Estimation of particle concentration profiles in a three-phase fluidized bed from experimental data and using the wake model

Knesebeck, Alexandre; Guardani, Roberto

doi:10.1590/s0104-66322004000100006

Cited by 5 publications

(5 citation statements)

References 16 publications

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“…The gravitational settling velocity depends primarily on the particle size and density, and is estimated in Equations – for the creeping (Stokian), intermediate, and Newtonian regimes, respectively:

v_{g} = \frac{D_{p}^{2} g false(ρ_{p} - ρ_{f} false)}{18 μ_{f}} for K \leq 3.3,

v_{g} = {((), \frac{D_{p}^{8 / 5} g false(ρ_{p} - ρ_{f} false)}{13.875 μ_{f}^{0.6} ρ_{f}^{0.4}})}^{5 / 7} for 3.3 < K \leq 43.6,

v_{g} = \sqrt{((), \frac{3.03 D_{p} g false(ρ_{p} - ρ_{f} false)}{ρ_{f}})} for 43.6 < K < 2, 360,

where ρ p is the particle density (1,000 kg/m 3 for the “classical aerodynamic diameter”), ρ f and μ f are the air density and viscosity, respectively, and K is a dimensionless constant that determines the range of the fluid‐particle dynamic laws [dimensionless] calculated based on Equation :

K = D_{p} {((), \frac{g ρ_{p} ρ_{f}}{μ_{f}^{2}})}^{1 / 3} .

…”

Section: Methodsmentioning

confidence: 99%

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Pollutant Ground Concentrations of Nonneutrally Buoyant Particles

et al. 2017

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A methodology is suggested for the estimation of the mass density and the cumulative ground deposition of a nonvolatile, nonneutrally buoyant, air pollutant (liquid or solid) released from a polluted column (following an explosion caused during routine operation in, e.g., the chemical industry or due to any kind of hostile act) and deposited on the ground via gravitational settling. In many cases, the deposited mass due to gravitational settling constitutes a significant fraction of the original inventory released from the source. Implementation of the methodology in preliminary risk assessments can serve as an efficient tool for emergency planning for both immediate and long-term measures such as evacuation and decontamination. The methodology considers, inter alia, an estimation of the critical particle diameter, particle size, and mass distributions along the polluted column. This methodology was developed to apply in rural regions since proper application of relevant meteorological input data can be accomplished mainly for such areas.

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v_{g} = \frac{D_{p}^{2} g false(ρ_{p} - ρ_{f} false)}{18 μ_{f}} for K \leq 3.3,

v_{g} = {((), \frac{D_{p}^{8 / 5} g false(ρ_{p} - ρ_{f} false)}{13.875 μ_{f}^{0.6} ρ_{f}^{0.4}})}^{5 / 7} for 3.3 < K \leq 43.6,

v_{g} = \sqrt{((), \frac{3.03 D_{p} g false(ρ_{p} - ρ_{f} false)}{ρ_{f}})} for 43.6 < K < 2, 360,

K = D_{p} {((), \frac{g ρ_{p} ρ_{f}}{μ_{f}^{2}})}^{1 / 3} .

…”

Section: Methodsmentioning

confidence: 99%

“…where h 200 = 200 m above ground level. The gravitational settling velocity depends primarily on the particle size and density, and is estimated in Equations (2)-(4) for the creeping (Stokian), intermediate, and Newtonian regimes, respectively (13)(14)(15) :…”

Section: Gravitational Settling From the Explosion Columnmentioning

confidence: 99%

Pollutant Ground Concentrations of Nonneutrally Buoyant Particles

et al. 2017

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“…Different theoretical and empirical correlations have been proposed by researchers for calculation of each of the abovementioned parameters [13]. A comprehensive description of this model can be found in the work of Tsutsumi et al [8] and Knesebeck et al [14].…”

Section: Reactor Types Distinctionmentioning

confidence: 99%

“…Based on Tsutsumi et al, the value of x for a system containing light and/or small particles cannot be greater than unity which means the solid concentration in the wake phase cannot exceed the solid concentration in the slurry phase. According to the available correlations [8,14], the value of b approach zero when x = 1. This means uniform distribution of solid particles in slurry bubble columns.…”

Section: Reactor Types Distinctionmentioning

confidence: 99%

Effect of Solid Particles on the Slurry Bubble Columns Behavior – A Review

Mahmoudi

Hlawitschka

2021

ChemBioEng Reviews

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A wide-ranging review is presented on the most focal aspects of gas-liquid-solid reactors to discuss the fresh headways towards the understanding of slurry bubble column reactors' behavior. In more detail, in this critical review, published works' findings concerning the effects of solid particles characteristics (size, concentration and density) on volumetric mass transfer coefficient, liquid-side mass transfer coefficient, gas-liquid interfacial area, gas hold-up and flow regime are deliberated. Besides, the effects of other pivotal parameters such as pressure, temperature, reactor size, height of liquid, gas distributor, density, and viscosity on the performance of slurry bubble column reactors are considered. Eventually, regarding the effects of each of the aforementioned parameters on the performance of reactor, logical conclusions are drawn.

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“…The K value determines the appropriate range of the fluidparticle dynamic laws that apply. If K < 3.3, then Stokes law Table 1 Friction coefficient (n) as a function of atmospheric stability condition (CCPS, 2000;Hanna et al, 1982;Irwin, 1979 (9)); if K > 43.6, Newton's law applies (equation (10)); and if K > 2360, equations (8)e(10) should not be used (Coker, 2007;Knesebeck and Guardani, 2004;Smith, 2005).…”

Section: Gravitational Settling Of Non-neutrally Buoyant Particlesmentioning

confidence: 99%