New model for single spherical particle settling velocity in power law (visco-inelastic) fluids

A FEM-DEM technique for studying the motion of particles in non-Newtonian fluids. Application to the transport of drill cuttings in wellbores

“…the steady state velocity reached by a particle falling freely in a liquid) can be found in several papers for different fluids [21,32]. In particular, Shah [33] proposed an estimation of the terminal velocity in power law fluids characterized by the following value of the (non linear) viscosity…”

“…Compute the drag coefficient for spherical (ϕ = 1) and non-spherical (ϕ = 1) particles via Eqs. (33) or (34) using the Reynolds number of Eq.(29). 3.…”

Experimental investigation of the settling velocity of spherical particles in Power-law fluids using particle image shadowgraph technique

“…There exists a wide range of opinions among investigators with respect to Power-law fluid applications and, unlike Newtonian fluids, there is no universally accepted general model for determining the settling velocities of spherical particles in Power law type fluids. Two different opinions prevail among researchers regarding the use of Newtonian drag curve for non-Newtonian fluid and on the dependency of drag coefficient on flow behavior index, n. Shah et al (2007), Dallon (1967), Prakash (1983, Reynolds and Jones (1989), Peden and Luo (1987), Koziol and Glowacki (1988), Machac et al (1995), Shah (1982, and Shah (1986) have all observed the strong dependency of drag coefficient on n. On the other hand, studies by Lali et al (1989), Chhabra (1990), Chhabra (2002), and Kelessidis (2004) have shown that the use of Newtonian drag curve for Power-law fluid yields equally good results.…”

“…Different concentrations of CMC-water mixtures (0.14-0.28 wt%) are used as test fluids for the experiments. A new empirical equation, which is an improved version of the Shah et al (2007) model, for predicting the settling velocity of a spherical particle in Power-law fluid is proposed. The new empirical model is found to give an average error of 10% in predicting the settling velocity.…”

Micromechanics of proppant agglomeration during settling in hydraulic fractures

“…Curve-fitting models were previously derived for predicting proppant settling rates, including the effects of the particle concentration in the fluid and the relative size of the fracture width relative to the proppant diameter. For proppant settling in pipes and narrow slots, existing experimental correlations relate average slurry settling velocity to a single particle settling velocity based on particle concentrations assuming uniform spatial distribution in the fluid (Hannah and Harrington 1981;Harrington et al 1979;Novotny 1977;Shah 1982Shah , 1993Shah and Lee 1986;Shah and Lord 1990;Shah et al 2007). Particle agglomerations and irregular particle motions were previously observed in several experimental studies on flow of particle-fluid mixtures in pipes and slot flow apparatus.…”