Systems and Methods for Modeling Drillstring Trajectories

• US 20130151217A1
• Filed: 02/08/2013
• Published: 06/13/2013
• Est. Priority Date: 03/24/2009
• Status: Abandoned Application

• Current Assignee: Landmark Graphics Corporation (Halliburton Company)
• Original Assignee: Landmark Graphics Corporation (Halliburton Company)
• Inventors: Mitchell, Robert Franklin
• Application Number:
  US13/763,526
• Publication Number:
  US 20130151217A1
• Time in Patent Office: Days
• US Class Current: 703/2
• CPC Class Codes: E21B 7/04 Directional drilling
• CPC Class Codes: G06F 30/20 Design optimisation, verification or simulation optimisation, verification or simulation of circuit designs G06F30/30

Abstract

Systems and methods for modeling drillstring trajectories by calculating forces in the drillstring using a traditional torque-drag model and comparing the results with the results of the same forces calculated in the drillstring using a block tri-diagonal matrix, which determines whether the new drillstring trajectory is acceptable and represents mechanical equilibrium of drillstring forces and moments.

Claims

1. A method for modeling a drillstring trajectory, comprising:

calculating an initial value of force and an initial value of moment for each joint along a drillstring model using a conventional torque-drag model, a tangent vector, a normal vector and a bi-normal vector for each respective joint;

calculating a block tri-diagonal matrix for each connector on each joint using displacement coefficients (U_n^k(ξ

),U_b^k(ξ

) for each joint and two unknown rotations (X_n,k,X_b,k) for each connector wherein;

2. The method of claim 1, further comprising:

calculating the tangent vector at each survey point using survey data at each respective survey point.

3. The method of claim 2, wherein the survey data comprises an angle (θ

), another angle (φ

), and a measured depth (s) for each survey point.

4. The method of claim 3, wherein the tangent vector includes directional components and is calculated by:

{right arrow over (t)}_j·

{right arrow over (i)}_N=cos(θ

_j)sin(φ

_j)

{right arrow over (t)}_j·

{right arrow over (i)}_E=sin(θ

_j)sin(φ

_j)

{right arrow over (t)}_j·

{right arrow over (i)}_z=cos(φ

_j)

5. The method of claim 4, further comprising calculating the normal vector at each survey point using the tangent vector calculated at each respective survey point.

6. The method of claim 5, further comprising calculating the bi-normal vector at each survey point using the tangent vector and the normal vector calculated at each respective survey point.

7. The method of claim 1, wherein:

8. The method of claim 1, wherein:

9. The method of claim 1, further comprising calculating a new value of force and a new value of moment for each joint along the drillstring model.

10. The method of claim 9, further comprising:

comparing the initial value of force and the initial value of moment with the new value of force and the new value of moment to determine if the values are sufficiently close for each joint along the drillstring; and

repeating the steps of calculating a block tri-diagonal matrix for each connector on each joint and modeling the drillstring trajectory by solving the block tri-diagonal matrix for the two unknown rotations at each connector if the initial values of force and moment are not sufficiently close to the new values of force and moment.

11. The method of claim 10, wherein the new values of force and moment are sufficiently close to the initial values of force and moment if the new values of force and moment are within a range of ±

2% of the initial values of force and moment.

12. A program carrier device for carrying computer executable instructions for modeling a drillstring trajectory, the instructions being executable to implement:

calculating an initial value of force and an initial value of moment for each joint along a drillstring model using a conventional torque-drag model, a tangent vector, a normal vector and a bi-normal vector for each respective joint;

calculating a block tri-diagonal matrix for each connector on each joint using displacement coefficients (U_n^k(ξ

),U_b^k(ξ

)) for each joint and two unknown rotations (X_n,k,X_b,k) for each connector wherein;

13. The program carrier device of claim 12, further comprising:

calculating the tangent vector at each survey point using survey data at each respective survey point.

14. The program carrier device of claim 13, wherein the survey data comprises an angle (θ

), another angle (φ

), and a measured depth (s) for each survey point.

15. The program carrier device of claim 14, wherein the tangent vector includes directional components and is calculated by:

{right arrow over (t)}_j·

{right arrow over (i)}_N=cos(θ

_j)sin(φ

_j)

{right arrow over (t)}_j·

{right arrow over (i)}_E=sin(θ

_j)sin(φ

_j)

{right arrow over (t)}_j·

{right arrow over (i)}_z=cos(φ

_j)

16. The program carrier device of claim 15, further comprising calculating the normal vector at each survey point using the tangent vector calculated at each respective survey point.

17. The program carrier device of claim 16, further comprising calculating the bi-normal vector at each survey point using the tangent vector and the normal vector calculated at each respective survey point.

18. The program carrier device of claim 12, wherein:

19. The program carrier device of claim 12, wherein:

20. The program carrier device of claim 12, further comprising calculating a new value of force and a new value of moment for each joint along the drillstring model.

21. The program carrier device of claim 20, further comprising:

comparing the initial value of force and the initial value of moment with the new value of force and the new value of moment to determine if the values are sufficiently close for each joint along the drillstring; and

repeating the steps of calculating a block tri-diagonal matrix for each connector on each joint and modeling the drillstring trajectory by solving the block tri-diagonal matrix for the two unknown rotations at each connector if the initial values of force and moment are not sufficiently close to the new values of force and moment.

22. The program carrier device of claim 21, wherein the new values of force and moment are sufficiently close to the initial values of force and moment if the new values of force and moment are within a range of ±

2% of the initial values of force and moment.