH (degrees)

0.00 1,000.00 1,100.00 1,200.00 1,300.00

0.00 0.00 3.00 6.00 9.00

N 0.00E N 0.00E N21.70E N26.50E N23.30E

1,400.00 1,500.00 1,600.00 1,700.00 1,800.00

12.00 15.00 18.00 21.00 24.00

N20.30E N23.30E N23.90E N24.40E N23.40E

1,900.00 2,000.00 2,100.00 2,200.00 2,300.00

27.00 30.00 30.20 30.40 30.30

N23.70E N23.30E N22.80E N22.50E N22.10E

2,400.00 2,500.00 2,600.00 2,700.00 2,800.00

30.60 31.00 31.20 30.70 31.40

N22.40E N22.50E N21.60E N20.80E N20.90E

2,900.00 3,000.00 3,100.00 3,200.00 3,300.00

30.60 30.50 30.40 30.00 30.20

N22.00E N22.50E N23.90E N24.50E N24.90E

3,400.00 3,500.00 3,600.00 3,700.00 3,800.00

31.00 31.10 32.00 30.80 30.60

N25.70E N25.50E N24.40E N24.00E N22.30E


3,900.00 4,000.00 4,100.00 4,200.00 4,300.00

31.20 30.80 30.00 29.70 29.80

N21.70E N20.80E N20.80E N19.80E N20.80E

4,400.00 4,500.00 4,600.00 4,700.00 4,800.00

29.50 29.20 29.00 28.70 28.50

N21.10E N20.80E N20.60E N21.40E N21.20E

Solution: Tangential Method

At 0 and 1,000 feet the inclination is 0, therefore, the wellbore position is 0 North and 0 East.

A survey at 1,100 feet shows the inclination to be 3o in the N21.7E direction (Azimuth = 21.7). Calculate the position of the wellbore at 1,100 feet. (The nomenclature is defined at the end of the chapter.)

12 MDMDMD =

000,1100,1 =MD '100=MD

The direction of the wellbore is given as N21.7E; however, in the equations, A must equal a value between 0 and 360 where:

N = 360 or 0

E = 90

S = 180

W = 270

When referring to the hole direction as being N21.7E, it is 21.7 East of North. Therefore, the azimuth is equal to 0+21.7 or 21.7.

Using the tangential method, calculate TVD ( )( )2ICosMDTVD = ( )( )= 3100 CosTVD

ftTVD 86.99=




Calculate the true vertical depth.

12 TVDTVDTVD +=

000,186.992 +=TVD

ftTVD 86.099,12 =

Calculate North( )( )( )22 ACosISinMDNorth = ( )( )( )= 7.213100 CosSinNorth

'86.4=North Calculate the North coordinate.

12 NorthNorthNorth +=

'0'86.42 +=North

ftNorth 86.42 =

Calculate East( )( )( )22 ASinISinMDEast = ( )( )( )7.213100 SinSinEast =

'94.1=East Calculate the East coordinate.

12 EastEastEast +=

'0'94.12 +=East

'94.12 =East

Calculate the position of the wellbore at the next survey point of 1,200.

12 MDMDMD =

'100,1'200,1 =MD '100=MD


The direction is N26.5E at 1,200 feet; therefore, the azimuth is 26.5.

( )( )2ICosMDTVD = ( )( )= 6100 CosTVD

'45.99=TVD

12 TVDTVDTVD +=

'86.099,1'45.992 +=TVD

'31.199,12 =TVD

( )( )( )22 ACosISinMDNorth = ( )( )( )= 5.266100 CosSinNorth

'35.9=North


'86.4'35.92 +=North

'21.142 =North

( )( )( )22 ASinISinMDEast = ( )( )( )= 5.266100 SinSinEast

ftEast 66.4=

12 EastEastEast +=

'94.1'66.42 +=East

ftEast 60.62 =

The same calculations are made at each survey depth, and the results are shown in Table 2-4.

Balanced Tangential Method

Calculate the position of the wellbore at 1,300 feet using the balanced tangential method given the values at 1,200 feet from Table 2-5.




12 MDMDMD =

'200,1'300,1 =MD ftMD 100=

The azimuth at 1,300 feet is 23.30.

( )122 ICosICosMDTVD +

=

( )+

= 692

100 CosCosTVD

'11.99=TVD

12 TVDTVDTVD +=

'59.199,1'11.992 +=TVD

ftTVD 70.298,12 =

( )22112 ACosISinACosISinMDNorth +

=

( )+

= 30.2395.2662

100 CosSinCosSinNorth

'86.11=North


'54.9'86.112 +=North

'40.212 =North

( )22112 ASinISinASinISinMDEast +

=

( )+

= 30.2395.2662

100 SinSinSinSinEast

'43.5=East

12 EastEastEast +=


Table 2-4. Survey Calculations for Directional Well No. 1 using the Tangential Method

RECTANGULAR COORDINATES

MEASUREDDEPTH

(feet)

INCLIN-ATION

(degrees)

AZIMUTH

(degrees)

COURSE LENGTH

(feet)

TRUE VERTICAL

DEPTH

(feet) NORTH EAST

VERTICAL SECTION 10 DEG

(feet)

DOGLEG SEVERITY

(deg/100)

0.00 1,000.00 1,100.00 1,200.00 1,300.00

0.00 0.00 3.00 6.00 9.00

0.00 0.00

21.70 26.50 23.30

0.00 1000.00 100.00 100.00 100.00

0.00 1,000.00 1,099.86 1,199.32 1,298.08

0.00 0.00 4.86

14.22 28.58

0.00 0.00 1.94 6.60

12.79

0.00 0.00 5.12

15.15 30.37

0.00 0.00 3.05 3.02 3.03

1,400.00 1,500.00 1,600.00 1,700.00 1,800.00

12.00 15.00 18.00 21.00 24.00

20.30 23.30 23.90 24.40 23.40

100.00 100.00 100.00 100.00 100.00

1,395.90 1,492.49 1,587.60 1,680.96 1,772.31

48.08 71.86

100.11 132.74 170.07

20.00 30.24 42.76 57.56 73.71

50.83 76.01

106.01 140.72 180.29

3.05 3.08 3.00 3.00 3.02

1,900.00 2,000.00 2,100.00 2,200.00 2,300.00

27.00 30.00 30.20 30.40 30.30

23.70 23.30 22.80 22.50 22.10

100.00 100.00 100.00 100.00 100.00

1,861.41 1,948.01 2,034.44 2,120.69 2,207.03

211.64 257.56 303.94 350.69 397.43

91.96 111.74 131.23 150.60 169.58

224.40 273.06 322.11 371.51 420.84

3.00 3.01 0.32 0.25 0.23

2,400.00 2,500.00 2,600.00 2,700.00 2,800.00

30.60 31.00 31.20 30.70 31.40

22.40 22.50 21.60 20.80 20.90

100.00 100.00 100.00 100.00 100.00

2,293.11 2,378.82 2,464.36 2,550.34 2,635.70

444.50 492.08 540.25 587.97 636.65

188.98 208.69 227.76 245.89 264.47

470.56 520.84 571.59 621.74 672.90

0.34 0.40 0.51 0.65 0.70

2,900.00 3,000.00 3,100.00 3,200.00 3,300.00

30.60 30.50 30.40 30.00 30.20

22.00 22.50 23.90 24.50 24.90

100.00 100.00 100.00 100.00 100.00

2,721.77 2,807.94 2,894.19 2,980.79 3,067.22

683.84 730.73 777.00 822.50 868.12

283.54 302.96 323.47 344.20 365.38

722.69 772.24 821.36 869.77 918.38

0.98 0.27 0.72 0.50 0.28

3,400.00 3,500.00 3,600.00 3,700.00 3,800.00

31.00 31.10 32.00 30.80 30.60

25.70 25.50 24.40 24.00 22.30

100.00 100.00 100.00 100.00 100.00

3,152.93 3,238.56 3,323.37 3,409.26 3,495.34

914.53 961.15

1,009.41 1,056.19 1,103.29

387.72 409.95 431.84 452.67 471.99

967.96 1,017.74 1,069.06 1,118.75 1,168.48

0.90 0.14 1.07 1.22 0.89

3,900.00 4,000.00 4,100.00 4,200.00 4,300.00

31.20 30.80 30.00 29.70 29.80

21.70 20.80 20.80 19.80 20.80

100.00 100.00 100.00 100.00 100.00

3,580.87 3,666.77 3,753.37 3,840.23 3,927.01

1,151.42 1,199.28 1,246.03 1,292.64 1,339.10

491.14 509.32 527.08 543.86 561.51

1,219.21 1,269.51 1,318.62 1,367.44 1,416.26

0.67 0.61 0.80 0.58 0.51

4,400.00 4,500.00 4,600.00 4,700.00 4,800.00

29.50 29.20 29.00 28.70 28.50

21.10 20.80 20.60 21.40 21.20

100.00 100.00 100.00 100.00 100.00

4,014.05 4,101.05 4,188.80 4,276.51 4,364.40

1,385.04 1,430.65 1,476.03 1,520.74 1,565.23

579.24 596.56 613.62 631.14 648.40

1,464.58 1,512.50 1,560.16 1,607.23 1,654.04

0.33 0.33 0.22 0.49 0.22




Table 2-5. Survey Calculations for Directional Well No. 1 using the Balanced Tangential Method

RECTANGULAR COORDINATES MEASURED

DEPTH

(feet)

INCLIN-ATION

(degrees)

AZIMUTH

(degrees)

COURSE LENGTH

(feet)

TRUE VERTICAL

DEPTH

(feet) NORTH EAST


(feet)

DOGLEG SEVERITY

(deg/100)

0.00 1,000.00 1,100.00 1,200.00 1,300.00

0.00 0.00 3.00 6.00 9.00

0.00 0.00

21.70 26.50 23.30

0.00 1000.00 100.00 100.00 100.00

0.00 1,000.00 1,099.93 1,199.59 1,298.70

0.00 0.00 2.43 9.54

21.40

0.00 0.00 0.97 4.27 9.69

0.00 0.00 2.56

10.14 22.76

0.00 0.00 3.05 3.02 3.03

1,400.00 1,500.00 1,600.00 1,700.00 1,800.00

12.00 15.00 18.00 21.00 24.00

20.30 23.30 23.90 24.40 23.40

100.00 100.00 100.00 100.00 100.00

1,396.99 1,494.20 1,590.04 1,684.28 1,776.63

38.33 59.97 85.98

116.43 151.41

16.39 25.12 36.50 50.16 65.64

40.60 63.42 91.01

123.37 160.51

3.05 3.08 3.00 3.00 3.02

1,900.00 2,000.00 2,100.00 2,200.00 2,300.00

27.00 30.00 30.20 30.40 30.30

23.70 23.30 22.80 22.50 22.10

100.00 100.00 100.00 100.00 100.00

1,866.86 1,954.71 2,041.23 2,127.57 2,213.86

190.86 234.60 280.75 327.31 374.06

82.84 101.85 121.49 140.92 160.09

202.34 248.73 297.58 346.81 396.18

3.00 3.01 0.32 0.25 0.23

2,400.00 2,500.00 2,600.00 2,700.00 2,800.00

30.60 31.00 31.20 30.70 31.40

22.40 22.50 21.60 20.80 20.90

100.00 100.00 100.00 100.00 100.00

2,300.07 2,385.96 2,471.59 2,557.35 2,643.02

420.97 468.29 516.16 564.11 612.31

179.28 198.83 218.22 236.82 255.18

445.70 495.70 546.22 596.66 647.32

0.34 0.40 0.51 0.65 0.70

2,900.00 3,000.00 3,100.00 3,200.00 3,300.00

30.60 30.50 30.40 30.00 30.20

22.00 22.50 23.90 24.50 24.90

100.00 100.00 100.00 100.00 100.00

2,728.74 2,814.85 2,901.06 2,987.49 3,074.00

660.24 707.29 753.87 799.75 845.31

274.01 293.25 313.22 333.83 354.79

697.79 747.47 796.80 845.57 894.08

0.98 0.27 0.72 0.50 0.28

3,400.00 3,500.00 3,600.00 3,700.00 3,800.00

31.00 31.10 32.00 30.80 30.60

25.70 25.50 24.40 24.00 22.30

100.00 100.00 100.00 100.00 100.00

3,160.08 3,245.75 3,330.96 3,416.31 3,502.30

891.33 937.84 985.28

1,032.80 1,079.74

376.55 398.83 420.90 442.26 462.33

943.17 992.85

1,043.40 1,093.91 1,143.62

0.90 0.14 1.07 1.22 0.89

3,900.00 4,000.00 4,100.00 4,200.00 4,300.00

31.20 30.80 30.00 29.70 29.80

21.70 20.80 20.80 19.80 20.80

100.00 100.00 100.00 100.00 100.00

3,588.10 3,673.82 3,760.07 3,846.80 3,933.62

1,127.35 1,175.35 1,222.65 1,269.33 1,315.87

481.56 500.23 518.20 535.47 552.69

1,193.85 1,244.36 1,294.06 1,343.03 1,391.85

0.67 0.61 0.80 0.58 0.51

4,400.00 4,500.00 4,600.00 4,700.00 4,800.00

29.50 29.20 29.00 28.70 28.50

21.10 20.80 20.60 21.40 21.20

100.00 100.00 100.00 100.00 100.00

4,020.53 4,107.69 4,195.07 4,282.66 4,370.46

1,362.07 1,407.84 1,453.34 1,498.38 1,542.98

570.37 587.90 605.09 622.38 639.77

1,440.42 1,488.54 1,536.33 1,583.70 1,630.64

0.33 0.33 0.22 0.49 0.22


'27.4'43.52 +=East

ftEast 70.92 =


Average Angle Method

Calculate the position of the wellbore at 1,400 feet using the averaging angle method and the survey data at 1,300 feet in Table 2-6.

12 MDMDMD =

'300,1'400,1 =MD ftMD 100=


+=2

21ICosMDTVD

+=2129100 CosTVD

ftTVD 33.98=

12 TVDTVDTVD +=

'80.298,1'33.982 +=TVD

ftTVD 13.397,12 =

+

+=22

2121 AACosIISinMDNorth

+

+=2

3.203.232129100 CosSinNorth

ftNorth 92.16=


'57.21'92.162 +=North

ftNorth 49.382 =




+

+=22

2121 AASinIISinMDEast

+

+=2

3.203.232129100 SinSinEast

ftEast 77.6=

12 EastEastEast +=

'19.9'77.62 +=East

ftEast 96.152 =


Radius of Curvature Method

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 MDMDMD =

'400,1'500,1 =MD ftMD 100=


( )( )( )( )12

12180II

ISinISinMDTVD =

( )( )( )( )1215

1215100180

= SinSinTVD

ftTVD 23.97=

12 TVDTVDTVD +=

'08.397,1'23.972 +=TVD

ftTVD 31.494,12 =


( ) ( )( )( )( )( )12122

12212180

AAIIASinASinICosICosMDNorth

=

( ) ( )( )( )( )( )3.203.231215

3.203.2315121001802

2

=

SinSinCosCosNorth

ftNorth 67.21=


'47.38'67.212 +=North

ftNorth 14.602 =

( ) ( )( )( )( )( )12122

21212180

AAIIACosACosICosICosMDEast

=

( ) ( )( )( )( )( )3.203.231215

3.233.2015121001802

2

=

CosCosCosCosEast

ftEast 67.8=

12 EastEastEast +=

'95.15'67.82 +=East

ftEast 62.242 =


Minimum Curvature Method

Calculate the position of the wellbore at 1,600 feet using the minimum curvature method and the survey data at 1,500 feet in Table 2-8.

12 MDMDMD =

'500,1'600,1 =MD ftMD 100=





For the minimum curvature method, all the data must be changed to radians.

= 151I or ( )( ) radians2618.018015 =

= 182I or ( )( ) radians3142.018018 =

= 30.231A or ( )( ) radians4067.018030.23 =

= 90.232A or ( )( ) radians4171.018090.23 =

Calculate the ratio factor.

( ) ( )[ ]{ }121212 11 AACosISinISinIICosD = ( ) ( )[ ]{ }4067.04171.012618.01342.02618.03142.01 = CosSinSinCosD

9986.01 =D

1112 2

1

= D

TanD

19986.0

12 21

= TanD

0538.02 =D

=22

22 DTan

DFC

=2

0538.00538.02 TanFC

0002408.1=FC

( ) FCICosICosMDTVD 212 +

= ( )

( )( 0002408.13142.02618.02

100 CosCosTVD +

= )


ftTVD 87.95=

12 TVDTVDTVD +=

'31.494,1'87.952 +=TVD

ftTVD 18.590,12 =

( ) ([ ]( )FCACosISinACosISinMDNorth 11222 +

= )

( ) ( )[ ]( )0002408.14067.02618.04171.03142.02

100 CosSinCosSinNorth +

=

ftNorth 02.26=


5 '98.9'02.262 +=North

ftNorth 00.862 =

( ) ([ ]( )FCASinISinASinISinMDEast 11222 +

= )

( ) ( )[ ]( )0002408.14067.02618.04171.03142.02

100 SinSinSinSinEast +

=

ftEast 38.11=

12 EastEastEast +=

2 '12.5'38.112 +=East

ftEast 50.362 =

The same calculations are made at each survey depths, and the results are shown in Table 2-8.




Table 2-6. Survey Calculations for Directional Well No. 1 using the Average Angle Method

RECTANGULAR COORDINATES MEASURED

DEPTH

(feet)

INCLIN-ATION

(degrees)

AZIMUTH

(degrees)

COURSE LENGTH

(feet)

TRUE VERTICAL

DEPTH

(feet) NORTH EAST

VERTICAL SECTION

10 DEGREES

(feet)

DOGLEG SEVERITY

(deg/100) 0.00

1,000.00 1,100.00 1,200.00 1,300.00

0.00 0.00 3.00 6.00 9.00

0.00 0.00

21.70 26.50 23.30

0.00 1000.00 100.00 100.00 100.00

0.00 1,000.00 1,099.97 1,199.66 1,298.80

0.00 0.00 2.57 9.73

21.57

0.00 0.00 0.49 3.70 9.19

0.00 0.00 2.62

10.23 22.84

0.00 0.00 3.05 3.02 3.03

1,400.00 1,500.00 1,600.00 1,700.00 1,800.00

12.00 15.00 18.00 21.00 24.00

20.30 23.30 23.90 24.40 23.40

100.00 100.00 100.00 100.00 100.00

1,397.13 1,494.36 1,590.25 1,684.51 1,776.90

38.49 60.17 86.19

116.65 151.64

15.96 24.63 36.00 49.66 65.16

40.68 63.53 91.14

123.50 160.65

3.05 3.08 3.00 3.00 3.02

1,900.00 2,000.00 2,100.00 2,200.00 2,300.00

27.00 30.00 30.20 30.40 30.30

23.70 23.30 22.80 22.50 22.10

100.00 100.00 100.00 100.00 100.00

1,867.16 1,955.04 2,041.55 2,127.89 2,214.19

191.11 234.86 281.01 327.57 374.32

82.36 101.39 121.02 140.45 159.63

202.50 248.90 297.76 346.99 396.35

3.00 3.01 0.32 0.25 0.23

2,400.00 2,500.00 2,600.00 2,700.00 2,800.00

30.60 31.00 31.20 30.70 31.40

22.40 22.50 21.60 20.80 20.90

100.00 100.00 100.00 100.00 100.00

2,300.40 2,386.29 2,471.92 2,557.68 2,643.35

421.23 468.55 516.43 564.37 612.57

178.82 198.37 217.76 236.36 254.72

445.88 495.88 546.39 596.84 647.50

0.34 0.40 0.51 0.65 0.70

2,900.00 3,000.00 3,100.00 3,200.00 3,300.00

30.60 30.50 30.40 30.00 30.20

22.00 22.50 23.90 24.50 24.90

100.00 100.00 100.00 100.00 100.00

2,729.07 2,815.19 2,901.39 2,987.82 3,074.34

660.51 707.56 754.14 800.02 845.58

273.55 292.80 312.76 333.38 354.34

697.98 747.65 796.99 845.75 894.26

0.98 0.27 0.72 0.50 0.28

3,400.00 3,500.00 3,600.00 3,700.00 3,800.00

31.00 31.10 32.00 30.80 30.60

25.70 25.50 24.40 24.00 22.30

100.00 100.00 100.00 100.00 100.00

3,160.41 3,246.08 3,331.30 3,416.66 3,502.64

891.60 938.12 985.56

1,033.08 1,080.02

376.09 398.38 420.45 441.81 461.88

943.36 993.04

1,043.60 1,094.11 1,143.82

0.90 0.14 1.07 1.22 0.89

3,900.00 4,000.00 4,100.00 4,200.00 4,300.00

31.20 30.80 30.00 29.70 29.80

21.70 20.80 20.80 19.80 20.80

100.00 100.00 100.00 100.00 100.00

3,588.45 3,674.17 3,760.42 3,847.15 3,933.97

1,127.64 1,175.64 1,222.95 1,269.63 1,316.17

481.12 499.78 517.75 535.02 552.24

1,194.05 1,244.57 1,294.27 1,343.24 1,392.07

0.67 0.61 0.80

.0.58 0.51

4,400.00 4,500.00 4,600.00 4,700.00 4,800.00

29.50 29.20 29.00 28.70 28.50

21.10 20.80 20.60 21.40 21.20

100.00 100.00 100.00 100.00 100.00

4,020.88 4,108.04 4,195.42 4,283.01 4,370.80

1,362.37 1,408.14 1,453.64 1,498.68 1,543.28

569.93 587.45 604.64 621.93 639.32

1,440.64 1,488.76 1,536.55 1,583.91 1,630.85

0.33 0.33 0.22 0.49 0.22


Table 2-7. Survey Calculations for Directional Well No. 1 using the Radius of Curvature Method


MEASURED DEPTH

(feet)

DRIFT ANGLE

(degrees)

DRIFT AZIMUTH

(degrees)

COURSE LENGTH

(feet)

TRUE VERTICAL

DEPTH

(feet) NORTH EAST

VERTICALSECTION 10 DEG

(feet)

DOGLEG SEVERITY

(deg/100) 0.00

1,000.00 1,100.00 1,200.00 1,300.00

0.00 0.00 3.00 6.00 9.00

0.00 0.00

21.70 26.50 23.30

0.00 1000.00 100.00 100.00 100.00

0.00 1,000.00 1,099.63 1,199.63 1,298.77

0.00 0.00 2.56 9.71

21.55

0.00 0.00 0.49 3.69 9.19

0.00 0.00 2.60

10.21 22.82

0.00 0.00 3.00 3.02 3.03

1,400.00 1,500.00 1,600.00 1,700.00 1,800.00

12.00 15.00 18.00 21.00 24.00

20.30 23.30 23.90 24.40 23.40

100.00 100.00 100.00 100.00 100.00

1,397.08 1,494.31 1,590.18 1,684.43 1,776.81

38.47 60.14 86.16

116.62 151.60

15.95 24.62 35.99 49.64 65.15

40.65 63.50 91.10

123.47 160.61

3.05 3.08 3.00 3.00 3.02

1,900.00 2,000.00 2,100.00 2,200.00 2,300.00

27.00 30.00 30.20 30.40 30.30

23.70 23.30 22.80 22.50 22.10

100.00 100.00 100.00 100.00 100.00

1,867.06 1,954.93 2,041.44 2,127.78 2,214.08

191.06 234.81 280.96 327.52 374.27

82.35 101.37 121.01 140.44 159.61

202.46 248.85 297.70 346.93 396.30

3.00 3.01 0.32 0.25 0.23

2,400.00 2,500.00 2,600.00 2,700.00 2,800.00

30.60 31.00 31.20 30.70 31.40

22.40 22.50 21.60 20.80 20.90

100.00 100.00 100.00 100.00 100.00

2,300.29 2,386.18 2,471.81 2,557.57 2,643.24

421.18 468.50 516.37 564.32 612.52

178.80 198.35 217.74 236.34 254.70

445.82 495.83 546.34 596.79 647.45

0.34 0.40 0.51 0.65 0.70

2,900.00 3,000.00 3,100.00 3,200.00 3,300.00

30.60 30.50 30.40 30.00 30.20

22.00 22.50 23.90 24.50 24.90

100.00 100.00 100.00 100.00 100.00

2,728.96 2,815.08 2,901.28 2,987.71 3,074.23

660.46 707.50 754.08 799.96 845.53

273.53 292.78 312.74 333.36 354.32

697.92 747.59 796.93 845.70 894.21

0.98 0.27 0.72 0.50 0.28

3,400.00 3,500.00 3,600.00 3,700.00 3,800.00

31.00 31.10 32.00 30.80 30.60

25.70 25.50 24.40 24.00 22.30

100.00 100.00 100.00 100.00 100.00

3,160.30 3,245.97 3,331.19 3,416.54 3,502.53

891.55 938.06 985.50

1,033.02 1,079.96

376.07 398.36 420.43 441.79 461.86

943.31 992.98

1,043.54 1,094.04 1,143.76

0.90 0.14 1.07 1.22 0.89

3,900.00 4,000.00 4,100.00 4,200.00 4,300.00

31.20 30.80 30.00 29.70 29.80

21.70 20.80 20.80 19.80 20.80

100.00 100.00 100.00 100.00 100.00

3,588.33 3,674.05 3,760.30 3,847.03 3,933.85

1,127.58 1,175.58 1,222.89 1,269.57 1,316.11

481.10 499.76 517.73 535.00 552.22

1,193.99 1,244.50 1,294.21 1,343.18 1,392.00

0.67 0.61 0.80 0.58 0.51

4,400.00 4,500.00 4,600.00 4,700.00 4,800.00

29.50 29.20 29.00 28.70 28.50

21.10 20.80 20.60 21.40 21.20

100.00 100.00 100.00 100.00 100.00

4,020.76 4,107.92 4,195.30 4,282.89 4,370.69

1,362.31 1,408.08 1,453.57 1,498.62 1,543.22

569.90 587.43 604.62 621.91 639.30

1,440.57 1,488.69 1,536.48 1,583.85 1,630.79

0.33 0.33 0.22 0.49 0.22




Table 2-8. Survey Calculations for Directional Well No. 1 using the Minimum Curvature Method


MEASURED DEPTH

(feet)

INCLIN-ATION

(degrees)

AZIMUTH

(degrees)

COURSE LENGTH

(feet)

TRUE VERTICAL

DEPTH

(feet) NORTH EAST


(feet)

DOGLEG SEVERITY

(deg/100) 0.00

1,000.00 1,100.00 1,200.00 1,300.00

0.00 0.00 3.00 6.00 9.00

0.00 0.00

21.70 26.50 23.30

0.00 1000.00 100.00 100.00 100.00

0.00 1,000.00 1,099.95 1,199.63 1,298.77

0.00 0.00 2.43 9.54

21.40

0.00 0.00 0.97 4.27 9.70

0.00 0.00 2.56

10.14 22.76

0.00 0.00 3.05 3.02 3.03

1,400.00 1,500.00 1,600.00 1,700.00 1,800.00

12.00 15.00 18.00 21.00 24.00

2030 23.30 23.90 24.40 23.40

100.00 100.00 100.00 100.00 100.00

1,397.08 1,494.31 1,590.18 1,684.44 1,776.81

38.34 59.98 86.00

116.45 151.44

16.40 25.12 36.51 50.17 65.65

40.61 63.44 91.03

123.40 160.54

3.05 3.08 3.00 3.00 3.02

1,900.00 2,000.00 2,100.00 2,200.00 2,300.00

27.00 30.00 30.20 30.40 30.30

23.70 23.30 22.80 22.50 22.10

100.00 100.00 100.00 100.00 100.00

1,867.06 1,954.93 2,041.45 2,127.79 2,214.08

190.90 234.66 280.81 327.37 374.12

82.86 101.88 121.51 140.94 160.11

202.39 248.78 297.64 346.87 396.23

3.00 3.01 0.32 0.25 0.23

2,400.00 2,500.00 2,600.00 2,700.00 2,800.00

30.60 31.00 31.20 30.70 31.40

22.40 22.50 21.60 20.80 20.90

100.00 100.00 100.00 100.00 100.00

2,300.29 2,386.19 2,471.81 2,557.58 2,643.25

421.02 468.34 516.22 564.16 612.36

179.30 198.86 218.25 236.85 255.20

445.76 495.76 546.27 596.72 647.38

0.34 0.40 0.51 0.65 0.70

2,900.00 3,000.00 3,100.00 3,200.00 3,300.00

30.60 30.50 30.40 30.00 30.20

22.00 22.50 23.90 24.50 24.90

100.00 100.00 100.00 100.00 100.00

2,728.96 2,815.08 2,901.29 2,987.72 3,074.23

660.30 707.35 753.92 799.80 845.37

274.03 293.28 313.24 333.86 354.82

697.86 747.53 796.86 845.63 894.14

0.98 0.27 0.72 0.50 0.28

3,400.00 3,500.00 3,600.00 3,700.00 3,800.00

31.00 31.10 32.00 30.80 30.60

25.70 25.50 24.40 24.00 22.30

100.00 100.00 100.00 100.00 100.00

3,160.31 3,245.98 3,331.20 3,416.55 3,502.54

891.39 937.90 985.34

1,032.86 1,079.80

376.57 398.86 420.92 442.28 462.36

943.23 992.91

1,043.47 1,093.97 1,143.68

0.90 0.14 1.07 1.22 0.89

3,900.00 4,000.00 4,100.00 4,200.00 4,300.00

31.20 30.80 30.00 29.70 29.80

21.70 20.80 20.80 19.80 20.80

100.00 100.00 100.00 100.00 100.00

3,588.34 3,674.06 3,760.31 3,847.04 3,933.87

1,127.42 1,175.42 1,222.72 1,269.40 1,315.94

481.59 500.26 518.23 535.50 552.71

1,193.91 1,244.43 1,294.13 1,343.10 1,391.92

0.67 0.61 0.80 0.58 0.51

4,400.00 4,500.00 4,600.00 4,700.00 4,800.00

29.50 29.20 29.00 28.70 28.50

21.10 20.80 20.60 21.40 21.20

100.00 100.00 100.00 100.00 100.00

4,020.77 4,107.94 4,195.31 4,282.90 4,370.70

1,362.14 1,407.91 1,453.40 1,498.45 1,543.05

570.40 587.93 605.12 322.41 639.80

1,440.49 1,488.61 1,536.40 1,583.77 1,630.71

0.33 0.33 0.22 0.49 0.22


The results of the survey calculations for Directional Well No. 1 in Example 2-2 are compared in Table 2-9 and Table 2-10. The comparison shows a significant difference when using the tangential method. The difference is much less pronounced with the other four methods. Table 2-10 shows the difference in the calculated TVD, North and East assuming the minimum curvature method is the most accurate. The average angle, balanced tangential and radius of curvature methods are all within one foot of each other at total depth. It must be remembered that as the distance between surveys increases, the average angle and balanced tangential errors will increase significantly.

Table 2-9. Comparison of the Survey Calculation Methods for Example 2-2 Results

METHOD TVD Feet

NORTH Feet

EAST Feet

Tangential 4,364.40 1,565.23 648.40 Balanced Tangential 4,370.46 1,542.98 639.77 Average Angle 4,370.80 1,543.28 639.32 Radius of Curvature 4,370.69 1,543.22 639.30 Minimum Curvature 4,370.70 1,543.05 639.80

Table 2-10. Relative Difference between the Survey Calculation Methods for Example 2-2 Results

METHOD

DIFFERENCE IN TVD

Feet

DIFFERENCE IN NORTH

Feet

DIFFERENCE IN EAST

Feet Tangential -6.30 22.18 +8.60 Balanced 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

CLOSURE AND DIRECTION

The line of closure is defined as "a straight line, in a horizontal plane containing the last station of the survey, drawn from the projected surface location to the last station of the survey." The line of closure is identified in Figure 2-9. Simply stated, the closure is the shortest distance between the surface location and the horizontal projection of the last survey point. The closure is always a straight line because a straight line is the shortest distance between two points. The closure is the polar coordinates at a given survey point as opposed to north and east being rectangular coordinates.

When defining closure, the direction must also be given. Without indicating direction, the bottomhole location projected in a horizontal plane could be anywhere along the circumference of a circle with the radius of the circle being equal to the closure distance. The direction and closure exactly specifies where the bottom of the hole is located in relation to the surface location.




Figure 2-9. Graphic Representation of the Difference between Closure Distance and Vertical Section in the

Horizontal Plane

The closure distance and direction are calculated using the following equations:

NorthEastTandirection Closure 1= Equation 2-27

( ) ( )22 EastNorthdistance Closure += Equation 2-28 These are the same equations used for calculating an angle and hypotenuse of a right triangle.

Example 2-3 Given: To illustrate the use of these equations, the closure and direction of the

Directional Well No. 1 in Example 2-2 for the results of the minimum curvature method are calculated below

From Table 2-7, the coordinates of the last survey point in the example well are:

North = 1,543.05 ft

East = 639.80 ft

( ) ( )22 EastNorthdistanceClosure +=


( ) ( )22 80.63905.543,1 +=distanceClosure ftdistanceClosure 43.670,1 =

= NorthEastdirectionClosure 1Tan

= 05.543,180.639Tan 1directionClosure

Closure direction = 22.52 or 22 31' Since the bottomhole location is in the northeast quadrant, the closure distance and direction are:

1,670.43 ft N22.52E

Then, the horizontal projection of the bottom of the hole is 1,670.43 feet away from the surface location in the N22.52E direction.

VERTICAL SECTION

The vertical section is the horizontal length of a projection of the borehole into a specific vertical plane and scaled with vertical depth. When the path of a wellbore is plotted, the vertical section is plotted versus TVD. The closure distance cannot be plotted accurately because the plane of closure (closure direction) can change between surveys. The vertical plot of a wellbore is in one specific plane. Figure 2-9 graphically shows the difference between the closure distance and vertical section. The closure distance and vertical section are equal only when the closure direction is the same as the plane of the vertical section.

The vertical section azimuth is usually chosen as the azimuth from the surface location to the center of the target. If multiple targets are present and changes in azimuth are required to hit each target, the vertical section azimuth is usually chosen as the azimuth from the surface location to the end of the wellbore.

The vertical section is calculated from the closure distance and direction. The equations for calculating the vertical section can be seen in Table 2-1 and are as follows:

( ) ( )distance ClosureAzAzCosVS clvs = Equation 2-29

Example 2-4 Given: The data of Directional Well No. 1 from the previous examples.

The plane of the vertical section is 10.

Calculate: The vertical section at the last survey point.




From the previous example:

Closure distance = 1,670.43 feet

Closure direction = 22.52

Calculate the vertical section:

( ) ( )distanceClosureAzAzCosVS clvs = ( ) ( )43.670,152.2210 = CosVS

ftVS 71.630,1=

Therefore, the distance of 1,630.71 feet would be plotted on the vertical section. Figure 2-10 and Figure 2-11 are respectively the plan view and vertical section for Example 2-2.


Plan View

0

200

400

600

800

1000

1200

1400

1600

1800

0 200 400 600 800 1000 1200 1400 1600

East, feet

Nor

th, f

eet

Figure 2-10. Plan View for Directional Well No. 1 of Example 2-2




Vertical Section

0

500

1000

1500

2000

2500

3000

3500

4000

4500

50000 500 1000 1500 2000 2500 3000 3500

Vertical Section, feet

True

Ver

tical

Dep

th, f

eet

Figure 2-11. Vertical Section for Directional Well no. 1 in Example 2-2


PROBLEMS

1. Given the following survey data, calculate the TVD, North and East using the average angle and radius of curvature methods.

MD1 = 1000 feet MD2 = 2000 feet I1 = 0 I2 = 40 A1 = S42W A2 = S42W

2. Given the following rectangular coordinates, calculate the vertical section of the survey point if the vertical section azimuth is 215.

North = -1643.82 feet and East = -822.16 feet

3 Given the following survey data, calculate the TVD, North and East using the average angle, radius of curvature and minimum curvature methods.

MD1 = 100 feet MD2 = 200 feet I1 = 1 I2 = 1 A1 = 0 A2 = 180

NOMENCLATURE

A1 = Azimuth angle at upper survey point.

A2 = Azimuth angle at lower survey point.

Azcl = Azimuth of closure or closure direction (0 to 360), degrees

Azvs = Azimuth of Vertical Section (0 to 360), degrees

Br = Build rate.

D1 = Intermediate calculation in minimum curvature method.

D2 = Intermediate calculation in minimum curvature method.

DLS = Dogleg severity in degrees per 100 feet.

FC = Ratio factor for minimum curvature

I1 = Inclination angle at upper survey point, degrees

I2 = Inclination angle at lower survey point, degrees

MD = Measured depth.

r = Radius of curvature.

VS = Vertical Section length

= Change in parameter




DEP = The change in the horizontal departure. East = The East coordinate at a survey point

East = The change in East coordinates between survey points. MD = The measured distance along the wellbore course between

survey points.

North = The North coordinate at a survey point North = The change in North coordinates between survey points. TVD = The change in true vertical depth between survey points.

1 = Subscript denotes upper or previous survey point

2 = Subscript denotes lower or last survey point

Documents

Survey Calculations Directional and Horizontal Drilling