Directional Drilling Survey Calculations

Interim Data

Average Angle Exercise

CL = 155.00’ Ī = 19.80°

MD

Ā = 74.95°

•

Inc

Az

TVD

N

E

VS

DLS

Survey 10 4787.00 19.30 72.00 4764.05 106.25 90.84 125.14 1.13 Survey 11 4942.00 20.30 77.90

Step 1 – Calculate the Course Length, Average Inclination, and Average Azimuth (use vector averaging if necessary) Course Length

Average Inclination

CL = MD 2 − MD1

I =

I1+ I 2

2

Average Azimuth

A=

A1 + A 2 2 72 .00 + 77 .90 2

CL = 4942.00 − 4787.00 I = 19.30° + 20.30° 2

A=

CL = 155.00'

A = 74.95°

I = 19.80°

16

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Average Angle Exercise • Now from a different perspective . . .

North East

North

106.25

East 90.84

8

Interim Data

Average Angle Exercise

CL = 155.00’ Ī = 19.80°

MD

Ā = 74.95°

Inc

Az

TVD

N

E

VS

DLS

Survey 10 4787.00 19.30 72.00 4764.05 106.25 90.84 125.14 1.13

Survey 11 4942.00 20.30 77.90 4909.89 Step 2 – Calculate the change in True Vertical Depth

•

()

ΔTVD = CL × cos I

ΔTVD = 155'× cos(19.80°)

Ī

ΔTVD = 155× ' (0.9409)

CL

ΔTVD

ΔTVD = 145 .84 '

145.84’ 145.84’

TVD11

TVD11 = TVD10 + ΔTVD

4909.89’ 4909.89’

TVD11 = 4764.05'+145.84' TVD 11 = 4909 .89 '

Make a Triangle!

Interim Data

Average Angle Exercise

CL = 155.00’ Ī = 19.80°

MD

Ā = 74.95°

•

Inc

Az

TVD

N

E

VS

DLS

Survey 10 4787.00 19.30 72.00 4764.05 106.25 90.84 125.14 1.13 Survey 11 4942.00 20.30 77.90 4909.89

Step 3 – Calculate the Horizontal Deviation

()

HD = CL × sin I HD = 155'× sin(19.80°)

Ī CL

HD = 155'× (0.3387 )

HD = 52 .50 ' HD

52.50’ 52.50’

9

Average Angle Exercise • Back to Horizontal Plane

North

106.25

HD

52.50’ 52.50’

East 90.84

Interim Data

Average Angle Exercise

CL = 155.00’ HD = 52.50’

MD

Ā = 74.95°

Inc

Az

TVD

N

E

VS

DLS

Survey 10 4787.00 19.30 72.00 4764.05 106.25 90.84 125.14 1.13 Survey 11 4942.00 20.30 77.90 4909.89

Step 4 – Calculate the change in rectangular coordinates (ΔN, ΔE)

•

ΔN = HD × cos( A)

Make another Triangle! North

ΔN = 52.50'× cos(74.95°) ΔN = 52.50'×(0.2597)

North

ΔN = 13.63'

106.25

ΔE = HD × sin( A) ΔE = 52.50' × sin(74.95°) ΔE = 52.50' × (0.9657)

ΔE 50.70’ 50.70’ ΔN

13.63’ 13.63’

Ā

HD

East 90.84

ΔE = 50.70'

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21

10

Interim Data CL = 155.00’ ΔN = 13.63’

Average Angle Exercise

ΔE = 50.70’

MD

Inc

Az

TVD

Survey 11 4942.00 20.30 77.90 4909.89

• Step 4 (Cont.) – Calculate the rectangular coordinates (Total) From Tie In Survey:

N10 = 106.25

From Previous Calculation:

ΔN

=

Add to obtain Survey 11 N

From Tie In Survey: From Previous Calculation:

N

E

VS

DLS

Survey 10 4787.00 19.30 72.00 4764.05 106.25 90.84 125.14 1.13

13.63

119.88 141.54

North

119.88’ 119.88’ E10 = ΔE =

90.84 50.70

Add to obtain Survey 11 E

50.70’ 50.70’ 13.63’ 13.63’

141.54’ 141.54’

East

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22

Vertical Section • Sometimes called: – VSA = 83° – Vertical Section Azimuth – Target Direction – Proposed Direction – Vertical Section Plane Azimuth

North Closure Distance

Target Location

East

Total Vertical Section

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23

11

Average Angle Exercise MD

Inc

Az

TVD

N

Survey 10 4787.00 19.30 72.00 4764.05 106.25

E

VS

DLS

90.84 125.14 1.13

Survey 11 4942.00 20.30 77.90 4909.89 119.88 141.54

Step 5 – Calculate Closure Distance (calculated from last survey)

•

North Closure Azimuth

Closure Distance

Closure Distance

CD = ( N ) 2 + ( E ) 2 CD = (119 .88) 2 + (141 .54 ) 2

CD = 185.49 ft

East

24

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Be Careful with Closure Azimuth… CLOSURE AZIMUTH = DIRECTION OF CLOSURE DISTANCE North

1 1 4

2 East

3 2 3

4

⎛E⎞ CA = tan -1 ⎜ ⎟ ⎝N⎠

⎛ 30.0 ⎞ CA = tan -1 ⎜ ⎟ ⎝ 40.0 ⎠

36.87° 36.87°

CA = 36.87

⎛ 25.0 ⎞ CA = tan -1 ⎜ ⎟ ⎝ − 30.0 ⎠

180+(180+(-39.81)=

⎛ − 35.0 ⎞ CA = tan -1 ⎜ ⎟ ⎝ − 50.0 ⎠

180+(34.99)=

CA = −39.81

140.19° 140.19°

CA = 34.99

214.99° 214.99°

⎛ − 50.0 ⎞ CA = tan -1 ⎜ ⎟ ⎝ 20.0 ⎠

360+(360+(-68.20)=

CA = −68.20

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291.80° 291.80° 25

12

Average Angle Exercise MD

Inc

Az

TVD

N

Survey 10 4787.00 19.30 72.00 4764.05 106.25

•

E

VS

DLS

90.84 125.14 1.13

Survey 11 4942.00 20.30 77.90 4909.89 119.88 141.54 Step 6 – Calculate Closure Azimuth (direction of closure distance) North Closure Distance

Closure Azimuth

Closure Azimuth

⎛E⎞ CA = tan-1 ⎜ ⎟ ⎝N⎠

⎛ 141.54 ⎞ CA = tan -1 ⎜ ⎟ ⎝ 119.88 ⎠

CA = 49.74° East

26

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Interim Data

Average Angle Exercise

CD = 185.49’ CA = 49.74°

MD

VSA = 83.00°

•

Inc

Az

TVD

N

Survey 10 4787.00 19.30 72.00 4764.05 106.25

E

VS

DLS

90.84 125.14 1.13

Survey 11 4942.00 20.30 77.90 4909.89 119.88 141.54 Step 7 – Calculate Vertical Section (total—not incremental)

DD = VSA − CA

North Closure Azimuth

Closure Distance

9’ 5.4 18

33.26° 33.26° East

155.10’ 155.10’

Target Location

DD = 83° − 49.74° DD = 33.26°

VS = CD × cos(DD) VS = 185.49'× cos(33.26°) VS = 155.10'

Target Direction

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27

13

Average Angle Exercise • Dogleg – The change in inclination and azimuth between two points – Measured in degrees • Dogleg Severity – The dogleg over a defined distance – Measured in degrees /100 ft • Severe dogleg severity may produce – ‘Keyseats’ – Problems with running casing – Stuck pipe – Drill pipe wear 28

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Average Angle Exercise MD

Inc

Az

TVD

N

Survey 10 4787.00 19.30 72.00 4764.05 106.25

•

E

VS

DLS

90.84 125.14 1.13

Survey 11 4942.00 20.30 77.90 4909.89 119.88 141.54 155.10 1.44

Step 8 – Calculate Dogleg and Dogleg Severity Dogleg

DL = cos−1[sin(I 1)sin(I 2 ) cos( A2 − A1) + cos(I 1) cos(I 2 )]

DL = cos −1[sin( 19 .3) sin( 20 .3) cos( 77 .9 − 72 ) + cos(19 .3) cos( 20 .3)]

DL = cos −1[0.99924]

DL = 2.23°

Dogleg Severity

DLS = DLS =

DL × Interval CL

2.23° × (100) ft 155'

DLS = 11.44 .44° / 100' © 2008 Baker Hughes Incorporated. All rights reserved.

29

14

Survey Calculations Dogleg and Dogleg Severity Closure and Vertical Section

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Objectives •

The student will be able to - demonstrate proficiency with their hand calculator. - list the main types of survey calculation. - perform average angle hand calculations. - explain what is meant by the terms “Dogleg” and “Dogleg Severity”. - hand calculate DL and DLS. - describe what these calculations indicate re Directional Drilling . - calculate closure. - calculate vertical section. - explain what the resulting calculation indicates. - list the information available from a standard drilling plot.

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1

Calculating The Wellbore Position •

When we survey a wellbore, we typically have MD, Inc and Az measurements at specific points along the wellbore

•

To plot/calculate the position of the wellbore, we need to somehow “join-the-dots”

•

There are many different mathematical ways to join the dots

•

Each method makes assumptions about the path between the survey stations

•

The most common survey calculation methods used in the drilling industry are – Minimum curvature – Radius of curvature – Average angle

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Survey Calculation Methods

•

Minimum curvature – Is generally recognised as the most appropriate survey calculation method in most circumstances – Is the most commonly used survey calculation method – Most of our customers worldwide use this (and want us to use this) – Assumes the line joining any two successive survey stations is a 3D curve (with curvature in 3 dimensions i.e. the wellpath lies on the surface of a sphere)

•

Radius of curvature – Used to be more common than it is now – Rarely used nowadays in the drilling industry – Assumes the line joining any two successive survey stations is a 3D curve (with curvature in 2 dimensions i.e. the wellpath lies on the surface of a cylinder)

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2

Survey Calculation Methods

•

Both minimum curvature and radius of curvature calculations are computationally complex

•

They are therefore typically done only with the aid of a computer program (e.g. WellArchitect, Advantage) or with a programmable calculator (with appropriately validated program)

•

Average Angle is a calculation method which is less computationally complex and can be hand calculated on a basic scientific calculator

•

The average angle method is adequate for field calculations, but would only be used in situations where for some reason a minimum curvature calculation is not available

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Average Angle Survey Calculations

•

We know the MD, Inc, and Az values at each survey station

•

The average angle method assumes that the path between any two survey stations is a straight line

•

This straight line will have an inclination and a direction

•

The inclination of the straight line is the average of the inclinations of the survey stations at each end of the straight line

•

The direction of the straight line is the average of the directions of the survey stations at each end of the straight line

•

The TVD, N and E coordinates can then be calculated using the properties of the right-angled triangle and basic trigonometry

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3

Average Angle Survey Calculations

•

For the straight line joining any two survey stations – Denote the average azimuth of this straight line by

Az

– Denote the average inclination of this straight line by •

Then, for the straight line between any two survey stations

Az = Az + Az 2 1

•

I

And

I = I + I 2 1

2

2

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Average Angle Survey Calculations

•

So we have, looking from the side

I

ΔTVD

MD1, I1, Az1

ΔTVD = CL × CosI CL

HD

HD = CL × Sin I

MD2, I2, Az2

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4

Average Angle Survey Calculations

•

And looking from above

N ΔE

ΔN = HD × Cos Az ΔN HD

ΔE = HD × Sin Az

Az

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Average Angle Survey Calculations

•

So we have the average angle formulae

ΔTVD = CL × CosI

HD = CL × Sin I ΔN = HD × Cos Az ΔE = HD × Sin Az

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5

Average Angle Survey Calculations

•

Note that the calculated values of ΔTVD, ΔN and ΔE are changes in these parameters from one survey station to the next

•

Therefore each of these Δ values needs to be added on to the appropriate absolute values on the previous line

•

Thus the survey calculation is an incremental calculation and a mistake in any line of the calculation will mean all subsequent calculations of that parameter will also be incorrect

•

Clearly, to start off we need to have a tie-on line with the TVD, N, and E coordinates specified – this is usually, but not always, ultimately a tieon line at surface

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Average Angle Survey Calculations

•

Note that you can usually spot gross errors if you pay a little attention to the numbers e.g. if the course length is 100 ft, then ΔN cannot be 300 ft

•

The direction of the average azimuth will tell you whether – N and E should be increasing or decreasing – ΔN should be bigger or smaller than the ΔE

•

ΔTVD may be a negative number – This means that the inclination is above 90°

•

ΔN and/or ΔE may be a negative number – This means the wellbore is going south and/or west

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6

Average Angle Calculation Exercise

•

Note that it is typically better to do the calculation by line rather than by column

•

Typically, these calculated values are quoted to 2 decimal places

•

You can either store previous line values on your calculator, or handenter them as appropriate

•

Depending on which you do, over multiple lines you’ll get very slight differences in your answers

•

Calculate TVD, N, and E for the first few lines on Exercise 1

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Dogleg and Dogleg Severity

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7

Dogleg •

Dogleg (DL) is a measure of the 3 dimensional change in trajectory (inclination and direction) of a bore-hole between two survey stations, expressed as a 3D angle.

•

DL = Cos-1 [ Sin I1 Sin I2 Cos (A2 - A1) + Cos I1 Cos I2 ]

•

With the same change in inclination and azimuth between two survey stations, the dogleg will be higher at higher inclinations.

•

The same amount of turn in the hole will produce a higher dogleg at higher inclinations.

•

1 degree of inclination change will give a 1 degree dogleg. This is NOT the case with azimuth change except for when the hole is horizontal.

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Dogleg changing with inclination Inclination

Azimuth

Dogleg

1 1

0 180

2.00

5 7

20 20

2.00

5 7

20 24

2.04

10 12

20 24

2.14

20 22

20 24

2.46

30 32

20 24

2.87

45 47

20 24

3.50

60 62

20 24

4.03

90 92

20 24

4.47

90 90

20 24

4.00

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8

Dogleg Severity •

The dogleg calculation is a function of inclination and azimuth values at each of two survey points

•

As such, it has limited practical value

•

It is much more useful to have a measure which takes account of course length (CL)

•

Dogleg severity is dogleg expressed over a particular interval (usually 100ft or 30m)

DLS = DL × Interval CL •

Dogleg and Dogleg Severity are NOT the same thing although the terms are often used interchangeably

•

A very short course length may give misleading DLS values

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DLS Calculation Exercise •

Once again, DLS values are usually quoted to 2 decimal places

•

Set your calculator to display 2 decimal places

•

What is Cos 1°, Cos 2°, Cos 3°, Cos 4° … (to 2 decimal places)?

•

This means if you are hand-entering intermediate values, you need to record 6 decimal places

•

If you are storing intermediate values in your calculator, you will automatically be using sufficient precision

•

Calculate DLS for the first few lines of the given survey in Exercise 1

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9

Drilling Map Closure and Vertical Section

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Drilling Map •

What information might be displayed on a drilling map? – Location information – Well information – Slot information (particularly slot coordinates) – Target information – Surface information (north reference, spheroid model, depth offsets, depth units) – Tie-on information – Logo – Wellplan – North arrow (correction to TN/GN, Dip, Bt) – Approval box – Plan view (wellpath map) – Etc.

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10

Drilling Map •

When we plot a survey on the plan view, what does that tell us?

•

It is a projection on a horizontal plane

•

It lets us know whether the drilled well is left or right of the plan (on the projection)

•

It doesn’t tell us how far off the line we are

•

It doesn’t always tell us if we need to steer right or left – we need more information than just one survey tell us this

•

More on the drilling map later

© 2008 Baker Hughes Incorporated. All rights reserved.

Closure and Vertical Section •

Later on we’ll talk about why we calculate VS and what it indicates

•

We’ll start by covering how to calculate Vertical Section – Most people do not find this a particularly easy calculation – As with most of the other survey calculations, it is very rarely done manually – Before you can calculate VS, you first have to do a calculation to find something we call closure – Calculating closure involves calculating two values • Closure distance • Closure direction – You need both of these values in order to calculate VS – Both closure and VS are calculated for a specific point on the wellbore, usually every survey station

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11

Closure • • •

Is the distance and direction on a horizontal projection to a given point P on an actual wellpath Closure distance is typically measured from the slot (assume the slot has coordinates (0,0) Closure direction is typically given as an azimuth, which like all azimuths is measured clockwise from N N P

1600

Cl o

Closure Direction

e sur

t Di s

ce an

E 2250

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Closure Distance N

Closure Distance =

1600 2 + 2250 2 = 2760.89

1600

C

ce an t s i eD ur s lo

2250

E

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12

Closure Direction N

Closure Direction = tan -1

2250 = 54.58 ° 1600

1600

2250

E

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Closure Calculation •

On a vertical well, there is no VS azimuth and hence no VS calculation

•

On a vertical well, therefore, closure parameters are typically of some interest

•

Closure information is not typically that useful for practical purposes on a directional well

•

It does not typically determine our future steering behaviour, for example

•

It is however necessary for calculating vertical section, which may be used to determine steering behaviour

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13

Directional Difference

•

We have calculated the closure direction

•

We define the VS azimuth (more on this later)

•

In our example we define the VS azimuth to be 60°

•

The difference between these two values is the Directional Difference (DD)

•

Thus, in our example, the DD = 60 – 54.58 = 5.42°

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Directional Difference N

Closure Direction = tan -1 VS Azimuth = 60°

2250 = 54.58° 1600

So the Directional Difference = 60 - 54.58 = 5.42° 1600

VS Azimuth

Directional Difference

Closure Direction

2250

E

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14

Vertical Section

The VS at point P is the length of the green line i.e. cos DD x closure distance

N

= cos 5.42 x 2760.89 = 0.996 x 2760.89 = 2749.85

1600

27 42 5.

60

P

9 .8

°

2250

E

© 2008 Baker Hughes Incorporated. All rights reserved.

Vertical Section •

Mathematically, VS = Cos DD x Closure distance

•

VS is a distance

•

It is the distance drilled (from some defined VS origin) projected onto a vertical plane oriented at a particular azimuth

•

The particular azimuth is called the VS azimuth (or plane, or direction)

•

Both the VS origin and the VS azimuth are defined (by a well-planner or the customer) and will be found on the drilling plot

•

For any particular point on the wellpath, VS is plotted against TVD on the section view of a drilling map

•

VS is used to give a visual indication of where a drilled wellpath is compared to where it should be (“above or below the line”)

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15

Drilling Map •

So we can add some additional information to the list we saw previously – Location information – Well information – Slot information (particularly slot coordinates) – Target information – Surface information (north reference, spheroid model, depth offsets, depth units) – Tie-on information – Logo – Wellplan – North arrow (correction to TN/GN, Dip, Bt) – Approval box – Plan view (wellpath map) – VS view (cross-section view) – VS azimuth – VS origin © 2008 Baker Hughes Incorporated. All rights reserved.

Drilling Map •

When we plot a survey on the section view, what does that tell us?

•

It is a projection on a vertical plane

•

This vertical plane is oriented at some azimuth (the vertical section azimuth)

•

It gives us an indication of whether the drilled well is above or below the plan (on the projection)

•

Strictly speaking, this is only true if we are drilling in a direction close to the VS azimuth

•

It doesn’t tell us how far off the line we are

•

It doesn’t always tell us if we need to steer up or down – we need more information than just one survey tell us this

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16

Vertical Section Calculation (summary) •

To calculate the VS at point P, you need to know – The VS azimuth (aka VS plane or VS direction) – The VS origin – The local N and E coordinates of point P

•

Calculate the closure of point P, both – The closure distance – The closure direction

•

Calculate the difference between the VS azimuth and the closure direction (this is the directional difference, DD)

•

Calculate the VS for point P – VS = Cos DD x Closure distance

© 2008 Baker Hughes Incorporated. All rights reserved.

Vertical Section Calculation •

If you’re doing this calculation manually, it’s always good to draw a diagram

•

If you’re drilling in a direction other than N and E, the formulae will take care of the different quadrants, as long as the directions are azimuths measured clockwise from N

•

If you’re using any right-angled triangles to calculate distances and angles, be careful to label accordingly and correct to azimuths as appropriate

•

When calculating the DD, just subtract the smaller number from the bigger for ease of calculation

© 2008 Baker Hughes Incorporated. All rights reserved.

17

Choice of Vertical Section Origin

•

The vertical section origin is usually, but not always, the slot

•

The customer may specify a point for VS origin that is not the slot

•

If the slot coordinates are not (0,0), you may have to correct appropriately when calculating the closure distance i.e. subtract the ΔN and ΔE of the slot coordinates from the coordinates of the point on the wellpath

•

When drilling a sidetrack, the sidetrack point may be the VS origin, with coordinates referenced to platform centre

© 2008 Baker Hughes Incorporated. All rights reserved.

Choice of Vertical Section Azimuth •

The vertical section azimuth is typically chosen to give the most useful view of the wellpath on the section view of the drilling plot

•

For a 2D wellplan, the vertical section azimuth will usually be the direction of a straight line drawn from the slot to the end of the wellpath

•

This gives the most useful view of the drilled versus planned wellpaths

•

The least useful view would be a vertical section azimuth perpendicular to this

•

For a 3D wellplan the choice of vertical section azimuth is a less obvious process

© 2008 Baker Hughes Incorporated. All rights reserved.

18

Choice of Vertical Section Azimuth •

The choice of vertical section azimuth will usually be up to us

•

Sometimes for a 3D plan it will be the same as for a 2D wellplan, i.e. the direction of a straight line drawn from the slot to the end of the wellpath

•

Or it could be the direction of a straight line from the origin to the end of the wellpath

•

Or it could be the direction of a straight line from any point on any azimuth

•

Sometimes it will be chosen to give a better view of the more critical part of the wellpath

•

Sometimes there will be multiple plots created, for different sections of the well, each with different vertical section azimuths

© 2008 Baker Hughes Incorporated. All rights reserved.

Vertical Section Calculation •

If the calculated VS is exactly the same as the closure distance, this means the point lies on the VS azimuth i.e. precisely on the line (of the plan view) for a simple 2D plan

•

If the calculated VS is 0, this means the point lies on a line perpendicular to the VS azimuth (in the plan view)

•

If the calculated VS is negative, this means the drilled well has gone “backwards” with respect to the VS azimuth and origin

•

This is fairly common in some types of hole

•

The plotted drilled versus proposed section view will only truly tell you if you’re above or below the line if you’re drilling in a direction close to the VS azimuth

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19

Curtain Section •

In the MWD world, there has historically been something called Incremental Section

•

This is not the same as VS, is now history, and can safely be forgotten about

•

There is however another type of cross section calculation referred to as Curtain Section, in which a 3D wellpath is “flattened out” along a straight plane

•

Both types of cross-section (VS and Curtain Section) can be generated in WellArchitect

•

Curtain section may be useful for visualisation of wellpaths in relation to earth models (formations)

© 2008 Baker Hughes Incorporated. All rights reserved.

VS Calculation Exercise •

Calculate VS for a few lines of the given survey in Exercise 1

•

Note that the VS Origin is the slot with coordinates (0 N, 0 E)

•

Check your answers

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20

Projecting Ahead

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Objectives The student will be able to •

explain what is meant by “Projecting Ahead”

•

explain why we might project from the last survey to the bottom of the hole

•

do simple hand calculation projections to – Calculate Inc and Az at BOH for a given build & turn – Calculate TVD for a projected Inc at a specified BUR – Calculate BUR required for a given TVD

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1

Projecting Ahead •

Is the process of calculating, one way or another, where we think the wellbore may be after a certain amount of drilling which we haven’t done yet

•

As such, it always involves some guesswork on our part as to what will happen to the wellbore over this as yet undrilled section

•

For example, it may build or turn at a relatively predictable rate

•

And if it does, then we may be interested in calculating various things: – The current inclination and/or direction at the bottom of the hole – The bottom hole location after a specified additional MD has been drilled – What inclination we will have at a certain TVD – Whether we will hit a specified target – etc

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Projecting Ahead •

It is common for a DD to project ahead, often after every survey – To estimate where the wellbore will be compared to the plan – To monitor potential collision issues – To find out if he needs to take remedial action

•

Projecting ahead may be something the DD does as an integral part of his own routine, or it may be laid down in procedures, either from INTEQ or from the customer

•

Either way, it is a useful, and often necessary, thing to do

•

Sometimes multiple projections are done using different parameters, so that the DD will have a good idea what he hopes to get in advance of the survey being taken

•

In collision-critical situations, there may be a designated hand, either at the rigsite or in town, dedicated to doing projection calculations

© 2008 Baker Hughes Incorporated. All rights reserved.

2

Projecting Ahead

•

For any specific BHA, the survey sensor is some fixed distance behind the bit

•

Surveys are almost always taken with the BHA off bottom

•

Therefore we never have definitive surveys of the bottom of the wellbore while drilling

•

It is usually good practice to project ahead from the last survey station to the bottom of the hole, and then to do any further projection from the bottom of the hole

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Projecting Ahead

•

Simple projections can be done on a hand-calculator, but can also be done with WA (“Projection To Bit”)

•

More complicated projections are usually done with WA (“Project Ahead”)

•

We will do some of the simpler hand-calculations now

•

We will do projections using WA later

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3

Projecting Ahead

•

There are various formulae that can be used when projecting ahead

•

These formulae are typically developed from the geometry of the circle and of the right-angled triangle

•

For most people, the derivation of these formulae is not a great matter of interest

•

What is important is how to use them to get the information you want

•

However, if you are interested …

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Derivation of formulae •

Any curved section in the wellbore can be regarded as an arc of a circle with a specific radius, rc, the radius of curvature

•

The circumference, C, of this circle is 2πrc

•

Since there is no exact value of π, any calculations using π will depend on the precision with which it is defined

•

If doing manual calculations, use the π button on your calculator

•

There is a fixed ratio between any arc length (AL) and the angle angle (AA) by that arc

•

Let’s assume we’re drilling in feet, so a typical arc length would be 100

•

So AL/AA = 100/BUR

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4

Arc Length and Arc Angle

Arc angle

Arc length

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Derivation of formulae •

In the limiting case of the entire circle the expression above would equal C/360

•

So 100/BUR = 2πrc/360

•

Rearranging this gives rc = 360 x 100 / (2π x BUR) = 5729.58/BUR

•

If we’re using metres, the BUR is usually expressed in °/30 m

•

So the expression becomes rc = 360 x 30 / (2π x BUR) = 1718.87/BUR

•

So if you’re using these formulae, the first thing you need to check is whether the BUR is expressed per 100, per 30, or whatever

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5

Projecting Ahead •

Some of the abbreviations used are – – – – – – –

I CL MD TVD Az VS BUR

= = = = = = =

– – – – – –

rc TF DL DLS BOH LSS

= = = = = =

inclination (degrees) course length (feet or metres) measured depth (feet or metres) true vertical depth (feet or metres) azimuth (hole direction) (degrees) vertical section (feet or metres) build up rate (º/interval) e.g. a BUR of 12º/100ft would be input into the formulas as 12 radius of curvature (feet or metres) toolface (degrees from highside) dogleg (degrees) dogleg severity (degrees/100 ft or degrees/30m) bottom of hole last survey station

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Calculating Inc and Az at BOH for given build & turn •

Assume we have taken two successive surveys at different depths

•

If we assume that the hole curvature between these two surveys continues to the bottom of the hole, then we can easily calculate first the BUR, then the inc and az at the bottom of the hole

•

Remember that the interval (for BUR) is typically 100 if using feet, and 30 for m

•

To determine the inclination and direction at the bottom of the hole: – Formulae BUR = (

I 2 - I1 MD 2 - MD1

I BOH = ( CL LSS -BOH ×

) × Interval

BUR ) + I2 Interval

Turn Rate = (

Az 2 - Az1 ) × Interval MD 2 - MD1

Az BOH = ( CL LSS -BOH ×

Turn Rate Interval

) + Az 2

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6

Calculating Inc and Az at BOH for given build & turn Example •

The following are the last two surveys a directional driller obtained (depths in ft): – MD Inc Az TVD – 4653 30 15 4643.99 – 4713 39 18 4693.38

•

The bit to sensor distance is 33 ft and surveys are taken 5 ft off of bottom

•

Assume the curvature between the last two survey stations will accurately reflect the build rate to the bottom of the hole

•

What is the projected inclination and direction at the bottom of the hole?

•

We first need to calculate the build rate and turn rate achieved between the last two survey stations using the appropriate formula

•

Then we need to project the inclination and direction at the bottom of the hole based on the calculated build rate and the distance from the survey sensor to the bottom of the hole

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Calculating Inc and Az at BOH for given build & turn Example BUR = (

I 2 - I1 ) × Interval MD 2 - MD1

Turn Rate = (

BUR = (

39 - 30 ) × 100 4713 - 4653

Turn Rate = (

BUR = 15° /100ft

BUR ) + I2 Interval

I BOH = (CL ×

I BOH = (38 ×

15 ) + 39 100

I BOH = 44.70°

Az 2 - Az 1 ) × Interval MD 2 - MD1

18 - 15 ) × 100 4713 - 4653

Turn Rate = 5°/100 ft

Az BOH = (CL ×

Az BOH = (38 ×

Turn Rate ) + Az 2 Interval 5 ) + 18 100

Az BOH = 19.9°

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7

Exercise

•

Do Ex 1 to find the inclination and direction at the bottom of the hole given the last two surveys

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Calculating TVD for a projected Inc at a specified BUR •

Assume that the DD now wants to know what the TVD will be (at a given inc) if he continues to build at the rate defined by the last two surveys

rc I1

TVD1 TVD2 ΔTVD

I2

TVD1 = rc × sinI 1 TVD 2 = rc × sinI 2 So ΔTVD = TVD 2 – TVD1 = rcsinI 2 – rcsinI 1 = rc (sinI 2 – sinI 1 )

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8

Calculating TVD for a projected Inc at a specified BUR Example •

Using the same data as in the previous example, let’s assume that the build rate between the last two survey stations is continued to the BOH

•

So, we can calculate what the TVD will be at the bottom of the hole

BUR = 15° /100 ft.

rc =

5729.58 BUR

=

5729.58 15

= 381.97 ft

ΔTVD LSS -BOH = rc × (sinI BOH – sinI LSS ) = 381.97 × (sin 44.7 – sin 39) = 28.29 TVD BOH = TVD LSS + ΔTVD BOH -LSS = 4693.38 + 28.29 = 4721.67 ft

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Exercise

•

Do Ex 2 to find the TVD at a projected inclination

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9

Calculating BUR required for a given TVD •

We may wish to do the previous calculation the other way round – for a given TVD (e.g. target TVD) and inclination, what is the required BUR?

•

From a previous slide, we have

ΔTVD = rc (sin I 2 – sinI 1 ) So rc =

(TVD2 – TVD1 ) (sin I 2 – sinI 1 ) (sin I 2 – sinI 1 ) ΔTVD

Since BUR =

=

5729.58 rc

Then BURRequired = 5729.58 ×

(sin I 2 – sinI 1 ) (TVD2 – TVD1 )

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Calculating BUR required for a given TVD •

So if we wish to calculate the BUR from the BOH to the target, then

BURRequired = 5729.58 ×

(sin I 2 – sin I1 ) (TVD 2 – TVD1 )

becomes

BURRequired = 5729.58 ×

(sin I (TVD

target target

– sin I BOH )

– TVDBOH )

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10

Calculating BUR required for a given TVD •

So, again using the same example data, if we wish to calculate the BUR from the BOH to the target, then

BURRequired = 5729.58 ×

(sin I (TVD

target target

– sin I BOH )

– TVD BOH )

becomes

(sin 89 – sin 44.7) (4930 – 4721.67 )

BURRequired = 5729.58 ×

= 8.15°/100 ft •

This 8.15°/100 ft BUR can then be compared against the calculated BUR when the next survey is taken

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Exercise

•

Do Ex 3 to find the BUR required to hit a particular TVD at a given inclination

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11

Miscellaneous •

Remember if the units are metres, use 1718.87 instead of 5729.58

•

These calculations have been concentrating on projections in the build plane i.e. inclinations

•

Similar formulae can be derived and applied to the turn plane i.e. azimuths

•

In practice, once the calculations become moderately complex, it is rare to do them by hand

•

Typically, WA is used if calculations are required to estimate – what’s required to hit the target (build, turn, front, back, top, bottom) – what’s required to get back on the line (profile, DLS, by a given TVD) at a given inc and az – etc.

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