Bottomhole assembly design method to reduce rotational loads

1. A method for estimating a location for disposing a tool in a drill tubular having a drill bit, the method comprising:

performing a modal analysis of the drill tubular to determine natural eigenfrequencies and corresponding eigenmodes of torsional oscillations of the model;

selecting a predominant natural eigenfrequency and corresponding eigenmode from the determined natural eigenfrequencies and corresponding eigenmodes, the predominant eigenfrequency having a frequency that is higher than the lowest determined eigenfrequency and providing a mode shape corresponding to the predominant eigenfrequency having an absolute single maximum amplitude of torsional deflection at the drill bit;

performing a forced modal analysis of the drill tubular at the predominant eigenfrequency with a force or moment acting on the drill bit to provide a correlation between forced torsional deflection amplitude and position; and

estimating the position to be within a range of positions wherein a vibration qualification of the tool is greater or equal to the torsional deflection amplitude throughout the range.

2. The method according to claim 1 , wherein the maximum torsional deflection magnitude occurs where the drill tubular is attached to the drill bit.

3. The method according to claim 1 , further comprising creating a mathematical model of the drill tubular, the model comprising a geometry of the drill tubular and a density and stiffness of a material of the drill tubular.

4. The method according to claim 3 , wherein the modal analysis is performed on the model.

5. The method according to claim 3 , wherein the forced modal analysis is performed on the model.

6. The method according to claim 1 , wherein the modal analysis is performed by experiment.

7. The method according to claim 6 , wherein the experiment is performed on a portion of interest of the drill tubular or a scale model of a portion of interest of the drill tubular.

8. The method according to claim 1 , wherein the drill tubular comprises a mud motor configured to turn the drill bit using energy from circulating drilling fluid.

9. A method for building a drill tubular having a drill bit, the method comprising:

performing a modal analysis of the drill tubular to determine natural eigenfrequencies and corresponding eigenmodes of torsional oscillations of the model;

selecting a predominant natural eigenfrequency and corresponding eigenmode from the determined natural eigenfrequencies and corresponding eigenmodes, the predominant eigenfrequency having a frequency that is higher than the lowest determined eigenfrequency and providing a mode shape corresponding to the predominant eigenfrequency having an absolute single maximum amplitude of torsional deflection at the drill bit;

performing a forced modal analysis of the drill tubular at the predominant eigenfrequency with a force or moment acting on the drill bit to provide a correlation between forced torsional deflection amplitude and position; and

estimating a position of a tool to be within a range of positions wherein a vibration qualification of the tool is greater than or equal to the torsional deflection

amplitude throughout the range; and

disposing the tool in the drill tubular at the estimated position.

10. The method according to claim 9 , wherein the tool comprises a plurality of tools and each tool is disposed in the drill tubular in a range of positions wherein a vibration qualification for each tool is greater than or equal to the torsional deflection amplitude throughout the corresponding range of positions.

11. The method according to claim 10 , wherein a spacer is disposed between a first tool and a second tool in the plurality of tools.

12. The method according to claim 9 , wherein the range of positions comprises a node where the torsional deflection amplitude is zero.

13. The method according to claim 12 , further comprising calculating a stress experienced by a drill tubular structure at the node.

14. The method according to claim 13 , further comprising comparing the calculated stress at the node to a threshold stress for a drill tubular structure at the node.

15. The method according to claim 14 , further comprising strengthening the drill tubular structure if the threshold stress is less than the calculated stress.

16. The method according to claim 14 , further comprising relocating the drill tubular structure to a location within a range of positions not having a node if the threshold stress is less than the calculated stress.

17. A method for assembling a set of tools in a bottomhole assembly (BHA) of a drill tubular having a drill bit, the method comprising:

disposing the set of tools in a first set of positions in the BHA;

performing a modal analysis of the drill tubular to determine natural eigenfrequencies and corresponding eigenmodes of torsional oscillations of the model;

selecting a predominant natural eigenfrequency and corresponding eigenmode from the determined natural eigenfrequencies and corresponding eigenmodes, the predominant eigenfrequency having a frequency that is higher than the lowest determined eigenfrequency and providing a mode shape corresponding to the predominant eigenfrequency having an absolute single maximum amplitude of torsional deflection at the drill bit;

performing a forced modal analysis of the model at the predominant eigenfrequency with a force or moment acting on the drill bit to provide a correlation between forced torsional deflection amplitude and position;

comparing a vibration qualification of each of the tools in the set to the forced torsional defection amplitude at the predominant eigenfrequency for the corresponding position of each of the tools; and

disposing the set of tools in a second set of positions in the BHA if the vibration qualification of one or more tools is less than the torsional deflection amplitude at the predominant eigenfrequency;

wherein each of the tools in the second set of positions have a vibration qualification that is greater than or equal to the torsional deflection amplitude at the predominant eigenfrequency for the corresponding position.

18. The method according to claim 17 , further comprising disposing a spacer between a first tool and a second tool in the set, the spacer being configured to maintain the positions of the first and second tools.

19. The method according to claim 17 , further comprising sensing the hardness of a subsurface material being drilled by the drill tubular using a hardness sensor disposed at the drill tubular and determining the force acting on the drill bit using the sensed hardness.

20. The method according to claim 17 , further comprising validating the second set of positions by comparing vibration data obtained from one or more accelerometers disposed at the BHA at each tool position while drilling a borehole to the vibration qualification of each of the tools.