Settling Velocity of Irregularly Shaped Particles

Abstract

Summary A new correlation has been developed to predict the settling velocity of irregularly shaped particles in Newtonian and non-Newtonian fluids for all types of slip regimes. The correlation was derived from extensive data on the drag coefficients and particle Reynolds numbers of irregularly shaped particles. The effective fluid viscosity at the settling shear rate is used in the correlation. A trial-and-error or numerical iteration method is required to predict the settling velocity for non-Newtonian fluids. The correlation predicted and verified the effects of fluid properties, particle properties, and operation parameters on the settling velocity. Introduction The settling process occurs in many petroleum, mining, and process engineering operations. Applications include lifting of drill cuttings, transportation of fracturing proppants, design of settling and separating tanks, pipeline transportation of mining and coal particles, and deposition of sediments in river channels. In most practical applications, the particles involved are irregularly shaped. The irregular shape changes the settling behavior compared with smooth, symmetrical particles. Another practical consideration is that the fluid medium, such as drilling fluid, polymer fluid, and clay slurry, through which the particles settle is often non-Newtonian. Non-Newtonian fluid rheology is more complex than that of Newtonian fluids. The viscosity of such fluids is generally shear-rate dependent. Some may have time- and history-dependent properties. Chien presented two empirical correlations for the settling velocity of drill cuttings for rotary drilling operations: one for determination of the settling velocity of cuttings in all slip regimes and the other a simplified version for the turbulent-slip regime. Since then, more experimental data on the settling velocity of irregularly shaped particles have been published, and new models describing the rheology of non-Newtonian fluids have been introduced. These developments have been incorporated into a new correlation. The viscosity used in the correlation is an effective viscosity at the settling shear rate. With the new correlation, effects of fluid and particle properties and operating parameters on the settling velocity are presented and compared with experimental observations. Background Settling Velocity, Slip Regime, and Settling Shear Rate. Richards reported settling-velocity data for galena and quartz particles in water for a wide range of diameters. Quartz particles have a density comparable with that of drill cuttings and silica sands. Fig. 1 shows the settling velocity of quartz particles as a function of nominal particle diameter. In a given fluid, the settling velocity increases with particle diameter, but the rate of increase is different for different particle-size ranges. The logarithmic plot in Fig. 1 shows three distinct regimes of settling behavior. For particles <0.018 cm in diameter, settling velocity increases approximately proportionally to the square of the particle diameter. For particles >0.13 cm in diameter, the settling velocity increases proportionally to the square root of the particle diameter. The settling behavior of the small-diameter range is known as laminar slip, and that of the large diameter range as the turbulent slip. Between these two regimes is the transitional-slip regime. In the laminar-slip regime, the settling velocity is affected by both the rheology and the density of the fluid, while in the turbulent-slip regime, the settling velocity is affected mainly by the density of the fluid and the surface characteristics of the particle.