Understanding the Enhancement Effect of Na2CO3 Additive on the

Dec 17, 2014 - The enhancement effect of Na2CO3 additive on the reaction of CaCO3 with SO2 and O2 at high temperature is a widely observed phenomenon;...
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Understanding the Enhancement Effect of Na2CO3 Additive on the Direct Sulfation of Limestone Zhenshan Li,* Peiting Liang, and Ningsheng Cai Key Laboratory for Thermal Science and Power Engineering of the Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China ABSTRACT: The enhancement effect of Na2CO3 additive on the reaction of CaCO3 with SO2 and O2 at high temperature is a widely observed phenomenon; however, its mechanism remains unclear. From the solid-state physics point of view, this study proposed that the defect formation caused by the additive may explain the enhanced sulfation. The single-crystal CaCO3 with a smooth surface was used as a sample for direct sulfation, and the morphology and Na element distribution was investigated with scanning electron microscopy and energy-dispersive spectroscopy. It is observed that the Na ion will diffuse into CaSO4 during sulfation, and it does not diffuse into the lattice of the CaCO3 crystal by itself. The relationship of the diffusion coefficient in the solid state with the additive fraction was established and integrated into a new sulfation model. This new model included a simplified rate equation model to describe the product island formation and an ionic diffusion model that describes the productlayer growth. The experimental data on the direct sulfation of limestone, with and without additive, were used to validate the newly developed models. some additives.9,10 The enhancement reason for both direct and indirect sulfation with additive is ascribed to the promotion of product-layer diffusion.5 Ionic diffusion is the movement of ions inside the solid and associated with lattice defects. Adding the additive into the solid will possibly produce defects and affect the diffusion of ions and therefore change the subsequent sulfation behavior. Thus, understanding the influence of additive is significant in improving the sorbent performance. The positive influence of additive on sulfation has been extensively supported; however, the mechanism on the effect of additive on sulfation has not been clarified. Accordingly, this problem is investigated in the present study. This study aims to (1) apply the theories of defect chemistry and ion diffusion to study the mechanism of direct sulfation enhanced by Na2CO3 additives and (2) discuss the effects of certain factors on the direct sulfation. The results can help further develop calcium-based sorbents and improve their reactivity.

1. INTRODUCTION O2/CO2 coal combustion in a circulating fluidized bed (CFB) boiler is one of the promising technologies for CO2 capture1 and is currently demonstrated in large-pilot-scale facilities such as the 30MW CIUDEN Oxy-CFB Boiler Demonstration Plant in Spain.2 In O2/CO2 coal combustion CFB systems, a high purity of oxygen is mixed with the flue gas, and then this gas mixture is introduced into the CFB furnace to burn the coal. Almost no nitrogen is introduced into the furnace; therefore, the CO2 content in the flue gas can be higher than 95%.1−4 For the O2/CO2 coal combustion CFB, the sulfur from the coal will be released into the flue gas to form SO2 pollutant; therefore, limestone is required in order to remove SO2 from flue gas. Because the temperature and CO2 fraction inside the CFB furnace are 800−900 °C and ∼95%, respectively, in this case, the limestone decomposition is limited by the chemical equilibrium, and the direct sulfation reaction between limestone with SO2 and O2 will occur as CaCO3(s) + SO2 (g) + 0.5O2 (g) → CaSO4 (s) + CO2 (g)

2. THEORY 2.1. Model for the Direct Sulfation Reaction. The first step for direct sulfation is chemisorption. The forces responsible for chemisorption arise from the overlap of adsorbate and surface wave functions, which leads to the formation of new bonds and, consequently, modification of their electronic structures. Chemisorption occurs only when the adsorbate makes direct contact with the active surface; thus, it is a single-layer process. The solid product has two possible states: (I) vibrating around its original lattice and (II) jumping to another site from its original lattice, i.e., solid-state diffusion. If the solid product only vibrates without jumping to another

(1)

The reaction kinetics and mechanisms of the direct sulfation of limestone with SO2 have been widely studied by researchers. A comprehensive literature review on the direct sulfation reaction has been published by Hu and Dam-Johansen.5 The initial stage of direct sulfation is controlled by chemical kinetics, whereas the next stage is controlled by solid product-layer diffusion. In addition, the diffusion in the product layer is ionic diffusion at the solid state rather than the molecular or Knudsen diffusion states because the activation energy is larger than that of molecular or Knudsen diffusion. To improve the sulfation kinetics, additives have been added into limestone to enhance its performance. Some inorganic salts, such as Li+, Na+, and K+, have been observed to enhance direct sulfation.6−8 At the same time, it was observed that the indirect sulfation of calcined limestone can also be enhanced by © 2014 American Chemical Society

Received: June 29, 2014 Revised: November 16, 2014 Published: December 17, 2014 278

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Figure 1. (a) Experimental result of the direct sulfation on a single crystal of CaCO3.12 (b) Principle of CaCO3 product formation, growth, and ion diffusion during the direct sulfation of CaCO3.

formation is relatively short in the initial stage, the assumption ignoring the time for solid island formation is reasonable. XI can be calculated as follows:

site, the reaction is limited to a single-molecule layer because chemisorption cannot occur and the solid product hinders the direct contact of the gas molecule with the active surface. For practical gas−solid reactions, the solid reactant is consumed continuously; thus, the solid product must jump to another site from its original lattice; i.e., solid-state diffusion takes place simultaneously with the chemical reaction. Solid-state diffusion has three types: surface diffusion, grain boundary diffusion, and lattice diffusion. The activation energy for surface diffusion is typically lower than those of grain-boundary diffusion and lattice diffusion; thus, the initial reaction stage is dominated by both reaction kinetics and surface diffusion. The surface diffusion of solid products leads to nucleation and growth, wherein the driving force is minimization of the surface free energy of the solid products.11 Thus, surface diffusion is important when understanding the nucleation and growth of the solid product. As previously discussed, the initial stage of the gas−solid reaction, such as the direct sulfation of CaCO3 with SO2 and O2, is fast and controlled by chemical kinetics and surface diffusion, whereas the next stage is slow and controlled by diffusion in the solid product layer. Our recent experimental results12 showed that the initial CaSO4 products occur and grow as island morphologies on the CaCO3 surface, as shown in Figure 1a; minimization of the surface free energy is the driving force for island morphology. The formation of CaSO4 “product islands” on the reacting CaCO3 surface can gradually cover the reactant CaCO3 surface, thereby reducing the conversion rate. Recently, a rate equation theory has been established to calculate the kinetics of gas−solid reactions.13,14 In this section, the rate equation theory can be used to develop a simplified, easy-to-use model for the reaction process. Figure 1b shows the simplified concept of the CaSO4 product formation during the direct sulfation reaction. The unreacted CaCO3 is assumed to be a thin film with thickness h0, and the surface area of CaCO3 is assumed to be a unit (1 m2). In an atmosphere with high CO2 concentration, decomposition of CaCO3 will not occur; thus, CaCO3 can be assumed to be nonporous. During the initial fast-stage reaction controlled by chemical kinetics and surface reaction, SO2 and O2 make contact with the CaCO3 surface. The direct sulfation reaction can occur on the CaCO3 surface, and CaSO4 will grow on the CaCO3 surface with the morphology of islands. Because of the fast reaction rate, a partial CaCO3 surface will be covered by CaSO4 islands with a critical thickness hc−hpc, as shown in Figure 1b. The uncovered area fraction of the CaCO3 surface after the fast-stage sulfation is α, whereas the area fraction of CaSO4 islands is 1 − α. To simplify the model, it is assumed that once the CaSO4 island is produced, the local CaCO3 covered by the product island has already reached critical conversion XI. Because the time for CaSO4 product island

XI =

h0 − hpc volume of reacted CaCO3 = volume of initial CaCO3 h0

(2)

where hpc is the thickness of unreacted CaCO3 when the local conversion reaches XI. On the basis of the volume relationship between reacted CaCO3 and CaSO4, the critical product-layer thickness can be expressed as Z(h0−hpc). The critical productlayer thickness is temperature-dependent and can be determined by calculation of the rate equation theory13,14 or by the experiments.12 After the thick product layer is formed on the CaCO3 surface in the fast reaction stage, the reaction rate suffers a dramatic decrease, which represents a transition from a fast reaction stage to a slow reaction stage controlled by product-layer diffusion. In the product-layer diffusion stage, there is little increase for the local CaCO3 conversion while the unreacted CaCO3 thickness decreases to hp. This increment of conversion during the product-diffusion-controlled stage XII can be given by XII =

hpc − hp h0

(3)

For a single product island, the local CaCO3 conversion is XI + XII, while for the uncovered CaCO3 surface (as seen in Figure 1b), the local CaCO3 conversion is zero. Therefore, the overall CaCO3 conversion can be written as follows: X = (XI + XII)(1 − α)

(4)

In the chemical-kinetics-controlled stage, CaSO4 islands with a local CaCO3 conversion XI cover the CaCO3 surface in the fraction of 1 − α, whereas the α fraction of the CaCO3 surface remains exposed to the gas phase. During this reaction stage, the consumption of CaCO3 can be calculated by the chemical kinetics rate equation as n2 FCaCO3 = αkCOn12CCO C 2 CaCO3

(5)

Because the CaCO3 surface is assumed to be a unit (1 m ), α can represent the reaction area. On the basis of the volume relationship, FCaCO3 can be expressed as 2

FCaCO3 =

h0 − hpc d(1 − α) M dt VCaCO 3

(6)

When combining eqs 5 and 6, the uncovered area fraction α can be derived as n1 α = exp( −ksCSO C n2 t ) 2 O2

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nil ⇄ VCa ′′ + VSO4••

where ks = kVM CaCO3 CCaCO3/(h0 − hpc). The CaSO4 product for the product-layer-diffusion-controlled stage covers the CaCO3 surface and hinders the direct contact of CaCO3 with the reactants from the gas phase. In this case, the direct sulfation reaction is controlled by ion diffusion through the CaSO4 product layer. As proposed by Fuertes and Fernandez,6 SO42− diffuses inward from the CaSO4/gas interface to the CaSO4/CaCO3 interface, whereas CO32− diffuses outward from the CaSO4/CaCO3 interface to the CaSO4/gas interface, as shown in Figure 1b. The diffusion fluxes of SO42− and CO32− are JSO42− and JCO32−. To maintain local and global charge balance, these diffusion fluxes satisfy the equation JSO 2− = JCO 2− 4

2CaSO4

Na 2SO4 ⎯⎯⎯⎯⎯⎯→ 2Na Ca′ + VSO4••

[VCa″][VSO4••] = K s(T )

4

2[VSO4••] = [Na Ca′] + 2[VCa″]

+

De

1 n1 kCSO C n2 2 O2

2−

••

[VSO4 ] =

(9)

where [SO4 ]0 is the concentration at the CaSO4/gas interface. For the direct sulfation of limestone, grain-boundary diffusion is esepcially significant because most of the atoms’ or ions’ movements occur on the grain boundary. The effective product-layer diffusion coefficient can be related to the lattice and grain-boundary diffusion coefficients.11,13 In this work, the effective diffusion coefficient has been assumed as a function of CaCO3 conversion, i.e.,

(10)

⎛ ΔHm ⎞ ⎛ ΔGm ⎞ ⎛ ΔS ⎞ ⎟ = υ exp⎜ m ⎟ exp⎜ − ⎟ ω = υ exp⎜ − ⎝ RT ⎠ ⎝ R ⎠ ⎝ RT ⎠

(

D 1−

XII 1 − XI

m

)

+

1 n1 kCSO C n2 2 O2

(20)

where υ represents the vibration frequency. When eqs 17−20 are combined, the diffusion coefficient can be expressed as

M VCaCO [SO4 2 −]0 /h0 3 1

(17)

4

The jump frequency (ω) can be expressed as15

(11)

When eqs 9−11 are combined, the CaCO3 conversion rate in the ion-diffusion-controlled stage can be obtained as follows: dXII = dt

[Na Ca′]2 + 16K s

where σ is a geometrical factor of the lattice structure, n/t is the number of jumps per unit time, and a0 is the jump distance. n/t depends on the jump frequency (ω) toward an adjacent site, the number of nearest-neighbor positions of the atom (ζ), and the fraction of vacancies ([VSO4••]; the particle only jumps if there is a vacancy on an adjacent site).15 Therefore, n = ωζ[VSO4••] (19) t

From eq 3, the following equation can be obtained: M VCaCO dXII 1 dh p 3 =− = J 2− dt h 0 dt h0 SO4

[Na Ca′] +

Equation 17 shows that the relationship of the defect concentration with the additive fraction has been established, and this equation is useful for investigating the effect of the additive on the defect concentration. Subsequently, the relationship between the diffusion coefficient in the solid state with the defect concentration is built. The diffusion coefficient in the solid state can be expressed as15 n D = σ a0 2 (18) t

SO42−

m ⎛ XII ⎞ De = DZh0(XI + XII)⎜1 − ⎟ 1 − XI ⎠ ⎝

(16)

When eqs 15 and 16 are combined, the concentration of the SO42− vacancies can be obtained as follows:

[SO4 2 −]0 h − hp

(15)

The expression of charge neutrality is as follows:

On the basis of the Fick diffusion law, the diffusion flux of SO42− is as follows: JSO 2− =

(14)

The mass-action expression for the Schotty defect formation reaction of CaSO4 is as follows:

(8)

3

(13)

(12)

D = σa0 2ζ[VSO4••]ω

The CaCO3 conversion during the ion-diffusion-controlled stage can be calculated with eq 12. When eqs 7 (describing product island formation) and 4 are combined, the overall CaCO3 conversion during the initial fast stage and the second slow stage can be calculated. 2.2. Effect of an Additive on the Defect Concentration and Diffusion Coefficient. When additive Na2CO3 is added to the solid phase, Na2CO3 will react with SO2 and O2 to form Na2SO4, and then Na2SO4 will be incorporated into the lattice of the CaSO4 product and more extrinsic defects will be produced inside CaSO4, causing enhancement of ion diffusion (i.e., increasing the diffusion coefficient). The Schottky disorder is the preferred form of intrinsic disorder and the Na ion occupies the Ca lattice. The negatively charged impurity center, NaCa′, is compensated for by SO42− vacancies. The Na incorporation reaction is presented as follows (with the Kröger−Vink notion in defect chemistry theory):

= αυa0 2ζ

[Na Ca″] +

⎛ ΔHm ⎞ ⎟ exp⎜ − ⎝ RT ⎠

[Na Ca″]2 + 16K s 4

⎛ ΔS ⎞ exp⎜ m ⎟ ⎝ R ⎠ (21)

Equation 21 shows that the relationship between the diffusion coefficient with the extrinsic defect concentration, and therefore the enhancement effect of the additive on the reaction, can be calculated quantitatively.

3. EXPERIMENTS 3.1. Sample. Single-crystal CaCO3 with a crystal orientation of ⟨100⟩ was used as the test sample. Both the length and width of the sample were 5 mm, and the thickness was 0.5 mm. The surface of the sample was polished, and the root mean square 280

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Figure 2. (a) Atomic force microscopy images of the single-crystal CaCO3 fresh surface. RMS = 1.2 nm. (b) SEM images of the single-crystal CaCO3 fresh surface.

Figure 3. CaCO3 conversion versus time for the direct sulfation of a CaCO3 crystal with and without Na2CO3 additive at different temperatures (3000 ppm of SO2 and 3 vol % O2, 77 vol % CO2, and balance N2): (a) 700 °C; (b) 750 °C; (c) 800 °C; (d) 850 °C.

and balance N2. The total gas flow was 100 mL/min. The CaCO3 sample was heated from room temperature to the test temperature (700, 750, 800, and 850 °C) with a heating rate of 50 °C/min. When the test temperature was reached, the sample was kept isothermal for 150 min in an atmosphere with 3000 ppm of SO2. The impregnation method was used to prepare the CaCO3 sample with Na2CO3 additive. Single-crystal CaCO3 was dipped into a 10 wt % Na2CO3 solution, and the wet sample was dried at 110 °C for 20 min. The polished surface of the sample was

(RMS) was less than 5 nm, as can be seen in Figure 2. The crystal structure of CaCO3 belongs to the hexagonal crystal system with space group R3̅c. The unit cell parameters are a = b = 0.4989 nm and c = 1.7062 nm. 3.2. Experimental Procedures. CaCO3 direct sulfation experiments were performed in a thermogravimetric analyzer (TA Instruments Q500). Because CaCO3 could decompose to CaO at high temperature, CO2 of high concentration (about 77 vol %) was set to prevent CaCO3 decomposition. Other gas compositions were maintained at 3 vol % O2, 3000 ppm of SO2, 281

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Figure 4. SEM images of a sample reacted at 700 °C with and without Na2CO3 after 150 min of reaction.

Figure 5. SEM images of a sample reacted at 800 and 850 °C with and without Na2CO3 after 150 min of reaction.

Figure 6. SEM cross-sectional images of a sample reacted at 850 °C with and without Na2CO3 after 150 min of reaction.

enhancement effect of Na2CO3 additive on the direct sulfation at higher temperatures such as 800 and 850 °C was more pronounced, as shown in Figure 3. Figures 4 and 5 show the SEM images of a sample reacted at different temperatures without Na2CO3. From a comparison of Figure 4a and parts a and c of Figure 5, it can be seen clearly that the product size increases with increasing temperature; that is to say, the temperature affects not only the reaction kinetics and product-layer diffusion but also the product morphology. These phenomena conform to the principle of minimization of the surface free energy, and a detailed discussion can be found in the literature.11 Figure 6 compares the effect of Na2CO3 addition on the cross section of a sample reacted at 850 °C after 150 min of reaction. From Figure 6, it can be seen clearly that Na2CO3 addition will produce more grain boundaries. Compared with the ion at the lattice, the bonding of the ion at the grain boundary is less tight, and the ion at the grain boundary will be more mobile than the lattice ion. That is to say, the activation energy of grain-boundary diffusion is normally lower than that of lattice diffusion. Therefore, with the formation of more grain boundaries, ion diffusion through the product layer is expected to be enhanced. For the experiments of the CaCO3 crystal, Na2CO3 was deposited on the crystal surface. The question is, how does the

kept upward in order for aqueous Na2CO3 to remain on the polished surface. Because the surface area of the CaCO3 sample was very small, only a small amount of the Na2CO3 solution could be deposited on the surface. 3.3. Characterization. Observation of the reacted sample surface morphology was obtained by scanning electron microscopy (SEM). The instrument used to inspect the morphology is a FEI SIRION 200 scanning electron microscope because it can provide both a full picture of the sample and details of a specific feature. Energy-dispersive spectroscopy (EDS; type EDAX) was used to analyze the component distribution on the surface. Except for the CaCO3 reacting surface, a cross section of the sample was also observed to study the diffusion of ions during the reaction. The sulfated CaCO3 sample was cut flat into two pieces with a fine steel wire. EDS was used to analyze the component distribution on the cross section.

4. RESULTS AND DISCUSSION 4.1. Results of a Single Crystal of CaCO3. Figure 3 shows CaCO3 conversion of a CaCO3 crystal with time at different temperatures with and without Na2CO3 additive. From Figure 3, it can be seen that the presence of Na2CO3 additive has a significant influence on CaCO3 conversion. Compared with the cases at lower temperatures such as 700 and 750 °C, the 282

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Figure 7. SEM cross-sectional image and EDS of a sample treated at 850 °C without SO2 after 150 min.

Figure 8. SEM cross-sectional images and EDS of a sample reacted at 850 °C with Na2CO3 after 150 min of reaction.

Figure 9. CaCO3 conversion versus time for the direct sulfation of limestone with and without Na2CO3 additive at different temperatures (2000 ppm of SO2 and 2.7 vol % O2 balanced with CO2): (a) 700 °C; (b) 750 °C; (c) 775 °C; (d) 800 °C; (e) 850 °C; (f) 875 °C (experimental data are from ref 6).

distribution of element Na with the depth inside a sample reacted at 850 °C with sulfation after 150 min. From the EDS results, it can be found that the Na element diffused into the sample, as did the S element; however, it seemed like the diffusion rate of Na was slower than that of S, as shown in Figure 8d, and this may be due to a small amount of Na2CO3 deposited on the surface. From the above discussion, the

additive diffuse during the direct sulfation process? In order to answer this question, the additive concentrations varying with the depth were measured, as shown in Figures 7 and 8. Figure 7 shows the distribution of element Na with the depth inside a sample reacted at 850 °C without sulfation after 150 min. It can be seen from the EDS results that the Na element did not diffuse into the lattice of the CaCO3 crystal. Figure 8 shows the 283

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Energy & Fuels conclusion is that the Na element will diffuse into CaSO4 during sulfation and it does not diffuse into the lattice of the CaCO3 crystal by itself, so the Na incorporation reaction presented in eq 14 is reasonable. 4.2. Results of Limestone Particles. The results presented in section 4.1 were obtained from single-crystal CaCO3. The purpose of using a single crystal is to investigate clearly the surface morphology of the solid product; however, the lattice structure of a single crystal is largely different from the limestone particles because the practical limestone will have many defects. In order to validate the proposed model, the experimental results of limestone were used. Figure 9 shows CaCO3 conversion with time at different temperatures, with and without Na2CO3 additive. Experimental data published by Fuertes and Fernandez6 were used to validate the developed model, and the experimental details can be found in the literature.6 The additive was deposited over CaCO3 particles by evaporation of a Na2CO3 solution, and it is believed that some Na2CO3 aqueous solution will penetrate the particle and diffuse into the interier of the particle because there are some pores and surface area inside the sample (0.43 m2/g).6 Figure 9 also shows that the direct sulfation reaction has a typically fast reaction stage and a slow product-layer diffusion stage, and the presence of Na2CO3 additive has a significant influence on CaCO3 conversion. A comparison between the calculated and experimental results during the initial stage and the second stage is also shown in Figure 9 to discuss the effects of the additive on the reaction rates and conversion. In the model calculation, the adjustable parameters are XI, D, and m. These parameters depend on the temperature. The calculations revealed that the temperature had almost no effect on m and 1 1 ksCnSO Cn2 (cm3/mol/s), and the value of ksCnSO Cn2 was 3.84 × 2 O2 2 O2 −6 3 10 cm /mol/s for all temperatures. The Na2CO3 additive had no influence on the reaction rate constant but affected m and D. The values of the parameters used in the calculation are given in Table 1. XI increases with increased temperature, which is

Figure 10. Activation energy of the direct sulfation of CaCO3 with/ without Na2CO3 additive.

that the diffusion coefficients of limestone with Na2CO3 additive are larger than those of the limestone without additive at all temperatures. Interestingly, the activation energy value (77.3 kJ/mol) of solid-state diffusion for a doped sample is the same as that for an undoped sample. During ion diffusion from one site to another inside the solid, the ion has to surmount energy barriers. The potential barrier height symbolizes the activation energy for ion diffusion. As discussed in section 4.1, the doped Na2CO3 changes the defect number inside the CaSO4 structure, while it may not change the potential barrier height of ion diffusion, and this may be an reason that the activation energy value (77.3 kJ/mol) of solid-state diffusion for a doped sample is the same as that for the undoped sample. The determined activation energy (77.3 kJ/mol) is smaller than that reported by other authors such as 145.9 kJ/mol (pure calcite),16 132.9 kJ/mol (limestone),17 and 148 kJ/mol (limestone).18 These high activation energy values reported by other researchers come from the claims that solid-state ion diffusion is only controlled by lattice diffusion and that the reaction rate will change with time, indicating that the diffusion coefficient changes with time, leading to a change in the activation energy with time. When the activation energy was obtained, these researchers did not consider grain-boundary diffusion and assumed that the product-layer diffusion stage was only controlled by lattice diffusion; however, this finding is not reasonable because numerous grain boundaries are formed during the gas−solid reaction progress.11−14 The grain boundary is the fast diffusing path of ions; thus, the activation energy of grain-boundary diffusion is smaller than that of lattice diffusion. The model developed in this work included grainboundary diffusion, and the activation energy determined for grain-boundary diffusion is 77.3 kJ/mol. For the enhancement mechanism, Fuertes and Fernandez6 proposed that the diffusion-controlled stage can be changed to a kinetic-controlled stage by adding Na2CO3. However, the results presented in this work indicated that the addition of Na2CO3 produced more crystal defects because the diffusion coefficient is directly related to the defect concentration and the diffusion coefficient is enhanced, as shown in eq 21. Figure 10 shows that the activation energy does not change with the addition of Na 2 CO 3 , and the additive increased the preexponential factor. The ratio of the preexponential factor with additive to that without additive is represented as follows:

Table 1. Values of the Parameters Used in the Calculationa parameter b

D

Dc XI

700 °C

750 °C

775 °C

800 °C

4.46 × 10−8 1.15 × 10−7 0.050

9.00 × 10−8

9.70 × 10−8 2.44 × 10−7 0.085

1.00 × 10−7

0.052

0.130

850 °C 1. 53 × 10−7 4.14 × 10−7 0.2

875 °C 2.09 × 10−7 4.99 × 10−7 0.22

n1 n ksCSO C 2 = 3.84 × 10−6 cm3/mol/s for all temperatures. [SO42−]0 = 2 O2 3 M 1/VM CaSO4 = 1/46 = 0.0217 mol/cm . h0 = d/2 = 17/2 = 8.5 μm. VCaSO3 2− −4 −2 2 −1 [SO4 ]0/h0 = 36.9/(8.5 × 10 )(2.17 × 10 ) = 9.42 × 10 cm . m = b a

0.80, without additive; m = 0.33, with additive. Diffusion coefficient without additive. cDiffusion coefficient with additive.

reasonable because the critical size of the solid product island depended on the temperature.11−14 With the parameters listed in Table 1, Figure 9 shows that the calculated results agreed well with the experimental data for the direct sulfation of CaCO3, and the developed model can capture the enhancement effect of the Na2CO3 additive on direct sulfation. The enhancement effect of the Na2CO3 additive on the direct sulfation at all temperatures was more obvious when the sulfation progress became diffusion-controlled, as shown in Figure 9. The relationship of the diffusion coefficient with temperature for a doped sample and the original limestone is presented in Figure 10 as an Arrhenius plot. Figure 10 shows 284

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[Na Ca″]2 + 16K s Ks

=

exp(0.4414) = 2.58 exp( −0.5081) (22)

This calculation indicated that the Na2CO3 additive enhanced the diffusion coefficient by 2.58 times. Meanwhile, the simulated results indicated that the values of m in eq 12 are 0.33 and 0.8, respectively, for the direct sulfation with and without Na2CO3 additive. The parameter m reflects the fraction of the grain boundary, wherein the smaller value of m means that more grain boundaries will be produced. Our experimental and modeling results indicated that the additive can produce more grain boundaries. The crystal size of the CaSO4 product observed by Chen et al.8 became smaller, and the morphology of the solid products became more irregular when Na2CO3 was added into the limestone. This observation implied that more grain boundaries inside the CaSO4 product were produced with Na2CO3 additive, thereby supporting our conclusion.

5. CONCLUSIONS An integrated model was developed to understand the enhancement effect of the Na2CO3 additive on the direct sulfation of CaCO3 with SO2 and O2. The product island formation and growth were described with simplified rate equation theory, and product-layer diffusion was described with solid-state ion diffusion theory. The enhancement effect of the Na2CO3 additive on the crystal defect was calculated with defect chemistry theory. A comparison of the calculated results with the experimental ones revealed that the developed model successfully explained the macroscopic behavior of the additiveinduced enhancement effect. The activation energy value (77.3 kJ/mol) of solid-state grain-boundary diffusion for a doped sample was the same as that for an undoped sample. The additive increased the preexponential factor and produced more grain boundaries, thereby enhancing the diffusion rate. The developed model built the link of the kinetics of the direct sulfation reaction with the defect chemistry.

■

■

hpc critical CaCO3 thickness, m Ji (i = SO42−, CO32−) flux of diffusing ions, mol/m2/s k chemical reaction rate constant for the reaction of CaCO3 with SO2 and O2, m4/mol2/s m parameter reflecting the grain-boundary fraction NaCa′ disorder formed by the Na ion occupying the Ca lattice [SO42−]0 concentration of SO42− at the CaSO4/gas interface, mol/m3 R universal gas constant T temperature, K 3 VM CaCO3 molar volume of CaCO3, 36.9 cm /mol 3 VM molar volume of CaSO , 46 cm /mol CaCO4 4 VCa′′ vacancy of the Ca ion VSO4•• vacancy of the SO42− ion X total CaCO3 conversion XI critical CaCO3 conversion XII CaCO3 conversion during the product-layer diffusioncontrolled stage Z ratio of the CaSO4 volume to the CaCO3 volume ΔSm entropy, J/mol/K ΔHm enthalpy, J/mol

REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*Telephone: 86-10-62789955. Fax: 86-10-62770209. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the National Natural Science Funds of China (Grant 51376105, 91434124), the Program for the New Century Excellent Talents in University (NCET-120304), and the Tsinghua University Initiative Scientific Research Program.

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NOMENCLATURE CCaCO3 CaCO3 concentration, mol/m3 CSO2 SO2 concentration, mol/m3 CO2 O2 concentration, mol/m3 FCaCO3 CaCO3 consumption, mol/s D grain-boundary diffusion coefficient, m2/s De effective diffusion coefficient, m2/s h0 initial thickness of the CaCO3 film, m hp thickness of the unreacted CaCO3, m 285

DOI: 10.1021/ef5014456 Energy Fuels 2015, 29, 278−286

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DOI: 10.1021/ef5014456 Energy Fuels 2015, 29, 278−286