Closure to “Settling Velocity of Spherical Particles in Calm Water”

Abstract Accurate description of cuttings slippage in the gas-liquid phase is of great significance for wellbore cleaning and the control accuracy of bottom hole pressure during MPD. In this study, the wellbore bubble flow environment was simulated by a constant pressure air pump and the transparent wellbore, and the settling characteristics of spherical particles under different gas volume concentrations were recorded and analyzed by highspeed photography. A total of 225 tests were conducted to analyze the influence of particle diameter (1–12mm), particle density (2700–7860kg/m^3), liquid viscosity and bubble volume concentration on particle settling velocity. Gas drag force is defined to quantitatively evaluate the bubble’s resistance to particle slippage. The relationship between bubble drag coefficient and particle Reynolds number is obtained by fitting the experimental results. An explicit settling velocity equation is established by introducing Archimedes number. This explicit equation with an average relative error of only 8.09% can directly predict the terminal settling velocity of the sphere in bubble containing Newtonian fluids. The models for predicting bubble drag coefficient and the terminal settling velocity are valid with particle Reynolds number ranging from 0.05 to 167 and bubble volume concentration ranging from 3.0% to 20.0%. Besides, a trial-and-error procedure and an illustrative example are presented to show how to calculate bubble drag coefficient and settling velocity in bubble containing fluids. The results of this study will provide the theoretical basis for wellbore cleaning and accurate downhole pressure to further improve the performance of MPD in treating gas influx.

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Settling-velocity and flume-behavior of non-spherical particles

Transactions American Geophysical Union ◽

10.1029/tr023i002p00621 ◽

1942 ◽

Vol 23 (2) ◽

pp. 621 ◽

Cited By ~ 50

Author(s):

W. C. Krumbein

Keyword(s):

Settling Velocity ◽

Spherical Particles

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Sedimentation of finite-size spheres in quiescent and turbulent environments

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.698 ◽

2016 ◽

Vol 788 ◽

pp. 640-669 ◽

Cited By ~ 49

Author(s):

Walter Fornari ◽

Francesco Picano ◽

Luca Brandt

Keyword(s):

Turbulent Flow ◽

Settling Velocity ◽

Solid Phase ◽

Density Ratio ◽

Finite Size ◽

Spherical Particles ◽

Volume Fractions ◽

Turbulent Environments ◽

The Mean ◽

Quiescent Fluid

Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behaviour of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform direct numerical simulations of sedimentation in quiescent and turbulent environments using an immersed boundary method to account for the dispersed rigid spherical particles. The solid volume fractions considered are ${\it\phi}=0.5{-}1\,\%$, while the solid to fluid density ratio ${\it\rho}_{p}/{\it\rho}_{f}=1.02$. The particle radius is chosen to be approximately six Kolmogorov length scales. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reductions with respect to a single particle in quiescent fluid are approximately 12 % and 14 % for the two volume fractions investigated. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails are associated with the intermittent fast sedimentation of particle pairs in drafting–kissing–tumbling motions. The particle lateral dispersion is higher in a turbulent flow, whereas the vertical one is, surprisingly, of comparable magnitude as a consequence of the highly intermittent behaviour observed in the quiescent fluid. Using the concept of mean relative velocity we estimate the mean drag coefficient from empirical formulae and show that non-stationary effects, related to vortex shedding, explain the increased reduction in mean settling velocity in a turbulent environment.

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Can terminal settling velocity and drag of natural particles in water ever be predicted accurately?

10.5194/dwes-2020-30 ◽

2020 ◽

Author(s):

Onno J. I. Kramer ◽

Peter J. de Moel ◽

Shravan K. R. Raaghav ◽

Eric T. Baars ◽

Wim H. van Vugt ◽

...

Keyword(s):

Drinking Water ◽

Measurement Errors ◽

Settling Velocity ◽

Particle Density ◽

Fixed Bed ◽

Drinking Water Treatment ◽

Liquid System ◽

Solid Particles ◽

Spherical Particles ◽

Fluidised Bed

Abstract. Natural particles are frequently applied in drinking water treatment processes in fixed bed reactors, in fluidised bed reactors, and in sedimentation processes to clarify water and to concentrate solids. When particles settle, it has been found that in terms of hydraulics, natural particles behave differently when compared to perfectly round spheres. To estimate the terminal settling velocity of single solid particles in a liquid system, a comprehensive collection of equations is available. For perfectly round spheres, the settling velocity can be calculated quite accurately. However, for naturally polydisperse non-spherical particles, experimentally measured settling velocities of individual particles show considerable spread from the calculated average values. This work aimed to analyse and explain the different causes of this spread. To this end, terminal settling experiments were conducted in a quiescent fluid with particles varying in density, size and shape. For the settling experiments, opaque and transparent spherical polydisperse and monodisperse glass beads were selected. In this study, we also examined drinking water related particles, like calcite pellets and crushed calcite seeding material grains, both applied in drinking water softening. Polydisperse calcite pellets were sieved and separated to acquire more uniformly dispersed samples. In addition, a wide variety of grains with different densities, sizes and shapes were investigated for their terminal settling velocity and behaviour. The derived drag coefficient was compared with well-known models such as Brown–Lawler. A sensitivity analysis showed that the spread is caused to a lesser extent by variations in fluid properties, measurement errors and wall effects. Natural variations in specific particle density, path trajectory instabilities and distinctive multi-particle settling behaviour caused a slightly larger degree of spread. In contrast, greater spread is caused by variations in particle size, shape and orientation.

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