Development of an applied relationship for pressure drop estimation in tri-cone drill bit using Bingham rheological model

In this study, non Newtonian fluid flow simulations are obtained through a tri-cone drilling bit. F-3 drill bit of size 7-7/8 inch is used for pressure drop calculations. The drilling bit contains three nozzles of equal size. Nozzle sizes of 7/32, 9/32, 10/32, and 11/32 inch are selected for simulations and each solution considered three nozzles of equal size. Eight drilling fluids of different density and rheological properties are selected and Bingham rheological model is employed in this study. Rheological data were obtained using a Fann 35 viscometer. To validate the results, calculated pressure drops from flow simulations are compared to experimental data and Eckel-Bielstein equation. The results show that flow simulations have predicted the pressure drop for all nozzle sizes with an absolute average percentage error of 9.66, whereas Eckel-Bielstein equation has an absolute average percentage error of 17.16. A new equation is proposed to calculate the pressure drop in the tri-cone bit for Bingham rheological model. The proposed equation considers effects of rheological parameters on the pressure drop. Comparison of results with experimental data revealed that the proposed equation can predict pressure drops with an absolute average percentage error of 8.31.