A mathematical model of the motion of cutting particles in reverse circulation air drilling

In reverse circulation air drilling, the cutting particles are carried by compressed air to the central channel at the bottom of the borehole and then up to the surface. Keeping the bottom of the borehole clean is a difficult; thus, a mathematical model was proposed for studying the motion of cutting particles. The model describes the motion of cutting particles in the radial and axial directions. In the radial direction, the aerodynamic drag force and frictional force of the rock were considered. The relationships among the radial velocity of the particle, the particle size, and the friction coefficient of the rock were obtained by calculating the model. The particle size was significantly affected, and the results were employed to design the structure of the bit. In the axial direction, the model was built by considering the aerodynamic drag force, the frictional force of the drill pipe, and the weight of particles. The cutting particles with the same size exhibited the same axial velocity, although they entered the central channel with different initial velocities. The results would be helpful in estimating the demand of air volume. To verify the effects of particle size on axial velocity, the axial velocity of cuttings from the Lunchuang field with different particle sizes was measured. The results showed that the application condition of the axial model is that the air velocity and the particle size produced by the advancement of the bit were in harmony, or the approximate circular particles were produced by normal drilling.