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A breakage model with different liquid properties for pressurized bubble columns in a homogeneous regime

  • Process Systems Engineering, Process Safety
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Abstract

The bubble breakage rate in gas-liquid bubble columns increases for organic liquid and at high pressure. This study developed a breakage model that accounts for different liquid properties in gas-liquid pressurized bubble columns in the homogeneous regime. The Luo (1996), Lehr (2002), and Wang (2003) breakage models, which are widely used for the population balance equation (PBE) of bubble columns, were compared in terms of the total breakage rate, daughter size distribution, and computational time. The model with two empirical equations, modified from Luo’s breakage kernel, was proposed. One represented bubble deformation behavior in different liquid properties in terms of buoyancy, surface tension, and viscosity. The other considered the effect of operating pressure (or gas density) on the breakage rate. The modified model was compared with experimental data and a rigorous breakage model from the literature. The proposed breakage model shows good agreement with experimental data and computational efficiency. This breakage model is applicable for computational fluid dynamics with PBE in pressurized bubble columns with organic liquids.

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Abbreviations

c:

reakage time constant [=1/8]

Cf :

parameter of surface energy increment [-]

Cd :

parameter of surface energy per unit volume [-]

d:

mother bubble diameter [m]

d′:

small daughter bubble diameter [m]

d*:

dimensionless bubble diameter [-]

dc :

critical bubble neck diameter [m]

dneck :

diameter of the bubble neck [m]

eγ :

kinetic energy of eddy [J]

e γ, crit :

critical kinetic energy of eddy [J]

ēγ :

mean kinetic energy of eddy [J]

fv :

bubble breakup volume fraction [-]

kM :

correction factor of breakup rate considering liquid property [-]

kP :

correction factor of breakup rate considering system pressure [-]

Mo:

morton number [-]

n:

number density of bubbles [1/m3]

nγ :

number density of eddies [1/m4]

P:

operating pressure [bar]

Pb :

breakup probability density function [-]

Pe :

breakup probability density function for eddy [-]

tb :

bubble breakup time [s]

uγ :

turbulent velocity of eddy [m/s]

ūγ :

mean turbulent velocity at a distance of db [m/s]

u γ, crit :

critical turbulent velocity of eddy [m/s]

We:

webber number [-]

α g :

gasvolumefraction[-]

β :

daughter size distribution [-]

ε :

turbulence energy dissipation rate [m2/s3]

γ :

bombarding eddy size [m]

γ min :

minimum size of eddy [m]

μ l :

liquid viscosity [Pa·s

v l :

kinematic viscosity of fluid [m2/s]

Ω γ :

collision frequency density of eddy [1/m5/s]

Ω :

totalbreakagerate [1/m3/s]

Ω k :

breakage ratekernel[1/m3/s]

Ω f :

breakage frequency [1/s]

Ω*:

dimensionless breakage rate [-]

ρ g :

gasdensity[kg/m3]

ρ g,0 :

air density at normal condition [=1.2 kg/m3]

ρ l :

liquid density[kg/m3]

σ :

surface tension [N/m]

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Acknowledgement

We acknowledge with gratitude the financial support from the R&D Convergence Program of the Ministry of Science, ICT and Future Planning (MSIP) and the National Research Council of Science & Technology (NST) of the Republic of Korea (CRC-14-1-KRICT). This research was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Ministry of Science and ICT (Grant number:2020R1F1A1066097).

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Authors and Affiliations

  1. Center of Sustainable Process Engineering (CoSPE), Department of Chemical Engineering, Hankyong National University, Jungang-ro 327, Anseong-si, Gyeonggi-do, 17579, Korea

    Bay Van Tran, Son Ich Ngo & Young-Il Lim

  2. Center for Convergent Chemical Process (CCP), 141 Gajeong-ro, Yuseong-gu, Daejeon, 34114, Korea

    Kang-Seok Go & Nam-Sun Nho

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  1. Bay Van Tran
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  2. Son Ich Ngo
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  3. Young-Il Lim
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  4. Kang-Seok Go
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Correspondence to Young-Il Lim.

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Tran, B.V., Ngo, S.I., Lim, YI. et al. A breakage model with different liquid properties for pressurized bubble columns in a homogeneous regime. Korean J. Chem. Eng. 38, 264–275 (2021). https://doi.org/10.1007/s11814-020-0717-9

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  • DOI: https://doi.org/10.1007/s11814-020-0717-9

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