A Dynamic Model for Rotary Rock Drilling

A rock drilling model is developed as a set of ordinary differential equations describing discrete segments of the drilling rig, including the bit and the rock. The end segment consists of a description of the bit as a “nonideal” transformer and a characterization of the rock behavior. The effects on rock drilling of bottom hole cleaning, drill string-borehole interaction, and tooth wear are represented in the model. Simulated drilling under various conditions, using this model, gave results which are similar to those found in field and laboratory drilling performance data. In particular, the model predicts the expected relationships between drilling rate and the quantities, weight on bit, differential mud pressure, and rotary speed. The results also suggest that the damping of the longitudinal vibrations of the drill string could be predominantly hydrodynamic as opposed to viscous. Pulsations in the mud flow are found to introduce “percussive” effects in the bit forces which seem to improve the penetration rate. However, it is known from field observations that drill pipe movements, if strong enough, may induce mud pressure surges which can cause borehole and circulation problems. Bit forces and torques are shown to be substantially coupled and the influence of certain rock parameters on variables which are measurable either at the bit or on the surface support the expectation that these signals can furnish useful data on the formation being drilled. Other results, though preliminary, show that the effects of the lateral deflections of the drill string may be large for the axial bit forces and significant for the torsional vibrations. For the latter, the unsteady nature of the rotation above the bit increases and the resistance to rotation due to rubbing contact between the drill string and the wellbore accounts for very large power losses between the surface and the bit.