Crystallization and Fracture: Product Layer Diffusion in Sulfation of

43, 18, 5653-5662 ... The product layer diffusivity increased with temperature, but decreased with increasing ... such a layer can be fractured by ste...
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Ind. Eng. Chem. Res. 2004, 43, 5653-5662

5653

Crystallization and Fracture: Product Layer Diffusion in Sulfation of Calcined Limestone Wenli Duo* Pulp and Paper Research Institute of Canada, 3800 Wesbrook Mall, Vancouver, British Columbia V6S 2L9, Canada

Karin Laursen Department of Chemical Engineering, Kyoto University, Kyoto-Daigaku Katsura, Nishikyo-ku, Kyoto 615-8510, Japan

Jim Lim and John Grace Department of Chemical and Biological Engineering, University of British Columbia, 2216 Main Mall, Vancouver, British Columbia V6T 1Z4, Canada

Sintered samples of calcined limestone were sulfated for extended times in a differential reactor to study the reaction kinetics after formation of a product layer. The reaction rate was controlled by product layer diffusion, except during the initial period. The product layer diffusivity increased with temperature, but decreased with increasing SO2 concentration. The diffusivity not only depends on current conditions, but also on previous conditions that led to the formation of the layer. The results support a crystallization and fracture model and a hypothesis that the ratelimiting mechanism changes from inward gas diffusion control in the early stages to outward ionic diffusion control after formation of a continuous product layer, a change attributed to the need for the reaction to do mechanical work to displace the product layer and make room for increased solid volume at the CaO/CaSO4 interface. A criterion is established to determine whether a product layer can be fractured. A gas containing 2250 ppm SO2 at 900 °C cannot fracture a product layer as thick as 233 nm, while such a layer can be fractured by steam at 250 °C and a partial pressure of 1 bar. Introduction Sulfur capture in fluidized bed combustion of coal and other sulfur-rich fuels1-4 involves rapid high-temperature limestone calcination to porous calcium oxide followed by sulfation:

CaO(s) + SO2(g) + 1/2O2(g) h CaSO4(s)

(1)

The sulfate product forms a barrier between the unreacted lime and gaseous reactants. The growth of the product layer augments the resistance to gas or solid phase diffusion though the product layer. For a porous particle, the reaction rate in the early stages of sulfation is generally considered5 to be controlled by diffusion of SO2 and O2 in intraparticle pores and by the reaction of SO2 and O2 with CaO on the surface of individual grains. Once a “continuous” product layer of CaSO4 has covered the grain surface, the rate tends to be controlled by diffusion through the product layer. However, for large particles the overall rate remains dependent on pore diffusion, since the pores become narrower and more constricted as the reaction proceeds. Pore blockage is commonly attributed to the molar volume of the solid product (CaSO4) exceeding that of the reactant (CaO). The shrinking unreacted-core model6,7 has been employed to describe the sulfation rate for both whole particles and individual CaO grains (in porous sor* To whom correspondence should be addressed. Tel.: 604222-3200. Fax: 604-222-3207. E-mail: [email protected].

bents).5 A key parameter is the product layer diffusion coefficient, Ds, particularly for the late stages, where diffusion of reactants through the product layer becomes rate-limiting.1,6,8 For product layer diffusion control with a constant diffusivity, Ds, Szekely et al.9 showed that

R - [R + (1 - R)(1 - X)] t )3 τs R-1

2/3

- 3(1 - X)2/3 (2)

where R is the volume expansion ratio (molar volume of CaSO4/molar volume of CaO), X is the conversion, and τs is the time required for complete conversion with no volume expansion (i.e. R ) 1), given by

τs )

FCaORp2 6MCaODsCSO2

(3)

Rp, FCaO, and MCaO represent the particle radius, density, and molar weight of the solid CaO, respectively, while CSO2 is the inlet concentration of SO2. The only parameter that cannot be measured directly is Ds. Several groups have found that Ds increases exponentially with temperature (in Arrhenius form). However, both the absolute values and the dependence on temperature vary greatly in the literature, with values2,5,6,10 at 850 °C ranging from 6 × 10-13 to 2 × 10-11 m2/s and activation energies1,2,11,12 from 51 to 159 kJ/mol. In a recent investigation of the mechanism of formation of product layers,13 the morphology of sulfated samples of sintered calcined limestone was studied to

10.1021/ie030837d CCC: $27.50 © 2004 American Chemical Society Published on Web 06/05/2004

5654 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004

characterize initial product layers, as well as fully developed layers. The reaction product was found to form by crystallization. The product did not form a true layer in the early stages of the reaction but isolated nuclei and crystals. A “continuous” product layer formed later was a monolayer of individual crystals with pores of 20-30 Å diameter along crystal boundaries. The structure of the product layer depends on the reaction conditions, with the product layer more porous when developed from a smaller number of larger stable nuclei formed by the initial reaction at higher temperatures and lower SO2 concentrations. These observations are consistent with a crystallization and fracture model (CFM).8,14,15 In this paper, a criterion is developed on the basis of the CFM to determine the conditions under which the CaSO4 product layer will fracture. It also examines how the product layer diffusivity depends on temperature and inlet SO2 concentration. Our previous work13 showed that the average thickness of the product layer formed on an unsintered particle was much thinner than on a sintered particle, even though the overall conversion in the former case was much higher than in the latter, due to the fact that the specific surface area of the unsintered particle was 30 times larger than that of the sintered particle. Although particles with large surface areas are of most practical interest, they are disadvantageous for studying intrinsic reaction kinetics. First, given the crystallization mechanism, a continuous product layer may never form on the internal surfaces. Second, even when the total porosity of the particle is high, there may be insufficient free space inside pores for the product crystals to grow, given the substantial volume expansion (R ) 2.7 for reaction 1). Therefore, a fully developed product layer may never form. Third, a uniform product layer thickness cannot be achieved because of pore diffusion and blockage. The extent to which these problems affect the apparent product layer diffusivity depends on the experimental conditions and the characteristics of the sorbent particles. The larger the specific surface area, the worse the problem. This is one reason reported Ds values vary so much. The surface area of calcined limestone decreases with increasing calcination temperature and duration,16-21 mainly because CaO sinters at high temperatures. In the present work, calcined limestone samples were deliberately sintered for a long time well above the sulfation temperature. Thus, no further sintering would occur in the subsequent sulfation, and the structure of the solid should be stable throughout the sulfation period. Fracture Analysis Product layer diffusion is a slow process at temperatures typical of fluidized bed combustion. If the product layer can be broken, then the reaction continues at a faster rate at the CaO/CaSO4 interface by inward diffusion of SO2 through the cracks. Some mechanical work must be done by the chemical reaction in order to fracture the product layer.8,14 The CFM expresses the total energy change, including mechanical work, owing to formation of a spherical product nucleus or crystal as

∆G ′ ) 4πr2σ + 4/3πr3(FCaSO4/MCaSO4)∆Gc + W ′ (4) where σ, MCaSO4, and FCaSO4 represent the specific surface

energy, molar weight, and density, respectively, of the product, CaSO4. W ′ is the mechanical work needed to make space at the reaction interface for the increased volume as CaO is converted to CaSO4, while r is the radius of the nucleus or crystal. The above expression may also be applied for addition of a single molecule of CaSO4 to an existing crystal during crystal growth. In such a case, the contribution from the first term on the right-hand side of eq 4 becomes negligible; r in the second term is the radius of CaSO4 molecules, and ∆G ′ and W ′ are calculated for a single molecule. ∆Gc, the free energy change of the reaction per mole of CaSO4 formed, is given by

∆Gc ) ∆G° - RT ln(PSO2PO21/2)

(5)

∆G°, the Gibbs free energy change at the standard state, is a function of temperature, and PSO2 and PO2 are the partial pressures of SO2 and O2 at the reaction interface, respectively. Fracture of the product layer requires collective action by many nuclei and crystals. The total work performed by the crystals depends on the geometry of the particle and the distribution of the product. For simplicity, we consider a spherical particle sulfated following the unreacted core model, as shown schematically in Figure 1. Suppose that the force imposed on the product layer by the increased volume during crystal growth is distributed uniformly over the entire interface (Figure 1a). The problem may then be converted to one of stress analysis of a pressure vessel of spherical shape with pressure p (Figure 1b). While the total force normal to the shell surface is 4πRc2p, the tangential force on any cross section through the center (Figure 1c) of the vessel wall can be expressed22 as

∑F ) πRc2p

(6)

where Rc is the radius of the unreacted core. The crosssectional area (ring shape, Figure 1b) may be approximated by 2πRch for a thin product layer of thickness h. (The cross-sectional area is more accurately calculated as 2π(Rc + h/2)h, particularly for a thick layer.) If the tensile stress in the product layer caused by the tangential force is S, then22

∑F ) 2πRchS

(7)

Here, the stress is assumed to be uniform throughout the layer thickness. For a small outward displacement, δ, of the layer, the total work performed by the growing crystals is, by definition, the product of the normal force and the displacement:

∑W ′ ) 4πRc2pδ

(8)

Inserting p from eqs 6 and 7 into eq 8 yields

∑W ′ ) 8πRchSδ

(9)

The magnitude of δ depends on the shape of the crystal being formed. As a simplified, qualitative estimate, δ is assumed to be the radius of a half-sphere (Figure 1a), the volume of which is equivalent to the extra volume generated by converting CaO to form a CaSO4 crystal of radius r, i.e.

δ ) [2(1 - 1/R)]1/3r ) λr

(10)

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The critical point is obtained by setting ∑∆G ′ ) 0, leading to

(Nc/3)r2(FCaSO4/MCaSO4)(-∆Gc) ) 2λRchKc(πa)-1/2 (13) The left side of this equation represents the combined force of Nc growing crystals, while the right side portrays the resistance. Equation 13 gives the minimum condition for fracture of the product layer. It also indicates which parameters are important. These parameters are influenced by the reaction conditions in a complicated manner. For example, for the initial reaction, -∆Gc decreases with increasing temperature, leading to the formation of fewer (but larger) nuclei.13 However, as shown by eq 5, -∆Gc increases with the gas concentration, which is higher at the CaO/CaSO4 interface at higher temperatures due to faster product layer diffusion. From geometry, the maximum number of growing crystals that can be accommodated by the CaO/CaSO4 interface is approximately

Nm ) 4Rc2/r2

(14)

From eq 13, if the conversion is low (small h), only a portion of the available driving power is needed (i.e. Nc < Nm) to fracture the product layer. Full power would be reached with all Nm crystals growing simultaneously at the CaO/CaSO4 interface. Substituting eq 14 into eq 13 yields

( ) h Rc

Figure 1. Schematic of a particle with product crystals performing mechanical work: (a) unreacted core model; (b) equivalence of product layer shell to pressure vessel wall; (c) top view of bs particle exterior surface with indication of tangential force. 2a is the largest flaw size.

where R ) MCaSO4FCaO/MCaOFCaSO4 and λ ) [2(1 - 1/R)]1/3. For N growing crystals of radius r, insertion of eqs 9 and 10 into eq 4 yields

∑∆G ′ ) N(4/3)πr3(FCaSO /MCaSO )∆Gc + 8λπRchrS 4

4

(11)

The term for contribution from the surface energy is eliminated from eq 11, as it is small in the later stages of the reaction when the crystal is relatively large. CaSO4, a ceramic, is brittle. The maximum tensile stress that the product layer can withstand before catastrophic failure, i.e., its fracture strength, is related to its fracture toughness, Kc, by23

S ) Kc/xπa

(12)

where a is the half-length of the longest flaw, as shown in Figure 1b,c, and Kc is a material property. It is probable that a increases with the size of the gaps or pores along CaSO4 crystal boundaries, which become wider with increasing crystal size. ∑∆G ′ must be 0.5 µm in unsintered samples, whereas the primary pores in the sintered sample were several microns in diameter. Experimental Apparatus. Sulfation of sintered calcines was carried out in a bench-scale quartz reactor at atmospheric pressure. The sulfation apparatus is shown schematically in Figure 3. The reactor was placed vertically in a cylindrical electrical furnace of 50 mm inside diameter. The simulated flue gas was drawn from three cylinders containing air, nitrogen, and 5% SO2 in N2. Mass flow controllers/meters measured and controlled the individual gas flows. The exit gas from the reactor was sent to a SO2 analyzer for continuous monitoring and then bubbled through a basic solution for complete SO2 removal. The reactor was 2 m long with an outside diameter of 38 mm. A removable top section (gas injector and thermocouple tube) and a removable bottom section, including a sample holder of inside diameter 26 mm, were attached to the main body of the reactor by ground

sintering

sulfation

sample size, g particle size, µm temperature, °C flow rate, NmL/min gas composition

25 500-710 1300-1350 na air

duration, min

1440

0.6 500-710 705-900 1600 225-2250 ppm SO2 + 3% vol O2 in N2 130-1800

joints. Samples could be conveniently unloaded and reloaded by removing the bottom section. The sample particles contained in the holder were spread evenly as a thin layer on a sintered quartz frit of pore size 60 µm. After being introduced through the inlet at the bottom of the reactor, the premixed sulfation gas was heated to the reaction temperature in the preheating zone, where the gas flowed upward in annular passages, then downward, up again, and finally downward one last time to the sample particles. Once through the packedbed, the reacted gas traveled down through an exhaust tube, leaving the reactor at the bottom. More details are given elsewhere.13 Two K-type thermocouples were inserted into the reactor. One, 40 mm above the packed bed, measured the temperature of the upstream gas, while the other, 6 mm below the packed bed, gave the approximate sample temperature. Prior to and right after each test, the gas stream by-passed the reactor for several minutes to measure the inlet SO2 concentration and to check for drift. The inlet SO2 concentration was also calculated from the flow rates of SO2, air, and carrier N2. Differences in inlet concentrations from these two methods were normally within (2%. All data, including temperatures, SO2 concentration, and flow rates, were continuously logged into a computer by a Visual Basic program. Analytical Methods. The calcium utilization was determined (a) by integration of the SO2 removal curve and (b) from the difference of sample weights before and after tests. The latter gives only the end result for each run, while the SO2 breakthrough curves record the entire sulfation history. The results from the two methods were generally within (3%. The specific surface areas of samples were determined using an ASAP 2010 analyzer (Micromeritics Instrument Corp.) by the multipoint N2 adsorption BET method. Pore size distribution measurements were based on the BJH method. While this method successfully determined pore size distributions in unsintered samples13 up to 0.3 µm, it only showed a high peak at 2-3 nm on the pore size distribution curves for sulfated sintered samples. However, there was no such peak for the presulfated samples. It was thus concluded that the size of the pores formed in the product layer was 2-3 nm. The primary pore diameter remained >0.3 µm after sulfation of the sintered samples. The experimental conditions are listed in Table 1. Results and Discussion A series of tests was carried out to examine the effect of temperature and inlet SO2 concentration on sulfation behavior for different reaction times. Two sorbent samples, A and B, were prepared under the same conditions to test the reproducibility of the experiments. As the two samples gave very similar results, the discussion is based on sample B, except where indicated. Sulfation proceeded typically in three stages, as de-

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scribed previously.13 The breakthrough concentration increased rapidly in the first few minutes (I) to a value close to the inlet concentration. It further increased, but slowly, over the next stage (II) up to a few hours. The SO2 concentration was then virtually constant over the third stage (III) for many hours. In general, the difference between the inlet and outlet concentrations was less than 10% of the inlet value for long runs, except during the first few minutes, indicating that the reactor was performing as a differential reactor. The solid conversion was calculated by integration of the breakthrough curves. The inlet concentration of SO2 was corrected2,13 to take account of loss by oxidation to SO3. The degree of sulfation increased rapidly and nonlinearly with time at first, but increased slowly and approximately linearly in the later stages. The resulting calcium utilization curves were shown in an earlier paper (Figures 6 and 7).13 By using sintered samples with large intergrain pores (Figure 2), the disadvantages of unsintered particles were avoided. It is thus assumed that (1) sulfation occurred over the entire particle surface, resulting in a uniform product layer thickness; (2) there was sufficient free space around CaO grains to allow a fully developed product layer to form without pore blockage (primary pore size > 0.3 µm); and (3) the overall reaction was not controlled by external mass transfer given the low reaction rate due to the low surface area of the particles.1 Under these assumptions, the shrinking unreacted core model may be applied to the later stages of the reaction to obtain the product layer diffusion coefficient. However, the SO2 concentration varied significantly during the initial reaction, making the simple model inapplicable for obtaining reaction rate constants. The product layer diffusivity was obtained from eqs 2 and 3. Product Layer Diffusivity. Equation 2 assumes that the reaction rate is controlled by product layer diffusion over the entire process.9 However, the ratelimiting step may change as the reaction progresses, with chemical reaction control in the initial stages, followed by combined control by chemical reaction and product layer diffusion and finally product layer diffusion control.8 Combined control may occur when there is partial occupation of the CaO surface by product nuclei and crystals.13 Duo et al.8 demonstrated that a modified form of eq 2 can be applied to determine the product layer diffusivity using experimental data obtained in the late stages of the reaction:

t - t0 ) F(X) - F(X0) τs

(16)

F(X), a function of solid conversion, is equal to the right side of eq 2; X0 is the solid conversion at t0, the time after which the reaction becomes controlled by product layer diffusion. From eq 16, F(X) should vary linearly with time during any period when reaction 1 is controlled by product layer diffusion. This is consistent with our experimental results, shown in Figures 4 and 5 (fitted R2 ) 0.96-0.99). The slope of each of the lines represents 1/τs, from which Ds can be determined using eq 3. Despite the shorter durations of the experiments at the lower temperatures (130 min at 705 °C, 330 min at 750 °C), the results should be valid for determining the product layer diffusivity. Literature data1,2,12 suggest

Figure 4. Linear correlation by the unreacted core model under product layer diffusion control, i.e., eqs 2 and 16. The experimental calcium utilizations as functions of time were obtained at different temperatures with an inlet gas composition of 2250 ppm SO2, 3% vol O2, balance N2.

Figure 5. Linear correlation by unreacted core model for product layer diffusion control, eqs 2 and 16. Experimental data were obtained with 3% vol O2 and 825 °C at different SO2 concentrations.

that product layer diffusion becomes rate-limiting under similar conditions for reaction 1 after only a few minutes of reaction. In particular, less reaction time is required to form a “continuous” product layer at lower temperatures.13 Although a uniform distribution of grain size is not expected for the sintered sorbent particles, for simplicity, a single characteristic grain radius, determined by2

Rg )

3 FCaOSg

(17)

where Sg, the specific surface area of the particles, is used to replace Rp in eq 3. Figure 6 indicates that the dependence of Ds on temperature for an initial SO2 concentration of 2250 ppm can be represented by an equation of Arrhenius form. Fitting leads to

Ds ) 3.61 × 10-5 exp(-19800/T) m2/s

(18)

Ds values reported by Borgwardt and Bruce2 are shown in Figure 6 for comparison. These values, based on samples of small particles (1 µm) of calcine, are slightly

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Figure 6. Product layer diffusivity as a function of inverse temperature. Points are from experiments at 2250 ppm SO2. The line is the Arrhenius correlation for sample B. Samples A and B were prepared separately by sintering under the same conditions. A has a slightly larger specific surface area.

Figure 7. Product layer diffusivity as a function of inlet SO2 concentration. Points are from experiments at 825 °C; the line is a linear correlation.

higher than the present ones, while the independently determined activation energies are very similar. The agreement confirms that sintered large particles can be employed to study sulfation kinetics. The product layer diffusivity depends not only on temperature, but also on SO2 concentration. As shown in Figure 7, Ds increases linearly with increasing reciprocal inlet SO2 concentration. The following correlation, shown by the fitted straight line, describes the relationship at 825 °C for inlet SO2 concentrations of 225-2250 ppm:

Ds ) 3.17 × 10-10(1/CSO2) + 4.63 × 10-13 m2/s (19) Borgwardt and Bruce2 found Ds proportional to 1/(CSO2)0.38 for temperatures from 760 to 1075 °C. Spartnos and Vayenas24 observed that at lower temperatures, 300600 °C, Ds increased with SO2 concentration in the range 5000-20 000 ppm. Further increasing the concentration led to a decrease. However, the dependence of Ds on SO2 concentration has not been systematically investigated in the literature. Although eq 19 was based on only a single temperature (a typical one for FBC) and the linear relationship may not apply at other temperatures, our results confirm those of Borgwardt and

Bruce2 that Ds decreases with increasing inlet SO2 concentration. Note that Borgwardt and Bruce2 did not consider the product volume expansion in developing their correlations. While the SO2 concentration in most studies of sulfation kinetics ranged from 1500 to 5000 ppm,3,25 2-3% has also been used.1,24 From eq 19, Ds is more sensitive to CSO2 at lower than at higher concentrations. For example, the smallest value (4.6 × 10-13 m2/s) projected from eq 19 at infinitive CSO2 is not far from the value obtained at 2250 ppm (6 × 10-13 m2/s), shown in Figure 7. Although the production of SO2 in a boiler varies with fuel type, SO2 emissions must be reduced to a low level (typically below ∼100 ppm). Therefore, a considerable portion of the injected sorbent reacts with gas at low SO2 concentrations, suggesting that our results are of practical importance. Effect of Morphology of Product Layers. The temperature-dependence of the product layer diffusivity has been interpreted2 as reflecting thermally induced solid-state ionic diffusion. The ions and vacancies are more mobile at higher temperatures within the product layer so that Ds increases with temperature. In addition, the product layer characteristics vary with formation temperature,13 with a higher porosity at a higher temperature contributing to increased product layer diffusion. The concentration dependence of Ds can be explained in a similar manner. As shown in Table 2, the BET surface areas (Sg) of the sulfated samples are consistently larger than those of the corresponding sintered presulfated calcines (A and B). The difference reflects the surface area of the product layer. The surface area of a porous particle does not necessarily increase with increasing particle porosity. The porosity depends heavily on the size and number of larger pores, whereas the surface area is mainly determined by the smaller pores. As the product layer is composed of nonporous crystals13 of CaSO4, the larger the crystals, the larger the pores between them (i.e. more porous) and the less the surface area for a given conversion. Therefore, the porosity, and hence the product layer diffusivity, should be lower at a higher product layer specific surface area. Although the effect of temperature and conversion on Sg is unclear, Table 2 indicates a lower product layer surface area formed at 225 ppm SO2 than at 2250 ppm (B-8 vs B-4). A complication is that the conversion for B-8 is significantly lower than for B-4. Note that the conversion is determined by a combination of inlet SO2 concentration, reaction temperature, and time. Since calcine samples A and B were prepared under the same conditions, sulfated samples A-1 and B-8 may be comparable. With the same conversion, A-1 has a much higher surface area, indicating that a combination of lower temperature and higher concentration can lead to product layers of higher surface area and lower porosity. These results support our earlier observations13 that product layers formed at low concentrations and high temperatures are composed of larger crystals. The higher Ds at low concentrations are therefore attributed to larger pores in the product layers. Two additional experiments involving two-stage sulfation of sintered CaO samples further tested the effect of SO2 concentration on product layer properties. In the first, the sample was sulfated at 825 °C with 2250 ppm SO2 for 100 min and then sulfated by a gas containing 225 ppm SO2 under otherwise identical conditions for

Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5659 Table 2. Measured Sample Surface Areas sample type sample no. sulfation T (°C) CSO2 (ppm) conversion (%) Sg (m2/s)

sintered calcine A

0 0.39

sulfated sintered calcine

B

A-1

A-3

B-2

B-4

B-5

B-9

B-8

0 0.37

750 2250 2.4 0.63

900 2250 3.6 0.60

750 2250 4.8 0.56

825 2250 13.1 0.58

900 2250 20.3 0.59

825 340 10.8 0.50

825 225 2.4 0.41

Figure 8. Effect of order of exposure on degree of sulfation. Both tests were conducted at 825 °C and involved sintered calcine (Sample B) with 3% vol O2 in N2.

a further 105 min. In the second test, the experimental conditions and procedures were the same, except that the exposure order was reversed, i.e., the sample was first sulfated with 225 ppm SO2, then with 2250 ppm SO2. Although a lower conversion (3%) was reached at the end of the first stage in the second test, as shown in Figure 8, the overall degree of sulfation in the second test was significantly greater than in the first. This suggests either that the reaction at 225 ppm SO2 did not form a “continuous” product layer after 100 min or that the product layer in the second test is more porous and mechanically weaker. A conversion of 3% was reached at 36 min in the first test. The literature data all suggest that product layer diffusion is rate-limiting after such a long time of reaction 1 for the conditions of the first test. From these tests we conclude, supported by observations of the product crystals,13 that the smaller number of larger product nuclei and crystals formed in the first sulfation stage at the lower SO2 concentration helped develop favorable product layer characteristics for the second stage. This also explains why the product layer diffusivity increases with decreasing inlet SO2 concentration (Figure 7). Alteration of Diffusion Mechanism. It was reported by Duo et al.13 that the pore size along the crystal boundaries in the product layers was in the range 2030 Å. Therefore, even a continuous product layer was not impervious to gas molecules or large ions such as SO42- diffusing through the product layer to the CaO/ CaSO4 interface. For example, using a literature correlation,26 the Knudsen diffusivity through the product layer of sample A-3 with a measured porosity of 0.003 was estimated to be 10-9 to 10-10 m2/s, a few orders of magnitude larger than Ds shown in Figures 6 and 7. This suggests that the reaction in the late stages of sulfation did not proceed as rapidly as the inward gas diffusion through the product layer would allow. In addition, the activation energy for product layer diffu-

sion, 164 kJ/mol from eq 18, is much higher than required for gas diffusion through the layer pore matrix. We propose that the reaction is limited by the mechanical work8,13,14 and can no longer occur at the CaO/ CaSO4 interface when the chemical potential becomes insufficient to provide the mechanical work required to displace the product layer and make room at the interface for the increased solid volume, as shown in eqs 4 and 11. This theory would also exclude the possibility of inward ionic diffusion. An alternative mechanism would be outward ionic diffusion, as proposed by Hsia et al.25,27 It is thus suggested that the diffusion mechanism changes with solid conversion and that the reaction is controlled by outward ionic diffusion after a product layer is fully developed. The removal of the solid reactant from the unreacted core creates free spaces at the CaO/CaSO4 interface. With sufficient inward gas diffusion capability, the reaction can then occur in the resulting voids without performing mechanical work. It is therefore possible that sulfation takes place at both CaO/CaSO4 and CaSO4/gas interfaces, with the rate controlled by outward ionic diffusion. We call this mode of reaction the “mode of mechanical work control.” Fracture of Product Layers. When the reaction ceases at the CaO/CaSO4 interface, gaseous reactants are no longer consumed there. Hence, the concentrations of SO2 and O2 in the pores within the product layer become equal to the corresponding bulk gas contents. The superficial concentration at the interface is then

(Ci)s ) s(Ci)b

(20)

where i represents either SO2 or O2 and subscript b indicates the bulk. The porosity of the product layer, s, for sample A-3 (Table 2) was found to be 0.003 based on N2 adsorption. Since SO2 molecules are significantly larger than N2, the above value should overestimate the chemical potential for reaction at the CaO/CaSO4 interface. Shelby et al.28 reported Kc values from 0.25 to 0.91 MN m-3/2 for different glasses. If the fracture toughness for CaSO4 lies in the above range and Kc is taken at the midpoint, 0.58 MN m-3/2, then (h/Rc)m is estimated by eq 15 for 900 °C, 2250 ppm SO2, and 3% O2 to be 0.025, 0.035, 0.043, and 0.096 for a ) 10, 20, 30, and 150 Å, respectively; h/Rc calculated with a measured conversion of 3.6% (or h ) 73 nm) is 0.033 (Duo et al.13). The largest flaw size in the product layer (2a) is expected to be larger than the measured pore size of 20-30 Å. Therefore, it is predicted that this thin product layer can be fractured by the reaction of further sulfation. However, when the conversion reaches 10.8% (or h ) 233 nm), the value of h/Rc would become 0.099. Even if the flaw size (2a) were as large as 300 Å, (h/ Rc)m would still be smaller than h/Rc and the thick layer would be predicted to remain intact. Equation 15 helps identify the diffusion mechanism. If product layers can be fractured, the reaction rate should be determined by inward gas diffusion; otherwise, it is determined by outward ionic diffusion.

5660 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004

Figure 9. SEM images of product layers: (a) after initial sulfation and (b) after hydration at 250 °C for 15 min with steam partial pressure of 0.9 atm and resulfation of initially sulfated sample. Initial sulfation and resulfation were at 825 °C for 90 min with 2250 ppm SO2, 3% vol O2, balance N2.

Figure 10. BSE images of embedded and cross-sectioned particles: (a) after initial sulfation of unsintered calcine at 825 °C with 2250 ppm SO2, 3% vol O2, balance N2 to 38% conversion and (b) after hydration of the above sample at 250 °C for 15 min with a steam partial pressure of 0.9 atm.

One way to enhance breakdown of the product layer is to introduce other gases to react with partially sulfated CaO particles. A good example is steam reactivation,17,29-32 where Ca(OH)2 is formed at the CaO/CaSO4 interface as the product of CaO hydration. Fast inward diffusion of steam through the CaSO4 layer is expected, because water molecules are substantially smaller than SO2 molecules. For steam at high partial pressures, a high concentration of water vapor at the reaction interface makes it possible for a large number of Ca(OH)2 crystals to grow simultaneously. A similar estimate of (h/Rc)m can be made for hydration of partially sulfated sintered CaO particles, with the chemical free energy change based on the hydration reaction

0.067, 0.095, and 0.116 for a ) 10, 20, and 30 Å, respectively. Again, h/Rc calculated for the initial sulfation degree at 3.6% and 10.8% is 0.033 and 0.099, respectively. Consequently, h/Rc < (h/Rc)m for both the thinner product layer (even if 2a < 20 Å) and the thicker layer if 2a > 50 Å. This is very likely, given the heterogeneity of the product layer with a mean pore size of 20-30 Å. Note that we used 2a ) 300 Å to analyze fracture of the thick product layer by the reaction between CaO and SO2. These analyses suggest that hydration should be able to fracture the product layer, in agreement with the images in Figure 9. Product layer a appears to be smoother, consisting of flaky crystals of CaSO4 oriented horizontally on the surface of CaO grains, whereas layer b looks rougher, consisting of crystals of similar shape, but apparently oriented at a greater angle to the surface. As a result, layer b appears to be weaker, looser, and more porous than a, even though b was exposed to high sulfation temperature for a much longer time (more sintering) than layer a. The difference is clearly due to the hydration process. A possible mechanism is that during hydration individual CaSO4 crystals in layer a were partially or completely pushed off the CaO surface by Ca(OH)2 crystals formed between the CaO surface and CaSO4 crystals. The localized fracture pattern may be due to weak contacts between CaSO4 crystals in the product layer, indicated by the arrow in Figure 9b, where some CaSO4 crystals appear to have become detached. Figure 10 illustrates a BSE image of cross-sectioned calcined limestone particles after “full” sulfation at 825 °C and following steam hydration at 250 °C. The CaSO4 product layer is indicated by light regions, while unre-

CaO + H2O h Ca(OH)2

(21)

The density and molar weight are based on Ca(OH)2, rather than CaSO4, and the volume expansion ratio for conversion of CaO to Ca(OH)2 is used to calculate λ. Since H2O molecules are smaller than N2, the porosity measured by N2 adsorption likely underestimates the steam pressure at the reaction interface. To estimate the maximum hydration effect, PH2O can be equated to (PH2O)b. Figure 9 shows SEM images of two product layers. The one in part a was formed after initial sulfation of a sintered CaO sample at 825 °C for 90 min to a conversion of 3%, while part b portrays the same sample after hydration at 250 °C and resulfation at 825 °C for a further 90 min. For hydration at 250 °C with steam at a partial pressure of 0.9 atm, (h/Rc)m is estimated to be

Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5661

acted CaO core corresponds to dark regions. Although “fully” sulfated, the conversion of the limestone was only 38% with few cracks in layer a. Subsequent steam hydration resulted in marked fracturing of the product layers. Since calcined limestone is porous, steam reaction with CaO over a large surface area in the unreacted core also caused core fracture, as demonstrated in Figure 10b. Calcium utilization was more than 80% when this hydrated sample was resulfated. Mechanical work is believed to be responsible for the cracks that helped greatly improve the utilization. Laursen et al.17,31 observed three different sulfation patterns for calcined limestone particles: unreacted core, network, and uniformly sulfated. Steam hydration could reactivate samples of the first two of these patterns, but not the third. Equation 15 cannot be directly applied in the former two cases, because, for example, for the unreacted core pattern, as shown in Figure 10, the surface area in the porous CaO core is much larger than 4πRc2. During hydration, the number of Ca(OH)2 crystals formed inside the CaO core of the particle can be much larger than given by eq 14. However, eq 15 may be applied to the uniform sulfation case, where each intraparticle grain behaves like a nonporous particle (i.e. grain model). Laursen et al.17 observed 43-59% CaO conversions in uniformly sulfated samples. The value of h/Rc calculated for 43% conversion is 0.45, much larger than (h/Rc)m (0.067-0.42 for 2a ) 20-800 Å), explaining why steam hydration does not reactivate limestones that sulfate in this manner. Conclusions Sintered calcined limestone samples were sulfated for extended times in a differential reactor to study the reaction kinetics after a thick product layer formed. The reaction rate was controlled by product layer diffusion, except during the initial period. The product layer diffusivity (Ds) increased with temperature, but decreased with increasing inlet SO2 concentration. The characteristics of the product layer formed by crystallization processes can vary as the reaction proceeds. Consequently, Ds not only depends on current conditions, but also on previous conditions during product layer formation. The results are consistent with the crystallization and fracture model, and a hypothesis that the rate-limiting mechanism changes from inward gas diffusion control in the early stages of the reaction to outward ionic diffusion control after a continuous product layer has formed. This change is attributed to the requirement that the reaction do mechanical work to displace the product layer and make room for increased solid volume at the CaO/CaSO4 interface. On the basis of the crystallization and fracture model and the unreacted core model, a criterion is suggested to determine whether a product layer can be fractured. Application of the criterion indicates that a gas containing 2250 ppm SO2 at 900 °C is unable to fracture a product layer as thick as 233 nm. However, a product layer can be fractured by steam at a partial pressure of 1 bar at 250 °C. SEM images are consistent with these predictions. Acknowledgment Financial support from Alstom Power is gratefully acknowledged. Assistance from Yuchen Chen and Poupak Mehrani with the experiments is also greatly appreci-

ated. Wenli Duo and Karin Laursen express their gratitude to John Grace for his interest, persistent support, and high commitment to this work. Nomenclature a ) half-length of largest flaw in product layer, m (Ci)s ) superficial concentration of species i at reaction interface (Ci)b ) concentration of species i in the bulk phase CSO2 ) SO2 concentration, ppm Ds ) product layer diffusion coefficient of gas, m2/s F ) force imposed on product layer by a crystal growing from inside, N F(X) ) function of sulfation degree, equal to right-hand side of eq 2 ∆G° ) chemical free energy change at standard state, J/mol ∆Gc ) chemical free energy change, J/mol ∆G ′ ) total energy change including mechanical work, J h ) product layer thickness, m Kc ) fracture toughness, MN m-3/2 (MN ) 106 Newtons) MA ) molar weight of substance A, kg/mol N ) total number of crystals growing at reaction interface Nc ) minimum number of growing crystals to cause product layer fracture Nm ) maximum number of growing crystals at reaction interface p ) pressure in imaginary pressure vessel, N/m2 (PA)b ) partial pressure of gaseous species A in the bulk phase, Pa PA ) partial pressure of gaseous species A at reaction interface, Pa R ) gas constant, J/mol K Rp ) radius of particle, m r ) radius of spherical product nuclei or growing crystal, m Rc ) radius of unreacted core, m Rg ) initial radius of grains, m S ) tensile stress in product layer, N/m2 Sg ) specific surface area, m2/g T ) temperature, K t ) reaction time, s t0 ) given time, s W ′ ) mechanical work, J X ) conversion of calcium or degree of sulfation X0 ) degree of sulfation at t ) t0 Greek Letters R ) volume expansion ratio δ ) product layer displacement, m s ) porosity of product layer σ ) specific surface energy of solid, J/m2 λ ) [2(1 - 1/R)]1/3, constant FA ) density of material A, kg/m3 τs ) parameter defined by eq 3, s Abbreviations BSE ) back-scattered electrons CFM ) crystallization and fracture model SEM ) scanning electron microscopy

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Received for review November 19, 2003 Revised manuscript received April 7, 2004 Accepted April 16, 2004 IE030837D