Evaluation of the Onda Correlations for Mass Transfer with Large Random Packings

Dvorak, Bruce I.; Lawler, Desmond F.; Fair, James R.; Handler, Neil E.

doi:10.1021/es950408+

Cited by 24 publications

(19 citation statements)

References 10 publications

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“…The expression used to determine the interfacial area for mass transfer depends on the pattern of interactions between the three phases. For a trickle flow bed, a commonly used expression based on Onda's work is 24,25 :

a_{normalG - normalL} = a_{t} ({}, 1 - \exp ([], - 1.45 {(\frac{σ_{normalC}}{σ_{normalL}})}^{0.75} {Re}_{L}^{0.1} {Fr}_{L}^{- 0.05} {We}_{L}^{0.2}))

where σ C (N m −1 ) is the critical surface tension of the packing material (2.17 × 10 −2 N m −1 at 20°C) and σ L (N m −1 ) is the surface tension of the liquid (7.28 × 10 −2 N m −1 at 20°C) 26 . Only a portion of the solid particles is wetted by the liquid flow in the trickle flow regime; the specific wetted area of the bed, a w (m −1 ), different from a G − L and used in Equations ), () and () for the weathering reactions, is given by 27

a_{w} = a_{t} ({}, 1 - \exp ([], - 1.986 {Fr}_{L}^{0.139} {Mo}_{L}^{0.0195} ε_{M}^{- 1.55}))

…”

Section: Model Developmentmentioning

confidence: 99%

Enhanced weathering to capture atmospheric carbon dioxide: Modeling of a trickle‐bed reactor

2021

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Enhanced weathering (EW) of alkaline minerals can potentially capture CO2 from the atmosphere at gigaton scale, but the reactor design presents great challenges. We model EW with fresh water in a counter‐current trickle flow packed bed batch of 1–10 mm calcite particles. Weathering kinetics are integrated with the mass transfer of CO2 incorporating transfer enhancement by chemical reaction. To avoid flooding, flow rates must be reduced as the particles shrink due to EW. The capture rate is mainly limited by slow transfer of CO2 from gas to liquid although slow dissolution of calcite can also play a role in certain circumstances. A bed height of at least 7–8 m is required to provide sufficient residence time. The results highlight the need to improve capture rate and reduce energy and water consumption, possibly through enriching the feed with CO2 and further chemical acceleration of the mass transfer.

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a_{normalG - normalL} = a_{t} ({}, 1 - \exp ([], - 1.45 {(\frac{σ_{normalC}}{σ_{normalL}})}^{0.75} {Re}_{L}^{0.1} {Fr}_{L}^{- 0.05} {We}_{L}^{0.2}))

a_{w} = a_{t} ({}, 1 - \exp ([], - 1.986 {Fr}_{L}^{0.139} {Mo}_{L}^{0.0195} ε_{M}^{- 1.55}))

…”

Section: Model Developmentmentioning

confidence: 99%

Enhanced weathering to capture atmospheric carbon dioxide: Modeling of a trickle‐bed reactor

2021

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“…Direct use of the advection-diffusion equation for prediction of the transfer rate is rarely feasible because the turbulent and otherwise complex near-interface fluid motions are difficult to measure or obtain from simulation. Simplifying models have been developed to allow prediction of transfer rates, but the typical uncertainty in these predictions is large and ranges between a factor of 2 and 10 (Belanger & Korzun 1991;Dvorak et al 1996;Piche, Grandjean & Larachi 2002;Wanninkhof et al 2004;Ho et al 2006). This paper reports laboratory measurements of near-surface motions and interfacial gas transfer rates in air-water systems in turbulent open-channel flows and wind-driven flows including microscale wave breaking.…”

Section: Introductionmentioning

confidence: 99%

Air–water gas transfer and near-surface motions

Turney

Banerjee

2013

J. Fluid Mech.

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Rates of gas transfer between air and water remain difficult to predict or simulate due to the wide range of length and time scales and lack of experimental observations of near-surface fluid velocity and gas concentrations. The surface renewal model (SR) and surface divergence model (SD) provide the two leading models of the process, yet they remain poorly tested by observation because near-surface velocity is difficult to measure. To contribute to evaluation of these models, we apply new techniques called interfacial particle imaging velocimetry (IPIV) and three-dimensional IPIV (3D-IPIV) for measuring water velocities within a millimetre of a moving deformable air-water interface. The latter technique (3D-IPIV) simultaneously measures the air-water interface topography. We apply these techniques to turbulent open-channel water flows and wind-sheared water flows with microscale breaking waves. Additional measurements made for each flow condition are bulk turbulent length scales, bulk turbulent velocity scales, air-water gas transfer rates, friction velocities, and wave characteristics. We analyse these data to test the surface divergence models for interfacial gas transfer. The first test is of predictions from the Banerjee (Ninth International Heat Transfer Conference, Keynote Lectures, vol. 1, 1990, pp. 395-418, Hemisphere Press) surface divergence model for gas transfer for homogeneous isotropic turbulence interacting with a planar free surface. The second test is of predictions from the McCready, Vassiliadou and Hanratty (AIChE J., vol. 32 (7), 1986, pp. 1108-1115) surface divergence model, as applied in both open-channel flow and wind-sheared wavy flows. We find the predictions of the Banerjee and McCready et al. models to agree with the experimental data taken for open-channel flow conditions. On the other hand, for wind-driven flows with wind waves we find disagreement between the McCready et al. predictions and our direct measurements of the gas transfer coefficient. The cause of the disagreement is investigated by Lagrangian tracking of surface divergence of surface water patches, and by analysis of the corresponding Lagrangian time series with advection-diffusion concepts. A quantitative criterion based on surface divergence strength and lifetime is proposed to distinguish the effectiveness of each near-surface motion toward causing interfacial gas transfer. Capillary waves are found to contribute to surface divergence but to have too short a time scale to cause interfacial gas transfer. As wind speed increases, the presence and intensity on the air-water interface of capillary waves and other ineffective near-surface motions is diminished by the rise of turbulent wakes from microscale breaking waves thus causing the disagreement of the surface divergence model's predicted transfer rates with measurements. A model of air-water gas transfer that combines the surface renewal and surface divergence models is formulated and † Email address for correspondence: dturney@ccny.cuny.edu Air-water gas transfer a...

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“…(0.0508 m). The Onda correlations were found to be fairly inaccurate to predict mass transfer with large random packings, especially at high gas flow rates and when the gas-side resistance is large (31). It has been reported that the Onda correlations underpredicted k G for the saddles by about 40% on average and overpredicted f f k G for the f f spheres by more than 50% (32).…”

Section: Recent Advancementsmentioning

confidence: 98%