Method and system for analyzing a drill string stuck pipe event

1. A method comprising:

receiving a plurality of drilling parameters from a drilling operation, wherein the plurality of drilling parameters includes a cuttings bed height and a friction factor between a drill string and a wellbore;

simulating an estimated cuttings bed length, wherein simulating the estimated cuttings bed length includes:

generating a seed for the estimated cuttings bed length;

applying the plurality of drilling parameters and the seed for the estimated cuttings bed length to a friction model comprising a function of the cuttings bed height to determine a comprehensive friction factor;

applying the comprehensive friction factor to the plurality of drilling; parameters to determine a required hook load of the drill string;

comparing the required hook load to a maximum allowable hook load;

comparing the required hook load to known, historical or experimental values; and

updating the seed for the estimated cuttings bed length in response to determining that the required hook load and the known, historical or experimental values do not converge; and

repeating the applying the plurality of drilling parameters and the seed for the estimated cuttings bed length, applying the comprehensive friction factor, comparing the required hook load to known, historical or experimental values and updating the seed until a convergence between the required hook load, the known, historical or experimental values and the maximum allowed hook load is detected;

providing an indication of a stuck pipe event, the indication based on the convergence of the required hook load, the known, historical or experimental values and the maximum allowed hook load; and

adjusting at least one of the plurality of drilling parameters in response to the indication of the stuck pipe event.

2. The method of claim 1 , wherein the plurality of drilling parameters includes a cuttings distribution.

3. The method of claim 1 , wherein the plurality of drilling parameters comprises:

a weight-on-bit; a hook load; a rate-of-penetration; a rotary speed of the drill string; a torque applied to the drill string; a drilling fluid pump pressure; an inclination of the drill string a length of drill string; or a drilling fluid flow rate.

4. The method of claim 1 , wherein the plurality of drilling parameters includes a cuttings plug contact force.

5. The method of claim 4 , wherein the cuttings plug contact force is based on a plurality of discrete cuttings plug contact forces.

6. The method of claim 5 , further comprising applying the plurality of discrete cuttings plug contact forces to an approximation model to determine an axial plug force.

7. The method of claim 6 , further comprising providing the indication of the stuck pipe event, the indication based on the required hook load and the axial plug force.

8. The method of claim 5 , further comprising identifying a maximum cuttings plug contact force, wherein the required hook load is equal to a maximum hook load of the drill string.

9. The method of claim 8 , further comprising correlating the maximum cuttings plug contact force to a maximum cuttings plug length.

10. The method of claim 9 , further comprising solving for the maximum cuttings plug length, wherein the required hook load is equal to the maximum hook load.

11. A method comprising:

receiving a plurality of drilling parameters from a drilling operation, wherein the plurality of drilling parameters includes a cuttings bed height and a friction factor between a drill string and a wellbore;

simulating an estimated cuttings bed length, wherein simulating the estimated cuttings bed length includes:

generating a seed for the estimated cuttings bed length;

applying the plurality of drilling parameters and the seed for the estimated cuttings bed length to a friction model comprising a function of the cuttings bed height to determine a comprehensive friction factor;

applying the comprehensive friction factor to the plurality of drilling parameters to determine a required torque of the drill string;

comparing the required torque to a maximum allowed torque;

comparing the required torque to known, historical or experimental values; and

updating the seed for the estimated cuttings bed length based in response to determining that the required torque and the known, historical or experimental values do not converge; and

repeating the applying the plurality of drilling parameters and the seed for the estimated cuttings bed length, applying the comprehensive friction factor, comparing the required torque to known, historical or experimental values and updating the seed until a convergence between the required torque the known, historical or experimental values and the maximum allowed torque is detected;

providing an indication of a stuck pipe event, the indication based on the convergence of the required torque, the known, historical or experimental values the maximum allowed torque; and

adjusting at least one of the plurality of drilling parameters in response to the indication of the stuck pipe event.

12. The method of claim 11 , wherein the cuttings bed height is normalized by a diameter of the wellbore.

13. The method of claim 11 , wherein the plurality of drilling parameters comprises:

a weight-on-bit; a hook load; a rate-of-penetration; a rotary speed of the drill string; a torque applied to the drill string; a drilling fluid pump pressure; an inclination of the drill string a length of drill string; or a drilling fluid flow rate.

14. The method of claim 11 , wherein the plurality of drilling parameters includes a cuttings plug contact force.

15. The method of claim 14 , wherein the cuttings plug contact force is based on a plurality of discrete cuttings plug contact forces.

16. A non-transitory computer-readable medium storing a program that, when executed by a processor, causes the processor to:

receive a plurality of drilling parameters from a drilling operation, wherein the plurality of drilling parameters includes a cuttings bed height and a friction factor between a drill string and a wellbore;

simulate an estimated cuttings bed length, wherein the estimated cuttings bed length is simulated by:

generating a seed for the estimated cuttings bed length;

applying the plurality of drilling parameters and the seed for the estimated cuttings bed length to a friction model comprising a function of the cuttings bed height to determine a comprehensive friction factor;

applying the comprehensive friction factor to the plurality of drilling parameters to determine a required hook load of the drill string;

comparing the required hook load to a maximum allowed hook load;

comparing the required hook load to known, historical or experimental values; and

updating the seed for the estimated cuttings bed length in response to determining that the required hook load and the known, historical or experimental values do not converge; and

repeating the applying the plurality of drilling parameters and the seed for the estimated cuttings bed length, applying the comprehensive friction factor, comparing the required hook load to known, historical or experimental values and updating the seed until a convergence between the required hook load, the known, historical or experimental values and the maximum allowed hook load is detected;

provide an indication of a stuck pipe event, the indication based on the convergence of the required hook load, the known, historical or experimental value and the maximum allowed hook load; and

wherein, when executed by a processor, the computer-readable medium causes the processor to adjust at least one of the plurality of drilling parameters in response to the indication of the stuck pipe event.

17. The computer-readable medium of claim 16 , wherein the plurality of drilling parameters includes a cuttings plug contact force.

18. The computer-readable medium of claim 17 , wherein the cuttings plug contact force is based on a plurality of discrete cuttings plug contact forces.

19. The computer-readable medium of claim 18 , wherein, when executed by a processor, the computer-readable medium causes the processor to apply the plurality of discrete cuttings plug contact forces to an approximation model to determine an axial plug force.

20. The computer-readable medium of claim 19 , wherein, when executed by a processor, the computer-readable medium causes the processor to provide the indication of the stuck pipe event, the indication based on the required hook load and the axial plug force.