Axial motion drill bit model

1. A method for predicting an amount of axial motion of a drill bit having one or more cutters for drilling a borehole into a formation rock, the method includes:

receiving lithology data for the formation rock;

receiving drilling parameters that include mud weight and drill bit depth for a drill rig that will operate a drill tubular coupled to the drill bit and drill bit design information;

calculating confined compressive strength of the formation rock using the received lithology data, drilling parameters, and drill bit design information;

calculating an area of cut into the formation rock by each of the one or more cutters;

calculating an effective back rake of each of the one or more cutters;

calculating a force applied to each of the one or more cutters using the calculated confined compressive strength of the formation rock, the area of cut and the effective back rake of the one or more cutters, and by accounting for an orientation of each of the one or more cutters with respect to a surface of the rock to be cut; and

summing the calculated forces applied to each of the one or more cutters to calculate the weight on bit (WOB) and torque on bit (TOB);

wherein the above method is implemented by a processor.

2. The method according to claim 1 , further comprising calculating the WOB and TOB to provide a prescribed rate of penetration.

3. The method according to claim 1 , further comprising calculating a rate of penetration (ROP) to provide a prescribed WOB.

4. The method according to claim 1 , further comprising representing the drill bit with a first set of virtual pickets and the formation rock with a second set of virtual pickets.

5. The method according to claim 4 , wherein the first set of pickets lines up with the second set of virtual pickets at the interface of the drill bit with the formation rock.

6. The method according to claim 4 , wherein the area of cut of each of the one or more cutters, the effective back rake of each of the one or more cutters, and the force applied to each of the one or more cutters are calculated on a picket by picket basis.

7. The method according to claim 6 , wherein summing comprises summing the forces on each of the pickets.

8. A non-transitory computer-readable medium comprising computer-executable instructions for predicting an amount of axial motion of a drill bit having one or more cutters for drilling a borehole into a formation rock that when executed by a computer processing system implements the following steps:

receiving lithology data for the formation rock;

receiving drilling parameters that include mud weight and drill bit depth for a drill rig that will operate a drill tubular coupled to the drill bit and drill bit design information;

calculating confined compressive strength of the formation rock using the received lithology data, drilling parameters, and drill bit design information;

calculating an area of cut into the formation rock by each of the one or more cutters;

calculating an effective back rake of each of the one or more cutters;

calculating a force applied to each of the one or more cutters using the calculated confined compressive strength of the formation rock, the area of cut and the effective back rake of the one or more cutters, and by accounting for an orientation of each of the one or more cutters with respect to a surface of the rock to be cut; and

summing the calculated forces applied to each of the one or more cutters to calculate the weight on bit (WOB) and torque on bit (TOB).