cfd simulation of results

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Chemical Engineering Science 61 (2006) 6511 6529www.elsevier.com/locate/ces

Simulations of chemical absorption in pilot-scale and industrial-scale packedcolumns by computational mass transfer

G.B. Liua, K.T. Yua, X.G. Yuana,, C.J. Liua, Q.C. Guob

aState Key Laboratory for Chemical Engineering (Tianjin University), Chemical Engineering Research Center and School of Chemical Engineering and

Technology, Tianjin University, Tianjin, 300072, ChinabInstitute of photoelectronics thin film devices and technique, Nankai University, Tianjin, 300071, China

Received 28 December 2005; received in revised form 22 May 2006; accepted 22 May 2006

Available online 3 June 2006

Abstract

A complex computational mass transfer model (CMT) is proposed for modeling the chemical absorption process with heat effect in packed

columns. The feature of the proposed model is able to predict the concentration and temperature as well as the velocity distributions at once

along the column without assuming the turbulent Schmidt number, or using the experimentally measured turbulent mass transfer diffusivity.

The present model consists of the differential mass transfer equation with its auxiliary closing equations and the accompanied formulations of

computational fluid dynamics (CFD) and computational heat transfer (CHT). In the mathematical expression for the accompanied CFD and

CHT, the conventional methods of k. and t2.t are used for closing the momentum and heat transfer equations. While for the mass transfer

equation, the recently developed concentration variance c2 and its dissipation rate c equations (Liu, 2003) are adopted for its closure. To test the

validity of the present model, simulations were made for a pilot-scale randomly packed chemical absorption column of 0.1 m ID and 7 m high,

packed with 1/2 ceramic Berl saddles for CO2 removal from gas mixture by aqueous monoethanolamine (MEA) solutions (Tontiwachwuthikulet al., 1992 ) and an industrial-scale randomly packed chemical absorption column of 1.9m ID and 26.6 m high, packed with 2 stainlesssteel Pall rings for CO2 removal from natural gas by aqueous MEA solutions (Pintola et al., 1993). The simulated results were compared

with the published experimental data and satisfactory agreement was found between them in both concentration and temperature distributions.Furthermore, the result of computation also reveals that the turbulent mass transfer diffusivity Dtvaries along axial and radial directions. Thus

the common viewpoint of assuming constant Dt throughout the whole column is questionable, even for the small size packed column. Finally,

the analogy between mass transfer and heat transfer in chemical absorption is demonstrated by the similarity of their diffusivity profiles.

2006 Elsevier Ltd. All rights reserved.

Keywords: Computational mass transfer (CMT); Turbulent mass transfer diffusivity; Simulation; Packed bed; Chemical absorption; Mathematical modeling

1. Introduction

In the chemical industry, packed columns have been widelyused in separation and purification processes involving gas and

liquid contact such as distillation and absorption due to its high

efficiency, high capacity and low pressure drop. Despite the suc-

cess of applying structured packing in the recent years (Gualito

et al., 1997; Spiegel and Meier, 2003), the randomly packed

columns are still commonly used in the separation processes.

The mass transfer process undertaking in a packed column,

Corresponding author. Tel.: +86 22 27404732; fax: +86 22 27404496. E-mail address: [email protected] (X.G. Yuan).

0009-2509/$ - see front matter 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ces.2006.05.035

especially the diffusion of species in the liquid phase, is strongly

coupled with the extent of turbulent flow as well as the heat

effect if involved. As the process is complicated, the behaviorand prediction of the mass transfer in packed column have been

an active research area for decades in both experimental work

and mathematical modeling. It is known that, in most case,

the conventional plug-flow assumption is not applicable due

to the presence of non-uniform packing and the creating tur-

bulence, especially in the case of column-to-particle diameter

ratios ( = aspect ratios) lower than about 10 (Wen et al., 2001;Giese et al., 1998; Ziolkowska and Ziolkowski, 1988; Lerou

and Froment, 1977; Bey and Eigenberger, 1997; Zhang, 1986;

Zhang and Yu, 1988; Yuan et al., 1989). Thus the investigation
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6512 G.B. Liu et al. / Chemical Engineering Science 61 (2006) 65116529

on the non-uniform distributions of velocity and temperature

in the packed column have been received much attention in the

past. The notable advance is coming from the use of compu-

tational fluid dynamics (CFD) and computational heat transfer

(CHT) to help the solution of this problem, as the velocity and

temperature profiles in the packed column can be predicted by

such methodology (Yin et al., 2000, 2002; Hjertager et al., 2002;Liu, 2001, Jiang et al., 2002a,b). However, for the prediction of

concentration profile, it is necessary to use the empirical turbu-

lent Schmidt numbers or the experimentally determined disper-

sion coefficients obtained by tracer technique as an approximate

substitution to the unknown turbulent mass transfer diffusivity

(Yin et al., 2000; de Lemos and Mesquita, 2003). Obviously,

the use of such empirical method for finding the concentration

distribution is not dependable, especially for the cases where

the empirical relationship or the experimental coefficients for

the investigated system are unavailable. The best way of over-

coming this difficulty is to eliminate the turbulent mass transfer

diffusivity from the differential mass transfer equation in the

model computation. The recently developed c2.c model pro-

posed by Liu (2003) is suitable for this purpose. With the idea

of using such model, Sun et al. (2005) successfully obtained the

concentration profiles on the sieve trays of a commercial-scale

distillation column without relying on the empirical correlation

of turbulent mass transfer diffusivity and showed satisfactory

agreement with the published experimental measurement.

The chemical absorption has been extensively used in gas

purification as well as in many chemical processes. For in-

stance, the absorption of CO2 in randomly packed columns by

alkaline solutions such as NaOH, monoethanolamine (MEA),

diethanolamine (DEA) and methyldiethanolamine (MDEA)

aqueous solutions is commonly adopted in acid gas treatments.Among them, the use of aqueous MEA solutions as absorbent

takes more share in the industrial process of CO2 removal, and

the research concerned have been reported (Danckwerts, 1979;

Hikita et al., 1979; Tontiwachwuthikul et al., 1992; Astarita

et al., 1964; Aboudheir et al., 2003). However, the investiga-

tions were mostly based on overall mass balances and plug

flow, without considering the non-ideal behaviors of flow, heat

and mass transfer in the randomly packed bed. The problem

of close modeling is remained to be solved.

With the increasing power of computer and rapid devel-

opment of numerical computational method, it is possible to

solve the problem by establishing a complex model to describein-depth the transport phenomena of the chemical absorption

process with a set of differential equations. Thus, a complex

computational mass transfer model (CMT) is proposed in this

paper for modeling the chemical absorption process with heat

effect. The present model consists of the differential mass trans-

fer equation, closing with the c2.c equations, and the accom-

panied formulations of CFD and CHT. In the mathematical

formulation of the accompanied CFD and CHT, the conven-

tional methods of k. and t2.t are used for closing the mo-

mentum and heat transfer equations. To testify the validity of

the proposed model, simulation was made to a pilot-scale and

an industrial-scale randomly packed columns undertaking the

chemical absorption of CO2 by aqueous MEA solution. The

simulated results on the distributions of temperature and con-

centration along the axial and radial directions were compared

with the published experimental data.

2. The reaction mechanism of CO2 absorption by aqueous

MEA solution

When CO2 is being absorbed and reacts with aqueous MEA

solutions, the following three overall reactions are taken place

at the condition of carbonation ratio (or CO2 loading) less than

0.5 mol of CO2 per mole of MEA. (Danckwerts, 1979; Astarita

et al., 1964):

CO2,g CO2,L + HA, (1)

CO2,L + 2BNH2 k2 BNHCOO + BNH+3 + HR, (2)

CO2,L + BNHCOO + 2H2O BNH+3 + 2HCO3 , (3)

where letter B denotes the group HOCH2CH2, step (1) repre-sents the physical absorption of CO2 by water, HA is the accom-

panied heat of solution. At very short times of the liquidgas

encountered in industrial absorbers, the reaction (3) can be ne-

glected, and only reaction (2) affects the absorption rate of CO2(Sada et al., 1976). Reaction (2) takes place in two steps:

CO2,L + BNH2 BNHCOO + H+, (4)

BNH2 + H+ BNH+3 . (5)

Reaction (4) could be considered as second order, and is the

rate controlling step, because reaction (5) is a proton transfer

reaction and virtually instantaneous. Therefore, the absorption

of CO2 in MEA solutions can be regarded as gas absorption

accompanied by an irreversible second-order reaction with a

stoichiometric coefficient of 2, and the overall reaction is rep-

resented by reaction (2). The reaction rate Rc can be expressed

by the following equation:

Rc = k2[CO2][MEA]. (6)

3. The experimental data available

The validity of the proposed model for the chemical absorp-

tion of CO2 by MEA solution can be testified by the compar-

ison between the model prediction and the experimental data.There are two sets of data available:

(1) The experimental data of a pilot-scale column were re-

ported by Tontiwachwuthikul et al. (1992). They conducted the

experiment for the absorption of CO2 from air by using aque-

ous MEA solution at total pressure of 103.15 kPa in a column

of 0.1m ID and packed with 1/2 ( 1.27cm) ceramic Berlsaddles with a total packing height of 6.55 m. The column con-

sisted of six equal-height sections, and the samples were taken

at the inlet and outlet of each section for analyzing the concen-

tration.

(2) The operating data of an industrial column were reported

by Pintola et al. (1993). The column was used for reducing the

CO2 content in the natural gas from approximately 2% to less
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G.B. Liu et al. / Chemical Engineering Science 61 (2006) 65116529 6513

than 100 ppm by the aqueous MEA solution absorption. The

column was 1.9 m in diameter and packed with 2 stainless steelPall rings in three sections with total packing height of 14.1 m.

The operating pressure was ranging from 5.39 to 7.60 atm. All

their experimental data were given only at the top and the

bottom of column.

4. The computational mass transfer (CMT) model for the

chemical absorption concerned

4.1. Assumptions

The following assumptions are made for the present CMT

model for simulating the chemical absorption of CO2 by aque-

ous MEA solution in randomly packed columns:

1. The pseudo-single-liquid model is used and the liquid

phase is assumed to be pseudo-continuous, and the gas phase

is considered to be uniform along the radial direction. The flow

is axis-symmetric.

2. The gas absorption operation is steady, and the liquid is

incompressible, which means the liquid density does not vary

with the liquid temperature and concentration. This assumption

is reasonable for the current cases where the changes of liquid

temperature and liquid concentration are not large enough to

make substantial variation of the liquid density.

3. Only the CO2 component in the gas phase is absorbed

by the aqueous MEA solutions, and the solvent water does not

transfer to the gas phase.

4. The heat of solution and reaction generated is all absorbed

instantaneously by the liquid phase, and the effect of packing

on the heat transfer is neglected. There is not heat transfer

between gas and liquid phases.5. The gas absorption process is adiabatic, which means that

there is no heat exchange between the column and environment.

This is reasonable and justified by Pandya (1983).

4.2. Model equations

The CMT model consists of the differential mass transfer

equation with its auxiliary closing equations and the accompa-

nied formulations of CFD and CHT.

4.2.1. The mass transfer equation and its auxiliary closing

equations(1) The equation for time average MEA mass fraction C in

liquid phase:

(huC) = (hDeffC) + MC , (7)where MC is the MEA sink term which comes from the chem-

ical reaction between absorbed CO2 and MEA aqueous solu-

tions, Deff is the effective diffusivity of MEA, which is defined

by

Deff = D + Dt, (8)where D is the molecular diffusivity of MEA in the liquid phase,

and Dt is the turbulent diffusivity for mass transfer, which can

be solved by using the c2.c model (Liu, 2003) as follows.

According to the c2.c model, the Dt can be expressed by

Dt = Cc0k

k

c2

c

1/2, (9)

where the concentration variance c2 and its dissipation rate care defined by

c2 cc, (10)

c D

jc

jxj

jc

jxj

. (11)

The detailed derivation of c2.c model was given by Liu

(2003) and Sun et al. (2005). The model equations used in this

paper are given below.

(2) The concentration variance c2

equation:

(huc2) h

D + Dt

c

c2

= 2hDtCC 2hc (12)

(3) The dissipation rate c equation:

(huc) h

D + Dt

c

c

= Cc1hDtCCc

c2 Cc2h

2c

c2 Cc3h

c

k. (13)

The constants in Eqs. (9)(13) are given as follows ( Zhang,2002):

Cc0 = 0.11, Cc1 = 1.8, Cc2 = 2.2, Cc3 = 0.8,c = 1.0 and c = 1.0.

4.2.2. The accompanied CFD equations

(1) The continuity equation:

(hu) = M, (14)

where is the liquid density, h is the volume fraction of liquid

phase based on pore space, u is the interstitial velocity vector,M is the source term of the continuity equation due to the

chemical absorption of CO2 from gas phase, which is equal to

the quantity of CO2 absorbed by the aqueous solutions per unit

volume and unit time.

(2) The momentum equation:

(huu) (heff(u + (u)T 23 uI))= hp + FLG + h(FLS + g), (15)

eff = + t, (16)

t = Ck2

, (17)


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where , t and eff represent the molecular, turbulent and

effective viscosities of the liquid, respectively. The turbulent

viscosity t is unknown and can be solved simultaneously by

the standard k- model equations given below, and I is the unit

tensor. FLG is the interface drag force between gas phase and

liquid phase, FLS is the flow resistance created by the random

packing, which is considered to be the body force.(3) The turbulent kinetic energy k equation:

(huk)

h

+ t

k

k

= heffu ((u + (u)T) 23 uI) h. (18)

(4) The turbulent dissipation rate equation:

(hu)

h

+ t

= c1heffu ((u + (u)T) 23 uI)

k

c2h2

k(19)

the parameters which appear in k. model Eqs. (17)(19) are

customarily chosen to be

C = 0.09, k = 1.0, = 1.3,c1 = 1.44 and c2 = 1.92.

4.2.3. The accompanied CHT equations

(1) The time averaged liquid temperature T equation:

(cphuT )

= (cph

effT )

+Q, (20)

where cp is the liquid phase specific heat and taken as a con-

stant; eff is the effective thermal diffusivity of liquid phase,

defined as eff=+t, in which and t are the molecular andturbulent thermal diffusivities, respectively, and t can be cal-

culated by the t2.t closing equation set given below; Q is the

thermal source term including the heat of solution and reaction

and other thermal effects.

(2) The temperature variance t2 equation: The model equa-

tions of temperature variance t2 and its dissipation rate t pro-

posed by Nagano and Kim (1988) were used. However, in this

paper, some terms of the t2 and t equations were neglected

due to their unimportance as compared with other terms. Thesimplified model equations were given as follows:

(hut2) h

+ t

t

t2

= 2htTT 2ht. (21)

(3) The dissipation rate t equation:

(hut) h

+ t

t

t

=Ct1ht

T

Tt

t2 Ct2h

2t

t2 Ct3h

t

k

, (22)

the model constants in t2.t equations are (Nagano and Kim,

1988):

Ct0 = 0.11, Ct1 = 1.8, Ct2 = 2.2, Ct3 = 0.8,t = 1.0 and t = 1.0.

The concentration and the temperature as well as the velocity

distributions in the absorption column can be obtained by the si-

multaneous solution of the foregoing model Eqs. (7), (12)(15),

(18)(22) without assuming the empirical Schmidt number or

knowing the experimental mass transfer diffusivity. However,

before the computation of foregoing equation system, the terms

of h, M, FLG, FLS, MC, Q appearing in the equations must

be determined. In this paper, most of these terms are obtained

from existing correlations as shown in the following sections.

4.3. Evaluation of various terms in the model

4.3.1. The volume fraction of liquid phase

The volume fraction of liquid phase h based on pore spacecan be determined from the total liquid holdup Ht and the

porosity under the operating condition of the gasliquid two

phases flow:

h = Ht/. (23)

The total liquid holdup can be obtained as follows:

Ht = Hs + Hop. (24)

Shulman et al. (1955) reported the value of static holdup Hsto be 0.0317 for 1/2-in ceramic Berl saddles. The static holdup

Hs for stainless steel Pall rings could be determined from thecorrelation by Engel et al. (1997):

Hs = 0.033 exp0.22 g

a2

. (25)

Otake and Okada obtained a correlation for the operating

holdup Hop, as reported by Sater and Levenspiel (1966):

Hop = 1.295(Re)0.676L (Ga)0.44L (adp), (26)

where (Re)L = dpL/ is the Reynolds number of liquid phase;(Ga)L = d3pg2/2 is the Gallileo number of liquid phase; ais the surface area per unit volume of packed bed; dp is the

nominal diameter of the packed particle.The porosity of randomly packed bed is changed from a

constant around the center to a maximum in the neighborhood

of the wall region, which were observed by many experimental

investigations (Giese et al., 1998; de Klerk, 2003; Roblee et al.,

1958). Thus the uneven porosity distribution should be consid-

ered and calculated by the following correlation given by Liu

(2001):

= +(1 )

2Er

(1 0.3pd)

cos 2

c + 1.6Er2

R r

pddp+ 0.3pd , (27)
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where is the porosity of an unbounded packing, R is theradius of the column, r is the position in radial direction, Er is

the exponential decaying function, which is given by

Er = exp1.2pdR r

dp

3/4

, (28)where pd is the period of oscillation normalized by the nominal

particle size and pd = 0.94 for Berl saddles, pd = 0.94 (2 +1.414)/3 for Pall rings; c is a constant depending on the ratio

of the particle size to column size:

c =2R

npddp 1.6exp

2.4pd

R

dp

3/4, (29)

where

n = int

2

1 + 1.6exp[2.4pd(R/dp)3/4]R

pddp

. (30)

4.3.2. The source term M in continuity equation

The source term M, the rate of mass transfer per unit volume,

can be determined from the following equation based on the

well-known two-film model:

M= KGaeffMCO2 (pCO2 pe,CO2 ), (31)

where the overall coefficient of gas phase KG is related to the

individual film coefficients as follows:

1

KG= 1

kG+ 1

kLEH e. (32)

In the foregoing equations, kL, kG are the film coefficients

of mass transfer of liquid phase and gas phase respectively; effis the effective area for mass transfer between the gas phase

and liquid phase; MCO2 is the molecular weight of CO2; pCO2

is the partial pressure of CO2 in main body of gas; pe,CO2 ispartial pressure of CO2 in equilibrium with the solution; E

is the enhancement factor for the mass transfer process with

chemical reaction; He is the Henrys constant.

The liquid phase and gas phase mass transfer coefficients kL,

kG are determined from the correlations by Onda et al. (1968):

kL = 0.0051g

1/3L

aw

2/3

DCO2,L

1/2(adp)

0.4,

(33)

kG=

5.23 GaG

0.7

GGDG

1/3

(adp)2RGT

aDG

1, (34)

where the wetted surface area aw is obtained from the following

correlation by Onda et al. (1968):

aw

a

=1

exp1.45

ct

0.75 L

a

0.1

L2a

2g

0.05

L2

a

0.2

.(35)

According to the research result by Onda et al. (1968),

the w in Eq. (35) is considered to be equal to eff, and the

flow rate of liquid is related to the local liquid velocity by

L = h|u|.The viscosity of aqueous MEA solutions can be calcu-

lated from the correlation developed from experimental data by

Weiland et al. (1998):

H2O =exp

100C(2373 + 2118.6C)[rc(2.2589 + 0.0093 T + 1.015C) + 1.0]

T2 , (36)

where rc is the carbonation ratio of aqueous MEA solutions.

The surface tension of aqueous MEA solutions is deter-

mined by following equation (Vazquez et al., 1997):

= H2O (H2O MEA)

1+ (0.630361.3 105(T 273.15))xH2O

1 (0.9472 105(T 273.15))xH2O

xMEA.

(37)

The pure liquid surface tensions of water and MEA are obtained

as follows:

H2O = 76.0852 0.1609(T 273.15), (38)MEA = 53.082 0.1648(T 273.15), (39)where xH2O and xMEA denote the molar fractions of water and

MEA in aqueous MEA solutions, respectively.

The enhancement factor E, which is definedas the ratio of the

mass transfer coefficient kR,L for the absorption with chemical

reaction to the mass transfer coefficient kL for the physical

absorption (Danckwerts, 1970), varies along the column height.

For the irreversible second-order reaction such as CO2MEA

reaction, Wellek et al. (1978) derived the following explicit

correlation for the calculation of enhancement factor E with

deviation less than 3%:

E = 1 + ((Ei 1)1.35 + (E1 1)1.35)1/1.35, (40)where

Ei = 1 +DXMEA

2DCO2,LXi,CO2, (41)

E1 =

H a

tanh

H a, (42)

H a = DCO2,Lk2XMEA(kL)

2. (43)

Here XMEA denotes the molar concentration of MEA in liquid

phase; DCO2,L represents the molecular diffusivity of CO2 in
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aqueous MEA solutions; and k2 is the second-order reaction

rate constant for CO2MEA reaction.

Due to the chemical reaction of CO2 with MEA, the molec-

ular diffusivity of CO2 in the MEA aqueous solution DCO2,Lcan be determined by the use of N2O analogy as follows:

DCO2,L = DN2O,L(DCO2 /DN2O)w. (44)The diffusivities of CO2 and N2O in the pure water are deter-

mined from the correlations by Versteeg and Vanswaaij (1988):

(DCO2 )w = 2.35 106 exp(2119/T ), (45)

(DN2O)w = 5.07 106 exp(2371/T ). (46)

The diffusivity of N2O in aqueous MEA solutions is deter-

mined by the correlation reported by Ko et al. (2001):

DN2O,L = (5.07 + 0.865XMEA + 0.278X2MEA)

exp2371.0 93.4XMEAT

106. (47)The diffusivity of MEA molecule in aqueous MEA solutions

is calculated by using the correlation given by Snijder et al.

(1993):

D = exp(13.275 2198.3/T 0.078142XMEA). (48)

The second-order reaction rate constant k2 for CO2MEA

reaction is obtained from the correlation by Hikita et al. (1979):

log k2 = 10.99 2152/T. (49)

According to Pohorecki and Moniuk (1988), the molar con-centration of CO2 at interface Xi,CO2 can be expressed in terms

of Henrys law:

Xi,CO2 = H eptyCO2 , (50)

where He is the Henrys constant for CO2 in MEA solutions; ptis the total pressure of gas phase; yCO2 is the volume fraction

of CO2 in gas phase. Similar to the calculation of DCO2,L, He

is also determined by the use of N2O analogy in the following

form:

H e

=H eN2O(H eCO2 /H eN2O)w. (51)

The Henrys constant for CO2 and N2O in water can be ob-

tained from the following correlations proposed by Versteeg

and Vanswaaij (1988):

(H eCO2 )w = (2.82 106 exp(2044/T))1, (52)(H eN2O)w = (8.552 106 exp(2284/T))1. (53)The Henrys constant for N2O in aqueous MEA solutions is

calculated from the semi-empirical model developed by Wang

et al. (1992):

ln H eN2O

=vMEA ln(H eN2O)MEA

+ vH2O ln(H eH2O)w + MEA,H2O, (54)

where the excess Henrys quantity MEA,H2O for the presentsystem can be determined by the correlation of Tsai et al.

(2000):

MEA,H2O = vMEAvH2O(4.793 7.446 103T 2.201vH2O), (55)

where vMEA and vH2O denote the volume fractions of MEAand water in aqueous MEA solutions respectively; the Henrys

constant (H eN2O)MEA for N2O in pure MEA liquid is obtained

from the correlation developed from the experimental data by

Wang et al. (1992):

(H eN2O)MEA = (1.207 105 exp(1136.5/T))1. (56)

In order to calculate the gas phase film coefficient kG, some

physical properties of gas phase, such as molecular diffusiv-

ity DG of CO2 in gas phase, viscosity G and density G of

gas phase, should be known. In this paper, DG in the gas mix-

ture is obtained from the Blancs law and the binary molecular

diffusivity was calculated by empirical correlation reported byPoling et al. (2001). The gas mixture viscosity G is calcu-

lated by Bromley and Wilke correlation reported by Perry and

Green (2001). The viscosity of air and pure CO2 is obtained

from Geankoplis (2003), and the vapor viscosity of pure hy-

drocarbons at low pressure is predicted by the method of Stiel

and Thodos reported by Perry and Green (2001). The density

of gas mixture and pure components can be obtained according

to the method of Lee and Kesler, which was reported by Perry

and Green (2001).

4.3.3. Interface drag force FLG

For irrigated packing, the pressure drop is greater than thedry bed pressure drop pd because of the presence of liquid

adhered to the packing surface. The part of increased pressure

drop, pL, represents the interfacial drag force between gas

and liquid phases. Robbins (1991) correlated the total pressure

drop including pd and pL for irrigated packing as follows:

pt = pd + pL, (57)pd = p1G2f 10p2Lf , (58)

pL = 0.774

Lf

20000

0.1(p1G

2f 10p2Lf )4, (59)

where p1=

0.04002, p2=

0.0199, Gf is the gas loading fac-

tor, and Lf is the liquid loading factor. Gf and Lf can be

determined by the following correlations:

Gf = G

1.2

G

0.5 Fpd65.62

0.5for pt1.0 atm, (60)

Gf = G

1.2

G

0.5 Fpd65.62

0.5 100.0187G for pt > 1.0atm,

(61)

Lf = L

1000

Fpd

65.62

0.50.2 for Fpd15, (62)

Lf = L1000

65.62

Fpd0.5

0.1

for Fpd < 15. (63)


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The term Fpd is a dry packing factor, specified for a given

packing type and size. For 1/2( 1.27cm) ceramic Berl sad-dles, Fpd = 900m1, and for 2 stainless steel Pall rings,Fpd = 79 m1. Since the total operating pressure of chemicalabsorption in this study is more than 1.0 atm, Eqs. (61) and (62)

are chosen to evaluate Lf and Gf.

Finally, the interface drag force FLG can be calculated by

FLG =pL

|uslip|uslip, (64)

where uslip is the slip velocity between gas and liquid phases,

which is defined by

uslip = uG u. (65)

As the quasi-single-liquid-phase CFD method is applied in the

present work, thus the average uG in axial direction is deter-

mined from gas phase flow rate G, and the uG in radial direc-

tion is set to be zero.

4.3.4. Body force FLSThe resistance of liquid flow due to the presence of random

packing is considered as body force, which can be calculated

by Ergun (1952) equation with replacing the mean porosity by the porosity distribution function .

FLS =

150(1 )22d2e

+ 1.75 (1 )de

|u|

u, (66)

where de is the equivalent diameter of random packing, which

is defined by

de =6(1 )

a. (67)

4.3.5. The sink term MC in C equation

The rate of MEA consumed per unit volume for absorbing

CO2 from the gas phase, MC, can be calculated according to

the chemical reaction (2) as follows:

MC = M44

61 2. (68)

4.3.6. The heat effect Q

The temperature of liquid phase will be increased due to theheat of absorption and reaction, and as a result, the parameters

such as H e, k2 and DCO2,L as well as the absorption rate of

CO2 will be changed. Therefore, the increase of temperature in

liquid must be properly evaluated. The total heat effect Q can

be calculated as follows:

Q = MMCO2

(HA + HR), (69)

where HA is the heat of physical absorption, HA = 1.9924 107 J kmol1 CO2 absorbed (Danckwerts, 1970), and HR de-notes the heat of chemical reaction, HR

=8.4443

107 J kmol1

CO2 (Kohl and Riesenfeld, 1985).

Fig. 1. The simulation domain and boundary conditions arrangement.

4.4. The boundary conditions

The computational domain and boundaries are shown in

Fig. 1. The boundary conditions for the above equation set are

specified as follows:

(1) Inlet: At the top of the column, the boundary condition

for the liquid phase is set to be u = uinlet, vinlet = 0, T = Tinlet,C = Cinlet, kinlet = 0.003u2inlet, inlet = 0.09(k1.5inlet/dH) (Khalilet al., 1975). The term dH denotes the hydraulic diameter of

random packing (Bird et al., 2002), which can be calculated by

dH = 4/a(1 ).The boundary condition for temperature variance t2 is

taken from the work of Tavoularis and Corrsin (1981a,b) andFerchichi and Tavoularis (2002). After averaging their results,

we get the following equation:

t2inlet = (0.082T )2. (70)

As the change of temperature due to the chemical absorption

at the inlet is infinitesimal or very small, the T is set to be

0.1 K for the convenience of computation.

There are no existing experimental measurements or empir-

ical correlations for the inlet condition of the concentration

variance c2. However, by the analogy between heat and mass

transfer, we may assume that

c2inlet = (0.082Cinlet)2. (71)

The inlet condition for c is a complicated problem and could

be obtained by using the basic relationship of turbulent mass

transfer diffusivity Dt and the time scale ratio R:

R k/

c2/c. (72)

Combining Eqs. (10) and (56), we get

R= Cc0

k2

1

Dt

2

. (73)
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Different values of the ratio R were reported in the literatures.

According to the viewpoint of Launder (1976), it may not be

a universal constant and may strongly depend on the nature

of the flow field. As an approximation, we may let R to be

a fixed value only at the inlet boundary, and such value can

be determined from the experimental dispersion coefficient ob-

tained by using inert tracer technique, which is applicable tothe end conditions ofC =0. The diffusivity Dt at C =0 for acolumn randomly packed with 1/2( 1.27cm) ceramic Berlsaddles was measured by using the inert tracer technique by

Sater and Levenspiel (1966), and correlated the coefficient of

dispersion of liquid phase , i.e. equivalent to the Dt, by the

following equation:Udp

Dt

= 7.58 103

dpL

0.7030.238, (74)

where U is the liquid superficial velocity. Later, Michell and

Furzer (1972) correlated the dispersion coefficient according to

their own and some published data in the following form:

|u|dpDt

= 1.00

uinterdp

0.7d3pg22

0.32. (75)

According to Eqs. (74) and (75), the order of magnitude for

Dt is about 103. By taking their average value of Dt, and

substituting into Eq. (73), the value ofR was found to be about

0.4. Therefore, the boundary condition at the inlet for c can

be given as follows:

c,inlet = 0.4inlet

kinlet c2inlet. (76)

By the analogy between heat and mass transfer, the boundary

condition for dissipation rate t of temperature variance is set

to be

t,inlet = 0.4inlet

kinlet

t2inlet. (77)

The specific values calculated from the foregoing relation-

ships for the inlet boundary condition of the present simulation

are listed in Appendix A.

(2) Outflow: The liquid flow at the bottom exit of the column

is considered to be close to the fully developed condition, so

the outflow boundary condition of zero normal gradient for

all flow variables except pressure is chosen under the platform

of the software FLUENT 6.1.

(3)Axis: Under the assumption that all variables are axially

symmetrical, we have j/jr = 0 at r = 0.(4) Wall: The no-slip condition is applied to the wall, and

the flow behavior in the near wall region is approximated by

using the standard wall functions. The zero flux condition is

applied for other variables.

4.5. Numerical procedure

The model equations were solved numerically by using the

commercial software FLUENT 6.1 with finite volume method.

The simulation was done under the condition of steady two-

dimensional flow of axial and radial symmetry. The well-known

SIMPLEC algorithm is used to solve the pressurevelocity cou-

pling problem in the momentum equations.

The grid arrangement for the simulation of pilot-scale col-

umn of 6.55 m height and 0.05 m radius is as follows: there

are 1310 nodes uniformly distributed along the column heightand 80 nodes non-uniformly distributed along the radial direc-

tion with high grid resolution at the near wall region, so the

total numbers are about 104 800 quadrilateral cells. While the

grid arrangement for simulating the commercial-scale column

of 14.1 m height and 0.95 m radius, there are 1000 nodes uni-

formly distributed along the column height and 75 nodes non-

uniformly distributed along the radial direction with higher grid

resolution at the near wall region, so the total numbers are

about 75000 quadrilateral cells. The one-order upwind spatial

discretization scheme was used for all differential equations.

5. Comparison between simulated results and

experimental data

5.1. Comparison between simulated and experimental results

for pilot-scale column

Twelve sets of experimental data for chemical absorption of

CO2 from mixture of CO2 and air by aqueous MEA solutions in

a pilot-scale column were reported by Tontiwachwuthikul et al.

(1992), including the variation of radial averaged carbonation

ration ( = CO2 loading), the temperature in the liquid phase andthe radial averaged CO2 concentration in the gas phase along

the column height. In this paper, only the simulated results on

experiments T13, T14, T17, and T22 are used as examples forcomparison.

In Figs. 25, the square and circle symbols represent the

experimental data, and the solid lines indicate the simulated

results which are obtained after radial average. As seen from

the figures, the simulated and experimental results on the CO2loading in liquid phase and the CO2 volume percentage in gas

phase are in satisfactory agreement.

It is interesting to compare the simulated results between

using the present model without knowing the coefficient of dis-

persion and using the conventional model with published ex-

perimental coefficient. The conventional simulated model used

is one-dimensional with axial mixing, and the axial dispersioncoefficient is calculated by Eq. (74). Take run T17 as an ex-

ample, the simulated results by the conventional model on gas

CO2 concentration and liquid CO2 loading profiles are shown

in Fig. 4(a) by the dash dot lines along the axial direction. It

should be pointed out that the column is taller than it is needed

for the separation concerned as seen on the axial concentration

profile, in which the change of liquid phase concentration is

becoming very small in the upper part of the column. It means

that the separation is approaching to the equilibrium state at

some distance from the column bottom and thus results almost

the same concentration regardless what model is being used

for the simulation. However, the difference is clearly seen at

the lower part of the column, as the simulation by using the
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Fig. 2. Predicted (solid lines) and experimental (points) results for Run

T13: (a) gas CO2 concentration and liquid CO2 loading profiles; (b) liquid

temperature and enhancement factor.

present model give better prediction than the conventional. In

order to display clearly the difference of the simulated results,

a table for comparison is given in Appendix B, in which the ex-

perimental measurements, the predictions by the present model

and the conventional one for run T17 are listed. It is seen that

the present model give better prediction.

As shown in Figs. 2(b)5(b), the predicted temperature pro-

files along the column show somewhat higher than the exper-

imental measurement, especially at the column bottom. The

discrepancy may be due to the following reasons: firstly, thepresent modeling neglects the heat transfer between gas and

liquid phases, that is the cooling of descending liquid by the

entering gas; secondly, the evaporation of solvent water in liq-

uid phase is also neglected, so that the liquid temperature is

overestimated; thirdly, the assumptions of adiabatic operation

and neglecting the heat transfer between the solid packing and

the fluid are also the causes of producing error.

5.2. Comparison between simulated and measured results for

industrial-scale column

Fifteen sets of data for chemical absorption of CO2 from

natural gas mixture by aqueous MEA solutions in an industrial-




scale column were reported by Pintola et al. (1993), including

the CO2 volume percentage in the gas phase and the CO2 load-

ing with temperature in the liquid phase. In this paper, only the

simulated results on experimental Run 115 was presented as an

example for comparison.

As shown in Fig. 6, the simulated top and bottom concentra-

tions by using the proposed model are closely checked by the

reported measurement. Furthermore, our simulation is better

than that given by Pintola et al. (1993), as shown inAppendix C.

For Run 115, the typical CO2 volume percentage in gasphase, the CO2 loading, the temperature of liquid phase and

the enhancement factor along the column are shown in Fig. 6.

It is seen from the figure that 99% of the CO 2 was absorbed

by aqueous MEA solutions in the bottom two sections of the

column, and only little CO2 was removed in the top section.

Figs. 710 show the radial variation of the CO2 concentration

in gas phase, the CO2 loading, the liquid temperature and the

free MEA concentration of liquid phase at different height of

the column.

As seen from Figs. 79, the CO2 concentration in gas phase,

the CO2 loading and the temperature of liquid phase are de-

creased from column center to column wall at different height

of the column. It could be explained that the flow of liquid
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Fig. 4. Comparisons between the predicted values by present model (solid

lines) and by one-dimensional with axial mixing model (dash dot lines) with

experimental (points) results for Run T17: (a) gas CO2 concentration and

liquid CO2 loading profiles; (b) liquid temperature and enhancement factor.

phase is slow down near the wall in the randomly packed

column, resulting in worse contact with the gas phase, and

consequently less CO2 to be absorbed, producing less exother-

mic heat of solution and reaction. It may be also noted from

Fig. 10 that, at a fixed axial position, the radial difference of

free MEA concentration in the liquid phase is larger at the bot-

tom of the column than at the top.

Fig. 11 shows the axial distribution of the CO2 concentration

in the gas phase, the CO2 loading, the free MEA molar con-

centration and the liquid temperature. It can be seen that mostabsorptions are taken place at the bottom part of the column,

and the top part has a little effect on the CO2 removal.

5.3. Liquid velocity profile

Due to the non-uniform packing structure and higher poros-

ity near the wall region, the fluid flow deviates from the plug

flow. As seen from Fig. 12, in both the pilot-scale and the

industrial-scale columns, the wall flow effect is clearly seen,

and the flow behaves relatively uniform only about 2dpapart

from the wall. This phenomenon has been confirmed by many

investigators (Liu, 2001; Giese et al., 1998).




5.4. Turbulent mass transfer diffusivity Dt

The turbulent mass transfer diffusivity or dispersion coeffi-

cient Dt is often neglected or assumed to be constant in the

packed column design. However, according to the calculated

Dt by using the proposed model, it varies from top to bottom

and from center to wall of the columns as shown in Figs. 13(a),

14 (a) and 15 (a). Furthermore, the calculated Dt for the in-

dustrial column are very closer to the reported experimental

measurements. From Fig. 14(a), the turbulent diffusivity Dt ob-

tained by the present model is ranging from 6.0104

m

2

/s to1.5 103 m2/s, while the values calculated from the empiri-cal correlations obtained by using inert tracer technique with no

mass transfer by Sater and Levenspiel (1966) and by Michell

and Furzer (1972) are 0.001011 and 0.00116 m2/s, respectively.

Although they are practically in the same order of magnitude,

the difference in values between them demonstrates that the Dtis changed somewhat due to the process effect of mass transfer.

The variations of Dt with radius at different axial positions

are presented in Figs. 13(a) and 14(a). Generally speaking, Dtis found to be substantially constant around the center region of

the packed bed, and increased to a maximum near the column

wall, and then decreased sharply to the wall surface for both the

pilot-scale column and the industrial-scale column. Such phe-
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115: (a) gas CO2 concentration and liquid CO2 loading profiles; (b) liquid


Fig. 7. Gas CO2 concentration profiles along the radial direction at different

height.

nomenon is consistent with the experimental results by Fahien

and Smith (1955) and Dorweiler and Fahien (1959) on using

gas phase tracer technique. The uneven Dt distribution is re-

lated to the mal-distributed fields of flow and concentration as

shown in Figs. 11(c) and 12.

Fig. 8. The CO2 loading profiles along the radial direction at different height.

Fig. 9. The temperature profiles of liquid along the radial direction at different

height.

Fig. 10. The free MEA concentration profiles along the radial direction at

different height.


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Fig. 11. Axial distributions of: (a) CO2 concentration; (b) CO2 loading; (c) free MEA concentration; and (d) liquid temperature for Run 115.

The predicted Dt along the column height varies little for the

pilot-scale column as shown in Fig. 13(a), which results from

the lower liquid Reynolds number and higher volume fraction

of CO2 in gas phase. While for the industrial column, the Dt is

gradually decreased as approaching to the bottom of the column

as shown in Fig. 14(a), which is probably due to the higher

liquid Reynolds number and lower volume fraction of CO2 in

gas phase. The axial distribution ofDt for the industrial column

is shown in Fig. 15(a).

5.5. Analogy between turbulent mass transfer and heat transfer

In applying the present model, both turbulent mass trans-

fer diffusivity Dt and turbulent heat transfer diffusivity t can


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Fig. 12. Relative axial velocity profile of the liquid along the radial direction for Run T22 and Run 115.

be solved and show in Figs. 1315. From these figures, It

can be clearly seen the similarity between them in spite of

having a little difference. For example, the volume average

values of Dt and t calculated for Run 115 of the industrial

column are 0.001049 and 0.001107 m2/s, respectively, while

those in the Run T22 of the pilot-scale column are 0.001144 and

0.001169m 2/s; the approximate equality of Dt and t demon-

strates the analogy between turbulent mass transfer and heat

transfer.

5.6. Distribution of radial average enhancement factor E

along the column

The enhancement factor E is an important parameter for

chemical absorption, and its accurate estimation is essential for

proper modeling the mass transfer process. The enhancement

factor is influenced by many aspects, such as the physical prop-

erties of liquid and gas, the MEA concentration in liquid phase,

the CO2 concentration in gas phase, the flow field, the reaction

rate and the others; therefore it is a varying parameter along

the column as shown in Figs. 2 (b)6 (b).

5.7. Study on the influence of grid number on the accuracy of

numerical simulation

Generally, the number of grid to be used in simulation has

considerable effect on the numerical result. Regarding this as-

pect, it is necessary to test whether the use of 75 grid points in

radial simulation is sufficient for the industrial scale absorption

column with 1.9 m in diameter. Taking Run 115 of the large

column concerned, it was simulated with 75 and 225 points

separately in the radial direction, and using the second order

upwind discretisation scheme for the differential equations in-

stead of first order upwind scheme. The simulated radial gas

CO2 concentration profiles with 75 and 225 radial grid points

are given in Fig. 16.

It can be seen from Fig. 16 that the difference of the simu-

lated results is small. It could be understood that, the numerical

accuracy of the present simulation with 75 radial grid points is

sufficient in practical sense, and it has very weak improvement

on the increasing number of grids beyond 75.

However, there is no doubt that the numerical accuracy could

be further improved by precise simulation with very large num-

ber of grid points.
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Fig. 13. Turbulent diffusivity profiles along radial direction for Run T22: (a) turbulent mass transfer diffusivity profiles; and (b) turbulent heat transfer diffusivity

profiles.

Fig. 14. Turbulent diffusivity along radial direction for Run 115: (a) turbulent mass transfer diffusivity profiles; and (b) turbulent heat transfer diffusivity profiles.

Fig. 15. Distribution of turbulent diffusivity for Run 115: (a) turbulent mass transfer diffusivity; and (b) turbulent heat transfer diffusivity.


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Fig. 16. The simulated gas CO2 concentration profiles with 75 and 225 grid

points in the radial direction at x = 13.0 m.

6. Conclusions

The following conclusions can be drawn from the present

work:

(1) A complex model of computational mass transfer is pro-

posed for simulating the concentration, temperature and

velocity distributions for a chemical absorption process

with heat effect. The proposed model is applied to a pilot-

scale packed column undertaking the chemical absorption

of CO2 from air by MEA aqueous solutions, and to an

industrial-scale packed column for the chemical absorption

of CO2 from natural gas mixture by aqueous MEA solu-

tion. The simulated results are in satisfactory agreementwith the experimental data reported by Tontiwachwuthikul

et al. (1992) and by Pintola et al. (1993).

(2) The proposed model is able to predict the turbulent mass

transfer diffusivity Dt, which shows varying along the axial

and radial directions.

(3) The computed profiles of Dt for mass transfer and t for

heat transfer are found to be very similar, and the calculated

volume average values ofDt and t are nearly equal, which

demonstrates the analogy between turbulent mass and heat

transfer.

(4) The enhancement factor of chemical absorption predicted

from the proposed model varies significantly along thecolumn.

(5) The proposed model is useful for simulating chemical ab-

sorption and relevant process with heat effect without re-

lying on the experimental measurement of turbulent mass

transfer and heat transfer diffusivities, especially for cases

where the empirical turbulent Schmidt number or the dis-

persion coefficients is not available.

Notation

a surface area per unit volume of packed

bed, 1/m

aeff effective area for mass transfer between

the gas phase and liquid phase, 1/m

aw wetted surface area, 1/m

c2 concentration variance, dimensionless

cp liquid phase specific heat, J/kg/K

c a constant depending on the ratio of the

particle size to column size, dimension-less

C average concentration of mass fraction,

dimensionless

C, c1, c2 model parameters in k model equa-

tions, dimensionless

Cc0, Cc1, Cc2, Cc3 model parameters in c2.c model equa-


Ct0, Ct1, Ct2, Ct3 model parameters in t2.t equations,

dimensionless

[CO2], [MEA] molar concentration of CO2 and MEAin solution, respectively, kmol/m3

de equivalent diameter of random pack-ing, m

dH hydraulic diameter of random pack-

ing, m

dp nominal diameter of the packed parti-

cle, m

D molecular diffusivity of MEA molecu-

lar in aqueous MEA solutions, m2/s

DCO2,L molecular diffusivity of CO2 in aque-

ous MEA solutions,m2/s

(DCO2 )w, (DN2O)w diffusivity of CO2 and N2O in the pure

water, respectively, m2/s

Deff effective diffusivity of MEA, m2

/sDG molecular diffusivity of CO2 in gas

phase, m2/s

DN2O,L diffusivity of N2O in aqueous MEA so-

lution, m2/s

Dt turbulent diffusivity for mass transfer,

m2/s

E enhancement factor, dimensionless

FLG interface drag force between gas phase

and liquid phase, N/m3

FLS flow resistance created by the randomly

packing, N/m3

Fpd dry packing factor, 1/m

g acceleration due to gravity, m/s2

G gas phase flow rate per unit cross-

section area, kg/m2/s

Gf gas loading factor, kg/m2/s

(Ga)L Gallileo number of the liquid phase, di-

mensionless

h volume fraction of liquid phase based

on pore space, dimensionless

HA physical absorption heat of mol CO2absorbed, J/kmol

Hop operating holdup, dimensionless

HR chemical reaction heat of mol CO2 ab-

sorbed, J/kmol


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Hs static holdup, dimensionless

Ht total liquid holdup, dimensionless

He Henrys constant for CO2 in MEA so-

lutions, kmol/m3/kPa

(H eCO2 )w,(H eN2O)w, Henrys constant for CO2 and N2O in

water, respectively, kmol/m3/kPa

H eN2O Henrys constant for N2O in aqueousMEA solutions, kmol/m3/kPa

(H eN2O)MEA Henrys constant for N2O in pure MEA

liquid, kmol/m3/kPa

k2 second-order reaction rate constant,

m3/kmol/s

kG gas phase mass transfer coefficient,

kmol/m/s/kPa

kL liquid phase mass transfer coefficient

without chemical reaction, m/s

kR,L liquid phase mass transfer coefficient

with chemical reaction, m/s

K turbulent kinetic energy, m2/s2

KG overall coefficient of gas phase,kmol/m2/s1/kPa

L liquid flow rate per unit cross-section

area, kg/m2/s

Lf liquid loading factor, kg/m2/s

M CO2 quantity absorbed by the aqueous

solution per unit volume and unit time,

kg/m3/s

MCO2 molecular weight of CO2, kg/kmol

MC sink term of MEA conservation equa-

tion, kg/m3/s

p1, p2 constants, dimensionless

pd period of oscillation normalized by thenominal particle size, dimensionless

pe,CO2 partial pressure of CO2 in equilibrium

with solutions, kPa

pt total pressure of gas phase, kPa

pd dry-bed pressure drop per meter pack-

ing, N/m3

pL wet-bed pressure drop per meter pack-

ing, N/m3

pt total pressure drop per meter packing,

N/m3

PCO2 partial pressure of CO2 in main body

of gas, kPa

Q thermal source term of temperature

equation, J/m3/s

rc carbonation ratio (CO2 loading) of the

aqueous MEA solutions, mol CO2/ mol

MEA

R position in radial direction, m

R radius of the column, m

RG gas universal constant, kJ/kmol/K

(Re)L Reynolds number of liquid phase, di-

mensionless

Rc the rate of reaction, kmol/m3/s

R velocity to concentration time scale ra-

tio, dimensionless

t2 temperature variance , dimensionless

T liquid temperature, K

u interstitial velocity vector of liquid, m/s

uG gas velocity vector, m/s

uslip slip velocity vector between gas phase

and liquid phase, m/s

U liquid superficial velocity, m/svMEA, vH2O volume fraction of water and MEA in

aqueous MEA solutions, respectively,

dimensionless

xH2O, xMEA molar fraction of water and MEA in

aqueous MEA solutions, respectively,

dimensionless

XCO2 molar concentration of CO2 in the liq-

uid bulk, kmol/m3

Xi,CO2 molar concentration of CO2 at inter-

face, kmol/m3

XMEA molar concentration of MEA in liquid

phase, kmol/m3

yCO2 volume fraction of CO2 in gas

phase,dimensionless

Greek letters

, eff, t molecular, turbulent and effective ther-

mal diffusivities, respectively, m2/s

porosity distribution of the random

packing bed along the radial direction,

dimensionless

porosity in an unbounded packing, di-mensionless

turbulent dissipation rate, m2s

3

c turbulent dissipation rate of concentra-

tion fluctuation, 1/s

t turbulent dissipation rate of tempera-

ture fluctuation, 1/s

, t, eff, liquid molecular, turbulent and effec-

tive viscosity, respectively, kg/m/s

G gas phase viscosity, kg/m/s

liquid density, kg/m3

G gas phase density, kg/m3

surface tension of aqueous MEA solu-

tions, dynes/cm, or N/m

ct critical surface tension of the pack-

ing material, N/m, for ceramic, ct =0.061N/m, for stainless steel, ct =0.071N/m

c, c model parameters in c2.c model equa-


H2O pure water surface tension, dynes/cm

k , model parameters in k model equa-


MEA pure MEA surface tension, dynes/cm

t, t model parameters in t2.t model equa-


MEA,H2O excess Henrys quantity, kmol/m

3/kPa

variable, dimensionless


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Table 1

The specific values for the inlet boundary condition of the present simulation

u (m/s) v (m/s) h C T (K) k (m/s)2 (m2/s3) c2 c (s1) t2(K2) (s1)

T13 0.0387 0 0.1563 0.121878 292.15 4.492E 6 6.106E 8 9.988E 5 4.073E 7 6.724E 5 2.742E 7T14 0.0387 0 0.1563 0.093115 292.15 4.492E 6 6.106E 8 5.830E 5 2.377E 7 6.724E 5 2.742E 7T17 0.0387 0 0.1563 0.121805 293.15 4.492E

6 6.106E

8 9.976E

5 4.068E

7 6.724E

5 2.742E

7

T22 0.0304 0 0.1399 0.182817 292.15 2.777E 6 2.967E 8 2.247E 4 7.204E 7 6.724E 5 2.742E 7Run 115 0.1372 0 0.0319 0.219380 312.95 5.651E 5 4.351E 7 3.236E 4 9.967E 7 6.724E 5 2.071E 7

Table 2

Comparison between experimental, two and one dimensional simulation results for Run T17

T17 CO2 concentration in gas phase (%) CO2 loading in liquid phase

Exp. Two dim. One dim. Exp. Two dim. One dim.

x = 0.0 m 0.0 0.0265 0.0389 0.237 0.237 0.237x = 1.05 m 0.0 0.1045 0.1101 (0.237) 0.238 0.238x = 2.15 m 0.8 0.4596 0.3288 0.243 0.241 0.240x

=3.25 m 2.0 1.4343 0.9797 0.256 0.252 0.247

x = 4.35 m 5.3 4.1456 2.8740 0.296 0.282 0.267x = 5.45 m 10.2 9.7249 7.7675 0.350 0.347 0.324x = 6.55 m 15.6 15.60 15.60 0.428 0.427 0.427

Table 3

Comparison of CO2 concentration in gas phase exit between the results of

experimental, by the proposed model and by Pintola et al. (1993)

Run

No.

Exp. CO2(ppm)

Simu. CO2 (proposed)

(ppm)

Simu. CO2 (Pintola et al.

1993) (ppm)

101 8.0 9.1 65.2

102 11.5 2.4 17.5

103 14.5 27.5 13.0104 8.7 10.0 30.6

105 9.7 4.7 19.1

106 12.0 2.1 13.1

107 6.5 8.1 39.1

108 15.0 7.4 45.3

109 8.7 5.0 45.4

110 16.0 8.0 55.5

111 13.0 4.8 37.4

112 5.3 9.1 54.7

113 28.0 9.3 60.4

114 74.0 2.2 41.5

115 4.8 8.5 41.5

Subscripts

eff effective, dimensionless

G gas, dimensionless

I interface, dimensionless

L liquid, dimensionless

R reaction, dimensionless

slip slip, dimensionless

S solid, dimensionless

time scale, dimensionless

Acknowledgments

The authors acknowledge the financial support by the Na-

tional Natural Science Foundation of China (Contract no.

20136010) and the assistance from the staff in the State Key

Laboratories for Chemical Engineering (Tianjin University).

Appendix A

The specific values for the inlet boundary condition of the

present simulation are given in Table 1.

Appendix B

Comparison between experimental, two and one dimen-

sional simulation results for Run T17 are given in Table 2.

Appendix C

Comparison of CO2 concentration in gas phase exit be-tween the results of experimental, by the proposed model and

by Pintola et al. (1993) are given in Table 3.

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