Effect of Pressure on the Sulfidation of Calcined Calcium-Based

Energy & Fuels 2004, 18, 761-769

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Effect of Pressure on the Sulfidation of Calcined Calcium-Based Sorbents F. Garcıá-Labiano,* J. Adańez, A. Abad, L. F. de Diego, and P. Gayań Instituto de Carboquı´mica (CSIC), Department of Energy and Environment, Miguel Luesma Casta´ n 4, 50015 Zaragoza, Spain Received October 13, 2003. Revised Manuscript Received February 16, 2004

The sulfidation process for two calcined limestones and a fully calcined dolomite was analyzed under pressurized conditions (up to 1.0 MPa), at temperatures of 723-1173 K, and with sorbent particle sizes of 0.25-2.0 mm. The sulfidation experiments were performed in a pressurized thermogravimetric analyzer and in a pressurized differential reactor. The effects of total pressure, temperature, sorbent particle size, and H2S concentration were analyzed. The sulfidation rate of the sorbents increased with total pressure when the volume fraction of H2S was constant. However, the sulfidation rate decreased with total pressure when the partial pressure of H2S was constant. A reaction order on H2S of 1 was obtained at the different total pressures that were analyzed. In addition, the rate of H2S retention decreased as the sorbent particle size increased. The changing grain-size model, with the effective gas diffusivity in the pores and the effective diffusivity in the product layer varying with the total pressure, was used to obtain the kinetic parameters of the sulfidation reaction and to predict the experimental data. The values of the activation energies varied for the different calcium-based sorbents, from 29 kJ mol-1 to 56 kJ mol-1 for the chemical reaction rate constant (ks) and from 154 kJ mol-1 to 217 kJ mol-1 for the product layer diffusion coefficient (Ds). A good agreement between measured and predicted conversion versus time curves was observed for any total pressure, temperature, particle size, and H2S concentration analyzed.

1. Introduction The integrated gasification combined cycle (IGCC) process that is used for power generation has proven itself to be a technology with high efficiency and low pollutants emissions. In this process, coal is gasified to produce a synthesis gas that is fired in a gas turbine for power generation. The sulfur contained in coal reacts in the reducing atmosphere of a gasifier, forming mainly H2S. This gaseous contaminant must be removed prior to combustion of the coal gas, either inside the furnace or in the gas clean-up system, to prevent damage to turbine equipment and to comply with the emissions legislation. High temperatures and high-pressure gas clean-up systems improve the efficiency of energy production and reduce the volume of the processing vessels. Calcium-based sorbents (limestone or dolomite) are normally used in high-temperature coal gas desulfurization processes. The level to which sulfur can be removed is dependent on the equilibrium properties of the gas mixture (gas composition and temperature). To enable the design of a reactor in which coal gas is desulfurized with calcium-based sorbents, the sulfidation kinetics must be known. Limestone is primarily composed of CaCO3 and dolomite is mainly CaCO3‚MgCO3. On heating, the MgCO3 decomposes to MgO and CO2. The CaCO3 can * Author to whom correspondence should be addressed. E-mail address: [email protected].

decompose to CaO and CO2 or remain as CaCO3, depending on the CO2 partial pressure and temperature in the system. Under typical operating conditions of an entrained bed gasifier, such as PRENFLO,1 which is characterized by low CO2 partial pressures and high temperatures, the CaCO3 decomposes to CaO and CO2. The CaO reacts with H2S to form calcium sulfide (CaS), but MgO does not. Thus, for calcined conditions, the reactions that occur for calcined limestone and fully calcined dolomite are

CaO + H2S a CaS + H2O

(1)

CaO‚MgO + H2S a CaS‚MgO + H2O

(2)

The thermodynamic equilibrium of these reactions is given by the following equation (from Barin2):

(7262 T )

Keq ) 1.127 exp

(3)

The sulfidation reaction of calcined limestone and fully calcined dolomite has been extensively studied at 0.1 MPa (by Efthimiadis and Sotirchos,3 Heesink and Van Swaaij,4 Fenouil and Lynn,5,6 and Adańez et al.7). However, the gas clean-up system in the IGCC process (1) Takematsu, T.; Maude, Ch. Coal Gasification for IGCC Power Generation; IEA Coal Research: London, 1991. (2) Barin, I. Thermochemical Data of Pure Substances; VCH: Weinheim, Germany, 1989. (3) Efthimiadis, E. A.; Sotirchos, S. V. Ind. Eng. Chem. Res. 1992, 31, 2311-2321.

10.1021/ef0301708 CCC: $27.50 © 2004 American Chemical Society Published on Web 03/23/2004

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Garcıá-Labiano et al.

Table 1. Chemical Analysis and Physical Characteristics of Sorbents

composition (wt %) CaCO3 MgCO3 others density, Fr (kg m-3) molar volume of reactant, VM,reac × 106 (m3 mol-1) molar volume of product, VM,prod × 106 (m3 mol-1) volume fraction of reactant, fV,CaO specific surface area, Sg (m2 g-1)a initial particle porosity, 0a a

Omyacarb limestone

Sa´stago limestone

Sierra de Arcos dolomite

97.1 0.2 2.7 3315 16.9 27.6 1.0 19.0 0.56

95.7 0.9 3.4 3315 16.9 27.6 1.0 6.8 0.66

52.5 40.5 7.0 3369 15.0 20.1 0.54 30.4 0.57

Calcined.

is conducted at medium pressures (1-3 MPa). Therefore, it is necessary to know the effect of total pressure in the sulfidation reaction of calcined limestone or fully calcined dolomite. Yrjas and co-workers8,9 studied the sulfidation of calcined limestone and fully calcined dolomite particles (125-180 µm) at 1223 K and 2 MPa. They concluded that the capture of H2S under those conditions was fast and high conversions were obtained. Matsukata et al.,10 working with only a particle size range of +0.71-1.0 mm at one temperature (1123 K), observed that the rate of sulfidation reaction decreased as the total pressure for a constant H2S partial pressure increased and that a CaS layer was developed from the surface to the interior of the particle during sulfidation. These authors assumed that the intraparticle diffusion was hindered with increasing total pressure. However, a shrinking-core model with chemical reaction and product layer diffusion control failed to explain the sulfidation behavior at high pressures. Thus, an empirical model was developed in which the apparent kinetic rate constant varied with total pressure and conversion. A similar effect of pressure on the sulfidation reaction of calcined calcium-based sorbents has been also observed in other noncatalytic gas-solid reactions, although there is no consensus about the reasons for it. Agnihotri et al.11 studied the high-pressure sulfidation reaction of uncalcined limestone powder. They found that an increase of the total pressure had a negative effect on the sulfidation reaction, and they assumed that the sulfidation of uncalcined limestone was inhibited at high pressures, on the basis of thermodynamics. Lin et al.12 also observed that the higher the total pressure, the lower the reactivity in the sulfidation of noncalcined limestone. Qiu and Lindqvist13 used the unreacted shrinking-core model to describe the sulfation reaction (4) Heesink, A. B. M.; Van Swaaij, W. P. M. Chem. Eng. Sci. 1995, 50, 2983-2996. (5) Fenouil, L. A.; Lynn, S. Ind. Eng. Chem. Res. 1995, 34, 23342342. (6) Fenouil, L. A.; Lynn, S. Ind. Eng. Chem. Res. 1995, 34, 23432348. (7) Adańez, J.; de Diego, L. F.; Garcıá-Labiano, F.; Abad, A. Energy Fuels 1998, 13, 617-625. (8) Yrjas, K. P.; Zevenhoven, C. A. P.; Hupa, M. Ind. Eng. Chem. Res. 1996, 35, 176-183. (9) Yrjas, P.; Iisa, K.; Hupa, M. Fuel 1996, 75, 89-95. (10) Matsukata, M.; Ando, H.; Ueyama, K.; Hosoda, S. Presented at the 15th International Conference on Fluidized Bed Combustion (Savannah, GA, 1999), ASME, Paper No. FBC99-0009. (11) Agnihotri, R.; Chauk, S. S.; Misro, S. K.; Fan, L.-S. Ind. Eng. Chem. Res. 1999, 38, 3802-3811. (12) Lin, S. Y.; Suzuki, T.; Aida, C.; Horio, M. In 13th International Conference on Fluidized Bed Combustion (Orlando, FL, 1995); ASME: Fairfield, NJ, 1995; pp 1043-1048. (13) Qiu, K.; Lindqvist, O. Chem. Eng. Sci. 2000, 55, 3091-3100.

and calculated the kinetic rate constant and the effective diffusivity of SO2 through the product layer at different pressures. Both parameters decreased as the total pressure increased. Qiu et al.14 studied the effect of pressure on the oxidation reaction of CaS to CaSO4. An increase in total pressure produced a decrease in the oxidation reaction rate for a constant partial pressure of oxygen. They suggested that this effect could be due to a decrease in the O2 diffusion rate. The negative effect of pressure has been also observed in the calcination reaction of CaCO3. Dennis and Hayhurst15 found that the rate of calcination was slower at higher pressures, even when there was no presence of CO2 in the bulk gases. They considered that there was a spurious partial pressure of CO2 at equilibrium that (i) was lower than that obtained from thermodynamic data and (ii) was dependent on temperature and total pressure. GarcıáLabiano et al.16 observed the same effect of pressure on the calcination reaction. They showed a detailed analysis of the possible causes of this effect and concluded that the decrease in the effective gas diffusivity, when the total pressure was increased, was the most-probable reason for it. The objective of this work was to analyze the sulfidation reaction of calcined limestone and fully calcined dolomite at medium pressures. The effects of several parameters were investigated, including total pressure, reaction temperature, H2S partial pressure, and particle size. The changing grain-size model proposed by Georgakis et al.17 was used to obtain the kinetic parameters of the sorbents. 2. Experimental Section 2.1. Materials. Two limestones (“Omyacarb” and “Sa´stago”) and a dolomite (“Sierra de Arcos”) were used in several narrow particle size intervals between 0.25 and 2.0 mm (ranges of +0.25-0.4 mm, +0.8-1.0 mm, and +1.6-2.0 mm). Table 1 shows the chemical analyses and physical characteristics of these sorbents. 2.2. Apparatus. The experiments were performed in two different pieces of equipments. The low-temperature experiments (723-973 K) were performed in a CAHN model TG2151 pressurized thermogravimetric analysis (PTGA) system. At higher temperatures, the external mass transfer, even working at the maximum gas flow, controlled the sulfidation (14) Qiu, K.; Anthony, E. J.; Jia, L. Fuel 2001, 80, 549-558. (15) Dennis, J. S.; Hayhurst, A. N. Chem. Eng. Sci. 1987, 42, 23612372. (16) Garcıá-Labiano, F.; Abad, A.; de Diego, L. F.; Gayań, P.; Adańez, J. Chem. Eng. Sci. 2002, 57, 2381-2393. (17) Georgakis, C.; Chang, C. W.; Szekely, J. Chem. Eng. Sci. 1979, 34, 1072-1075.

Pressure Effect on Sulfidation of Ca-Based Sorbents

Figure 1. Schematic diagram of the pressurized differential reactor.

Energy & Fuels, Vol. 18, No. 3, 2004 763

Figure 2. Effect of flow gas (sample weight of W ) 1.3 g; gas flows of (4) 50, (]) 110, and (0) 280 cm3 s-1) and sample weight (gas flow rate of 110 cm3 s-1; sample weights of (9) 0.35, ([) 1.3, and (2) 2.0 g) in the conversion-vs-time curves obtained in the differential reactor for dolomite (particle size of +0.81.0 mm) at 1173 K and 1 MPa, in an environment of 0.5 vol % H2S, 5 vol % H2, 5 vol % H2O, with N2 as the balance. Table 2. Kinetic Parameters of Sorbents

reaction in the thermobalance. To avoid this effect, a differential reactor was used for the high-temperature (10731173 K) experiments. 2.2.1. PTGA (Cahn TG-2151). The thermobalance consists of a quartz tube (inside diameter (ID) of 31 mm) placed in an oven that can be operated at pressurized conditions. The sample holder, to reduce mass-transfer resistance around the sorbent sample and to prevent corrosion, was a wire mesh platinum basket (11 mm in diameter and 4 mm in height). The temperature and the sample weight were continuously measured and recorded on a computer. The reacting gas mixture (83 cm3 s-1 STP) contained H2S in the desired concentration, with 5 vol % H2 and N2 as the balance. The H2 was supplied to suppress the H2S dissociation to elemental sulfur and H2. The sulfidation of the sorbents was performed at different temperatures (723-973 K) and pressures (0.1, 0.5, and 1.0 MPa). In addition, to investigate the influence of H2S on the sulfidation reaction, different H2S partial pressures in the range of 0.25-1 vol % were used. For each experiment, the sample weight (∼10 mg) was loaded in the platinum basket. The system was closed and pressurized in a CO2 atmosphere. The experiments were conducted in two steps: calcination and sulfidation. The calcination conditions were always the same, to avoid the effect of this step on the sulfidation. The sorbents were heated up to 1173 K with a heating rate of 20 K/min in a CO2 atmosphere. Under these conditions, the MgCO3 present in the dolomite calcined. Later, the CO2 was replaced by N2 and maintained for 5 min to allow the CaCO3 to calcine, obtaining a fully calcined dolomite or limestone. The temperature was then set at the sulfidation conditions and the reacting gases were introduced when the entire system was stable. 2.2.2. Differential Reactor. Figure 1 shows a schematic diagram of the pressurized differential reactor. The reactor consists of a tube (27 mm ID, 700 mm in length) of Khantal alloy 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 that was located just above the sample. The composition of the reacting gas (220 cm3 s-1 STP) was as follows: 0.5 vol % H2S, 5 vol % H2, 5 vol % H2O, and the balance was N2. The sulfidation reaction was performed at different temperatures (1073, 1123, and 1173 K), pressures (0.1, 0.5, and 1.0 MPa), and particle sizes (+0.25-0.4 mm, +0.8-1.0 mm,

P (MPa) ks,0 (m s-1) Ea (kJ mol-1) Ds,0 (m2 s-1) E0 (kJ mol-1) 0.1a 0.5 1.0

1.3 × 10-3 2.5 × 10-4 1.4 × 10-4

0.1a 0.5 1.0

80 × 10-3 17 × 10-3 8.2 × 10-3

0.1a 0.5 1.0 a

Omyacarb limestone 29 3.7 × 10-3 29 7.5 × 10-4 29 3.5 × 10-4 Sa´stago limestone 56 14.4 56 2.8 56 1.5

Sierra de Arcos dolomite 3.8 × 10-3 42 4.4 × 10-5 -4 7.8 × 10 42 8.9 × 10-6 3.9 × 10-4 42 4.2 × 10-6

165 165 165 217 217 217 154 154 154

From Adańez et al.7

and +1.6-2.0 mm). The H2S concentration at the exit was measured by a Varian Star 3400cx gas chromatograph with a flame photometric detector (FPD) in a semi-continuous way. After the operating conditions (pressure, temperature, and gas concentration) were stable, the sample was loaded from a pressurized reservoir that was located just above the reactor. The sorbent calcination was very quick, and the sulfidation occurred on the CaO that formed. The sulfidation conversion was obtained from the measurements of the H2S concentration that were obtained at the gas exit. Several experiments were initially performed to select the operating conditions. Figure 2 shows the conversion-versustime curves obtained at different gas flows (Fg) and sample weights (W). The limits of the operating conditions needed to avoid the external mass-transfer resistance and to be considered as a differential reactor were a minimum gas flow of 110 cm3 s-1 (STP) and up to 1.3 g of sample. The operating conditions finally used were Fg ) 220 cm3 s-1 (STP) and W ) 1 g. 2.3. Particle Model. The changing grain-size model proposed by Georgakis et al.17 was used to predict the experimental results of the sulfidation reaction at pressure. This model was previously used to determine the kinetic parameters of the sulfidation reaction at 0.1 MPa.7 The results obtained in that work are shown in Table 2 for the different sorbents used. The model assumes that the particle consists of nonporous spherical grains of uniform initial radius r0. As the reaction

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proceeds, the grain size (r1) grows, while the size of the unreacted core (r2) shrinks. The reaction occurs all over the particle, although conversion profiles can exist. The relative importance of the resistances that control the reaction (pore diffusion, chemical reaction, or diffusion in the product layer) is dependent on the operating conditions.7 The assumptions adopted in the model were the following: (i) the solid reactant is a porous spherical particle, the outer radius of which remains constant during reaction; (ii) the solid is an isothermal particle; (iii) changes in the solid structure occur slowly enough so that the pseudo-steady-state hypothesis for the gas concentration profile in the particle is valid; (iv) the chemical reaction between the gas and the solid reactant is first-order, with respect to the H2S, and is irreversible; and (v) the chemical reaction on the CaO surface is the limiting step for an individual grain until a conversion of 10% is reached; thereafter, the reaction of a grain is controlled by diffusion of H2S through the CaS product layer and by the chemical reaction on the CaO surface.7 The calculation of the overall reaction rate, in terms of the solid conversion, as a function of time, requires the solution of the following equations with appropriate boundary conditions: (1) A differential mass balance equation for the gas diffusion and reaction within the spherical particle, assuming pseudosteady-state conditions, which yields the following gas concentration profile through the particle:

∂C 1 ∂ ∂C DeR2 - (r)s ) )0 ∂R ∂t R2 ∂R

(

)

(4)

The boundary conditions required for the solution of this equation, when external mass transfer is not affecting the overall reaction rate, are as follows:

C ) C0

(at R ) R0 and t > 0)

(5)

∂C )0 ∂R

(at R ) 0 and t > 0)

(6)

(2) A differential mass balance equation for the gas diffusion in the product layer, which gives a relation between the concentration in the pores of the particle and the concentration at the reaction interface. The analytical solution of this differential mass balance allows us to express the local reaction rate, in terms of the gas concentration in the pores, using the equation

(r)s )

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

(7)

with r0 ) r1) r2 at t ) 0. (3) An equation for the movement of the reaction interface, which is determined from the chemical reaction rate that is occurring at the reaction interface. The grain size (r1) and the unreacted core size (r2), at each time and position inside the particle, are calculated using the equations

dr2 ksCVM,CaO ) dt 1 + (ksr2/Ds)[1 - (r2/r1)]

(8)

r31 ) Zsr30 + (1 - Zs)r32

(9)

where Zs is defined as

Zs )

VM,prod VM,reac

(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 area (S0) is calculated from the relation

S0 ) SgFr(1 - 0)fV,CaO

(12)

The effective diffusivity is calculated as a function of the particle porosity and a combination of the molecular and Knudsen diffusivity: -1 -1 2 De ) [DH + D-1 κ ] p 2S

(13)

The porosity changes inside the particle with sulfidation conversion are calculated using the expression proposed by Hartman and Coughlin:18

p(R,t) ) 0 - (Zs - 1)(1 - 0)X(R,t)

(14)

The local conversion at each time and position inside the particle is calculated using the relation

X(R,t) ) 1 -

( ) r2(R,t) r0

3

(15)

The mean conversion at each time in the entire particle is calculated by integration of the local conversions:

X(t) )

∫

R0

0

4πR2X(R,t) dR /3πR30

4

(16)

3. Results and Discussion The effect of total pressure on the sulfidation of calcium-based sorbents was analyzed at several temperatures in the range of 723-1173 K. First, experiments with a constant molar fraction of H2S were performed at three total pressures (0.1, 0.5, and 1.0 MPa). Figure 3 shows some of the results obtained with the dolomite. At high temperatures, the reaction rate increased as the total pressure increased, whereas at 723 K, the effect was the opposite. The use of the kinetic parameters obtained at 0.1 MPa was not valid to predict the sulfidation of the dolomite at pressure, because they overpredicted the experimental data. However, in the aforementioned experiments, the increase of pressure was followed by an increase in the H2S partial pressure. To analyze only the effect of total pressure, other experiments were performed while a constant H2S partial pressure was maintained. Figure 4 shows the experimental results obtained during the sulfidation of dolomite, with a H2S partial pressure of 2.5 kPa and different total pressures. In this case, the reaction rate decreased with total pressure in all cases. Other authors have also observed this negative effect of the pressure in the sulfidation of calcined calciumbased sorbents,10 and in other gas-solid reactions.11-16 Figure 4 also shows the model predictions using the kinetic parameters obtained at a total pressure of 0.1 MPa. In this case, the model predicted a decrease in the reaction rate with increasing total pressure, because of the decrease of the effective pore diffusivity through the decrease of the molecular diffusivity. However, the (18) Hartman, M.; Coughlin, R. W. AIChE J. 1976, 22, 490-498.


Figure 3. Effect of total pressure on the sulfidation of dolomite (particle size of +0.8-1.0 mm) at 723 and 1123 K and 0.5 vol % H2S ((9) 0.1 MPa, ([) 0.5 MPa, and (2) 1.0 MPa). Also shown are model predictions with the kinetic parameters obtained at (0) 0.1, (]) 0.5, and (4) 1.0 MPa.

Figure 4. Effect of total pressure on the sulfidation reaction with a constant H2S partial pressure (2.5 kPa) for dolomite (particle size of +0.8-1.0 mm) at 973 K ((9) 0.1 MPa, ([) 0.5 MPa, and (2) 1.0 MPa). Also shown are model predictions with the kinetic parameters obtained at (0) 0.1, (]) 0.5, and (4) 1.0 MPa.

model predictions did not fit the experimentally observed results. Taking into account the results of Figures 3 and 4, it can be concluded that the use of kinetic parameters obtained at 0.1 MPa are not valid to predict the sulfidation reaction performed at higher pressures. To determine the kinetic parameters of the sulfidation reaction at pressure, different experiments were performed at two pressures (0.5 and 1.0 MPa) and at temperatures of 723-1173 K. Figure 5 shows the effect of temperature on the sulfidation rate of the three sorbents at 1.0 MPa and 0.5 vol % H2S, using a particle size of +0.8-1 mm. The experiments at temperatures of 723-973 K were performed in the PTGA system, and the rest were conducted in the differential reactor. The sulfidation reaction increased as the temperature for the dolomite and the Sa´stago limestone increased, although this effect was lesser at the highest temperatures. However, for the Omyacarb limestone, an increase in the temperature above 873 K produced a slight decrease in the sulfidation reaction, which indicated that the gas diffusion through the porous system of the particles controlled the sulfidation at temperatures above 873 K. It was also observed for all sorbents that, at low temperatures, the reaction was quick until conversions


of ∼10% were obtained, and then there was a sharp decrease. This effect had been observed in the previous experiments that were performed at 0.1 MPa,7 and it was in agreement with the results obtained by Attar and Dupuis.19 They found that the chemical reaction on the flat calcite crystal surface was the limiting step until 78 CaS layers were formed; thereafter, the reaction was limited by solid-state diffusion through the CaS product layer. On the other hand, at the high temperatures, the dolomite reached complete conversion in short time periods and, meanwhile, the porous Sa´stago limestone exhibited a sharp decrease in the sulfidation reaction at conversion values of ∼80%, probably because of the CaS sintering. These results are in fair agreement with the values reported by Yrjas et al.8,9 at pressures above 0.1 MPa. To determine the best kinetic parameters of the sulfidation reaction with the aforementioned model, the Nelder and Mead20 method was used by curve fitting the experimental conversion-versus-time data obtained at each temperature and pressure for the different calcium-based sorbents with a particle size of +0.8-1.0 mm. It was assumed that the reaction order on H2S (equal to 1) was not dependent on total pressure. The values obtained both for the chemical reaction (ks) and the product layer diffusion (Ds) at the different temperatures were dependent on the total pressure for all the sorbents. As an example, Figure 6 shows the results obtained for the dolomite. An Arrhenius-type dependence was assumed for ks and Ds:

( ) ( )

ks,P ) ks0,P exp -

Ea RgT

(17)

Ds,P ) Ds0,P exp -

E0 RgT

(18)

Table 2 shows the values of the kinetic parameters obtained for the sulfidation reaction at the different pressures, together with the values obtained at 0.1 MPa.7 The activation energies were the same, independent of the pressure, and the pre-exponential factors decreased as the total pressure increased. Although there was not a clear reason for this behavior, several authors have used an empirical fit of their kinetic parameters with pressure in several gas-solid reactions.10,13 In this way, the effect of pressure on the preexponential factors were fitted to the following equations:

() ()

ks0,P ) ks0,P0

P0 PT

Ds0,P ) Ds0,P0

P0 PT

a

(19)

b

(20)

where P0 is the reference pressure (0.1 MPa in this case). Figure 7 shows the results obtained with the different sorbents. In all cases, a value of 1 was obtained for the constants a and b. This means that the apparent kinetic constant and the product layer diffusivities were (19) Attar, A.; Dupuis, F. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 607-618. (20) Nelder, J. A.; Mead, R. Comput. J. 1964, 7, 308-313.

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Figure 5. Effect of temperature on the sulfidation reaction ((a) dolomite, (b) Sa´stago limestone, and (c) Omyacarb limestone) at a total pressure of 1.0 MPa, particle size of +0.8-1.0 mm, and 0.5 vol % H2S ((b) PTGA, (O) differential reactor, and (s) model predictions with eqs 19 and 20).

Figure 6. Arrhenius plot for the chemical reaction rate constant and the product layer diffusion coefficient for the dolomite.

inversely proportional to the total pressure, and the values of ks0,P0 and Ds0,P0 corresponded to that obtained at atmospheric pressure. With the use of eqs 17-20, it is possible to adequately predict the sulfidation conversion of the calcium-based sorbents at different temperatures and pressures, as shown in Figure 5. However, it must take into account that all the aforementioned results corresponded to a particle size of +0.8-1.0 mm. There is no theoretical explanation for the variation of the reaction rate kinetic constant with the total pressure, but it is in agreement with that found by other authors10,13 using only one particle size interval. Nevertheless, it is necessary know the effect of the particle size in the sulfidation reaction. Figure 8 shows the effect of particle size on the sulfidation of the sorbents at 1123 K and 1 MPa. The sulfidation rate decreased as the particle size increased for all sorbents, because of the higher resistance to gas diffusion in the pores. This figure also shows the model predictions with the kinetic parameters previously determined at pressure with a particle size of +0.8-1.0 mm. The model underpredicted the experimental results for the smallest particles (+0.25-0.4 mm) and overpredicted the results for the highest particles (+1.6-2.0 mm). Therefore, important differences can be found using eqs 19 and 20, as used by several authors,10,13 to predict the effect of

Figure 7. Fitting of the pre-exponential factors ks0,P ((9) Omyacarb, ([) Sa´stago limestone, and (2) dolomite) and Ds0,P ((0) Omyacarb, (]) Sa´stago limestone, and (4) dolomite), as a function of the total pressure.

pressure with other particle sizes different than those used for the kinetic determination. However, the experiments that were conducted at atmospheric pressure6 did not show these deviations. Several authors have proposed different explanations for the effect of the total pressure on the gas-solid reactions. Agnihotri et al.11 proposed that the increase in the number of moles of gas produced during the sulfidation of noncalcined calcium-based sorbents was responsible for the effect of pressure. This explanation makes no sense for the sulfidation of calcined sorbents, because, in this case, the number of moles of gas remains constant. Matsukata et al.10 and Qiu et al.14 explained the effect of total pressure by the inhibition of the gas diffusion in the porous system of the particles. Garcıá-Labiano et al.16 proposed an equation where the molecular diffusivitysand, thus, the effective diffusivity in the poresswas more affected by the total pressure than that given by the Fuller et al.21 equation. In this way, it was possible to predict the calcination of calciumbased sorbents over a wide range of total pressure, temperatures, CO2 concentrations, and particle sizes. (21) Fuller, E. N.; Schettler, P. D.; Giddings, J. C. Ind. Eng. Chem. 1966, 58, 19-27.



Figure 8. Effect of particle size on the sulfidation of different calcium-based sorbents (dolomite, Sa´stago limestone, and Omyacarb limestone) at a total pressure of 1 MPa and temperature of 1123 K (dp ) (9) +0.25-0.4 mm, ([) +0.8-1.0 mm, (2) +1.6-2.0 mm; (- - -) model predictions with eqs 19 and 20; (s) model predictions with eqs 21 and 22).

Figure 9. Effect of total pressure on the sulfidation of the different calcium-based sorbents (dolomite, Sa´stago limestone, and Omyacarb limestone) with a particle size of +0.8-1.0 mm, with 0.5 vol % H2S, at 723 K ((0) 0.1 MPa, (]) 0.5 MPa, (4) 1.0 MPa) and 1123 K ((9) 0.1 MPa, ([) 0.5 MPa, (2) 1.0 MPa). Solid lines represent model predictions with eqs 21 and 22.

A variation of the effective diffusivity in the pores affects the sulfidation reaction when the resistance to the pore diffusion is relatively important, with respect to other resistances. This happened at temperatures above 823 K.7 The experimental effect of the pressure and particle size previously observed can be explained by means of a further decrease on the effective H2S diffusivity in the pores with increasing total pressure than that predicted using eq 13. Therefore, an additional decrease of this factor with increasing pressure was proposed, by means of the following equation:

De,P ) De,P0

() P0 PT

m

(21)

where De,P0 was the effective diffusivity calculated by eq 13 at PT. At lower temperatures (723-773 K), the product layer diffusion in the grain controlled the sulfidation reaction. In this case, a similar equation was proposed to calculate the dependence of the product layer diffusion coefficient with pressure:

Ds,P ) Ds,P0

() P0 PT

s

(22)

The changing grain-size model with the kinetic parameters obtained at atmospheric pressure7 and both eqs 21 and 22, to take into account the effect of pressure,

have been used to predict the experimental results. The values of the parameters m and s were determined by fitting the sulfidation experimental curves obtained at different temperatures, pressures, and particle sizes. Values of 0.4 and 1 were obtained for the parameters m and s, respectively, which were valid for all the sorbents studied. Figures 8-10 show some examples of how the model, with eqs 21 and 22, adequately predicted the sulfidation reaction over a wide range of reaction variables. Figure 8 shows the effect of pressure for different particle sizes of sorbent. Figure 9 shows the experimental results and the model predictions for the sulfidation of the different sorbents at different pressures and temperatures. It can be observed that the increase in the reaction rate obtained by increasing the total pressure from 0.5 MPa to 1.0 MPa is relatively small, compared to that obtained by increasing the total pressure from 0.1 MPa to 0.5 MPa. Matsukata et al.10 also found no considerable increase of conversion level with further increases in the total pressure from 1.1 MPa to 2.1 MPa. The model proposed adequately predicted these facts. Figure 10 shows the effect of total pressure while the H2S partial pressure for the dolomite sulfidation is maintained constant. As previously noted, an increase of the total pressure while the H2S partial pressure was maintained constant decreased the reaction rate. A good agreement between experimental and predicted results was ob-

768


Figure 10. Effect of total pressure ((9) 0.1 MPa, ([) 0.5 MPa, and (2) 1.0 MPa) on the sulfidation of dolomite with a constant H2S partial pressure (PH2S ) 2.5 kPa) and a particle size of +0.8-1.0 mm. Solid lines represent model predictions with eqs 21 and 22.


temperatures, the sulfidation reaction rate increased as the pressure increased, whereas, at low temperatures, the effect was the opposite. Second, the total pressure was varied while the H2S partial pressure was maintained constant. In this case, the sulfidation reaction always decreased as the pressure increased. A changing grain-size model with different resistances to the global reaction (pore diffusion, product layer diffusion, and chemical reaction) has been used to determine the kinetic parameters of the sorbents. A dependence with total pressure (PT) in the effective diffusivity in the pores (De) and in the product layer (Ds) has been proposed to predict the experimental results. The effective diffusivity in the pores was inversely proportional to PT0.4 and the effective diffusivity in the product layer was inversely proportional to PT for all the calcium-based sorbents. The changing grain-size model with the kinetic parameters determined, at 0.1 MPa, a reaction order of 1, with respect to H2S, and the equations that were proposed to consider the effect of total pressure on De and Ds, predicted the sulfidation of calcium-based sorbents over a wide range of temperature, total pressure, H2S concentration, and particle size. Acknowledgment. This research was performed with financial support from the Comisioń Interministerial de Ciencia y Tecnologıá (Project No. AMB980883). Nomenclature

Figure 11. Effect of H2S concentration ((9) 0.25, ([) 0.50, (2) 0.75, and (b) 1.0 vol %) on the sulfidation of the dolomite at 1 MPa, a temperature of 848 K, and a particle size of +0.81.0 mm. Solid lines represent model predictions with eqs 21 and 22.

served over the entire range of pressures and particle sizes that were analyzed. Finally, the effect of the H2S concentration at pressures above the atmospheric pressure was analyzed. Figure 11 shows the conversion versus time curves for the sulfidation of the dolomite at different H2S concentrations in the range of 0.25%-1%. An increase in the H2S concentration produced an increase in the sulfidation reaction. A good prediction of the experimental results was observed, assuming a reaction order on H2S of 1 for the sulfidation reaction. It was concluded that this reaction order on H2S was valid to describe the sulfidation reaction of calcium-based sorbents at any pressure. Conclusions The effect of pressure on the sulfidation reaction of calcium-based sorbents was analyzed in two ways. First, the total pressure was varied while the gas composition of the reacting gas was maintained constant. At high

a ) total pressure exponent in eq 19 b ) total pressure exponent in eq 20 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 PT (m2 s-1) De,P0 ) effective diffusivity of H2S within the sorbent particles calculated by eq 13 at PT (m2 s-1) DH2S ) molecular diffusion coefficient of H2S (m2 s-1) DK ) Knudsen diffusion coefficient (m2 s-1) Ds ) product layer diffusion coefficient (m2 s-1) Ds,P ) product layer diffusion coefficient at pressure PT (m2 s-1) Ds,P0 ) product layer diffusion coefficient at P0 ) 0.1 MPa (m2 s-1) Ds0,P ) pre-exponential factor of the product layer diffusion coefficient at pressure (m2 s-1) Ds0,P0 ) pre-exponential factor of the product layer diffusion coefficient at P0 ) 0.1 MPa (m2 s-1) E0 ) activation energy of the product layer diffusion coefficient (J mol-1) Ea ) activation energy of the chemical reaction rate constant (J mol-1) fV,CaO ) volume fraction of CaO in the sorbent Fg ) gas flow (cm3 s-1) ks ) chemical reaction rate constant (m s-1) ks,P ) chemical reaction rate constant at pressure PT (m s-1) ks0,P ) pre-exponential factor of the chemical reaction rate constant at pressure (m s-1) ks0,P0 ) pre-exponential factor of the chemical reaction rate constant at P0 ) 0.1 MPa (m s-1) Keq ) equilibrium constant for the sulfidation reaction of calcined sorbents

Pressure Effect on Sulfidation of Ca-Based Sorbents m ) total pressure exponent in eq 21 PT ) total pressure (MPa) P0 ) reference pressure (MPa) r0 ) initial grain radius (m) r1 ) grain radius after some reaction (m) r2 ) radius of unreacted grain core (m) (r)s ) reaction rate (mol m-3 s-1) R ) radial coordinate within the particle (m) R0 ) particle radius (m) Rg) ideal gas constant (J mol-1 K-1) s ) total pressure exponent in eq 22 S0 ) initial reaction surface (m2 m-3) Sg ) specific surface area (m2 g-1) t ) time (s) T ) temperature (K)

Energy & Fuels, Vol. 18, No. 3, 2004 769 VM,CaO ) molar volume of the CaO (m3 mol-1) VM,prod ) molar volume of the CaS in limestones and CaS‚MgO in dolomites (m3 mol-1) VM,reac ) molar volume of the CaO in limestones and CaO‚ MgO in dolomites (m3 mol-1) W ) sample weight (g) X ) sulfidation conversion Zs ) expansion ratio Greek letters 0 ) initial particle porosity p ) particle porosity Fr ) true solid density (g m-3) EF0301708

Effect of Pressure on the Sulfidation of Calcined Calcium-Based

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