The effect of drilling mud damping on vertical vibrations of deep rotary drilling assemblies

We analyse the effect of damping of drilling fluids on vertical vibrations in rotary drilling systems. The vibrations are modelled by an impact oscillator excited by vertical impacts produced by the roughness of the borehole floor. This results in a detachment and bit bounce (chatter). These vibrations are influenced by the presence of the drilling mud in the borehole as it provides viscous damping for the oscillations. We investigate the influence of the rheology of the drilling mud on chatter assuming that the mud is shear-thinning and subsequently non-Newtonian. The Herschel-Bulkley fluid model is used to characterise non-Newtonian drilling muds. It is found that accounting for nonlinear fluid rheology may have significant impact on the value of estimated chatter. In the case of a mud with the Herschel-Bulkley viscosity the chatter can be reduced by increasing the consistency index and the power-law exponent.