Chemical Engineering Science 66 (2011) 5938–5944

Contents lists available at SciVerse ScienceDirect

Chemical Engineering Science

0009-25

doi:10.1

� Tel.

E-m

journal homepage: www.elsevier.com/locate/ces

Dynamics of CO2 adsorption on sodium oxide promotedalumina in a packed-bed reactor

Mingheng Li �

Department of Chemical and Materials Engineering, California State Polytechnic University, Pomona, CA 91768, United States

a r t i c l e i n f o

Article history:

Received 29 June 2011

Received in revised form

25 July 2011

Accepted 7 August 2011Available online 16 August 2011

Keywords:

CO2 adsorption

Sodium oxide promoted alumina

Packed-bed

Dynamics

Breakthrough curve

Modeling

09/$ - see front matter & 2011 Elsevier Ltd. A

016/j.ces.2011.08.013

: þ1 909 869 3668; fax: þ1 909 869 6920.

ail address: minghengli@csupomona.edu

a b s t r a c t

CO2 adsorption in packed-bed reactors has potential applications in flue gas CO2 capture and adsorption

enhanced reaction processes. This work focuses on CO2 adsorption dynamics on sodium oxide

promoted alumina in a packed-bed reactor. A comprehensive model is developed to describe the

coupled transport phenomena and is solved using orthogonal collocation on finite elements. The model

predicted breakthrough curve matches very well with experimental data obtained from a pilot-scale

packed-bed reactor. Several dimensionless parameters are also derived to explain the shape of the

breakthrough curve.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Fossil fuels supply around 98% of energy over the entire world.The use of fossil fuels is the major source of CO2 emissions.According to International Energy Outlook 2010, the worldwideconsumption of fossil fuels is projected to increase by about 50%by 2035 from 2007, primarily due to the economical growth ofnon-OECD (Organization for Economic Co-operation and Devel-opment) countries (U.S. Energy Information Administration,2011). In view that CO2 is a greenhouse gas that contributes toglobal climate warming, more stringent government regulationshave been proposed to reduce the emission of CO2 from the use offossil fuels, e.g., The American Clean Energy and Security Act of2009 (Waxman and Markey, 2009). This has significantly moti-vated the research and development of technologies for moreefficient use of fossil fuels (e.g., hydrogen fuel cell technologyKolb, 2008) as well as cost-effective CO2 capture and sequestra-tion techniques (Yang et al., 2008; Aaron and Tsouris, 2005).Among existing CO2 capture techniques such as absorption(Rao and Rubin, 2002), membrane separation (Zhao et al., 2008),cryogenic fractionation (Hart and Gnanendran, 2009), and adsorp-tion (Chue et al., 1995), the last one has advantages of low energyrequirement and low capital investment cost. Its working princi-ple is based on preferential adsorption of CO2 on a solid adsorbent

ll rights reserved.

and subsequent desorption at a different condition. Throughcyclic operations over several packed-beds (e.g., pressure swingadsorption or PSA), CO2 is separated from the mixture.

More recently, CO2 adsorption has found applications in adsorp-tive reaction processes where CO2 is a by-product. The adsorptivereactor concept enables natural separation of CO2 from the productmixture, and therefore, enhances yield and selectivity of thedesired product, leading to process intensification (Stankiewicz,2003). One such example is adsorption enhanced reforming (AER),which was originated by Sircar and coworkers (Carvill et al., 1996)and further developed by several groups around the world togenerate fuel cell grade hydrogen (Ding and Alpay, 2000; Reijerset al., 2006; Koumpouras et al., 2007; Stevens et al., 2007; Lindborgand Jakobsen, 2009; Duraiswamy et al., 2010). The author’s groupand Intelligent Energy, Inc. (Long Beach, CA) have recently devel-oped a bench-scale AER-based hydrogen generator. It incorporatesa novel pulsing feed concept that further improves hydrogen yieldand purity and allows the AER to be operated at low steam/carbonratios (Duraiswamy et al., 2010). The unit consists of four reactionbeds packed with ceria supported rhodium as the catalyst andhydrotalcite as the adsorbent. The beds run alternately and con-tinuously produces high-purity hydrogen for use in conjunctionwith fuel cells. The system is operated around 500 1C, significantlylower than the conventional steam methane reforming process(about 850 1C). During reforming step, CO2 is adsorbed and boththe reforming and water gas shift (WGS) reactions are enhanced(Li, 2008). As a result, H2 is produced with little CO and CO2

impurities. The CO2 adsorption also suppresses carbon formation

M. Li / Chemical Engineering Science 66 (2011) 5938–5944 5939

according to the author’s thermodynamic analysis (Li, 2009).During regeneration step, cathode off-gas of the fuel cell or steamis sent from the reversed direction and CO2-rich exhaust gas exitsthe reactor from the other end. The AER fuel cell system, if success-fully commercialized, would have a better process efficiency and alower CO2 emission than the combustion engine based route forpower generation.

The commonly used CO2 adsorbents include zeolite (Chue et al.,1995), activated carbon (Chue et al., 1995), and alkali composites,e.g., lithium zirconate (Xiong et al., 2003), calcium oxide (Li et al.,2009), aluminum oxide (Lee et al., 2007a) and hydrotalcite (Yang andKim, 2006; Yong et al., 2001). It has been shown that impregnation ofpotassium or sodium oxide enhances CO2 adsorption (Xiong et al.,2003; Lee et al., 2007a,b). This work aims to investigate the dynamicsof CO2 adsorption in packed-bed reactors, which is a part of theauthor’s research effort on adsorption enhanced reaction and separa-tion processes (Duraiswamy et al., 2010; Li, 2008, 2009; Li et al., inpress). The adsorbent chosen for this study is Sud Chemie ActiSorb s

CL2 adsorbent, which contains 85–95% alumina and 5–15% sodiumoxide. As compared to hydrotalcite used in the author’s previousexperimental work (Duraiswamy et al., 2010), sodium promotedalumina works at a relatively low temperature and has potentialapplications in adsorption enhanced methanol reforming and WGS(Li et al., in press) and in CO2 capture from flue gases. However, thedeveloped modeling can be extended to other adsorbents. The paperwill first present a comprehensive mathematical model to describevarious transport phenomena in the packed-bed. Different from theconstant velocity assumption often employed in literature (e.g., Choiet al., 2003; Stevens et al., 2007), this work explicitly accounts for itsevolution with respect to time and space. Several dimensionlessparameters are also derived to clearly reveal the kinetics andthermodynamics of the adsorption process.

2. Mathematical model

Consider the flow through a porous packed-bed with simulta-neous adsorption, the mass conservation equation of species j isdescribed by the following equation:

e@Cj

@tþrb

@qj

@t¼�

@ðvCjÞ

@zþ@

@zDz@Cj

@z

� �, j¼ 1, . . . ,s ð1Þ

where Cj is the concentration of species j, t is the time, e is the bedporosity, respectively, z is the axial location, v is the superficialvelocity (volumetric flow _Q ¼ vA), rb is the bulk density of thepacked material (total mass of the adsorbent in the reactor overthe reactor volume), qj is the loading of species j on the adsorbent,Dz is the axial dispersion coefficient, and s is the total number ofspecies.

It is assumed that the gases follow the ideal gas law, or

C ¼P

RTð2Þ

where C is the total molar concentration (C ¼Ps

i ¼ 1 Cj), P is thepressure and T is the temperature. Let yj be the fraction of speciesj in the gas phase, or Cj ¼ yjC, it can be derived from Eqs. (1)and (2) that

e@yj

@tþeyj

RT

@P

@t�eyjC

T

@T

@tþrb

@qj

@t¼�vC

@yj

@z�vyj

@C

@z�Cyj

@v

@z

þDz C@2yj

@z2þyj

@2C

@z2þ2

@C

@z

@yj

@z

!ð3Þ

The overall mass balance is then described by

Xs

j ¼ 1

yj ¼ 1 ð4Þ

It is also assumed that the adsorption follows the lineardriving force (LDF) model (Sircar and Hufton, 2000). Based onthis model, the changing rate of loading of species j on theadsorbent is described by:

@qj

@t¼ kads,jðq

n

j �qjÞ ð5Þ

where kads,j is the effective LDF mass transfer coefficient (Yang,1987). qn

j is the loading of species j on the adsorbent at a partialpressure of Pj when equilibrium is reached. According to theLangmuir isotherm model, qn

j ¼mjbjPj=ð1þPs

j ¼ 1 bjPjÞ, where mj

and bj are the saturated capacity and the adsorption parameter,respectively.

The momentum balance for flow over a pack-bed is describedusing the Ergun equation (Bird et al., 1960):

0¼�@P

@z�

150mð1�eÞ2

d2pe3

v�1:75ð1�eÞ

dpe3rgv2 ð6Þ

where P is the pressure, dp is the equivalent diameter of thepacked material, and rg is the gas density. rg ¼

Psj ¼ 1 CjMj ¼

CPs

j ¼ 1 yjMj ¼ ðP=RTÞPs

j ¼ 1 yjMj, where Mj is the molecularweight of species j and T is the temperature.

The energy balance equation is described as follows:

ðergcvg þrbcpbÞ@T

@tþrb

Xs

j ¼ 1

DHads,j

@qj

@t

� ��e @P

@t

¼�@ðvrgcpg TÞ

@zþ@

@zkz@T

@z

� �þ

4U

DsðTw�TÞ ð7Þ

where cvg and cpg are the gas heat capacities under constantvolume and constant pressure, respectively, and cpb

is the heatcapacity of the packed-bed material, DHads,j is the enthalpychange of adsorption of species j, Ds is the diameter of the reactorand U is the overall heat transfer coefficient between the wall andthe packed material.

Danckwerts (1953) boundary conditions are applied to theequations describing concentration and temperature. For exam-ple, the boundary conditions to Eq. (1) or (3) are

@Cj

@z¼�

v0

DzðCj,0�CjÞ, x¼ 0

@Cj

@z¼ 0, x¼ L ð8Þ

where v0 and Cj,0 are the superficial velocity and concentration ofspecies j at the inlet of the packed-bed, respectively.

The dynamic model composed by Eqs. (3)–(7) is a partialdifferential-algebraic equation (PDAE) which can be solvednumerically. The independent variables will be yj (j¼ 1, . . . ,s), P,T and u. Note that C is a dependent variable of P and T based onEq. (2). Moreover, the first- and second-order spatial derivativesof C can be explicitly described as functions of P and T using theequations below:

@C

@z¼

1

RT

@P

@z�

C

T

@T

@z

@2C

@z2¼

1

RT

@2P

@z2�2R

@C

@z

@T

@z�CR

@2T

@z2

� �ð9Þ

The numerical method is based orthogonal collocation onfinite elements, which has been used to solve diffusion-convec-tion-reaction processes (Li and Christofides, 2008). The centralidea of the orthogonal collocation method is to discretize thevariables in the spatial domain based on the zeros of someorthogonal polynomials and to transfer the PDAE to a set of DAEs.For example, a variable xðz,tÞ (which may be yj, P or T in this work)can be written as a sum of N finite elements within the spatial

Table 1Parameters used in the simulation.

Parameters Value

Ds 0.076 m

L 1.22 m

e 0.57

rb 785 kg/m3

cpb1000 J/kg/K

P 1.48 bar

T0 225 1C

Q0 18.8 slpm

v0 0.091 m/s

yA00.16

TW 225 1C

U 50 W/m2/K

kads 2.2�10�2 s�1

0100

200300

0

0.5

10

0.05

0.1

0.15

0.2

t/τz/L

y CO

2

Fig. 1. Spatial-temporal profile of CO2 fraction in the gas phase.

M. Li / Chemical Engineering Science 66 (2011) 5938–59445940

domain, or xðz,tÞ ¼PN

i ¼ 1 liðzÞxðzi,tÞ at time t, where li(z) is theLagrange interpolation polynomial of ðN�1Þ th order:

liðzÞ ¼YN

j ¼ 1,ja i

z�zj

zi�zjð10Þ

which satisfies

liðzjÞ ¼0, ia j

1, i¼ j

(ð11Þ

Based on the orthogonal collocation scheme, the collocationelements (zi) and the Lagrange interpolation polynomial may bedetermined a priori without information from the structure of thePDE. Therefore, the partial derivatives of xðz,tÞ with respect to thespatial coordinate can be expressed as follows:

@xðzk,tÞ

@z¼XN

i ¼ 1

xðzi,tÞdliðzkÞ

dz¼XN

i ¼ 1

Ak,ixðzi,tÞ ð12Þ

and

@x2ðzk,tÞ

@z2¼XN

i ¼ 1

xðzi,tÞd2liðzÞ

dz2¼XN

i ¼ 1

Bk,ixðzi,tÞ ð13Þ

where A and B are both constant matrices.For collocation points 2�ðN�1Þ, all the spatial derivatives in

Eqs. (3)–(7) are converted to weighted sums of variables at thesecollocation points. For collocation points 1 and N, the boundaryconditions (e.g., Eq. (8)) are converted to algebraic equations.Note that all the temporal derivatives in Eqs. (3)–(7) are on theleft hand side. Therefore, the original PDAE model is converted toa DAE as follows:

Mdx

dt¼ f ðx,tÞ, xð0Þ ¼ x0 ð14Þ

where x¼ ½y11, . . . ,y1N

, . . . yS1, . . . ,ySN

,T1, . . . TN ,u1, . . .uN ,P1, . . . PN�T

and M is a matrix. As one can see from Eq. (14), the velocity isfully coupled with other variables. Eq. (14) can be solved bystandard solvers (e.g., ode15s in Matlab).

Even though the focus of this work is dynamic modeling, it isworth nothing that the presented numerical method may be usedfor future model reduction and optimization of adsorption-basedprocesses (Agarwal et al., 2009). For example, Karhunen–Loeveexpansion can be used to derive empirical eigenfunctions, whichin turn, are used as basis functions to derive reduced-ordermodels to capture the dominant process dynamics. Thereduced-order system is then used for model-based control andoptimization to enhance process performance. Interested readersmay refer to literature for finite-dimensional approximation andcontrol of process systems described by nonlinear parabolicpartial differential (Christofides and Daoutidis, 1997; Baker andChristofides, 2000).

3. Results and discussion

The developed mathematical model can be applied to multi-component adsorption in general. However, for sodium oxidepromoted alumina in this work, CO2 is assumed to be the onlyadsorbate. The parameters used in the simulation are shown inTable 1, which are based on a pilot-scale experimental system at theauthor’s lab, and now at Intelligent Energy, Inc. (Long Beach,California). The temperature of the packed-bed is controlled around225 1C using an external heater. This temperature is suitable for WGSand steam reforming of methanol with simultaneous CO2 adsorption(Li et al., in press). At this temperature, our Thermogravimetricanalysis (TGA) study indicates that CO2 adsorption on sodium oxidepromoted alumina approximately follows the Langmuir isotherm

with parameters mA¼0.39 mol/kg and bA¼5.2�10�4 Pa�1, wheresubscript A represents CO2. The packed-bed reactor is loaded with3.8 kg adsorbent, corresponding to a bulk density of 785 kg/m3. Theresidence time calculated based on the inlet superficial velocity(t¼ Le=v0) is about 7.6 s. The axial dispersion coefficient Dz is esti-mated to be about 2.4�10�4 m/s2 using an empirical equation(Edwards and Richardson, 1968). The thermodynamic and transportproperties are calculated as functions of temperature and composi-tion using formulas and coefficients based on the NASA CEA program(Gordon and McBride, 1996). The pressure drop along the packed-bed calculated from the Ergun equation is less than 100 Pa, or theprocess may be considered isobaric.

The formulated mathematical model is solved using Matlab.Default error control settings are used (the relative tolerance is0.1% and the absolute error tolerance is 10�6). The contours ofCO2 fraction in the gas phase and CO2 loading on the adsorbentare shown in Figs. 1 and 2, respectively. The spatial-temporalprofile of CO2 behaves similar to the step response in a tubularreactor where dispersion and convection occur simultaneously(Li and Christofides, 2008). However, the breakthrough time ismuch longer than t. For a dispersion–convection process with noadsorption or reaction, the concentration of CO2 at the exit of thereactor is about 50% of the feeding condition at t¼t (Li andChristofides, 2008). When adsorption is coupled with dispersionand convection, all CO2 fed to the reactor is adsorbed near theentrance of the packed-bed at t¼t, and therefore, no CO2 comesout of the reactor. As time proceeds, the loading of CO2 on theadsorbent increases and the wave fronts of both CA and qA move

0100

200300

0

0.5

10

0.1

0.2

0.3

0.4

t/τz/L

q CO

2 (mol

/kg)

Fig. 2. Spatial-temporal profile of CO2 loading on the adsorbent.

0100

200300

0

0.5

1224

226

228

230

232

t/τz/L

T (°

C)

Fig. 3. Spatial-temporal profile of bed temperature.

0100

200300

0

0.5

10.07

0.08

0.09

0.1

t/τz/L

v (m

/s)

Fig. 4. Spatial-temporal profile of superficial velocity.

0 30 60 90 120 1500

0.05

0.1

0.15

0.2

y CO

2, e

t/τ

ExperimentModel

Fig. 5. Comparison between model predicted breakthrough curve and experi-

mental measurement.

M. Li / Chemical Engineering Science 66 (2011) 5938–5944 5941

forward along the reactor. Eventually, the concentration wavereaches the outlet of the reactor, and the breakthrough occurs.

The temperature contour of the bed is shown in Fig. 3. BecauseCO2 adsorption is exothermic, the bed temperature rises and heatis transferred from the packed-bed to the wall. As CO2 adsorptionapproaches equilibrium, the heat release rate from adsorptiondrops below the heat dissipation through the wall and thetemperature begins to drop. Therefore, one can see the propaga-tion of temperature wave along the reactor. Finally, the bedtemperature equals the wall temperature when the steady stateis reached.

The superficial velocity is shown in Fig. 4. Initially, the super-ficial velocity suddenly drops below v0 because of CO2 adsorptionon the adsorbent. The velocity gradually increases as the CO2

adsorption rate reduces (due to smaller and smaller driving forcefor adsorption). As the loading of CO2 on the adsorbent reaches itssaturated value, the superficial velocity is slightly higher than v0

because of an elevated bed temperature. As the bed temperaturebecomes the same as the wall temperature at steady state, thesuperficial velocity equals v0.

The model predicted and measured breakthrough curves ofCO2 mole fraction at the exit of the reactor are shown in Fig. 5. Itis seen that a very good match between mathematical modelingand measurement can be obtained using mA¼0.39 mol/kg insteadof 0.38 mol/kg derived from TGA measurement. The discrepancybetween TGA and packed-bed measurements is about 3%. More-over, the adsorption kinetic parameter kads is chosen to be a

constant (2.2�10�2 s�1) in the model to best match the model-ing results with the experimental data. As will be shown later, achange in kads will affect the slope of the breakthrough curve.

A mass balance equation may be derived to provide anin-depth understanding of the relationship between the break-through curve and the adsorbent capacity. Based on the assump-tions that the adsorption of carrier gas is negligible and that thecarrier mass flow rate at the exit of the reactor is the same as theone at the feed, a mass balance may be written as follows:

ðrbqn

A0þeCA0

ÞLAc ¼

Z 10

_ncg,0yA0

1�yA0

� _ncg,eyAeðtÞ

1�yAeðtÞ

� �dt ð15Þ

where _ncg is the molar flow rate of the carrier gas, and Ac is thecross-sectional area of the packed-bed. It can be readily derivedfrom Eq. (15) that:

Xþ1¼G ð16Þ

where X¼ rbqn

A0=eCA0

, and G¼ ð1=tÞR1

0 ½1�yAeðtÞð1�yA0

Þ=yA0

ð1�yAeðtÞÞ�dt, which is equal to the area between 1 and the corrected

dimensionless mole fraction yAeðtÞð1�yA0

Þ=yA0ð1�yAe

ðtÞÞ in Fig. 6.A numerical integration shows that G¼ 87:9, almost the same asXþ1¼ rbqn

A0=eCA0

þ1¼ 87:8.It is interesting to note that X is a very important parameter also

used in the author’s thermodynamic analysis of adsorption enhancedreaction process (Li, 2008, 2009). These studies have indicated that

0 50 100 150 2000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

y CO

2,e

(1−y

CO

2,0)

/yC

O2,

0 (1

−yC

O2,

e)

t/τ

Fig. 6. Temporal profile of the corrected dimensionless molar fraction at the exit

of the reactor.

0 500 1000 1500 20000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1C

/C0

Pe = 100Pe = 200Pe = 400

t/τ

Fig. 7. Effect of Pe on the breakthrough curve.

0 500 1000 1500 20000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Da = 0.075Da = 0.15Da = 0.3

C/C

0

t/τ

Fig. 8. Effect of Da on the breakthrough curve.

M. Li / Chemical Engineering Science 66 (2011) 5938–59445942

X uniquely determines the equilibrium composition of a reactivesystem with simultaneous adsorption at a given temperature, pres-sure and initial composition. The larger the X, the more the enhance-ment in reaction. The physical meaning of X is the ratio of CO2 on theadsorbent to the one in the gas phase at equilibrium. In this sense,X may be considered as the dimensionless adsorbent capacity of anadsorbent corresponding to CA0

(note that the volumetric adsorptioncapacity [mol A/m3]¼rbqn

A0¼XeCA0

).If CO2 concentration is low, it is shown that its adsorption

dynamics on a packed-bed may be well characterized using onlythree dimensionless parameters including X. Note that a low CO2

concentration implies a roughly constant bed temperature. There-fore, the mathematical model is formulated as follows:

e @CAðz,tÞ

@tþrb

@qAðz,tÞ

@t¼�v

@CAðz,tÞ

@zþD

@2CAðz,tÞ

@z2

@qAðz,tÞ

@t¼ kadsðq

n

A�qAðz,tÞÞ

s:t: vCA0¼ vCAð0,tÞ�Dz

@CAðz,tÞ

@z

����z ¼ 0

@CAðz,tÞ

@z

����z ¼ L

¼ 0 ð17Þ

To write the above PDE in a dimensionless form, the followingvariables are defined: t¼ Le=v (the characteristic time of thereactor), Pe¼ Lv=Dz (the Peclet number, or the rate of convectionover the one of axial dispersion), Da¼ kadst (the Damkohlernumber for adsorption, or the residence time over the timescale for adsorption), z ¼ z=L, t ¼ t=t, C ¼ CA=CA0

, q ¼ qA=qn

A0and

X¼ rbqn

A0=eCA0

. At a low CO2 concentration, bPA51, andqn

A ¼mbPA=ð1þbPAÞ �mbPA. Therefore, qn

A=qA0� C . As a result,

Eq. (17) can be written in a dimensionless form as follows:

_C þX _q ¼�C0þ

1

PeC00

_q ¼DaðC�qÞ

s:t: 1¼ C ð0,tÞ�1

PeC0ð0,tÞ

0¼ C0ð1,tÞ ð18Þ

It is seen from Eq. (18) that the process dynamics and thebreakthrough curve are primarily dependent on three importantdimensionless parameters: Pe, Da and X. Eq. (18) can be readilysolved using numerical methods such as finite difference andorthogonal collocation on finite elements (Li, 2008; Li andChristofides, 2008). Possible infinite series solution to Eq. (18)

will be investigated in future work. The base case conditions inthe parametric analysis are chosen to be Pe¼200, Da¼0.15 andX¼ 800. The effect of each parameter is shown in Figs. 7–9. It isobserved that Pe or Da affects the slope of the breakthrough curve.X has the most prominent influence on the slope as well asthe taking-off location of the breakthrough curve. Based on theassumption of a low CO2 concentration in the gas phase, G inEq. (16) can be simplified as:

G¼1

t

Z 10

1�yAeðtÞð1�yA0

Þ

yA0ð1�yAe

ðtÞÞ

� �dt¼

1

t

Z 10

1�yAeðtÞ

yA0

� �dt¼

Z 10ð1�C ð1,tÞ dt

ð19Þ

which is equal to the area between 1 and the breakthrough curvein Figs. 7–9.

If the adsorption kinetics is very fast (or Da is sufficientlylarge), adsorption equilibrium may be reached instantaneously.As a result, q ¼ C , and Eq. (18) becomes:

ð1þXÞ _C ¼�C0þ

1

PeC00

s:t: 1¼ C ð0,tÞ�1

PeC0ð0,tÞ

0¼ C0ð1,tÞ ð20Þ

0 500 1000 1500 20000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

C/C

0

Ξ = 400Ξ = 800Ξ = 1600

t/τ

Fig. 9. Effect of X on the breakthrough curve.

M. Li / Chemical Engineering Science 66 (2011) 5938–5944 5943

An approximate analytic solution of C ð1,tÞ may be derivedfollowing an approach similar to the one in Li and Christofides(2008). The result is as follows:

C ð1,tÞ ¼1

2erfc

1�t=ðXþ1Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4t=ðXþ1Þ=Pe

p" #

ð21Þ

which implies that:

C ð1,Xþ1Þ ¼ 0:5 ð22Þ

Eq. (22) provides an efficient way to estimate X and thecapacity of the adsorbent based on the experimentally measuredbreakthrough curve, provided that the adsorption is fast enough.It is found that Eq. (22) can be used to estimate X in all casesshown in Figs. 7–9 with a very reasonable accuracy. For thenon-dilute case presented in Fig. 6, t=t corresponding toyAeðtÞð1�yA0

Þ=yA0ð1�yAe

ðtÞÞ ¼ 0:5 is 85.9, which is also close tothe actual value of Xþ1, or 87.8.

4. Concluding remarks

A comprehensive mathematical model is formulated andsolved to describe the CO2 adsorption dynamics on sodium oxidepromoted alumina in a packed-bed reactor. The modeling resultmatches the experimental data very well with mA¼0.39 mol/kgand kads¼2.2�10�2 s�1 at a bed temperature around 225 1C. Thecapacity data are also close to TGA derived value 0.38 mol/kg.

Several dimensionless parameters (X, Pe and Da) may be usedto explain the breakthrough curve. In particular, X, or the dimen-sionless adsorbent capacity, significantly affects both the taking-off location and slope of the breakthrough curve. It is explained asthe area between 1 and the corrected dimensionless mole fractionin the breakthrough curve. The value of X may also be quicklyestimated with reasonable accuracy when the corrected dimen-sionless mole fraction reaches 0.5, provided that Da is largeenough. X also links this study to the author’s previous work onthermodynamic analysis of adsorption-reaction system.

Acknowledgments

This work is partly supported by the American ChemicalSociety Petroleum Research Fund (PRF# 50095-UR5). The author

would like to thank Dr. Duraiswamy at Intelligent Energy, Inc.(Long Beach, CA) for discussions.

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