Abstract: A method of controlling drill bit trajectory in a subterranean formation includes receiving drilling parameters for operating a specific bottomhole assembly (BHA), constructing, with a computer processor, a directional drill-ahead simulator including a computer model of the BHA and the subterranean formation, calculating axial motion and lateral motion of a drill bit connected to a bottom end of the BHA using formation parameters and drilling parameters, predicting bit walk of the drill bit by accounting for and calculating contact forces and frictional forces between the BHA and a wall of a borehole in the subterranean formation using the computer model of the BHA, and determining an adjusted drill bit trajectory to account for the predicted bit walk. The method includes determining adjusted drilling parameters for operating the BHA to substantially follow the adjusted drill bit trajectory and operating the BHA according to the adjusted drilling parameters.

Abstract: A method for predicting a path of a borehole that will be drilled in a rock formation by a bottomhole assembly (BHA) having a drill bit includes: constructing a model of the BHA; calculating confined compressive strength of the rock formation using an axial motion drill bit model that receives drilling parameter, drill bit design and lithology information; calculating lateral motion of the drill bit using a lateral motion drill bit model; calculating a ratio of lateral motion to axial motion using the lateral motion drill bit model; calculating an inclination angle and an azimuthal direction of the BHA using a BHA steering model that receives the ratio; and iterating the above steps by updating the BHA model to include extending the borehole an incremental distance in the direction of the inclination angle and the azimuthal direction and displacing the BHA the incremental distance in the extended borehole.

Abstract: A method for predicting a change in lateral displacement with a change in axial displacement of a drill bit drilling in a formation rock includes: constructing a virtual representation of the drill bit and the formation rock, the drill bit having a gage pad configured to remove rock by wearing or crushing the rock during moving contact and a cutter configured to cut into the rock during moving contact with the rock; adjusting lateral penetration depth until rock reactive force equals a side force applied to the drill bit to provide an adjusted lateral penetration depth; removing formation rock to where the pad and the cutters contact the rock at the adjusted lateral penetration depth and to a selected axial displacement of the drill bit; moving the drill bit in a drilling direction to the end of the currently drilled borehole; and iterating the adjusting, the removing, and the moving.

Abstract: A method for predicting an amount of axial motion of a drill bit having one or more cutters for drilling formation rock includes: receiving lithology data for the formation rock; receiving drilling parameters; calculating confined compressive strength (CCS) of the rock using the received 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 CCS, the area of cut and the effective back rake of the one or more cutters, and by accounting for an orientation of each cutter 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 and torque on bit.

Abstract: A method of controlling drill bit trajectory in a subterranean formation includes receiving drilling parameters for operating a specific bottomhole assembly (BHA), constructing, with a computer processor, a directional drill-ahead simulator including a computer model of the BHA and the subterranean formation, calculating axial motion and lateral motion of a drill bit connected to a bottom end of the BHA using formation parameters and drilling parameters, predicting bit walk of the drill bit by accounting for and calculating contact forces and frictional forces between the BHA and a wall of a borehole in the subterranean formation using the computer model of the BHA, and determining an adjusted drill bit trajectory to account for the predicted bit walk. The method includes determining adjusted drilling parameters for operating the BHA to substantially follow the adjusted drill bit trajectory and operating the BHA according to the adjusted drilling parameters.

Abstract: A method of generating a directional response of a drill bit based on one or more drilling parameters includes performing actual or simulated tests with a drill bit in a test material having a strength under different experimental drilling parameters and recording the results of the plurality of tests. A representation of an expected directional response of the drill bit is formed based on the results. Current drilling parameters are receiving current drilling parameters at a computing device and the directional response is generated based on the current drilling parameters by utilizing the representation.

Abstract: A method for predicting a change in lateral displacement with a change in axial displacement of a drill bit drilling in a formation rock includes: constructing a virtual representation of the drill bit and the formation rock, the drill bit having a gage pad configured to remove rock by wearing or crushing the rock during moving contact and a cutter configured to cut into the rock during moving contact with the rock; adjusting lateral penetration depth until rock reactive force equals a side force applied to the drill bit to provide an adjusted lateral penetration depth; removing formation rock to where the pad and the cutters contact the rock at the adjusted lateral penetration depth and to a selected axial displacement of the drill bit; moving the drill bit in a drilling direction to the end of the currently drilled borehole; and iterating the adjusting, the removing, and the moving.

Abstract: A method for predicting a path of a borehole that will be drilled in a rock formation by a bottomhole assembly (BHA) having a drill bit includes: constructing a model of the BHA; calculating confined compressive strength of the rock formation using an axial motion drill bit model that receives drilling parameter, drill bit design and lithology information; calculating lateral motion of the drill bit using a lateral motion drill bit model; calculating a ratio of lateral motion to axial motion using the lateral motion drill bit model; calculating an inclination angle and an azimuthal direction of the BHA using a BHA steering model that receives the ratio; and iterating the above steps by updating the BHA model to include extending the borehole an incremental distance in the direction of the inclination angle and the azimuthal direction and displacing the BHA the incremental distance in the extended borehole.

Abstract: A method for predicting an amount of axial motion of a drill bit having one or more cutters for drilling formation rock includes: receiving lithology data for the formation rock; receiving drilling parameters; calculating confined compressive strength (CCS) of the rock using the received 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 CCS, the area of cut and the effective back rake of the one or more cutters, and by accounting for an orientation of each cutter 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 and torque on bit.

Abstract: A method of predicting behavior of a drill bit includes: generating, by a processor, a representation of at least one component of the drill bit, the representation representing a three-dimensional object as a combination of at least two two-dimensional polygons; representing a borehole formed in an earth formation during a drilling operation by generating a mathematical representation of a borehole surface defined by a plurality of nodes; simulating operation of the drill bit within the borehole with the application of one or both of axial load and a side load; determining whether the three-dimensional object is in contact with the borehole surface by determining if one of the nodes is within both of the two-dimensional polygons during the simulation; and estimating an amount of lateral motion of the drill bit during the simulation.

Abstract: A method of predicting behavior of a drilling assembly includes generating, by a processor, a mathematical representation of a geometry of drill bit that includes a plurality of earth contacting portions, the plurality of earth contacting portions including a plurality of cutters and one or more additional components; estimating, with a separate model for each earth contacting portion, contact with the earth formation during a drilling operation; and estimating one or more forces on the one or more earth contact portions during the drilling operation based on the estimated contact.

Abstract: A method of designing a drill bit includes: defining a representation of a first drill bit including at least a first cutter having a first face, the first cutter being disposed on the representation of the first drill bit in a first orientation; simulating in a first simulation on a computing device off-axis rotation of the first drill bit in a simulated subterranean formation; determining that the first face included, during the first simulation, a first face orientation direction that was oriented different than a face cutting direction by an amount that exceeds a predetermined threshold; and defining the first drill bit such that the first cutter is disposed in a second orientation.

Abstract: A method of generating a directional response of a drill bit based on one or more drilling parameters includes performing actual or simulated tests with a drill bit in a test material having a strength under different experimental drilling parameters and recording the results of the plurality of tests. A representation of an expected directional response of the drill bit is formed based on the results. Current drilling parameters are receiving current drilling parameters at a computing device and the directional response is generated based on the current drilling parameters by utilizing the representation.