Systems and methods for determining the moments and forces of two concentric pipes within a wellbore

• US 8,855,933 B2
• Filed: 06/24/2011
• Issued: 10/07/2014
• Est. Priority Date: 06/24/2011
• Status: Active Grant

• Current Assignee: Landmark Graphics Corporation (Halliburton Company)
• Original Assignee: Landmark Graphics Corporation (Halliburton Company)
• Inventors: Mitchell, Robert F.
• Primary Examiner(s): Breene, John
• Assistant Examiner(s): HWANG, TIMOTHY
• Application Number:
  US13/980,913
• Publication Number:
  US 20140032115A1
• Time in Patent Office: 1,201 Days
• Field of Search: 731/524.9, 731/524.8
• US Class Current: 702/9
• CPC Class Codes: E21B 47/007 Measuring stresses in a pipe string or casing for locating blocked portions of pipes E21B47/09
• CPC Class Codes: E21B 47/09 Locating or determining the position of objects in boreholes or wells , e.g. the position of an extending arm; Identifying the free or blocked portions of pipes

Abstract

Systems and methods for determining the bending moment and shear force of tubing and casing when the tubing buckles and contacts the casing.

Claims

1. A method for determining the moments and forces of two concentric pipes within a wellbore, comprising:

determining an external pipe displacement using a computer processor;

determining whether the external pipe contacts the wellbore based on the external pipe displacement;

determining a bending moment and a shear force of an internal pipe and the external pipe based on contact between the internal pipe and the external pipe and the external pipe displacement if the external pipe does not contact the wellbore;

determining whether contact forces between the internal pipe and the external pipe and between the external pipe and the wellbore are greater than or equal to zero if the external pipe contacts the wellbore;

determining the bending moment and the shear force of the internal pipe and the external pipe, using the computer processor, based on contact between the internal pipe and the external pipe and contact between the external pipe and the wellbore if the contact forces between the internal pipe and the external pipe and between the external pipe and the wellbore are greater than or equal to zero;

determining a displacement solution using a contact force between the internal pipe and the external pipe equal to zero if the contact forces between the internal pipe and the external pipe and between the external pipe and the wellbore are not greater than or equal to zero;

determining whether there is another displacement solution using a contact force between the external pipe and the wellbore equal to zero if the contact forces between the internal pipe and the external pipe and between the external pipe and wellbore are not greater than or equal to zero; and

determining the bending moment and the shear force of the internal pipe and the external pipe based on the displacement solution or the another displacement solution if the contact forces between the internal pipe and the external pipe and between the external pipe and the wellbore are not greater than or equal to zero.

2. The method of claim 1, further comprising selecting the displacement solution to determine the bending moment and the shear force of the internal pipe and the external pipe if there is not another displacement solution.

3. The method of claim 1, further comprising selecting the displacement solution to determine the bending moment and the shear force of the internal pipe and the external pipe if the displacement solution produces a total potential energy for a system represented by the internal pipe and the external pipe that is less than a total potential energy for the system produced by the another displacement solution.

4. The method of claim 1, further comprising selecting the another displacement solution to determine the bending moment and the shear force of the internal pipe and the external pipe if the another displacement solution produces a total potential energy for a system represented by the internal pipe and the external pipe that is less than a total potential energy for the system produced by the displacement solution.

5. The method of claim 1, further comprising performing a stress analysis of the internal pipe and the external pipe based on the bending moment and the shear force of the internal pipe and the external pipe.

6. The method of claim 1, wherein

7. The method of claim 1, wherein

8. The method of claim 1, wherein

9. The method of claim 1, wherein

10. The method of claim 1, wherein

11. The method of claim 10, wherein

12. The method of claim 11, wherein

13. The method of claim 3, wherein

U=½

(E_cI_cr_oc²+E_tI_tr_ic²)β

⁴+½

(Fr_oc²−

Pr_oc²)β

²

is used to determine the total potential energy for the system;

E_c is Young'"'"'s modulus of the casing;

I_c is moment of inertia of the casing, r_oc is nominal radial clearance between the casing and exterior wellbore;

E_t is Young'"'"'s modulus of the tubing;

I_t is moment of inertia of the tubing;

r_ic is r_oc−

t_c;

t_c is the thickness of the casing;

β

is a possible displacement solution;

F is axial tension in casing; and

P is axial compression in tubing.

14. A non-transitory program carrier device tangibly carrying computer executable instructions for determining the moments and forces of two concentric pipes within a wellbore, the instructions being executable to implement:

determining an external pipe displacement;

determining whether the external pipe contacts the wellbore based on the external pipe displacement;

determining a bending moment and a shear force of an internal pipe and the external pipe based on contact between the internal pipe and the external pipe and the external pipe displacement if the external pipe does not contact the wellbore;

determining whether contact forces between the internal pipe and the external pipe and between the external pipe and the wellbore are greater than or equal to zero if the external pipe contacts the wellbore;

determining the bending moment and the shear force of the internal pipe and the external pipe based on contact between the internal pipe and the external pipe and contact between the external pipe and the wellbore if the contact forces between the internal pipe and the external pipe and between the external pipe and the wellbore are greater than or equal to zero;

determining a displacement solution using a contact force between the internal pipe and the external pipe equal to zero if the contact forces between the internal pipe and the external pipe and between the external pipe and the wellbore are not greater than or equal to zero;

determining whether there is another displacement solution using a contact force between the external pipe and the wellbore equal to zero if the contact forces between the internal pipe and the external pipe and between the external pipe and wellbore are not greater than or equal to zero; and

determining the bending moment and the shear force of the internal pipe and the external pipe based on the displacement solution or the another displacement solution if the contact forces between the internal pipe and the external pipe and between the external pipe and the wellbore are not greater than or equal to zero.

15. The program carrier device of claim 14, further comprising selecting the displacement solution to determine the bending moment and the shear force of the internal pipe and the external pipe if there is not another displacement solution.

16. The program carrier device of claim 14, further comprising selecting the displacement solution to determine the bending moment and the shear force of the internal pipe and the external pipe if the displacement solution produces a total potential energy for a system represented by the internal pipe and the external pipe that is less than a total potential energy for the system produced by the another displacement solution.

17. The program carrier device of claim 14, further comprising selecting the another displacement solution to determine the bending moment and the shear force of the internal pipe and the external pipe if the another displacement solution produces a total potential energy for a system represented by the internal pipe and the external pipe that is less than a total potential energy for the system produced by the displacement solution.

18. The program carrier device of claim 14, further comprising performing a stress analysis of the internal pipe and the external pipe based on the bending moment and the shear force of the internal pipe and the external pipe.

19. The program carrier device of claim 14, wherein

20. The program carrier device of claim 14, wherein

21. The program carrier device of claim 14, wherein

22. The program carrier device of claim 14, wherein

23. The program carrier device of claim 14, wherein

24. The program carrier device of claim 19, wherein

25. The program carrier device of claim 20, wherein

26. The program carrier device of claim 16, wherein

U=½

(E_cI_cr_oc²+E_tI_tr_ic²)β

⁴+½

(Fr_oc²−

Pr_oc²)β

²

is used to determine the total potential energy for the system;

E_c is Young'"'"'s modulus of the casing;

I_c is moment of inertia of the casing, r_oc is nominal radial clearance between the casing and exterior wellbore;

E_t is Young'"'"'s modulus of the tubing;

I_t is moment of inertia of the tubing;

r_ic is r_oc−

t_c;

t_c is the thickness of the casing;

β

is a possible displacement solution;

F is axial tension in casing; and

P is axial compression in tubing.

27. A method for determining the moments and forces of two concentric pipes within a wellbore, comprising:

determining an external pipe displacement using a computer processor;

determining whether the external pipe contacts the wellbore based on the external pipe displacement; and

determining a bending moment and a shear force of an internal pipe and the external pipe, using the computer processor, based on at least one of contact between the internal pipe and the external pipe and contact between the external pipe and the wellbore.

28. The method of claim 27, wherein determining the bending moment and the shear force of the internal pipe and the external pipe is based on contact between the internal pipe and the external pipe and the external pipe displacement if the external pipe does not contact the wellbore.

29. The method of claim 27, wherein determining the bending moment and the shear force of the internal pipe and the external pipe is based on contact between the internal pipe and the external pipe and contact between the external pipe and the wellbore if the contact forces between the internal pipe and the external pipe and between the external pipe and the wellbore are greater than or equal to zero.

30. The method claim 27, wherein determining the bending moment and the shear force of the internal pipe and the external pipe is based on a displacement solution or another displacement solution if the contact forces between the internal pipe and the external pipe and between the external pipe and the wellbore are not greater than or equal to zero.

31. The method of claim 30, wherein the displacement solution is determined using a contact force between the internal pipe and the external pipe equal to zero.

32. The method of claim 30, wherein the another displacement solution is determined using a contact force between the external pipe and wellbore equal to zero.

33. The method of claim 30, wherein the displacement solution is used to determine the bending moment and the shear force of the internal pipe and the external pipe if there is not another displacement solution.

34. The method of claim 30, further comprising selecting the displacement solution to determine the bending moment and the shear force of the internal pipe and the external pipe if the displacement solution produces a total potential energy for a system represented by the internal pipe and the external pipe that is less than a total potential energy for the system produced by the another displacement solution.

35. The method of claim 30, further comprising selecting the another displacement solution to determine the bending moment and the shear force of the internal pipe and the external pipe if the another displacement solution produces a total potential energy for a system represented by the internal pipe and the external pipe that is less than a total potential energy for the system produced by the displacement solution.

36. A non-transitory program carrier device tangibly carrying computer executable instructions for determining the moments and forces of two concentric pipes within a wellbore, the instructions being executable to implement:

determining an external pipe displacement;

determining whether the external pipe contacts the wellbore based on the external pipe displacement; and

determining a bending moment and a shear force of an internal pipe and the external pipe based on at least one of contact between the internal pipe and the external pipe and contact between the external pipe and the wellbore.

37. The program carrier device of claim 36, wherein determining the bending moment and the shear force of the internal pipe and the external pipe is based on contact between the internal pipe and the external pipe and the external pipe displacement if the external pipe does not contact the wellbore.

38. The program carrier device of claim 36, wherein determining the bending moment and the shear force of the internal pipe and the external pipe is based on contact between the internal pipe and the external pipe and contact between the external pipe and the wellbore if the contact forces between the internal pipe and the external pipe and between the external pipe and the wellbore are greater than or equal to zero.

39. The program carrier device claim 36, wherein determining the bending moment and the shear force of the internal pipe and the external pipe is based on a displacement solution or another displacement solution if the contact forces between the internal pipe and the external pipe and between the external pipe and the wellbore are not greater than or equal to zero.

40. The program carrier device of claim 39, wherein the displacement solution is determined using a contact force between the internal pipe and the external pipe equal to zero.

41. The program carrier device of claim 39, wherein the another displacement solution is determined using a contact force between the external pipe and wellbore equal to zero.

42. The program carrier device of claim 39, wherein the displacement solution is used to determine the bending moment and the shear force of the internal pipe and the external pipe if there is not another displacement solution.

43. The program carrier device of claim 39, further comprising selecting the displacement solution to determine the bending moment and the shear force of the internal pipe and the external pipe if the displacement solution produces a total potential energy for a system represented by the internal pipe and the external pipe that is less than a total potential energy for the system produced by the another displacement solution.

44. The program carrier device of claim 39, further comprising selecting the another displacement solution to determine the bending moment and the shear force of the internal pipe and the external pipe if the another displacement solution produces a total potential energy for a system represented by the internal pipe and the external pipe that is less than a total potential energy for the system produced by the displacement solution.