Short Radius Presentation

Short Radius Well CalculationsCalculating the Radius of Curvature

USDDSM0DFT © Copyright 1998, Sperry-Sun, a division of Dresser Industries, Inc. 1May 29, 1998

Short Radius Well Calculations

Calculating the Radius of Curvature

Knowing the build-up rate (BUR), you can calculate the value of the radius of curvature, Rc, for the build-up section of a well. Knowing the values for inclination at the start of the arc (I1) and the end of the arc (I2), you can find the incremental values for horizontal displacement (HD), vertical depth (VD), and measured depth (MD).

The radius of curvature is normally expressed in degrees/100' (degrees/30 m). To calculate a build or drop radius, the formula is:

Note: .

In our examples, we will use approximate values of 5730 and 1719.

Radius

180π

--------- 30×

Build Rate----------------------------=Radius

180π

--------- 100×

Build Rate----------------------------=

Feet Meters

180π

--------- 100× 5729.5780=180π

--------- 30× 1718.8734=


2 © Copyright 1998, Sperry-Sun, a division of Dresser Industries, Inc. USDDSM0DFTMay 29, 1998

Figure 1 Radius of curvature - relationships among angles

Feet Meters

1.

2.

3.

4.

KOP (Kick Off Point)

TV

D(T

rue

Vert

icalD

epth

)Displacement

Rad

ius

R

180π

--------- 100×

BUR------------------------ 5730

BUR------------= = R

180π

--------- 30×

BUR--------------------- 1719

BUR------------= =

Radius TVD Displacement= = Radius TVD Displacement= =

BUR5730TVD------------= BUR

1719TVD------------=

BUR5730DISP--------------= BUR

1719DISP--------------=

Curve Length∆Inc 100×

BUR---------------------------= Curve Length

∆Inc 30×BUR

------------------------=



Figure 2 Calculation example

Determine TVD1, DISP1, and MD1

On the plot, Angle 1 is the angle at the end of the build.

Prove Angle 1(end of build angle) = Angle 2(∆Inclination).

1. and

2.

Subtract 1 from 2.

Add Angle 1 to both sides of the eqation.

Complete the addition.

KOP

TVD1

Displacement

Rad

iusR 1

MD

1

DISP1

1

2

3

180° Right Angle Angle 3 Angle 2+ +=

180° Right Angle Angle 3 Angle 1+ +=

180° 180°– Rt Angle Angle 3 Angle 2 Rt Angle Angle 3 Angle 1–––+ +=

0 Angle 2 Angle 1–=

0 Angle 1+ Angle 2 Angle 1– Angle 1+=

Angle 1 Angle 2=



Figure 3 Calculation example

Determine: Calculate:

1. TVD1 1. R1

2. DISP1 2. DISPB

3. MD1

Calculate: Formulas used:

1.

2.

3.

4.

Note:

KOP

TVD1

Displacement

Rad

iusR 1

MD

1

DISP1

DISPB DISPA

1

2

3

TVD1 sin Angle 2 Radius×= Opposite asin Hypotenuse×=

DISPA cos Angle 2 Radius×= Adjacent acos Hypotenuse×=

DISP1 Radius cos Angle 2 Radius×( )–=

MD1∆Inc 100×

BUR--------------------------=

DISP1 DISPB=

Short Radius Well CalculationsExample #1


Example #1

Given:

1. Your target TVD is 8641 feet at an inclination of 90°.

2. Your current TVD is 8560 feet at an inclination of 72°.

Figure 4 Example #1

Questions

1. What is the radius of curvature?

2. What is the remaining measured depth?3. What is the remaining vertical section?4. What is the build rate to target?

Short Radius Well CalculationsExample #1 Answers


Example #1 Answers


You use the following formula:

Figure 5 Example #1 Question #1 Illustration

Radius of curvatureTarget TVD Survey TVD–

sin (Target inclination) sin (Survey inclination)–----------------------------------------------------------------------------------------------------------------------=

Radius of curvature8641 8560–

sin 90( ) sin 72( )–---------------------------------------------=


1.000000 0.951057–---------------------------------------------------=

Radius of curvature81

0.048943----------------------=

Radius of curvature 1654.97feet=



2. What is the remaining measured depth?



Remaining measured depth2 π× Radius of curvature×

360------------------------------------------------------------------ ∆inclination to target×=

Remaining measured depth2 π× 1654.97×

360-------------------------------------- 18×=

Remaining measured depth6.283185 1654.97×

360------------------------------------------------ 18×=

Remaining measured depth10398.48

360---------------------- 18×=

Remaining measured depth 28.884676 18×=

Remaining measured depth 519.92feet=



3. What is the remaining vertical section?



Remaining vertical section Radius of curvature cos (Target inc) cos(Survey inc)–( )×=

Remaining vertical section 1654.97 cos 90( ) cos 72( )–( )×=

Remaining vertical section 1654.97 0 0.309017–( )×=

Remaining vertical section 511.41feet=



4. What is the build rate to target?



Build rate to targetDifference in inclination to target

Remaining measured depth-------------------------------------------------------------------------------- 100×=

Build rate to target90 72–519.92------------------ 100×=

Build rate to target18

519.92---------------- 100×=

Build rate to target 0.034621 100×=

Build rate to target 3.46 degrees/100 feet=



Example #2

Given:

1. Your target TVD is 7873 feet at an inclination of 89°.

2. Your current TVD is 7800 feet at an inclination of 2°.

Figure 9 Example #2

Questions


2. What is the measured depth?3. What is the displacement?4. What is the build rate to target?



Example #2 Answers




Radius of curvatureTarget TVD Survey TVD–

sin (Target inclination) sin Survey inclination( )–-----------------------------------------------------------------------------------------------------------------------=


sin 89( ) sin 2( )–------------------------------------------=


0.999848 0.034899–---------------------------------------------------=


0.964948----------------------=

Radius of curvature 75.65feet=



2. What is the measured depth?



Remaining measured depth2 π× Radius of curvature×

360------------------------------------------------------------------ ∆inclination to target×=

Measured depth2 π× 75.65×

360-------------------------------- 87×=

Measured depth475.322968

360---------------------------- 87×=

Measured depth 1.320342 87×=

Measured depth 114.87feet=



3. What is the displacement?



Remaining Displacement Radius of curvature cos Target inc( ) cos Survey inc( )–( )×=

Displacement 75.65 cos 89( ) 2( )cos–( )×=

Displacement 75.65 0.017452 0.999391–( )×=

Displacement 75.65 0.981938×=

Displacement 74.28feet=



4. What is the build rate to target?



Build rate to targetDifference in inclination to target

Measured depth-------------------------------------------------------------------------------- 100×=

Build rate to target89 2–114.87---------------- 100×=

Build rate to target87

114.87---------------- 100×=

Build rate to target 0.757378 100×=

Build rate to target 75.74 degrees/100 feet=



Example #3

Given:

1. Current inclination = 88°

2. Current dogleg = 3°/100 feet3. Drill bit is at penetration of water.

Figure 14 Example #3

Questions

1. What is the measured depth (MD)?

2. What is the depth of penetration (TVD)?3. What is the length of penetration while drilling (HD)?



Example #3 Answers

1. What is the measured depth (MD)?



Measured depth∆Inc 100×

BUR---------------------------=

Measured depth2 100×

3------------------=

Measured depth2003

---------=

Measured depth 66.67feet=



2. What is the depth of penetration (TVD)?



Radius of curvature5730BUR------------=


3------------=

Radius of curvature 1910feet=



2. What is the depth of penetration (TVD)? (continued)

Then use the following formula:


Incremental vertical depth RC Inclinationsin RC×( )–=

Incremental vertical depth 1910 sin 88( ) 1910×( )–=

Incremental vertical depth 1910 0.9993908 1910×( )–=

Incremental vertical depth 1910 1908.84–=

Incremental vertical depth 1.16feet=



3. What is the length of penetration while drilling (HD)?



Displacement cos Inclination( ) Radius of curvature×=

Displacement cos 88( ) 1910×=

Displacement 0.034899 1910×=

Displacement 66.66feet=



3. What is the length of penetration while drilling (HD)? (continued)

You then use the following formula:


Total displacement Displacement 2×=

Total displacement 66.66 2×=

Total displacement 133.32feet=

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