Predicting fiber drag coefficient and settling velocity of sphere in fiber containing Newtonian fluids

In petroleum industry, fiber containing fluids are widely used as drilling fluids or fracturing fluids to improve the efficiency of cuttings transport during drilling or proppant transport during fracturing. Accurate prediction of fiber drag coefficient and settling velocity of sphere in fiber containing fluids is beneficial to design and optimization of fiber drilling/fracturing fluids applications. In this paper, a visualization apparatus and high-speed camera system are used to record the settling process in fiber containing Newtonian fluids. 283 tests involving different fiber concentrations (0.00%-0.10%), sphere diameters (1-10 mm), particle densities (2680, 4450 and 7960 kg/m3) and fluid viscosities are conducted. The fiber drag force is redefined to be suitable for spheres with different density. The effects of fiber length and fiber concentration on fluids viscosity and particle settling are investigated. The relationship between fiber drag coefficient and particle Reynolds number is obtained based on the experimental data. An explicit settling velocity equation which directly predicts settling velocity of sphere in fiber containing Newtonian fluids is proposed by correlating the total drag coefficient with the dimensionless sphere diameter. The average relative error is 4.4%, which indicates predictions of settling velocity are in good agreement with measured settling velocity. The models for predicting fiber drag coefficient and settling velocity are valid with particle Reynolds number ranging from 0.05 to 167 and fiber concentration ranging from 0.00% to 0.10%. Besides, a trail-and-error procedure and an illustrative example are presented to show how to calculate fiber drag coefficient and settling velocity in fiber containing fluids. Results of this study may provide some basis for the better field applications of fiber containing fluids.