Method and system for designing bottom hole assembly configuration

1. A method of designing the configuration of a bottom hole assembly including components that include at least one stabilizer, the bottom hole assembly being connected with a drill string that also includes a drill bit, the method including:

modeling the bottom hole assembly configuration using Lubinski's bottom hole assembly equations by dividing the bottom hole assembly components into modules and segments such that the bottom hole assembly is characterized by not more than two nonlinear equations associated with two unknowns, wherein the modeling comprises:

calculating profiles of the segments in a first, upper module;

determining a first non-linear equation for a first segment that solves for a distance between the drill bit and a tangential point;

calculating a side force at a lower stabilizer in another of any additional modules;

calculating profiles of the segments of another of any additional modules;

calculating a side force at a lower stabilizer and profiles of the segments for remaining modules except a last, bit module;

calculating a side force at the drill bit;

calculating profiles of the segments in the bit module;

determining a second nonlinear equation for a bit segment that solves for a side force at an upper stabilizer; and

calculating a distance between the drill bit and a tangential point and a side force at the upper stabilizer using the first and second non-linear equations;

resolving the unknowns by iteration to determine the bottom hole assembly configuration; and

displaying the bottom hole assembly configuration.

2. The method of claim 1 further including:

determining boundary conditions at the stabilizers by comparing the direction of a deflection with the direction of the side forces; and

verifying that a wellbore clearance is greater than a deflection profile of the bottom hole assembly.

3. The method of claim 2 further including repeating the modeling the configuration of the components based on a revised set of assumptions.

4. The method of claim 1 , further including designing the configuration of the bottom hole assembly in real time while at a wellbore drilling location.

5. A method of drilling a wellbore with a steerable tool and a drill bit including:

planning a well trajectory including an expected build rate as a function of measured depth;

determining components for a bottom hole assembly, the components including at least one stabilizer;

designing a configuration of the bottom hole assembly, including:

modeling the bottom hole assembly configuration using Lubinski's bottom hole assembly equations by dividing the bottom hole assembly components into modules and segments such that the bottom hole assembly is characterized by not more than two nonlinear equations associated with two unknowns, wherein the modeling comprises:

calculating profiles of the segments in the upper module;

determining a first non-linear equation for a first segment that solves for a distance between the bit and a tangential point;

calculating a side force at a lower stabilizer in another of any additional modules;

calculating profiles of the segments of another of any additional modules;

calculate a side force at a lower stabilizer and profiles of the segments for remaining modules except a last, bit module;

calculating a side force at the drill bit;

calculating profiles of the segments in the bit module;

determining a second nonlinear equation for a bit segment that solves for a side force at an upper stabilizer; and

calculating a distance between the drill bit and a tangential point and a side force at the upper stabilizer using the first and second non-linear equations; and

resolving the unknowns by iteration to determine the bottom hole assembly configuration;

drilling the wellbore using the bottom hole assembly configuration;

measuring a measured build rate as a function of measured depth; and

comparing the measured build rate with the expected build rate.

6. The method of claim 5 further including revising at least one drilling or operating parameter of the steerable tool as a function of measured depth based on the measured build rate.

7. The method of claim 6 wherein comparing the measured build rate with the expected build rate and revising at least one drilling parameter or operating parameter of the steerable tool are performed using a downhole processor.

8. The method of claim 5 further including:

determining boundary conditions at the stabilizers by comparing the direction of a deflection with the direction of the side forces; and

verifying that a wellbore clearance is greater than a deflection profile of the bottom hole assembly.

9. The method of claim 8 further including repeating the modeling the configuration of the components based on a revised set of assumptions.

10. The method of claim 9 further comprising logging the set of assumptions as a function of depth in drilling the wellbore.

11. The method of claim 5 , further including designing the configuration of a bottom hole assembly in real time while at a wellbore drilling location.

12. A computer-readable medium including software that, when executed by a processor causes the processor to design a configuration of a bottom hole assembly including components that include at least one stabilizer, the bottom hole assembly being connected with a drill string that also includes a drill bit, the designing including:

modeling the bottom hole assembly configuration using Lubinski's bottom hole assembly equations by dividing the bottom hole assembly components into modules and segments such that the bottom hole assembly is characterized by not more than two nonlinear equations associated with two unknowns, whereing the modeling comprises:

calculating profiles of the segments in a first, upper module;

determining a first non-linear equation for a first segment that solves for a distance between the drill bit and a tangential point;

calculating a side force at a lower stabilizer in another of any additional modules;

calculating profiles of segments of another of any additional modules;

calculating a side force at a lower stabilizer and profiles of the segments for remaining modules except a last, bit module;

calculating a side force at the drill bit;

calculating profiles of segments in the bit module;

determining a second nonlinear equation for a bit segment that solves for a side force at an upper stabilizer; and

calculating a distance between the drill bit and a tangential point and a side force at the upper stabilizer using the first and second non-linear equations; and

resolving the unknowns by iteration to determine the bottom hole assembly configuration.

13. The computer-readable medium of claim 12 modeling the bottom hole assembly configuration further includes:

determining boundary conditions at the stabilizers by comparing the direction of a deflection with the direction of the side forces; and

verifying that a wellbore clearance is greater than a deflection profile of the bottom hole assembly.

14. The computer-readable medium of claim 13 , further including repeating the modeling of the configuration of the components based on a revised set of assumptions.

15. The computer-readable medium of claim 12 , wherein the design of the configuration of a bottom hole assembly is performable in real time while at a wellbore drilling location.