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A PBM-CFD Model with Optimized PBM-Customized Drag Equations for Chemisorption of CO2 in a Bubble Column

  • Qi Liu , Xiao-Fei Liang , Xian-Jin Luo EMAIL logo and Zheng-Hong Luo EMAIL logo
Published/Copyright: March 21, 2018

Abstract

In this work, a computational fluid dynamics (CFD) approach based on two-fluid model (TFM) is introduced to describe the reversible two-step reactions found in the chemisorption process of CO2 by an aqueous NaOH solution in a lab-scale bubble column reactor. The population balance model (PBM) is applied to track the bubble size distribution with considering the coalescence and breakage terms, which then leads to a CFD-PBM model for describing the chemisorption of CO2 in an aqueous NaOH solution. Drag force is considered for the interfacial momentum transfer and a modified PBM-customized drag model with the correction factor is subsequently adopted, in which the contribution of different bubble size groups in each computational cell is computed. The tested boundary conditions include superficial gas velocities, gas-inlet sparger and the reactor dimension. Detailed and comprehensive investigations are done in the evolution of gas holdup, pH value, concentration distribution and bubble diameter distribution which are essential in optimizing the reactor performance in terms of yield and selectivity. Importantly, the current CFD-PBM model is able to predict the entire reaction process.

Funding statement: The authors thank the National Ministry of Science and Technology of China (No. 2017YFB0602401), the National Natural Science Foundation of China (No. 21625603 and 21776173) and the Center for High Performance Computing, Shanghai Jiao Tong University for supporting this work.

Nomenclature

B&C

Breakage and coalescence

BCRs

Bubble column reactors

BCs

Bubble columns

CFD

Computational fluid dynamics

E-E

Euler-Euler

E-L

Euler-Lagrange

NSEs

Navier–Stokes equations

PBEs

Population balance equations

PBM

Population balance model

QMOM

Quadrature method of moments

RTD

Residence time distribution

SMM

Standard method of moments

TFM

Two-fluid model

UDFs

User-defined functions

UDS

User-defined scalar

ai,j

bubble aggregation rate, s1

a

contact interphase area, m2

bv,v

bubble breakup rate, s1

CD

drag coefficient

bubble diameter, m

dc

critical size of bubbles having wake effect for bubble coalescence, m

E

enhancement factor

Eo

Eotvos number

f

value fraction

F

interphase force

FD

drag force

g

gravity, m2.s1

G

the production rate of turbulent energy, W.m3

H

Henry’s constant

Ha

Hatta number

I

ionic concentration, kmol.m3

k

turbulent kinetic energy, m2.s2

kb,large

correction factor for bubble wake effect

ki,j

the covariance of the velocities of phase i and phase j

Ki

equilibrium constant for ith reaction, m3.kmol1

m˙

interphase mass transfer, kg.s1

Mo

Morton number

n

number of particles per unit volume, m3

p

pressure, Pa

Re

Reynolds number

Sh

Sherwood number

c

Schmidt number

t

time, s

tdrainage

film drainage time, s

tcontact

bubble contact time, s

T

temperature, K

ui,j

the relative velocity between the liquid and dispersed phases

U

velocity vector, m.s1

Ug

superficial gas velocity, m.s1

v

bubble volume, m3

xi

pivot bubble size of the bubble interval (vi, vi+1), m3

Greek Letters

α

phase hold-up

βv,xk

daughter bubble size distribution function

ε

turbulent dissipation rate, m2.s3

λv,xi

bubble redistribution coefficient

μ

viscosity, kg.m1.s1

ξ

eddy size ratio

Πk,i

bubble-induced turbulence term, W.m3

Πε,i

bubble-induced turbulence term, W.s1.m3

ρ

density, kg.m3

σ

surface tension, N.m1

τ

viscous stress tensor

ψ,k

transfer coefficient of bubble breakup

ωi,jk

transfer coefficient of bubble coalescence

Subscripts

b

bubble index

g

gas index

i,j

phase index

l

liquid index

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Received: 2017-9-14
Revised: 2018-2-8
Accepted: 2018-3-12
Published Online: 2018-3-21

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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