WELLBORE COMPLETIONS DESIGN FOR A VERTICAL GAS WELL

EXECUTIVE SUMMARY

By Daevin Dev

A vertical gas completion was to be designed using 2-7/8” tubing. Minimal constraints were present in

the well. However, the well needed to be stimulated using acid. Based on these conditions several

analysis were performed to determine the safest and most economical type of tubing and completion

equipment to be used in completing this well. The final chosen tubing was the API type N80 2-7/8”

6.5ppf EUE. A brief description of the different types of analysis performed and its corresponding

outcomes are outlined below.

An initial selection of the tubing type was done through burst and collapse analysis. A worst case

scenario for burst and collapse were devised based on the available conditions and potential fluids that

would be in the tubing and in the annulus throughout the life of the well. Next, the minimum tubing

strength requirements were calculated, based on potential loads and backups, and compared against

available tubing data tables. An initial tubing selection was made based of this initial analysis. This tubing

was then used as the basis for further analysis.

The next analysis performed was testing the chosen tubing for potential failure through excessive

elongation or excessive force applied at the tubing at packer depth. This analysis tests the whether or

not the tubing will be able to withstand the potential high pressure and temperature differentials that

are bound to exist during stimulation and/or production. Additionally, this analysis would also indicate

whether or not the tubing can be landed or lathed at the packer. The specifics of this analysis are

outlined in the Excel™ file that was uploaded along with this summary. The outcome of this analysis was

that the preselected tubing, from above, would not fail and that it could be latched if a slack-off weight

was imposed on the tubing and if an annular surface pressure was introduced so as to offset some of the

pressure differential at the packer depth.

Consequently, the completions equipment that was to accompany the tubing needed to be selected.

The packer chosen was the retrievable type PMDJ Production Mechanical Packer by Schlumberger. It has

a high working pressure and is designed to support acid and frack stimulations, which suits the

requirements perfectly. Additionally, it also has an emergency release system which would prove handy

in the event of an emergency. A Nitrile type elastomer was chosen to seal the tubing and the packer

because of Nitrile’s high pressure & temperature resistance. A landing seating nipple is to be placed

above the packer to assist other tools in passing through the tubing. A sliding sleeve is incorporated into

the design to allow for ease of unloading the well. Two side pocket mandrels will be placed above the

sliding sleeve with a generous spacing to account for the possibility of artificial lift. The last two

completions equipment is the subsurface safety vale, for emergency production conduit closures, and

the tubing head and hanger to support the whole tubing string.

The projected estimated cost for the tubing is $127,920 at a footage cost of about $10/ft. The additional

completions equipment is estimated to cost about $21,775. This brings the total estimated cost of

completing the well to about $150,000. This cost does, however, exclude the cost of the tubing head

and other additional costs that will be incurred during the stimulation job.

All sample calculations and related diagrams have been uploaded, separately, along with this summary.

The Excel™ file outlines, to as much detail as possible, the necessary dimensions and specifics of the

completions design mentioned in this summary.

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Sample Calculations

All equations were obtained from Module 4: Tubing Design, PEGN 361: Completions Engineering, Colorado School of Mines.

1. Tubing Cross-sectional Area

𝐴𝑐𝑠 = 𝜋

4× (2.8752 − 2.4412)

𝐴𝑐𝑠 = 1.812𝑖𝑛2

2. Packer Bore Area

𝐴𝑝 = 𝜋

4× (3.252)

𝐴𝑝 = 8.296𝑖𝑛2

3. Outside Tubing Area

𝐴𝑜 = 𝜋

4× (2.8752)

𝐴𝑜 = 6.492𝑖𝑛2

4. Inside Tubing Area

𝐴𝑖 = 𝜋

4× (2.4412)

𝐴𝑖 = 4.68𝑖𝑛2

5. Tubing-To-Casing Clearance, ∆r

∆𝑟 = 6.366 − 2.875

2

∆𝑟 = 1.7455𝑖𝑛

6. Moment Of Inertia, I

𝐼 = 𝜋

64× (2.8754 − 2.4414)

𝐼 = 1.612𝑖𝑛4

7. Weight Of Fluid Inside Tubing, Wi

𝑊𝑖 = 0.0034 × 2.4412 × 9.5

𝑊𝑖 = 0.1924𝑙𝑏𝑚/𝑖𝑛

8. Weight Of Fluid Outside Tubing, Wo

𝑊𝑜 = 0.0034 × 2.8752 × 11.5

𝑊𝑜 = 0.3232𝑙𝑏𝑚/𝑖𝑛

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9. Ratio Of OD to ID, R

𝑅 = 2.875

2.441

𝑅 = 1.178

10. Pressures At The Packer For Initial & Final Conditions

a. Initial Tubing Conditions

𝑃 = 8.3

19.25× 12250

𝑃 = 5282𝑝𝑠𝑖

b. Final Tubing Conditions

𝑃 = 9500 +9.5

19.25× 12250

𝑃 = 14321𝑝𝑠𝑖

c. Initial Annulus Conditions

𝑃 = 8.3

19.25× 12250

𝑃 = 5282𝑝𝑠𝑖

d. Final Annulus Conditions

𝑃 = 1700 +11.5

19.25× 12250

𝑃 = 9018.2𝑝𝑠𝑖

11. Change In Pressure In Tubing At Packer Depth, ∆Pi

∆𝑃𝑖 = 14321 − 5282

∆𝑃𝑖 = 9039𝑝𝑠𝑖

12. Change In Pressure In Annulus At Packer Depth, ∆Po

∆𝑃𝑜 = 9018 − 5282

∆𝑃𝑜 = 3736𝑝𝑠𝑖

13. Change In Average Pressure In Tubing, ∆̅𝑃𝑖

∆̅𝑃𝑖 = 14321 + 9500

2−

5282 + 0

2

∆̅𝑃𝑖 = 9269𝑝𝑠𝑖

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14. Change In Average Pressure In Tubing, ∆̅𝑃𝑜

∆̅𝑃𝑜 = 9018 + 1700

2−

5282 + 0

2

∆̅𝑃𝑜 = 2718𝑝𝑠𝑖

15. Force Due to Piston Effect, F1

𝐹1 = [(8.296 − 6.492) × 3736] − [(8.296 − 4.68) × 9039]

𝐹1 = −25943 𝑙𝑏𝑓

16. Length Change Due To Piston Effect, ∆L1

𝐿1 =−25943 × 12250

30,000,000 × 1.812

𝐿1 = −70.4𝑖𝑛

17. Length Change Due To Buckling Effect, ∆L2

𝐿2 = −1.74552 × 8.2962 × (9039 − 3736)2

8 × 30,000,000 × 1.612 × (6.512 + 0.1924 − 0.3232)

𝐿2 = −37.1𝑖𝑛

18. Neutral Point Of Tension & Compression, n

𝑛 = (12250 × 12) −8.296 × (14321 − 9018)

(6.512 + 0.1924 − 0.3232)

𝑛 = 39961𝑖𝑛

19. Adjusted Length Change Due To Buckling, ∆L2 Adj

𝑆𝑖𝑛𝑐𝑒 𝑛 𝑖𝑠 𝑛𝑜𝑡 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 0 𝑜𝑟 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 𝐿, ∆𝐿2 𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑 = ∆𝐿2

∆𝐿2 𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑 = −37.1𝑖𝑛

20. Force Due to Ballooning Effect, F3

𝐹3 = 2 × 0.3 × (2718 × 6.492 − 9269 × 4.68)

𝐹3 = −15440𝑙𝑏𝑓

21. Length Change Due To Ballooning Effect, ∆L3

∆𝐿3 = (2 × 0.3 × 12250 × 12

30,000,000) × [

1.178 × 2718 − 9269

1.1782 − 1]

∆𝐿3 = −41.9𝑖𝑛

22. Force Due To Temperature Effect, F4

𝐹4 = 207 × 1.812 × −62.5

𝐹4 = −23443𝑙𝑏𝑓

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23. Length Change Due To Temperature, ∆L4

∆𝐿4 = 6.9 × 10−6 × 12250 × −62.5 × 12

∆𝐿4 = −63.4𝑖𝑛

24. Total Force, Fp

𝐹𝑝 = −25943.3 − 15440 + 10000 − 23443

𝐹𝑝 = −54825.9𝑙𝑏𝑓

25. Length Change Due To Slackoff Effect, ∆Lm

∆𝐿𝑚 = (10,000 × 12250

30,000,000 × 1.812) + (

1.74552 × 10,0002

8 × 30,000,000 × 1.612 × (6.512

+ 0.1924 − 0.3232))

∆𝐿𝑚 = −29.1𝑖𝑛

26. Total Length Movement, Lp

𝐿𝑝 = −70.4 − 37.1 − 41.9 + 29.1 − 63.4

𝐿𝑝 = −183.8𝑖𝑛

27. Actual Force At Packer, Fa

𝐹𝑎 = [(8.296 − 4.68) × 9039] − [(8.296 − 6.492) × 3736]

𝐹𝑎 = 35514𝑙𝑏𝑓

28. Top Joint Tension, Ftgs

𝐹𝑡𝑔𝑠 = 35514 − 54825.9 + 10000

𝐹𝑡𝑔𝑠 = 60638.2 𝑙𝑏𝑓

29. Outer Wall Stress For Slack-Off Weight, So

𝑆𝑜 =10,000

1.812+

2.875 × 1.7455 × 10000

4 × 1.612

𝑆𝑜 = 13306.7𝑝𝑠𝑖

30. Axial Stress, σa

𝜎𝑎 =35514

1.812

𝜎𝑎 = 19599.1𝑝𝑠𝑖

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31. σb

𝜎𝑏 = 2.875 × 1.7455 × 8.296 × (9039 − 3736)

4 × 1.612

𝜎𝑏 = 34275𝑝𝑠𝑖

32. Inner Tubing Wall Stress, σi

𝜎𝑖 = √3 × [1.1782(14321 − 9018)

1.1782 − 1]

2

+ [14321 − 1.1782 × 9018

1.1782 − 1+ 19599 +

34275

1.178]

2

𝜎𝑖 = 62689𝑝𝑠𝑖

33. Outer Tubing Wall Stress, σo

𝜎𝑜 = √3 × [(14321 − 9018)

1.1782 − 1]

2

+ [14321 − 1.1782 × 9018

1.1782 − 1+ 19599 + 34275]

2

𝜎𝑜 = 63155𝑝𝑠𝑖