Study of CO2 Diffusion and Adsorption on Calcined Layered Double

6150

Ind. Eng. Chem. Res. 2008, 47, 6150–6157

SEPARATIONS Study of CO2 Diffusion and Adsorption on Calcined Layered Double Hydroxides: The Effect of Particle Size Megha Dadwhal, Tae Wook Kim, Muhammad Sahimi, and Theodore T. Tsotsis* Department of Chemical Engineering, UniVersity of Southern California, UniVersity Park, Los Angeles, California 90089-1211

This paper describes a study of CO2 diffusion and adsorption in layered double-hydroxide (LDH) adsorbents using a gravimetric method. Four different particle size fractions, namely, 53-75, 75-90, 90-180, and 180-300 µm, were used in the study. The LDH materials were calcined in situ prior to the experiments, which resulted in significantly higher CO2 adsorption capacities than previously reported. The CO2 adsorption was shown to follow a Sips-type isotherm, while the adsorption capacity at saturation was found to be independent of the particle size. Two models, the homogeneous surface diffusion model (HSDM) and the bidisperse pore model (BPM), were used to fit the experimental data and to estimate the diffusivities. The main assumption made in the BPM is that the adsorbent particle is an agglomerate of a number of equalsized, single-crystal microparticles, and before a CO2 molecule is adsorbed in the microparticles, it has to diffuse through the intercrystalline porous region. Both models perform well in fitting the experimental data. However, the HSDM yields diffusivities that are a strong function of the particle size, whereas the diffusivities estimated using the BPM are almost independent of the particle size. 1. Introduction CO2 levels in the atmosphere have increased substantially since the Industrial Revolution and are expected to continue rising in the future.1 Measurements of CO2 levels throughout the world indicate a continuing buildup in the atmosphere of this greenhouse gas, thought to be chiefly responsible for global warming. Fossil fuel combustion for power generation is responsible from 1/4 to up to one-third of man-made CO2 emissions.1 The advantage that one has in power generation, with respect to other anthropogenic CO2 sources, is because emissions are generated in centralized stationary locations, there is potentially a broader range of options for dealing with them. In the short term, increasing power-plant efficiency will offer the most benefits. Longer-term, however, improving plant efficiencies will not suffice for meeting the CO2 environmental targets, and new processes must be developed for CO2 capture/ sequestration.1 A key requirement for such processes is that they are efficient and integrated within the power plant, so that energy needs for CO2 capture are minimized. The most direct way of capturing and sequestering CO2 from power plants is by separating it from the flue gas using conventional techniques, such as absorption, adsorption, or membrane separation. This, however, is not economically viable due to the dilute concentrations of CO2 found in the flue gas of conventional power plants. Oxy-combustion, in which oxygenenriched air is used during the combustion step, may significantly simplify this separation step but faces its own challenges in terms of the added costs of the oxygen-enrichment step. IGCC (integrated gasification combined cycle)-type power plants represent a third option currently studied, with the promise to meet future CO2 environmental targets for environmentally benign power generation.1 In these plants, coal or natural gas are first gasified to synthesis gas, which is then processed further * To whom correspondence should be addressed. Phone: 213 740 2069. Fax: 213 740 8053. E-mail: [email protected].

in a dual water gas-shift reactor (WGSR) system to produce additional H2. The WGSR exit stream must then be further treated to separate the H2 which, in turn, is used for clean power generation. The WGSR exit stream contains H2, CO2, H2O, and N2 (if air is used in the gasification), together with small amounts of other species (e.g., CO). Conventionally, CO2 separation during H2 production is carried out using absorption or adsorption methods. Both are, however, energy-intensive operations and require substantial capital outlays. The dual catalytic WGSR, itself, is also capital-intensive. In place of the technically complex IGCC plants, our group has developed a reactive separation technology,2,3 termed the HAMR (hybrid adsorbent membrane reactor) process, which implements the H2 production and CO2 separation steps in a single stage, through the combined use of high temperature, CO2-selective membranes and adsorbents. This new technology has many advantages over the conventional one. Coupling the separation with reaction into a single process is expected to provide significant synergy. It accelerates the reaction step, thus eliminating the need for incorporating a high-temperature water gas-shift (WGS) step, while simultaneously providing a sequestration-ready CO2 stream. The key challenge with the HAMR process is finding membranes and adsorbents that will function effectively (and reversibly in the case of the adsorbents) in the high-temperature conditions (523-573 K) required. For example, though a number of high-performance CO2 adsorbents, such as silica,4 zeolite,5,6 carbon molecular sieves,7 CaO and dolomite exist, they do not perform well under such conditions. In our studies we have utilized layered double hydroxide (LDH) materials and carbon molecular sieve membranes. The LDH materials belong to a class of ionic lamellar solids made-up of positively charged layers containing two kinds of metallic cations and exchangeable interlayer chargebalancing anions.8 They are also often referred to as hydrotalcites (HT), as well as anionic clays. They contain

10.1021/ie701701d CCC: $40.75  2008 American Chemical Society Published on Web 07/12/2008

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important functional groups, and have a well-defined layered structure with nanometer (0.3-3 nm) interlayer distances. They are widely studied today as catalysts and catalyst supports,9,10 antacids,9,11 anion scavengers,12,13 polymer stabilizers,9,14 molecularsieves,ionexchangers,andadsorbents.15,16 They have also been shown to be effective and reversible adsorbents of CO2 in steam environments akin to those encountered under the WGS reactive conditions.3 In an earlier study17 we investigated the thermal evolution of the structure of these materials (in particular Mg-Al-CO3 LDH) under an inert atmosphere and proposed a model to describe the structural changes that take place (the structural evolution of these materials with respect to temperature was also studied by Hutson et al.18 in a later study). In a subsequent study19 we investigated the sorption characteristics and thermal reversibility of the same materials under both inert as well as steam- and CO2-containing atmospheres. The experimental observations in this latter study were shown to be consistent with the structural model for the LDH that was previously proposed.17 Other groups have also recently studied CO2 adsorption on LDH.20–26 Lee et al.,22 for example, studied the chemisorption of CO2 on a potassium-carbonate-promoted HT, which was shown to be a reversible sorbent for CO2. Ritter and co-workers23–26 also studied the adsorption and desorption of CO2 from flue gas on potassium-carbonate-promoted HT and developed a nonequilibrium kinetic model to explain the observed behavior. Othman et al.27 prepared Mg-Al hydrotalcite coatings on zeolite adsorbents in order to improve their CO2 adsorption characteristics. In our most recent study describing the HAMR process, the CO2 adsorption kinetics were described by an overall effective rate equation.2,3 Though capable of fitting the process data, such a rate expression offers little insight into the phenomena that take place during CO2 adsorption in these materials. In this paper two detailed models are used to interpret the experimental adsorption data with these materials, the homogeneous surface diffusion model (HSDM), and the bidisperse pore model (BPM). The HSDM assumes that the adsorbent consists of homogeneous spherical particles, and adsorption is determined by intraparticle diffusion resistance in the form of surface diffusion within the adsorbent particle. The main assumption made in the BPM is that the adsorbent particle is an agglomerate of a number of equal-sized, single-crystal microparticles, so that before a CO2 molecule gets adsorbed on the microparticle, it has to diffuse through the intercrystalline porous region. These models were previously tested for describing adsorption in these materials of trace levels of arsenic and selenium from the aqueous phase.16 In the present study, the CO2 adsorption data generated with the LDH adsorbents of various particle sizes are fitted using both models, and the effect of particle size on the CO2 adsorption and diffusion are analyzed and reported. 2. Experimental Section 2.1. Preparation of the LDH. The Mg-Al-CO3-LDH utilized in the experiments was prepared in our laboratory by the coprecipitation method.15 In this method, 140 mL of a solution containing 0.7 mol of NaOH and 0.18 mol of Na2CO3 were added all at once to a second solution containing 0.115 mol of Mg(NO3)2 · 6H2O (90 mL) and 0.04 mol of Al(NO3)3 · 9H2O (90 mL) (corresponding to a Mg/Al ratio equal to 2.87) under vigorous stirring. The thick gel obtained was aged for 24 h at 333 K, followed by filtration and washing with distilled water and was then dried at 333 K. ICP-MS analysis of the resulting LDH material indicated that its Mg/Al mole

Figure 1. SEM pictures of the calcined LDH with particle sizes of (a) 53-75, (b) 75-90, (c) 90-180, and (d) 180-300 µm.

ratio is ∼2.9, close to the Mg/Al ratio of the starting salts. The as-prepared LDH was crushed and sieved using standard testing sieves (VWR) into four different fractions with particle sizes in the range of 53-75 (200-270 mesh fraction), 75-90 (170-200 mesh), 90-180 (80-170 mesh), and 180-300 µm

6152 Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008

(with a heating rate of 2 K/min), where it was kept (calcined) for 4 h. Then, the temperature was lowered to 473 K (again at the rate of 2 K/min). After the temperature of the system became stable at 473 K, UHP (ultrahigh-purity) dry Ar (99.999% pure) was allowed to completely fill the system volume, and the sample was left overnight at the same temperature in flowing Ar. The next day, Ar was allowed to flow continuously at a flow rate of 70 mL/min, until the TGA microbalance became stable prior to the initiation of the experiments. The adsorption isotherms were generated using mixtures of UHP Ar and instrumental grade CO2 (99.999% pure), which were prepared using Brooks 5850E mass flow controllers. Ar was utilized as the inert purge gas in order to minimize, to the degree possible, the buoyancy effects when switching from purge gas to pure CO2 (for the diffusivity experiments), or to Ar/CO2 mixtures (for the adsorption experiments). Though, in principle, not a concern neither during the isotherm experiments nor the kinetic runs used to validate the models (since they involve switching from pure Ar to pure CO2) we did, nevertheless, carry out independent adsorption experiments in order to investigate the effect of the overall flow rate. The rate of 70 mL/min was found to be sufficient for eliminating any influences on the weight gain curves, without unduly impacting the operation of the microbalance. 2.3. Characterization. SEM, using a Cambridge 360 SEM instrument (Cambridge Instruments, U.K.), was used to measure the adsorbent particle sizes before and after calcination. The SEM images were analyzed using the software Image J, in order to obtain the particle size distribution (PSD), to be used in the simulation studies. 3. Theory 3.1. Homogeneous Surface Diffusion Model. We focus first on the HSDM, which is used to fit the experimental adsorption data and to estimate the diffusion coefficient of CO2 in the LDH. According to this model, the governing equation for the concentration C of the species diffusing into a spherical homogeneous sorbent particle of radius, R, is given by

Figure 2. Particle size distribution profiles for various particle size ranges for the calcined LDH.

(50-80 mesh). Prior to the adsorption and diffusion experiments, the LDH materials were calcined in situ at 773 K for 4 h (see further discussion below). The particle size characteristics of both the uncalcined and calcined particles were investigated by scanning electron microscopy (SEM). The surface area, the BJH (Barret-Joyner-Halenda) mesopore volume, and the HK (Horvath-Kawazoe) micropore volume, as well as the pore size distribution of the calcined adsorbent particles of various sizes were measured by N2 adsorption using a Micrometrics ASAP 2010 instrument. Prior to adsorption, the particles were pretreated at 423 K under vacuum overnight. The solid density of the calcined particles was also measured using an Electronic Densimeter (model SD-200L, from Geneq Inc.). 2.2. Diffusivity Measurements and Adsorption Isotherms. The adsorption kinetics and isotherms of CO2 on Mg-Al-CO3 LDH were studied at 473 K by the gravimetric method (using a Cahn TGA 121 instrument). Approximately 130 mg of sieved uncalcined LDH was utilized in each experiment. The LDH sample was spread as a thin layer on a bowl-shaped quartz container in the TGA apparatus in order to minimize the effect of external mass-transfer resistance. The sample was first degassed by evacuation at 13.33 Pa, and then heated to 773 K

(

∂C ∂2C 2 ∂C ) DS + ∂t ∂r2 r ∂r

)

(1)

where DS (cm2/s) is the intraparticle diffusion coefficient, which is assumed to be concentration-independent. Equation 1 is accompanied by the following initial (IC) and boundary (BC) conditions: C ) 0, t ) 0

(2)

∂C ) 0, r ) 0 ∂r

(3)

C ) C0, r ) R

(4) 28

The solution of eqs 1– 4 is given by eq 5, in terms of Mt, the total amount of CO2 (mg/(g of particle)) that has diffused and adsorbed in the spherical particle at time t,

(

∞ Mt DSn2π 2t 1 6 )1- 2 exp M∞ π n)1 n2 r2

∑

)

(5)

where M∞ is the amount (mg/(g of particle)) adsorbed at large times (t f ∞). 3.2. Bidisperse Pore Model. The BPM assumes that the adsorbent particle is an agglomerate of a number of equal-sized, single-crystal microparticles and that a porous intercrystalline region is present between these microparticles. Before the CO2

Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008 6153 Table 1. Arithmetic and Volume Mean Averaged Diameters for the Particles with Different Sizes before and after Calcination after calcinations dav (µm)

before calcinations dav (µm) mesh size

particle size (µm)

200-270 170-200 80-170 50-80

53-75 75-90 90-180 180- 300

AM

VM

AM

VM

60.94 84.68 128.82 258.82

62.06 86.54 135.68 270.23

63.04 84.01 130.48 251.76

64.55 86.05 136.75 258.44

Table 2. Measured Densities and Porosities for the Calcined LDH with Different Particle Sizes particle size (µm)

solid density (g/cm3)

porosity (ε)

particle density (g/cm3)

53-75 75-90 90-180 180- 300

2.798 2.742 2.682 2.619

0.36 0.39 0.49 0.50

1.791 1.673 1.368 1.310

Mt )

[

]

(6)

subject to the following IC and BC CM ) 0, t ) 0

(7)

∂CM ) 0, rM ) 0 ∂rM

(8)

CM ) C0, rM ) RM

(9)

( )

(10)

subject to the following IC and BC qµ ) 0, t ) 0

(11)

∂qµ ) 0, rµ ) 0 ∂rµ qµ )

1 + KCMn(rM, t)

RM

0

[(1 - ε)Fsqµ + εCM]rM2 drM

qµ )

3 Rµ3

∫

Rµ

0

qµrµ2 drµ

(14)

(15)

The gravimetric analysis, most likely, measures only the first term of eq 14 (excess adsorption, assuming that Ar and CO2 access the same intercrystalline space, which is likely to be true). However, for experiments at atmospheric pressures involving gases, the second term in eq 14 (the CO2 in the intercrystalline region) is insignificant compared to the first term (the CO2 adsorbed in the microparticles).

4.1. Particle Size Distribution. Figure 1 shows the SEM pictures of the in situ calcined LDH materials corresponding to the four different particle size ranges. For each particle size range, several SEM pictures were taken and used to determine the PSD of the adsorbent particles. The PSD of the calcined LDH particles are shown in Figure 2. For the simulations, an average particle size is required. There are a number of ways to define and to determine the average particle size for a batch of particles with a PSD in a certain size range. We utilize here the two most popular definitions,29 namely, 1. arithmetic mean (AM):

∑nd

(16)

i i

∂qµ ∂qµ Dµ ∂ ) 2 rµ2 ∂t ∂r ∂rµ r µ

KqsCMn(rM, t)

∫

4. Results and Discussion

where CM is the CO2 concentration in the intercrystalline porous region (mg/L), qjµ is the volume-averaged CO2 concentration in the solid phase (microparticles; mg/g)ssee eq 15 belowsRM is the particle external radius, and ε is the void fraction in the porous region. Diffusion and adsorption in the microparticles are described by

µ

3 FRM3

Equations 6–14 must be solved with qjµ given by

molecule adsorbs inside the microparticle structure, it must diffuse from the particle surface, through the intercrystalline porous region, to the surface of the microparticles. The BPM assumption is consistent with the presence of a mesoporous region, as indicated by our BET measurements and by the TEM studies of the adsorbent particles.19 In the intercrystalline porous region, diffusion is described by the following equations,16 ∂CM (1 - ε) ∂qµ DM ∂ ∂CM + Fs ) 2 rM2 ∂t ε ∂t ∂r ∂rM rM M

In the BPM, the total amount of CO2 entering the sphere is the sum of the amount of CO2 adsorbed in the microspheres and the CO2 found in the intercrystalline porous region and is given by

(12)

,

rµ ) Rµ

(13)

where qµ is the CO2 concentration (mg/g) in the microparticle, Dµ (cm2/s) is the microparticle diffusivity, and Rµ is the microparticle radius (cm). Equation 13 is the Sips isotherm equation that is used here (see discussion below) in order to analyze the adsorption data. The experimental data were fitted using eq 13, and the relevant parameters, qs, K, and n, were calculated, where qs and K are the maximum sorption capacity and the Sips constant, respectively, and n is a parameter which is thought to characterize adsorbent surface heterogeneity.

d10 )

i

N where N ) ∑i ni, i is an index corresponding to particle i in a population of particles, and di is its particle diameter.

( )

2. volume mean (VM):

∑nd

3 1⁄3

i i

d30 )

(17)

i

N Fairly similar average particle sizes are obtained on the basis of the two definitions (generally, d30 is somewhat larger than d10). The results are shown in Table 1 for both the uncalcined and the calcined LDH materials. Given the uncertainty in measuring the PSD, the results in Table 1 indicate that the calcination process has a minimal effect on the average size of the LDH particles (a slight reduction of ∼5% is observed for the largest size range of the particles). Table 2 presents the measured densities and porosities for the four samples. The porosities reflect the pore volume, as measured by BET, occupied by pores with diameters in the range of 1.7-300 nm. The solid matrix densities are fairly similar (they vary by ∼6%); however, the porosities and particle densities vary somewhat

6154 Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008

by other investigators29,30 and were also observed with the conditioned LDH in our previous study.16 The true solid densities, reported in Table 2, are ∼30% higher than the values previously measured16 and calculated (with molecular simulations) for the conditioned materials. For comparison, the solid densities for MgO, Al2O3, and the MgAl2O4 spinel are 3.58, 3.97, and 3.54-3.63 g/cm3 correspondingly. 4.2. Adsorption Isotherms of CO2 on the LDH. Figure 3 shows the CO2 adsorption isotherms for the calcined LDH at 473 K. To analyze the adsorption data, they were fitted with the Sips equation. In the figure, the points represent the experimental data, while the solid lines represent the Sips fitting. The fitted Sips parameters, qs, K, and n, are reported in Table 3. The parameters qs and K are almost the same (less than 4% variation) for all the particle size ranges (similar observations were also previously made with arsenic adsorption on LDH16). The same is true for n where, other than the value for the smallest size particles (for which the experimental data fit is not as good as that for the largest size particles), there is again less than 4% variation in the value of the parameter. The parameter n is thought to relate to the degree of surface heterogeneity of the adsorbent; the smaller n is the higher is the degree of heterogeneity. Since n does not change much, as the particle size increases; this would seem to suggest that solid surface heterogeneity also does not change with increasing particle size. The CO2 adsorption saturation capacity qs obtained for the various particle sizes varies from 0.749 to 0.798 mmol/g at 473 K. It is quite large when compared to the results obtained by previous investigations for unpromoted hydrotalcites. Previous studies by our group19 of CO2 sorption using uncalcined LDH, for example, in the temperature range of 423-623 K, indicated the CO2 capacities being ∼0.4-0.45 mmol/g at 473 K. Reddy et al.31 studied the CO2 adsorption capacity of Mg-Al-CO3-LDH (Mg/Al ) 2.9) calcined at 673 K and reported it to be ∼0.49 mmol/g at 473 K. Their lower capacities may be due to the lower calcination temperature, but potentially also because their samples were stored under atmospheric condition for 48 h, prior to the adsorption studies. 4.3. Experiments for Model Validation. Parts a-d of Figure 4 show the CO2 uptake curves at 473 K for the four samples with different particle sizes. Each figure contains two experimental runs (each utilitzing a different sample from the same batch of adsorbent with a certain particle size range), as well as the fitted curves obtained with both the HSDM and BPM using the arithmetic mean average diameter. However, the simulations for the various particle sizes were carried out using both the arithmetic mean and the volume mean average diameters, with the corresponding values being reported in Tables 4 and 5. The fitted surface diffusivities for the HSDM vary as a function of average diameter (dav). Two observations are clear for the HSDM. First, the agreement between the calculated values for the two sets of experiments is reasonable. Second, there is a great difference in the values calculated for the diffusivity between the small and large particles (they vary by more than 1 order of magnitude). Similar observations were made in our previous paper16 on arsenic adsorption on condiTable 3. Sorption Isotherm Parameters for CO2 Uptake on Calcined LDH with Different Particle Sizes Figure 3. Adsorption isotherm on calcined LDH for various particle sizes and the Sips isotherm model fit.

with particle size (by ∼28 and 27% correspondingly). Variations in the porosity with particle size were previously also reported

particle size (µm) 53-75 75-90 90-180 180- 300

qs (mg/g)

K (L/mg)

n

R2

42.1 42 42.1 42.05

0.02830 0.02833 0.02780 0.0273

0.664 0.698 0.724 0.719

0.94 0.96 0.99 0.98

Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008 6155

tioned LDH. We observed, for example, that the HSDM estimated diffusivities that were also a strong function of particle size (the D values varied from 1.64 × 10-11 cm2/s for 53-75 µm particle size to 10.03 × 10-11 cm2/s, for the 180-300 µm particle size). Defining the dav differently, and even taking into account the measured PSD, did not improve things in that regard. Using a concentration-dependent diffusivity (following the Darken correlation) did not improve things much, either. Table 5 shows the calculated values for DM and Dµ/Rµ2 corresponding to the data fit in Figure 4 using the BPM model. Other data used in these calculations include the corresponding Sips isotherm parameters (Table 3), as well as the experimentally measured solid densities and the total porosities (from the nitrogen adsorption studies). For comparison, we show in the same table the calculated Knudsen diffusivity values (DK) corresponding to the average mesopore radius measured by BET. Note that the diffusivity values obtained with the BPM vary comparatively (to the HSDM) little with the particle size and that the calculated values are very close to each other for the two different samples with the same PSD. This observation is consistent with the understanding that the Dµ/Rµ2 value for the microparticles should remain unaffected by the overall size of the aggregate particle. It is also observed that the fitted DM values are fairly close to DK calculated by the following:32 4 DK ) rp 3



2RgT πM

(18)

where Rg is the ideal gas law constant (J/(g mol K)), M is the molecular weight of CO2 (g/mol), rp is the average pore radius (cm) of the adsorbent particle obtained from the analysis of the BET data, and T is the temperature (K). Note, also, that in the BPM case the calculated diffusivities for the two samples with the same PSD are much closer to each other than in the HSDM case. Though both the HSDM and BPM successfully fit the experimental adsorption data, it is probably reasonable to conclude that the BPM offers a more accurate representation of the phenomena that occur than does the commonly utilized HSDM. This is true for both gas as well as liquid adsorption, since similar results using the BPM were also previously observed during fitting of the As adsorption data on LDH.16 5. Conclusions CO2 adsorption on calcined layered double hydroxide adsorbents was investigated. It was shown to follow a Sips isotherm with an adsorption capacity at saturation which is independent of the particle size, and significantly larger than what has been previously reported with the same materials.31 Two different models, the conventional homogeneous surface diffusion model and the bidisperse pore model, were used to fit the experimental data. The main assumption made in the BPM is that the Table 4. Surface Diffusion Coefficients for CO2 in Calcined LDH with Various Particle Sizes Calculated Using the HSDM DS (×109 cm2/s) particle size (µm)

dav

expt I

expt II

53-75

AM VM AM VM AM VM AM VM

3.44 3.61 4.14 4.35 10.45 11.48 54.35 57.27

3.30 3.46 4.43 4.65 10.32 11.34 55.62 58.61

75-90 Figure 4. Observed experimental data (dashed line) and model predictions (HSDM and BPM using the AM average diameter) for CO2 adsorption on calcined LDH with various particle sizes: (a) 53-75, (b) 75-90, (c) 90-180, and (d) 180-300 µm.

90-180 180-300

6156 Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008 Table 5. Diffusivity (DM, Dµ/Rµ2) Values for Calcined LDH with Various Particle Sizes Calculated Using the BPM, and the Estimated Knudsen Diffusivity (DK) expt I

expt II

particle size (µm)

dav

DM (×10 cm /s)

Dµ/ Rµ (×10 s )

DM (×10 cm /s)

Dµ/ Rµ2 ( × 104s-1)

DK (×102cm2/s) (from BET)

53-75

AM VM AM VM AM VM AM VM

1.51 1.53 1.68 1.67 2.05 2.04 2.07 2.06

5.77 5.77 5.61 5.63 5.57 5.59 5.56 5.60

1.51 1.53 1.67 1.65 2.06 2.07 2.08 2.11

5.76 5.77 5.61 5.60 5.65 5.59 5.60 5.57

0.76

75-90 90-180 180-300

2

2

2

4

-1

adsorbent particle is an agglomerate of a number of equal-sized, single-crystal microparticles, so that before a CO2 molecule gets adsorbed on the microparticle, it has to diffuse through the intercrystalline porous region. Both models fit the adsorption data well. However, the surface diffusivities calculated using the HSDM exhibit strong particle size dependence, while the BPM yields values that are particle size independent, as one may expect. These results, obtained for gas adsorption, are consistent with observations made during As adsorption from the liquid phase, as reported in our previous study.16

2

2

0.80 1.42 2.05

Subscripts 0 ) intial conditions M ) particle µ ) microparticle s ) saturation condition Greek Symbols ε ) void fraction in the porous region F ) particle density (g/cm3) Fs ) solid density (g/cm3)

Acknowledgment This research was supported by NASA and the U.S. Department of Energy. Nomenclature C ) CO2 concentration in the solid phase, HSDM model (mg/g) C0 ) initial gas-phase CO2 concentration (mg/L) CM ) CO2 concentration in the intercrystalline region, BPM model (mg/L) d10 ) arithmetic mean diameter (µm) d30 ) volume mean diameter (µm) dav ) average mean diameter of the particle size range (µm) di ) particle diameter of the ith particle (cm) DK ) Knudsen diffusivity (cm2/s) DM ) mesopore diffusivity (cm2/s) Dµ ) micropore diffusivity (cm2/s) DS ) intraparticle diffusion coefficient (cm2/s) K ) Sips constant (L/mg) n ) exponential factor in the Sips isotherm ni ) number of particles with particle diameter di N ) total number of particles qµ ) CO2 concentration in the microsphere (mg/g) qjµ ) volume-averaged adsorbate concentration in the microsphere (mg/g) qs ) saturation loading (mg/g) M ) molecular weight of CO2 (g/mol) Mt ) volume averaged adsorbate concentration in the particle (mg/ g) M∞ ) volume averaged adsorbate concentration in the particle at large times (equilibrium) (mg/g) r ) radial distance in the particle (cm) R ) particle radius (cm) Rg ) ideal gas law constant (J/(g mol K)) rM ) radial distance in the particle in the bidisperse model (cm) RM ) particle radius in the bidisperse model (cm) rµ ) radial distance in the microparticle (cm) Rµ ) microparticle radius (cm) rp ) average pore radius (cm) t ) time (s) T ) temperature (K)

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ReceiVed for reView December 12, 2007 ReVised manuscript receiVed May 8, 2008 Accepted May 15, 2008 IE701701D