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Carbonation Characteristics of IsolatedCalcium Oxide Nanoparticles for Thermal

Energy Storage

Krishna V. Valavala a , Hongxiang Tian a & Sanjiv Sinha aa

Department of Mechanical Science and Engineering , University of

Illinois at Urbana Champaign , Urbana , Illinois

Published online: 27 Jun 2013.

To cite this article: Krishna V. Valavala , Hongxiang Tian & Sanjiv Sinha (2013) Carbonation

Characteristics of Isolated Calcium Oxide Nanoparticles for Thermal Energy Storage, Nanoscale and

Microscale Thermophysical Engineering, 17:3, 204-215, DOI: 10.1080/15567265.2013.776153

To link to this article: http://dx.doi.org/10.1080/15567265.2013.776153

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Nanoscale and Microscale Thermophysical Engineering, 17: 204215, 2013

Copyright Taylor & Francis Group, LLC

ISSN: 1556-7265 print / 1556-7273 online

DOI: 10.1080/15567265.2013.776153

CARBONATION CHARACTERISTICS OF ISOLATEDCALCIUM OXIDE NANOPARTICLES FOR THERMALENERGY STORAGE

Krishna V. Valavala, Hongxiang Tian, and Sanjiv SinhaDepartment of Mechanical Science and Engineering, University of Illinois at

Urbana Champaign, Urbana, Illinois

Carbonation of lime is an attractive system for thermal energy storage. The typical use of

10-m particles creates well-known recycling problems. We propose the use of isolatednanoparticles dispersed over a high surface area to avoid sintering and model the conversion

time characteristics of such particles. Our calculations show that reactions on the surface

dominate in particles smaller than 70 nm, leading to fast conversion times. We compare

our predictions against experimental data on micrometer- and nanometer-size particles to

establish the validity of the model. This work shows that isolated nanoparticles arranged in

scaffolds are an ideal system for realizing fast and repeatable conversion for thermal storage

with high storage density.

KEY WORDS: porous CaO nano-particles, carbon sequestration, energy storage, random

pore model, shrinking core model, carbonation

INTRODUCTION

The recent focus on thermal energy storage [1] stems from the widespread availability

of waste heat and the inadequacies of current energy storage technologies. Thermochemical

energy storage has a potential cost advantage over electrochemical and mechanical storage

based on simple chemistries of abundant materials. Among thermochemical storage

systems, carbonation of lime provides one of the largest heats of reaction at 1.78 MJ/kgand is an attractive process for thermal energy storage in applications such as concentrated

solar power generation [2]. Though widely deployed in industrial processes and extensively

studied, carbonation suffers from poor recycling characteristics [3]. Unlike its reverse

calcination reaction, the carbonation reaction does not reach completion and the quality

of calcium oxide as a CO2 sorbent declines over repeated calcinationcarbonation cycles

[4]. In this work, we show that the incompleteness of the carbonation reaction is inherently

linked to the particle size: Nanoparticles exhibit fast conversion times and complete

reactions. We show that the loss of surface area caused by sintering results in reduced

Manuscript received 3 October 2012; accepted 10 February 2013.

The authors acknowledge support from the National Science Foundation under grant NSF-CBET-09-54696-

CAREER.

Address correspondence to Krishna V. Valavala, Department of Mechanical Science and Engineering,

University of Illinois at Urbana Champaign, 235 W. Mechanical Engineering Building, 1206 W. Green St., Urbana,

IL 61801. E-mail: [email protected]

204

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CARBONATION OF LIME 205

NOMENCLATURE

C concentration of CO2, mol/m3

De intraparticle diffusivity, m2/s

DP product layer diffusivityk reaction constant, m4/mol/s

km convective mass transfer coefficient,

m/s

L length of the pores per unit volume of

space, 1/m2

M molecular weight of CaO, kg/mol

R radius of the particle, m

S area of the unreacted CaO surface in the

pores per unit volume of space, 1/m

Sh Sherwood number

t time, s

V volume enclosed in the pores by the

unreacted CaO surface per unit volume

of space

X ratio of volume of CaO consumed to

initially available CaO at a given radial

position

X ratio of total volume of CaO consumed

to the total initial volume of CaO avail-

ableZ ratio of molar volumes of CaCO3 to

CaO

Greek Symbols

product layer thickness, m

nondimensional radial position, r/R0 density of CaO, kg/m3

Subscripts and Superscript

0 value at the beginning of the reaction

b bulk stream

e at equilibrium

i CaOCaCO3 interface

s outer surface nondimensionalized

reactivity. Sintering changes the surface texture over multiple cycles with the formation of

macroscopic pores as well as the shrinkage of microscopic pores. Such structural changes

largely dictate the decline by more than 60% over as few as 10 cycles [5, 6].Several methods such as sorbent doping, hydration, and preparation by wet precipita-

tion have been suggested [7, 8], with limited success to increase the reactivity and to sustain

it over repeated cycles. Based on our theoretical predictions, we suggest the use of isolated

nanoparticles dispersed on a scaffold to solve this issue in principle. Sub-100-nm isolated

particles offer the distinct advantage of short heat (4 ns) and mass diffusion times (8 nsfor CO2 in CaCO3). In 1974, Barker [9] experimentally demonstrated enhanced reactivity

of10 nm size particles in a powder to93% with no detectable decline over 30 cycles in a24-h period. More recent work [10] has demonstrated high conversion for nanometer-sized

CaO particles at even faster rates. Experiments on nanoparticles reported in the literature

[4, 5] did not yield repeatability in conversion over a large number of cycles mainly due tothe use of powdered samples that sinter easily. Advanced manufacturing techniques such as

electrohydrodynamic printing [11] can disperse isolated nanoparticles on textured surfaces

with high areas, avoiding sintering.

Figure 1 illustrates a conceptual scaffold that holds calcium oxide particles with-

out sintering. The scaffolding mesh structure has micrometer-scale pillars to increase the

surface area per volume of the structure. Calcium oxide particles are placed on the micropil-

lars such that the successive particles are separated by a distance greater than the expected

radial expansion of the particles in the carbonation reaction. This avoids sintering during

carbonation. We estimate an 30% increase in size in a 100-nm particle. Therefore, 100-nm particles should be placed with a minimum center-to-center gap of 130 nm to prevent

sintering. In this article, we assume that the calcium oxide particle held in a scaffoldingstructure could be treated as an isolated particle suspended in a gas mixture containing

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206 K.V. VALAVALA ET AL.

Figure 1 Concept design of a scaffolding structure to hold CaO particles without sintering. The supporting

structure has a high surface area per unit volume due to the micropillars shown in the figure. The distance

between any two successive calcium oxide particles should be greater than the radial expansion of the particle

upon carbonation to prevent sintering.

carbon dioxide. The model and the results presented in this article advance the use of iso-

lated sub-micrometer-sized lime particles in calcium looping as a means to achieve carbon

sequestration and thermochemical energy storage.

THEORY

An estimate of the carbonation time characteristics of CaO nanoparticles requires

consideration of the pore structure, CO2 diffusion rates, and reaction kinetics. The seminal

random pore model is a useful starting point in analyzing conversion behavior. In their

earliest version of the random pore model [12], Bhatia and Perlmutter assumed kinetic

control for reactions inside pores and correlated the local reaction extent X to the pore

structure parameter as X= 1 exp

1 +

4

, where is a dimensionless time

incorporating kinetics and porosity. Assuming uniform reaction extent within the particle

and a kinetic regime for reactions on the external surface, the overall conversion was given

as X= 1 1 3 exp1 + 4 , where the new parameter includes the effectof particle size. However, the pores inside CaO particles result in a CO2 concentration

gradient, leading to a nonuniform reaction extent within the particle, thereby invalidating

the assumption of uniform reaction extent. The kinetic control regime assumption is also

invalid for CaO carbonation reactions because CO2 diffusion through the product layer

controls the reaction rate. For these reasons, the expression above cannot be used to study

the particle size dependence of CaO carbonation reaction times. In a later version of the

random pore model [13], the effects of intraparticle diffusion resistance and the product

layer diffusion resistance were incorporated to account for the nonuniform reaction extent

X inside the pores. However, the reaction on the external surface of the particle, which is

important at nanometer scales, was not considered in calculating the overall reaction extent.

In our model, we calculate conversion in the pores as well as on the external sur-

face considering all possible resistances involved in the reaction. We calculate the reaction

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extent in the pores X(, t)using the random pore model and combine it with reaction on the

external surface calculated using the shrinking core model to obtain the overall conversion

X(t) as

X(t) = 1 3Ri (t)

R0

=0(1 X(, t))2d, (1)

where is the radial position nondimensionalized with respect to the particle radius RO,

and Ri(t) is the position of the external reacting surface at time t obtained by using the

shrinking core model.

Diffusion and Conversion Inside the Nanoparticle

In this section, we describe the random pore model used to calculate the reaction

extent in the core of the nanoparticle. We assume that the CaO nanoparticle is a porous

sphere exposed to a carbon dioxide and nitrogen gas mixture at a temperature of 650C and1 atm pressure with a CO2 mole fraction of 0.15.

As depicted in Figure 2, the concentration of CO2 decreases from Cb in the bulk

stream to Cs at the particle surface due to external mass transfer resistance, Rm,ER. It fur-

ther decreases to C(, t) due to intrapellet resistance, Rm,IPR, offered by the pores inside the

Figure 2 Schematic of a CaO nanoparticle suspended in a mixture of CO 2 and N2 environment at 650C. Carbon

dioxide gas diffuses into the particle through the pores (white) and the calcium carbonate product layer (grey) to

reach the reaction surface of calcium oxide (black) where the carbonation reaction takes place. Notations used for

concentration of CO2 at various positions with respect to the particle are shown along the horizontal line at thebottom of the figure.

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particle. Finally, the concentration drops to Ci(, t) at the reaction surface inside the pores

due to resistance from the CaCO3 product layer, Rm,PLR. The concentrations are nondimen-

sionalized using bulk concentration Cb as the normalizing quantity and are represented with

asterisks.

We assume pseudo-steady-state conditions during the carbonation reaction. Thisimplies that the change in CO2 concentration at any position over a short period of time

due to the reaction is negligible compared to the CO 2 flow rate. Under this assumption, the

diffusionconsumption equation for CO2 diffusion and the subsequent reaction is

1

2

2De

C

= R

2o

MDe0Cb(1 V0)

dX(, t)

dt. (2)

The associated boundary conditions reflecting the spherical symmetry and external mass

transfer resistance are

C

=0

= 0 (3)

C

=1

= Sh(1 C)

De. (4)

Solving Eqs. (2)(4) provides the local conversion profile X(, t), which can be used to

evaluate the overall conversion time characteristics.

We now describe the variables that are present in the above equations and provide

expressions to evaluate these variables. The initial intrapellet diffusivity De0 at the begin-ning of the reaction is defined as the harmonic mean of molecular diffusivity DM of CO2and Knudsen diffusivity DK through the pores

1

De0= 1

DM+ 1

DK. (5)

The intrapellet diffusivity De (, t) normalized with respect to its initial value De0 isexpressed in terms of the local conversion, X(, t) as

De (, t) =De

De0 = 1 (Z

1)(1

V0)X(, t)

V02

. (6)

The Sherwood number (Sh) in Eq. (4) defined as Sh = kmRO/De0 requires evaluation ofthe convective mass transfer coefficient km. The continuum flow regime expressions for Sh

cannot be used here because the mean free path of the gas is comparable to size of the

particle. The mean free path of CO2N2 gas mixture at 650C and 1 atm pressure is 0.3

m and the Knudsen number varies from, Kn 3 to 0.3 as the particle size varies from100 nm to 1 m. In our calculations, we use an interpolation formula for effective mass

transfer coefficient that is valid across various flow regimes [14, 15]:

km = DMRo

1 + Kn

43 Kn + 1.0161

43

Kn + 11

. (7)

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The rate of conversion dX/dt in Eq. (2) is expressed in terms of the concentration profile

C(, t) by correlating changes in the pore structure to the chemical kinetics of the reactionusing modifications to the random pore model [13]. The random pore model assumes that

pores are cylindrical with size distribution f(r), where f(r) is the length of pores with radius

in the range r and r+ dr. By assuming that no pores are formed or destroyed during thereaction, the following equation can be written to balance the number of pores

f

t+

t

f

dr

dt

= 0. (8)

Assuming that the reaction is of first order with respect to the concentration of CO 2 and is

proportional to the surface area of the solid reactant CaO available, the rate of change of

the pore radius is given by

dr

dt = k(Ci Ce), (9)

where k is the rate constant of the carbonation reaction, and Ce is the CO2 equilibrium

concentration in the carbonationcalcination reaction. Total pore length LE, pore surface

area SE, and pore volume VE per unit volume of space are obtained in terms of their initial

values L0, S0, and V0 by multiplying Eq. (8) by 1, 2r, and r2, respectively, and integrating

over the pore radius from zero to infinity. LE, SE, and VE are then corrected to account for

pore overlap [16] to obtain corresponding corrected expressions L, S, and V. The corrected

expression for the volume enclosed by the unreacted CaO surface V is given by

V= 1 (1 V0)expkCb t

0

(Ci

Ce

)dt

1 V0 . (S0 + kL0Cb t0(Ci Ce )dt)

. (10)

In the random pore model, the concentration of CO2 at the unreacted CaO surface, Ci, is

assumed to be independent of time and the integration is written as Ci t. Here we accountfor the changing concentration using t0(Ci Ce )dtinstead.

Using Eq. (10), the local conversion X(, t) inside the particle at the radial posi-

tion is

1 X(, t) = (1 V)(1 V0)

= expkCb t0(Ci Ce )dt

1 V0. (S0 + kL0Cb t0(Ci Ce )dt)

.

(11)

Differentiating Eq. (11) with respect to tprovides the local conversion rate dX(, t)/dtas

dX(, t)

dt= kCbSo

(1 V0)(Ci Ce )(1 X(, t))

1 + 2kL0Cb

t0(C

i Ce )dt

So

. (12)

Equation (12) expresses dX(, t)/dt as a function ofCi , and the left-hand side of Eq. (2) isa function ofC. Therefore, in order to be able to use dX(, t)/dt from Eq. (12) in Eq. (2),

Ci needs to be expressed in terms of C. This relation is obtained [13] by analyzing the

resistance offered by the CaCO3 product layer to the flow of CO2 from the CaCO3 surface

to the unreacted CaO surface. Assuming that the product layer thickness is small, growthof the product layer can be expressed as

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= ZkCbt

0

(Ci Ce )dt. (13)

Balancing the CO2 diffusion rate through the product layer of diffusivity Dp and the rate of

consumption of CO2 at the CaCO3CaO interface, we get

Dp(C Ci )

= k(C

i Ce )

M. (14)

Eliminating from Eqs. (13) and (14), the concentration of CO2 at the reaction surface

Ci can be related to the concentration of CO2 in the pores, C. Now, Eqs. (2)(4) can be

discretized and solved using the control volume method for concentration profiles C(, t),which, in turn, provides the local conversion profile X(, t) in the pores.

Conversion at the External Surface

As the reaction proceeds, the outer CaO reacting surface recedes from RO to Ri(t).

Because the molar volume of CaCO3 formed is greater than that of CaO, the particle radius

itself expands to Rs(t), given by

4

3 (Rs(t)

3 Ri(t)3) = Z4

3(R3O Ri(t)3). (15)

As discussed previously, the external surface reaction is incorporated in the overall calcula-

tion in the form of the upper limit Ri(t)/RO of the integral in Eq. (1). We calculate the radial

position of the external reaction surface Ri(t) by using the shrinking core model under a

pseudo-steady-state assumption [17]. The overall resistance to the flow of CO2 at time t,Hex, is [18]

Hex =1

4

1

kmR2O

+ 1DP

1

Ri(t) 1

Rs(t)

+ M

kRi(t)2

. (16)

The three terms in Eq. (15) are the external mass transfer resistance, product layer diffu-

sion resistance, and carbonation reaction resistance, respectively. The external resistance in

Eq. (16) was calculated using the convective mass transfer coefficient given in Eq. (7) and

was found to be 8 orders of magnitude smaller than other resistances even for particles as

small as 50 nm. The rate of mole consumption of CO2 during the time interval t to t+

dt

is now given by (Cb Ce)/Hex. Stoichiometry considerations provide the rate of change ofthe radial position of the CaCO3CaO interface as

Cb CeHex

= M

d

dt

4R3

3

Ri

= 4 M

Ri(t)2 dRi(t)

dt. (17)

RESULTS

The equations presented in the previous section were numerically solved by using

the control volume method [19]. The rate and diffusion constants were obtained from

experimental results [2022]. We validated the calculation methodology by matching ournumerical results to the analytical results obtained in the random pore model at particle

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sizes above 1 m. In this section, we compare our numerical results with experimental

data for both micrometer- and nanometer-sized particles. We follow this comparison with

a discussion on relative contribution of various flow resistances to the overall conversion

characteristics at various particle sizes.

For the purpose of comparing our theoretical model with experimental results, wechose two data sets [23, 24] in which the particle size is in the regime of interest and

information regarding pore distribution, carbonation conditions, and the conversion time

characteristics are available. The first data set was from the experiments of Martavaltzi

and Lemonidou [24] on pure nonisolated CaO obtained from calcium acetate with a par-

ticle radius of 550 nm. The second data set was from the work of Broda and Mller

[23], whose sorbent preparation method produces particles of radius 85 nm with mayen-

ite (Ca12Al14O33) as the inert supporting material. The weight percentage gain data in the

second publication were converted to conversion time data by assuming that all Al 2O3 was

converted to mayenite and, therefore, the remaining CaO weight percentage in the sorbent

was 69%.Figure 3 compares predictions from the model with experimental results. Because the

flow rate of CO2 increases from zero to its steady value in a thermogravimetric analyzer, the

initial reaction rates from experiments were smaller than those predicted at the beginning

stages of the reaction. The experiments did not provide measurements of product layer

diffusivity. Because the product layer diffusivity value is not universal but varies depending

on the source of CaO, precursor type, and preparation technique [25], we used the product

layer diffusivity as a fitting parameter in these calculations. The values used for the fit

were close to the experimentally determined values of product layer diffusivities [20, 21,

26], thereby establishing the validity of our model. The fitted activation energy and the

preexponential factor for the product layer diffusivity were 178.5 KJ/mol and 2.25

105

m2/s respectively for the first data set, yielding a diffusivity of 4.7 1015 m2/s at 690C,which is very close to the corresponding value of 4.85 1015 m2/s obtained at the same

Figure 3 Comparison of conversion time characteristics from our theoretical model and experimental results for

CaO particles with a radius of 85 nm (squares) and a radius of 550 nm (circles). The advantage of using isolatednanoparticles over nonisolated micrometer-sized particles can be seen from the results shown in the figure.

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temperature by Grasa et al. [21]. The fit to the second data set employed the same activation

energy and the preexponential factor was 8 105 m2/s. We suspect that the higher valueof product layer diffusivity in the alumina-supported CaO particles compared to the pristine

particles could arise from additional CO2 diffusion through unfused CaO grain boundaries.

The results in Figure 3 highlight the advantage of using nanometer-sized particles that aresupported by an inert framework over unsupported micrometer-sized particles.

We now investigate the impact of decreasing size on intraparticle diffusion. Diffusion

inside pores results in carbonation proceeding faster away from the center of the par-

ticle. For large particle sizes, the CO2 concentration gradient is significant and leads to

nonuniform reaction rates, decreasing the overall conversion. Figure 4 shows the effect of

intraparticle resistance on the conversion time characteristics for three particle sizes. The

solid lines in the figure were obtained by assuming the initial intraparticle diffusivity, Deo,

to be infinite. Under this assumption, the concentration of CO2 and therefore the reaction

extent are uniform throughout the particle. Thus, CaO particles reach complete conversion

regardless of size under this condition. However, smaller particles reach completion faster.This is due to reaction on the external surface, discussed later in this section.

The dotted lines in Figure 4 were calculated using the value of initial intraparticle

diffusivity obtained from Eq. (12). With finite intraparticle diffusivity, the concentration

of the CO2 decreased as we move from the external surface to the center of the particle.

Consequently, the local reaction rate was slower at the center of the particle and was faster

away from the center. In time, pores further away from the center of the particle closed

down and the reaction remained incomplete near the center. This was evident in particles

of size greater than 1.5 m. For example, in particles of size 5 m, conversion stopped

at around 75%. A finite intraparticle diffusivity did not lead to pore closure in particles

smaller than

1.5 m. Thus, pore closure is not an important issue with nanoparticles.

The large surface area available in nanoparticles significantly accelerates conversion.Based on measurements of specific surface area of pores [12], the ratio of external area to

Figure 4 Conversion time characteristics for isolated CaO particles with radii of 50 nm, 100 nm, and 5 m with

finite (dotted lines) and infinite (solid lines) intraparticle diffusivity. Particles larger than 1.5m experience poreclosure.

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Figure 5 Influence of external surface reaction on conversion time at various particle sizes. Reaction on the

external surface contributes significantly toward the overall conversion rate for particle size less than 500 nm.

pore surface increased twofold from 0.7 to 1.4 as the particle size decreased from 100 to

50 nm. Figure 5 shows the difference in times taken to reach half conversion with and with-

out inclusion of the reaction on the outer surface. The solid horizontal line corresponds to

the original random pore model and shows that the conversion time remained independent

of particle size, depending only on the pore structure. The dashed line represents the half

times calculated using the modified model including external surface reaction. It can beseen from Figure 5 that conversion time for a 100 nm particle is five times lower than that

for a 3 m particle due to availability of external surface area. This advantage is lost when

particles sinter, resulting in low conversion of nanoparticles [5].

Finally, we comment on thermal energy storage density for a system of dispersed

nanoparticles. The theoretical limit of storage density for CaCO3 is 4.8 GJ/m3. Recentadvances in the fabrication of high-surface-area alumina templates [27] make these an

ideal scaffold for dispersing nanoparticles. The hexagonal cells (50-nm periodicity) in thealumina template enable large area fraction coverage (>75%) of nanoparticles. Using two

particles per pore led to an effective storage density >0.2 GJ/m3, excluding CO2 storage.

CONCLUSION

In conclusion, we investigated the theoretical carbonation of CaO nanoparticles for

thermochemical storage using a modified random pore model. Comparisons with exper-

imental data validated the proposed model and clearly highlight the advantage of using

isolated nanoparticles. Our model further provides insight into three important advantages

of using isolated nanoparticles to achieve fast and repeatable conversions. First, pore clo-

sure is unimportant for particles smaller than1.5m. Second, reaction on external surfacedominates over reaction in pores in particles smaller than70 nm. Irrespective of the domi-nating reacting surface, sub-micrometer sized particles achieve complete conversion. Third,

subcontinuum transport of the reactant to the nanoparticle surface does not pose any limi-tation on the conversion time, even when the Knudsen number is 6 (for a 50-nm particle).

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All of the above advantages of using nanoparticles are lost if particles are allowed to sinter.

However, the use of templates or scaffolds potentially avoids this issue and represents an

important direction for future experimental work in this area.

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