Terminal settling velocity of a single sphere in drilling fluid

The accurate prediction of terminal settling velocity of solid spheres in non-Newtonian liquids is important for various fluid-particle systems such as slurry pipelines, separation processes, hole-cleaning in drilling operations, and mineral processing. The standard practice for the prediction involves an implicit procedure that requires repeated iterations using Newtonian correlations. Wilson et al. developed an explicit method that allows direct (noniterative) prediction of the velocity in non-Newtonian liquids. Although very useful, the original Wilson model has an empirical constraint that limits its application. In this study, experiments are performed to measure the terminal settling velocity of precision spheres in Newtonian liquid (water) and non-Newtonian drilling fluids (Flowzan solutions). The Herschel-Bulkley three parameter model satisfactorily modeled the non-Newtonian rheology. Experimental data and similar measurements available in the literature are presented in this paper. The data exhibited the standard relationship between the drag coefficient and the Reynolds number. The original Wilson model was tested for these data points and was modified in this study to address its limitations. Consequently, it was observed that the modified version yielded more accurate results than the original model. Its prediction was especially better when the value of corresponding Reynolds number was more than 10.