Direct Sulfidation of Half-Calcined Dolomite under Pressurized

4132

Ind. Eng. Chem. Res. 2004, 43, 4132-4139

Direct Sulfidation of Half-Calcined Dolomite under Pressurized Conditions J. Ada´ nez,* A. Abad, L. F. de Diego, F. Garcı´a-Labiano, and P. Gaya´ n Instituto de Carboquı´mica (CSIC), Department of Energy and Environment, Miguel Luesma Casta´ n 4, Zaragoza 50015, Spain

There are pressurized gasification systems in which the desulfurization process is carried out with Ca-based sorbents at noncalcining conditions. At these conditions, the H2S reacts directly with CaCO3. The direct sulfidation reaction of a half-calcined dolomite was analyzed under atmospheric and pressurized conditions (up to 1.0 MPa), temperatures between 923 and 1123 K, and with sorbent particle sizes between 0.4 and 2.0 mm. The half-calcined dolomite reacts quickly up to high conversions (>85%), and it is an effective sorbent at noncalcining conditions. The sulfidation experiments were performed in an atmospheric thermogravimetric analyzer and a pressurized differential reactor. The effects of the reaction pressure and temperature, sorbent particle size, and H2S concentration were analyzed. The changing grain size model was used to predict the experimental results and to determine the kinetic parameters of the direct sulfidation reaction. The resistances to the global reaction considered in the model were the pore diffusion, diffusion through product layer, and chemical reaction. A reaction order on H2S of 1 was obtained. The values of the activation energies were 267 kJ mol-1 for the chemical reaction rate constant, kS, and 25 kJ mol-1 for the product layer diffusion coefficient, DS. The sulfidation rate of the sorbents increased with total pressure, but less than expected. To predict the experimental data, an effective gas diffusivity in the pores and an effective diffusivity in the product layer varying with total pressure was used. In this way, good agreement between measured and predicted conversion-time curves was observed for any total pressure, temperature, particle size, and H2S concentration analyzed. 1. Introduction In the integration gasification combined cycle (IGCC) process, coal is gasified to produce a synthesis gas that is fired in a gas turbine for power generation. In the reducing atmosphere of a gasifier the sulfur contained in coal is mainly evolved to H2S, which must be removed prior to combustion of the coal gas to prevent damage to turbine equipment and infringement of emissions legislation. To improve the efficiency of energy production and to reduce the volume of processing vessels, the cleanup of the coal gas can be carried out in a hightemperature and high-pressure process using Ca-based sorbents such as limestone or dolomite. Limestone is primarily CaCO3 and dolomite is CaCO3‚ MgCO3. At the conditions existing in the gas cleaning systems, the MgCO3 always decomposes into MgO, but MgO does not react with H2S. However, depending on the temperature and the CO2 partial pressure in the system the CaCO3 can decompose into CaO and CO2 or remain as CaCO3. The calcination temperature of CaCO3 at conditions corresponding to some gasification processes (for example in the high-temperature Winkler, HTW, fluidized bed gasifier, or in the DOW entrained flow gasifier) can be as high as 1250-1300 K.1 If the temperature of the desulfurization process is lower than this calcination temperature, the CaCO3 does not calcine. The reactions taking place at these noncalcined conditions are the * To whom correspondence should be adddressed. Tel.: 34-976733977. Fax: 34-976733318. E-mail: jadanez@ carbon.icb.csic.es.

direct sulfidation of the limestone or the half-calcined dolomite

CaCO3 + H2S a CaS + CO2 + H2O

(1)

CaCO3‚MgO + H2S a CaS‚MgO + CO2 + H2O

(2)

The thermodynamic equilibrium2 of these reactions is given by the following equation:

Keq )

PH2OPCO2 PH2S

(

13212 T

) 4.66 ‚1012 exp -

)

(3)

The ultimate level to which sulfur can be removed depends on the equilibrium properties of the gas mixture (gas composition, temperature, and total pressure). The H2S concentration at the equilibrium increases for lower temperatures and higher total pressures. The resulting CaS is a hazardous product and must be stabilized before disposal. There are different methods to solve this problem. The most typical alternative is to oxidize CaS to produce the stable CaSO4, although other regenerative processes have been proposed to reduce the sorbent requirements as well as waste handling.3 The direct sulfidation of Ca-based sorbents has been studied by several authors. The limestones exhibited a high initial reaction rate but it then quickly fell off, reaching very low sulfidation conversions, ∼3-15%, at any operating pressure.4-11 The half-calcined dolomite was significantly more efficient in capturing H2S than uncalcined limestone and exhibited a great reactivity

10.1021/ie030804y CCC: $27.50 © 2004 American Chemical Society Published on Web 06/10/2004

Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004 4133 Table 1. Chemical Analysis and Physical Characteristics of the Dolomite “Sierra De Arcos” chemical analysis composition (wt %) CaCO3 MgCO3 others physical characteristics Fr (kg m-3)a fV,CaCO3(-)a Sg (m2 g-1)a  (-)a a

Table 2. Gas-Phase Compositions (vol %) Used in the TGA Experiments 873 K 898 K 923 K 948 K 973 K 1023 K 1073 K 1123 K

52.5 40.5 7.0 2915 0.72 9.6 0.35

half-calcined.

at both at atmospheric pressure4,8,12 and higher pressures.5,11,13 According to Fenouil and Lynn,4 and Yrjas et al.,5 the maximum conversion obtained in the direct sulfidation of half-calcined dolomite was a function of the MgCO3/CaCO3 molar ratio. Therefore, dolomite with a Mg/Ca molar ratio more than one was the only sorbent that could be completely sulfided. To enable the design of a reactor in which coal gas is desulfurized with Ca-based sorbents at medium pressures under noncalcining conditions, the reaction kinetic and the effect of total pressure on the direct sulfidation of the sorbents must be known. There are few works in the literature about kinetics related with the direct sulfidation of half-calcined dolomite. Fenouil and Lynn4 reported a value of 163 kJ mol-1 for the activation energy of the direct sulfidation reaction at atmospheric pressure, and Lin et al.14 found a value of 180 kJ mol-1 at 1 MPa. However, Yrjas et al.13 found values for the activation energy as high as 300-400 kJ mol-1 for the direct sulfidation of half-calcined dolomite at 2 MPa. It is also necessary to know the effect of the total pressure on the direct sulfidation of Ca-based sorbents. Lin et al.15 found that the higher the total pressure, the lower the reactivity of limestone, although they concluded that more studies had to be done to know the reasons. Agnihotri et al.10 found that the pressure had a negative effect on the sulfidation reaction of uncalcined limestone. They associated this fact with the increase in the number of gaseous moles during the reaction. However, several authors have found a similar effect of pressure on different noncatalytic gas-solid reactions even when there was not variation in the number of moles.10,15-20 There is not until now a clear reason to explain the effect of total pressure on the different reactions. The objective of this work was to analyze the direct sulfidation reaction of a half-calcined dolomite. The effects of several variables such as total pressure, reaction temperature, H2S partial pressure, and particle size were investigated. The effect of the total pressure on the reaction was analyzed with special attention because the desulfurization process take place at medium pressures. The changing grain size model was used to obtain the kinetic parameters of the sorbent and to predict the experimental results. 2. Experimental Section 2.1. Materials. A dolomite, Sierra de Arcos, was used in four narrow particle size intervals: +0.4-0.63, +0.81.0, +1.25-1.6, and +1.6-2.0 mm. The chemical analyses and physical characteristics of this sorbent are shown in Table 1. The MgCO3/CaCO3 molar ratio of this dolomite was 0.93. All the experiments were carried out with half-calcined dolomite.

CO2 CO H2 H2O H2S

83.0 8.5 1.5 5.6

82.5 8.6 1.4 6.2

82.0 8.6 1.4 6.7

81.5 81.0 8.6 8.7 1.4 1.3 7.2 7.7 0.5-2.0

80.0 8.8 1.2 8.5

79.0 8.9 1.1 9.2

78.0 9.0 1.0 9.6

2.2. Experimental Facilities. The apparatus used for the experimental work were a thermogravimetric analyzer (TGA), Setaram TGC-85 type, and a differential reactor. The TGA was used for the atmospheric pressure experiments and the differential reactor was used for the experiments at higher pressures. (a) TGA Setaram TGC-85. The thermobalance consisted of a quartz tube (15-mm i.d.) placed in an oven which can be operated at temperatures up to 1300 K. The sample holder, to reduce mass transfer resistance around the sorbent sample and to prevent corrosion, was a wire mesh platinum basket (5-mm diam and 8-mm height). The temperature and the sample weight were continuously measured and recorded in a computer. Conversion versus time evolution was obtained from the corresponding weight versus time data. The reacting gas mixture (5.6 cm3 s-1 STP) simulated the coal-gas composition and contained H2S, CO2, CO, H2, H2O, and N2 in the desired concentrations. The H2S concentration was usually 1 vol %, although to investigate the influence of H2S on the sulfidation reaction, different H2S partial pressures between 0.5 and 2.0 vol % were used. The direct sulfidation reaction was studied at temperatures between 923 and 1123 K. The inlet gas mixture, shown in Table 2, corresponded to the equilibrium composition at the reacting temperature. The CO2 partial pressure was enough to prevent CaCO3 calcination in all cases. For each run, between 10 and 15 mg of sorbent was loaded in the basket. Dolomite samples were introduced into the furnace at room temperature and heated (20 K min-1) in pure CO2 to 1073 K. This temperature was maintained constant during 5 min to allow the MgCO3 to calcine. The temperature was then changed to the specified value and the reaction gas mixture was introduced for the sulfidation reaction. Initially, to establish whether external film mass transfer and/or interparticle diffusion were affecting the reaction rate, the gas flow rate and the sample weight were changed in the following intervals: gas flow 4-8 cm3 s-1 STP and sample weight 4-20 mg. No differences were observed in the results obtained. Therefore, the gas flow rate and the sample weight used in this work were enough to avoid the influence of these resistances. (b) Differential Reactor. The reactor consisted of a tube (27-mm i.d., 700-mm length) of Khantal to avoid corrosion problems. The reactor was heated by an external furnace. The sample was loaded over a layer of quartz wool and the temperature was measured by a thermocouple located just above the sample. The reacting gas was composed by 0.5 vol. % of H2S, and a mixture of CO2, CO, H2, H2O, and N2 in the desired concentrations. Experiments with different gas flows (110-300 cm3 s-1 STP) and sample weights (0.3-1.5 g) were first carried out to find the optimum operating conditions. The limits of the operating conditions to avoid the external mass transfer resistance and to be considered as a differential reactor were a minimum gas flow of

4134 Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004 Table 3. Gas-Phase Compositions (vol %) Used in the Differential Reactor Experiments 0.1 MPa CO2 CO H2 H2O H2S

0.5 and 1 MPa

923 K

973 K

1023 K

1073 K

1123 K

923 K

973 K

1023 K

1073 K

1123 K

5.0 1.5 4.7 7.8

7.7 2.3 4.0 8.5

10.0 2.9 3.4 9.1

26.8 4.4 1.9 10.7

81.5 8.9 1.4 7.7

1.4 0.6 5.7 6.8

1.3 0.7 5.6 6.9

4.4 1.9 4.4 8.1

7.3 2.7 3.5 9.0

7.1 2.9 3.4 9.2

0.5

110 cm3 s-1 (STP) and up to 1.3 g of sample. The operating conditions finally used were 220 cm3 s-1 (STP) of gas flow and 1 g of sample. The sulfidation reaction was carried out at different temperatures (923-1123 K), pressures (0.1, 0.5, and 1.0 MPa) and particle sizes (+0.4-0.63, +0.8-1.0, +1.251.6, and +1.6-2.0 mm). Table 3 shows the gas composition as a function of the temperature and total pressure. These compositions were selected to avoid sorbent calcination and to minimize COS formation ( 0

(5)

∂C )0 ∂R

at R ) 0 and t > 0

(6)

2. An expression for the local reaction rate in terms of the gas concentration in the pores:

(r)s )

ksCS0(r2/r0)2 ksr2 r2 1+ 1Ds r1

( )

(7)

with r0 ) r1 ) r2 at t ) 0. This expression takes into account the diffusion in the product layer.22 3. An equation for the movement of reaction interface. The grain size, r1, and the unreacted core size, r2, at each time and position inside the particle, are calculated with the equations:

dr2 ksCVM,CaCO3‚MgO ) ksr2 r2 dt 1+ 1Ds r1

( )

r13 ) Zs r03 + (1 - Zs) r23

(8)

(9)

where Zs is defined as

Zs )

VM,CaS‚MgO VM,CaCO3‚MgO

(10)

The initial radius of the grain, r0, can be derived from the specific surface area, Sg, from the relationship

r0 )

3 SgFr

(11)

The initial reaction surface, S0, is calculated as

S0 ) SgFr (1 - 0)fV,CaCO3

(12)

The effective diffusivity was calculated as a function of the particle porosity and a combination of the molecular and Kundsen diffusivities

De ) [DH2S-1 + DK-1]-1p2

(13)

The porosity changes inside the particle with sulfidation conversion were calculated using the following equation:23

p(R,t) ) o - (Zs - 1)(1 - o)X(R,t)

(14)

Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004 4135

Figure 1. Effect of temperature on the direct sulfidation of half-calcined dolomite (0.1 MPa; 1% vol. H2S), T (K): 9 923; ] 948; 2 973; O 1023; b 1073; 4 1123; s model predictions.

The local conversion at each time and position inside the particle was calculated with the equation

X(R,t) ) 1 - (r2(R,t)/r0)3

(15)

The mean conversion at each time in the whole particle was calculated by integration of local conversions

∫0R

0

X(t) )

4π R2X(R,t)dR 4 πR 3 3 0

(16)

4. Results 4.1. Kinetic Determination at Atmospheric Pressure. An analysis of the direct sulfidation of the halfcalcined dolomite was first carried out in the TGA at atmospheric pressure. Figure 1 shows the effect of temperature with three different particle sizes. The sulfidation rate increased with temperature, although this increase was lower at the highest temperatures. Moreover, for a same temperature, the sulfidation rate decreased with increasing particle size due to a more important effect of the gas pore diffusion. A high conversion of the dolomite was reached in all cases. These results agree with those of Yrjas et al.,5 who found proportionality between the final conversion and the MgCO3/CaCO3 molar ratio for half-calcined dolomites. They explained this behavior by the fact that natural dolomites consist of a mixture of dolomite particles (Mg/Ca molar ratio equal to 1) and limestone particles (CaCO3). In the beginning of the reaction, the sulfidation was mainly due to the dolomite particles and when all dolomite particles were sulfided the reaction continued with the limestone particles which reacted very slowly. In the Sierra de Arcos dolomite, the Mg/Ca molar ratio was 0.93, and conversions about 95% were reached. The kinetic parameters corresponding to the chemical reaction, ks, and product layer diffusivity, Ds, of the CGS model were obtained from the experimental data obtained at different temperatures and particle sizes, as shown in Figure 1. It must be remarked that the same values of the parameters were obtained for the different particle sizes. An Arrhenius type dependence with the temperature was assumed for both parameters

ks ) ks,0 exp(-Es/RgT)

(17)

Ds ) Ds,0 exp(- E0/RgT)

(18)

Figure 2. Arrhenius plot for the chemical reaction rate constant and the product layer diffusion coefficient. 0 chemical reaction rate constant, ks; ] product layer diffusion coefficient, Ds. Table 4. Kinetic Parameters Obtained at Different Total Pressures for the Direct Sulfidation of the Half-Calcined Dolomite P (MPa)

ks,o (m s-1)

Es (kJ mol-1)

Ds,o (m2 s-1)

E0 (kJ mol-1)

CGSM with eqs 19 and 20; Valid for dp ) 0.8-1.0 mm 0.1a 2.2 × 109 267 ( 5 6.8 × 10-12 25 ( 1 0.5 4.3 × 108 267 ( 5 3.0 × 10-12 25 ( 1 1.0 2.2 × 108 267 ( 5 2.2 × 10-12 25 ( 1 CGSM with eqs 21 and 22; Valid for all PT, T, and dp 0.1a 2.2 × 109 267 ( 5 6.8 × 10-12 25 ( 1 0.5 2.2 × 109 267 ( 5 3.0 × 10-12 25 ( 1 1.0 2.2 × 109 267 ( 5 2.2 × 10-12 25 ( 1 a

Both in TGA and differential reactor.

Figure 2 shows the Arrhenius dependences, and Table 4 shows the values of the kinetic parameters obtained in TGA at atmospheric pressure. The activation energies obtained for ks and Ds were 267 and 25, respectively. Fenouil and Lynn7 also obtained a value of 267 kJ mol-1 for the direct sulfidation of limestone at temperatures above 973 K, which would indicate a kinetic control of the reaction. The values of activation energy reported by other authors4,6,24 for the direct sulfidation reaction normally varied between 155 and 176 kJ mol-1, which can be due to a mixed control of chemical reaction and product layer diffusivity. Figure 1 shows the model predictions with the kinetic parameters here-determined, which represent a good agreement with the experimental data. Figure 3 shows the effect of the particle size on the direct sulfidation of the half-calcined dolomite, which varied with temperature. The sulfidation reaction was almost independent of particle size at 923 K, but it was dependent at higher temperatures. This was due to the

4136 Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004

Figure 3. Effect of particle size on the direct sulfidation of halfcalcined dolomite (0.1 MPa) dp (mm): 9 +0.4-0.63, [ +0.8-1.0, 2 +1.25-1.6; s model predictions.

Figure 4. Effect of H2S concentration on the direct sulfidation of half-calcined dolomite at 923 K (filled symbols) and 1073 K (open symbols) (0.1 MPa; +0.8-1.0 mm H2S (vol %)): 0 0.5, ] 1.0, 4 1.5, O 2.0; s model predictions.

relative influence of the different resistances affecting the sulfidation reaction. At low temperatures, the reaction was controlled by the chemical reaction and the product layer diffusion, whereas at higher temperatures the pore gas diffusion was also important. This effect was similar to that found in a previous work on the sulfidation of a full-calcined dolomite.22 To adequately predict the experimental results, it was necessary to consider several resistances to the global reaction including pore diffusion, product layer diffusion, and chemical reaction. The model predictions shown in Figure 3 corroborated the validity of the model within the range of temperatures and particle sizes used in this work. The effect of the H2S concentration on the direct sulfidation of the dolomite was also investigated. Figure 4 shows this effect at two different temperatures, together with the model predictions. The sulfidation rate increased with increasing H2S in all cases. It can be observed that the model with a reaction order of 1 for the chemical reaction and the kinetic parameters shown in Table 4 was valid to predict the experimental data. Fenouil and Lynn7 found that the apparent reaction order of the direct sulfidation of limestones decreased from 1 to 0.5 when the temperature increased. They suggested that at low temperatures the reaction was controlled by the chemical reaction, whereas higher temperatures dominated the product layer diffusion. The model used in this work took into account both resistances, and the reaction order was associated with the chemical reaction, which was maintained constant and equal to 1 at all the temperatures. 4.2. Experiments at Pressures above 0.1 MPa. The experiments to analyze the effect of the pressure

Figure 5. Effect of total pressure on the direct sulfidation of halfcalcined dolomite (differential reactor, +0.8-1.0 mm; 0.5 vol % H2S); pressure (MPa): 9 0.1, [ 0.5, 2 1.0; - - - model predictions with kinetic parameters determined at 0.1 MPa; s model predictions with eqs 21 and 22.

on the direct sulfidation of the half-calcined dolomite were carried out in a differential reactor. Experiments with a 0.5 vol % in H2S and three different pressures (0.1, 0.5, and 1 MPa) were used. Figure 5 shows the results obtained at 923 and 1073 K. An increase in the total pressure always produced an increase in the reaction rate, because of the higher partial pressure of H2S in the reacting gases. However, this increase was not as high as would be expected from the CGS model predictions when using the kinetic parameters obtained at atmospheric pressure. At 923 K the model predictions were similar to those experimentally obtained but those were clearly over-predicted by the model at 1073 K. It must be considered that at high temperature, the pore diffusion is an important resistance to the reaction. Therefore, the model proposed together with the kinetic parameters obtained at 0.1 MPa was not valid to predict the pressurized data on direct sulfidation of dolomite. There are in the literature different explanations about the effect of total pressure on several gas-solid reactions. In the CaCO3 calcination, Dennis and Hayhurst16 assumed that there was a “spurious” partial pressure of CO2 at equilibrium. The calcination is a reversible reaction, and they supposed that the equilibrium CO2 pressure at pressures above the atmospheric was lower than the given by the thermodynamic equilibrium. In this way, the reaction rate predicted by the model decreased with an increase of total pressure. In the case of the direct sulfidation reaction, the so-called “spurious” H2S partial pressure should have had a very strong dependency with total pressure, which was difficult to believe. In the sulfidation of calcined limestone, Matsukata et al.17 developed an empirical model with the apparent kinetic rate constant varying with total pressure and conversion. Qiu and Lindqvist18 used an unreacted shrinking core model to describe the sulfation reaction and calculated the kinetic rate constant and the effective diffusivity of SO2 through the product layer at different pressures. Both parameters decreased with rising total pressure. Although there was not a theoretical explanation for the variation of the kinetic parameters with total pressure, this idea was used to predict the experimental data on direct sulfidation. Figure 6 shows the experimental results obtained at three pressures (0.1, 0.5, and 1 MPa) and different temperatures from 923 to 1123 K. The sulfidation rate increased with increasing temperature, although this increase was lower for the highest temperatures, similarly to that found with the experiments carried at 0.1 MPa. The maximum conversion obtained at atmospheric pressure was about 95%.

Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004 4137

Figure 6. Effect of temperature on the direct sulfidation of half-calcined dolomite (1.0 MPa, +0.8-1.0 mm; 0.5 vol % H2S); T (K): 9 923, ] 973, 2 1023, O 1073; b 1123; s model predictions with eqs 21 and 22.

However, this value decreased to about 85% when the sulfidation took place at 0.5 and 1.0 MPa, because the reaction rate for higher conversions was extremely slow, as it can be observed in Figures 5 and 6. The reasons for this behavior were not clear and a more detailed analysis will be necessary. Table 4 shows the kinetic parameters (kinetic constant and product layer diffusivity) as a function of pressure obtained by fitting the experimental data with the CGS model. An Arrhenius type dependence with temperature was assumed for both parameters. The preexponential factor decreased with increasing total pressure although the activation energy was the same for any total pressure. It must be remarked that the values of the preexponential factor and activation energy obtained at 0.1 MPa in the differential reactor experiments were the same as those determined in the atmospheric TGA with a H2S concentration of 1 vol %. The kinetic parameters could be fitted to the following expressions

() ()

ks,P ) ks,P0

P0 PT

Ds,P ) Ds,P0

P0 PT

(19)

0.5

(20)

where ks,P0 and Ds,P0 were the kinetic parameters obtained at the reference pressure P0, in this case 0.1 MPa. In this way, it was possible to predict the direct sulfidation data with a particle size of +0.8-1.0 mm at different temperatures and pressures. Finally, the effect of the particle size on the direct sulfidation of dolomite was investigated. Figure 7 shows the conversion versus time curves obtained at 1123 K and 1 MPa with three different particle sizes. The sulfidation rate decreased with increasing particle size because of the higher resistance to pore gas diffusion. This figure also shows the model predictions with eqs 19 and 20 and the kinetic parameters previously determined with a particle size of +0.8-1.0 mm. The model clearly under-predicted the experimental results for the smallest particles (+0.4-0.63 mm) and overpredicted the results for the highest particles (+1.62.0 mm). Therefore, important differences can be found by using eqs 19 and 20, as used by several authors, to predict the effect of pressure with other particle sizes different from those used for the kinetic determination. These deviations had not been detected with the experiments carried out at atmospheric pressure. It was

Figure 7. Effect of particle size on the direct sulfidation of halfcalcined dolomite (1.0 MPa, 1123 K), dp (mm): 9 +0.4-0.63, [ +0.8-1.0, 2 +1.6-2.0; - - - model predictions with eqs 19 and 20; s model predictions with eqs 21 and 22.

concluded that the gas diffusion resistance in the porous system of the dolomite should be higher than that given by eq 13 when working at pressures above atmospheric. These results agree with those found by Matsukata et al.17 on the sulfidation reaction of calcined Ca-based sorbents and by Qiu et al.19 on the oxidation of CaS, who explained the effect of total pressure by the inhibition of the gas diffusion in the porous system of the particles. Garcı´a-Labiano et al.,20 in their work about sorbent calcination, proposed an equation where the molecular diffusivity, and so the effective diffusivity in the pores, was more affected by the total pressure than that given by the Fuller et al.25 equation. To determine the effect of total pressure on the different resistances to the global reaction, the kinetic parameters ks and Ds were determined at each total pressure by fitting the experimental data at all temperatures and particle sizes (see Table 4). To consider the inhibition of the pore diffusivity, the following equation was proposed:

De,P ) De

() P0 PT

0.4

(21)

where De was the effective pore diffusivity given by eq 13 at pressure PT. The chemical reaction rate constant was always the same but the diffusional parameters decreased with total pressure. This negative effect on total pressure followed the next dependence:

()

Ds,P ) Ds,P0

P0 PT

0.5

(22)

where Ds,P0 was the product layer diffusivity obtained

4138 Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004

at the reference pressure, P0, in this case 0.1 MPa. It was found that the product layer diffusivity was affected by total pressure. It must be considered that this is a solid-state process that depends on the internal structure of the material.26 Agnihotri et al.27 found that in sulfidation of Ca-based sorbents sulfidation there is an inward diffusion of S2- ion through the CaS product layer. Therefore, the effect of PT on the Ds found in this work could be due to differences in the product layer structure formed at different pressures. In fact, Harvey et al.28 found different CaS structures in the sulfidation of sorbents at 0.1 and 2.1 MPa. They concluded that there is little or no difference in the crystal size of the CaS formed, but at high pressure the crystals formed tended to be blocky (cubic), whereas at low pressure they were more rounded. A more thorough analysis would be necessary to confirm this behavior at molecular scale. However, from the practical viewpoint, some values of Ds are necessary to predict the experimental results on direct sulfidation of sorbents, and these are affected by total pressure. In this sense, the parameters determined in this work are valid to predict the direct sulfidation of half-calcined dolomite at different total pressures (0.1-1 MPa), temperatures (923-1123 K), and particle sizes (0.4-2.0 mm), as can be observed in figures 5 to 7. 5. Conclusions The direct sulfidation reaction of a half-calcined dolomite has been investigated. The effect of temperature, particle size, and H2S concentration has been analyzed at three different pressures: 0.1, 0.5, and 1 MPa. The half-calcined dolomite reacts quickly up to high conversions (>85%), and it is an effective sorbent at noncalcining conditions. A changing grain size model has been used to determine the kinetic parameters of the sulfidation reaction. To predict the experimental data in a wide range of operating conditions, the model must include several resistances, including pore diffusion, the product layer diffusion, and the chemical reaction. The values of the activation energies were 267 kJ mol-1 for the chemical reaction rate constant, kS, and 25 kJ mol-1 for the product layer diffusion coefficient, DS. At temperatures above 973 K, the pore diffusion resistance is important and an increase in the particle size produced a decrease in the reaction rate. The pressure had an important effect on the direct sulfidation reaction. An increase in total pressure produced a higher sulfidation rate because of the higher H2S concentration in the reacting gases. However, this increase was lower than that predicted by the model when using the kinetic parameters obtained at 0.1 MPa. Therefore, an additional negative effect of pressure must exist, which was in fair agreement with the findings of several authors in different gas-solid reactions. In this work, the pore diffusivity and the product layer diffusivity were detected to be the resistances to the global reaction affected by total pressure. This negative effect on total pressure followed the next dependence:

De,P )

(

) () ()

1 1 + DH 2S DK

Ds,P ) Ds,P0

-1

2

P0 PT

0.5

P0 PT

0.4

Therefore, the changing grain size model with the kinetic parameters obtained at 0.1 MPa, and the previous equations to consider the effect of total pressure, and a reaction order on H2S of 1, were valid to predict the direct sulfidation of half-calcined dolomite in a wide range of temperature, pressure, and particle size. Acknowledgment This research was carried out with financial support from the Comisio´n Interministerial de Ciencia y Tecnologı´a (Project AMB98-0883). Nomenclature C ) H2S local concentration, mol m-3 C0 ) bulk H2S concentration, mol m-3 dp ) particle diameter, m De ) effective diffusivity of H2S within the sorbent particles, m2 s-1 De,P ) effective diffusivity of H2S within the sorbent particles at pressure P, m2 s-1 DH2S ) molecular diffusion coefficient of H2S, m2 s-1 DK ) Kundsen diffusion coefficient, m2 s-1 Ds ) product layer diffusion coefficient, m2 s-1 Ds,0 ) preexponential factor of the product layer diffusion coefficient, m2 s-1 Ds,P ) product layer diffusion coefficient at pressure P, m2 s-1 Ds,P0 ) product layer diffusion coefficient at atmospheric pressure, m2 s-1 E0 ) activation energy of the product layer diffusion coefficient, J mol-1 Es ) activation energy of the chemical reaction rate constant, J mol-1 fV,CaCO3 ) volume fraction of CaCO3 in the sorbent ks ) chemical reaction rate constant, m s-1 ks,0 ) preexponential factor of the chemical reaction rate constant, m s-1 ks,P ) chemical reaction rate constant at pressure P, m s-1 ks,P0 ) chemical reaction rate constant at atmospheric pressure, m s-1 Keq ) equilibrium constant for the direct sulfidation reaction Pi ) partial pressure of gas i, Pa PT ) total pressure, Pa P0 ) reference pressure, Pa r0 ) initial grain radius, m r1 ) grain radius after some reaction, m r2 ) radius of unreacted grain core, m R ) radial coordinate within the particle, m R0 ) particle radius, m Rg ) ideal gas constant, J mol-1 K-1 (-r)s ) reaction rate, mol m-3 s-1 Sg ) specific surface area, m2 g-1 S0 ) initial reaction surface, m2 m-3 t ) time, s T ) temperature, K VM,i ) molar volume of the solid i, cm3 mol-1 X ) sulfidation conversion Zs ) expansion ratio Greek letters 0 ) initial particle porosity p ) particle porosity Fr ) true solid density, kg m-3

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Resubmitted for review March 3, 2004 Revised manuscript received March 3, 2004 Accepted April 30, 2004 IE030804Y