Kinetic Model for Parallel Reactions of CaSO4 with CO in Chemical

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Kinetic Model for Parallel Reactions of CaSO4 with CO in Chemical-Looping Combustion Min Zheng, Laihong Shen,* Xiaoqiong Feng, and Jun Xiao Thermoenergy Engineering Research Institute, School of Energy & Environment, Southeast University, Nanjing 210096, Jiangsu Province, China ABSTRACT: Chemical-looping Combustion (CLC) has been proposed as an energy-efficient combustion method for in situ capture of CO2. Kinetic model for parallel reactions of the CaSO4 oxygen carrier with CO in a CLC process is explored in this paper. Tests on an isothermal reaction were carried out in a Thermogravimetric Analyzer coupled with Fourier Transform Infrared spectrum (TGA-FTIR), and the instantaneous evolutions of SO2 and COS were monitored by the FTIR quantitative analysis. The reaction temperature was varied between 850 and 1050 C, while 5-28% CO concentrations were utilized. The experiments showed that the reduction of CaSO4 by CO was a complex process, with the products of either sole CaS or both CaS and CaO depending on the reaction temperature as well as the concentration of CO reactant. The parallel reactions of CaSO4 with CO were investigated in terms of the selectivity based on the nucleation and growth model under isothermal conditions. According to the fitting results, the nucleation and growth model fit well the conversiontime data, and some of the kinetic parameters were obtained.

1. INTRODUCTION Chemical-looping combustion (CLC) has been suggested as a promising combustion technology to control the greenhouse gas emission because CO2 is inherently separated in the process.1,2 The CLC, which is proposed as an alternative to conventional combustion technique by Richter and Knoche in 1983,1 is an indirect combustion of both gaseous and solid fuels by use of oxygen carrier.117 And the CLC system, which can also be applied in combined cycle power plants, would be more potentially efficient than systems with conventional combustion.1821 The chemical-looping combustion typically consists of two separate reactors: an air reactor and a fuel reactor. An oxygen carrier, which circulates between the two reactors, transfers oxygen from air to fuel. The metal oxides NiO, Fe2O3, CuO, Mn2O3, and CoO are the main focus of the oxygen carriers for fuels.217 However, the utilization of the metal oxygen carriers may be limited because of the high cost, sulfur poisoning, and bad environmental sound. Recently CaSO4 is becoming an attractive oxygen carrier for the commercial application of CLC because of its easy availability and low price. Previous investigations2231 have been performed on CLC of gaseous and solid fuels with the CaSO4 oxygen carrier and many promising results have been obtained. Although the potential sulfur release partially resulted in a decline in the reactivity of the CaSO4 oxygen carrier during the cyclic use, the CaSO4 oxygen carrier had high reduction reactivity and stability in a long-time reductionoxidation test by using the gaseous fuels in a laboratory fixed/fluidized bed reactor.2729 Thus, the CaSO4 oxygen carrier may be a low-cost alternative oxygen carrier with high oxygen capacity even though the sulfur release problem exists. Figure 1 shows a schematic of the CLC process based on the CaSO4 oxygen carrier with CO. The general technical approach is demonstrated below. In the fuel reactor, CaSO4 is reduced to CaS r 2011 American Chemical Society

by CO 1 1 θ ¼ 43:5kJ=mol CaSO4 þ CO f CaS þ CO2 ΔH298 4 4 ðR1Þ

And then the reduced oxygen carrier CaS is oxidized by air to CaSO4 in the air reactor, where the oxygen is transferred from air to CaSO4 θ CaS þ 2O2 f CaSO4 ΔH298 ¼ 958:0kJ=mol

ðR2Þ

Although a fraction of SO2 may be produced during the periodic shifts between CaSO4 reduction and CaS oxidization, it could be recaptured and then recycled to CaSO4 by adding a small amount of sorbent, such as lime or limestone, into the CLC system.26,29 In this way, the stream from the air reactor is composed of atmospheric N2 and residual O2, and the stream from the fuel reactor almost consists of CO2 without the dilution of N2 from the air. In the process of CaSO4 reaction with CO, the sulfur emission is primarily ascribed to the side reaction R3 θ ¼ 220:0kJ=mol CaSO4 þ CO f CaO þ CO2 þ SO2 ΔH298

ðR3Þ According to the previous studies,26,3236 the reaction R3 is thermodynamically favored at a high reaction temperature and low reductive potential of the gas phase, as represented by the ratio of partial pressure PCO/PCO2. Thus, the CO reduction of CaSO4 to CaO can be eliminated partially under higher reductive Received: November 7, 2010 Accepted: March 8, 2011 Revised: March 4, 2011 Published: March 23, 2011 5414

dx.doi.org/10.1021/ie102252z | Ind. Eng. Chem. Res. 2011, 50, 5414–5427

Industrial & Engineering Chemistry Research

Figure 1. Schematic of the CLC process based on the CaSO4 oxygen carrier with CO.

potential of the gas phase and at lower temperatures, while less SO2 could be released from the reaction R3. The sulfur release accounts for a small fraction of the total amount of the oxygen carrier and could be recycled to CaSO4 by adding lime or limestone. The sorbent reacts with SO2 to form CaSO3 in the fuel reactor. Then the sulfidation product is expected to be oxidized to CaSO4 in the air reactor and can be used as oxygen carrier in the following cycle. In the previous studies,3739 the mechanism of CaSO4 reaction with CO under isothermal conditions was described by two kinds of kinetic models. One is the nucleation and growth model, and the other is the spherical unreacted-core shrinking model. Oh and Wheelock37 reported that the reaction rate of CaSO4 with a mixture of CO, CO2, SO2, and N2 varied linearly with CO concentration at 1150 C, and as the reaction proceeded, it had usually an initial induction period followed by a constant and rapid reaction period.37 This was a feature of a nucleation and growth process.37,40 Diaz-bossio et al.38 also found that the CO reduction of CaSO4 to CaO in a TGA reactor was first order with respect to the concentration of CO on condition that the reaction temperature was varied between 900 and 1180 C, while 1-6% CO concentration and 25% CO2 concentration were utilized. The unreacted-core shrinking model fit well the conversiontime data with the assumption of chemical reaction control and spherical grains.38 Talukdar et al.39 also used the spherical unreacted-core shrinking model to describe the reduction of CaSO4 to CaO, which was carried out in a coal-fired fluidized bed. During the reaction process, the CaSO4 was treated with a low CO concentration (e4%) and in the presence of oxygen within the temperature range of 800-900 C. However, the reaction environment used in this literature3739 is different from that in a fuel reactor of a CLC system based on the CaSO4 oxygen carrier. On one hand, the suitable reaction temperature of a fuel reactor in a CLC system should be between 900 and 950 C.26 On the other hand, the reduction of the CaSO4 oxygen carrier by CO in a fuel reactor of a CLC system should be conducted without the presence of oxygen. It seems that the kinetic knowledge on the reduction of the CaSO4 oxygen carrier by CO in a CLC system is limited. Besides, just the reaction R3 rather than the two parallel reactions R1 and R3 has been considered for the kinetic modeling in the literature.38,39 Additionally, the majority of the investigations of CaSO4 reductive decomposition3739 has been carried out in a TGA or fluidized reactor, and a few fundamental kinetic data are available due to the challenge of quantitative measurement on products. For instance, in the TGA reactor, the respective mass changes of the simultaneous products CaS and

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CaO with reaction time cannot be clearly distinguished from the overlapped TGA curves, which were caused by the simultaneous formations of the two solid components. In order to perform the quantitative analysis for the overlapped TGA transitions, the FTIR tool could be introduced to the TGA experiments. The TGA-FTIR has been successfully used in many fields for the quantitative analysis during the decomposition or solidgas reactions taking place in the TGA reactor.4145 Usually, it requires a calibrating procedure to obtain the quantitative data from the FTIR online gas phase measurements. The general technique used for the quantitative FTIR determinations of gaseous compounds is based on the calibration with the gaseous mixtures containing certain concentrations of the compounds of interest.43,4648 According to the LambertBeer’s law, the strength of the absorption is proportional to the concentration of the absorbing compound. Note that the law is not obeyed at high concentrations, so it is desirable to keep the strength of the absorption for no more than 0.7 for the FTIR quantitative analysis. In a previous study,26 the FTIR instrument has been applied to identify the gas products of CaSO4 reduction with CO. In this paper, the FTIR tool is used further for the quantitative analyses of the evolved gaseous substances formed in the TGA-FTIR runs, where CaSO4 is reduced to either sole CaS or both CaS and CaO by the gas CO. Thus, the reaction course and the reaction characteristics of the reaction can be clearly described. In the parallel reactions of CaSO4 with CO, it is necessary to promote the CaSO4 reduction to CaS (R1) and to restrain the side reaction of CaSO4 reduction to CaO (R3), and design criteria, in which the effects of chemical reaction are taken into account, are needed. Currently, the simultaneous reactions R1 and R3 of CaSO4 with CO are investigated in terms of the selectivity based on the nucleation and growth model under isothermal conditions. The concept of the selectivity, which is commonly used in the field of catalysis, is introduced to the analysis of the simultaneous noncatalytic solidgas reactions by Wen and Wei.49 In this study, the selectivity is defined as the ratio of the flux of the desired product CaS to that of the side product CaO. Then the model parameters can be determined by using the TGA data and the FTIR quantitative data on the evolved gaseous products. The kinetic model should be quite valuable for optimizing the reaction condition in chemical-looping combustion.

2. EXPERIMENTAL SECTION The reactions of CaSO4 reductive decomposition under CO atmosphere were investigated by a Setaram TG-DTA92 thermogravimetric analyzer (TGA) and a Bruker Vector 22 Fourier Transform Infrared (FTIR) spectrum and under isothermal condition. The CaSO4 particles with a mean particle diameter of 2.562 μm were used in this experiment. The measurement of the particle sizes were carried out by a Beckman Coulter LS 13 320 Particle Size Analyzer. The molar density of the particle was 23,610 mol/m3. The experiments in the TGA reactor were performed within the temperature range of 850-1050 C, and the reactant gas was the mixture of CO and nitrogen, with the CO concentration varying from 5 to 28%. To eliminate the resistance of CO mass transfer, a sufficiently high gas flow rate of 80 mL/min (under the standard condition of 1 atm and 25 C) was used through the experimental period. For each run, approximately 24 mg of chemically pure CaSO4 particles were placed in a ceramic basket, which was positioned inside the TGA reactor. The reactor was heated to the desired temperature in a N2 atmosphere at a flow rate of 80 mL/min and then kept at the desired temperature with the 5415

dx.doi.org/10.1021/ie102252z |Ind. Eng. Chem. Res. 2011, 50, 5414–5427


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Figure 2. Concentration-based calibration results for (a) SO2 and (b) COS.

desired reductive gas mixture. Afterward, the reaction of CaSO4 reduction by CO took place under isothermal conditions and at the pressure of 1 atm. The decrease in the sample weight during the reaction was continuously recorded. Most experiments were conducted until the sample showed no further mass change. The absorptances of the flue gas during the reaction process were recorded online by the FTIR analyzer placed at the exit of the TGA reactor, and from the absorption results, quantitative analyses of the sulfur emissions (SO2 and COS) were carried out by means of the calibration profiles and the peak-height method. Calibration operations were performed with SO2 and COS gases. The following gaseous mixtures were used for SO2 and COS calibration runs at the respective wavenumbers of 1371.1 cm1 and 2073.1 cm1: The fraction of SO2 in N2 atmosphere ranged from 0.0013 to 0.0072, and the fraction of COS in N2 atmosphere is from 0.0002 to 0.0018. Figure 2 shows the concentration-based calibration results for SO2 and COS, and the linear relationships between the absorptances and the concentrations of the absorbing species SO2 and COS are also represented respectively in Figure 2.

3. RESULTS 3.1. Distribution Profiles of Gas Products. A few terms were introduced to describe the distributions of the gas products. The emission rates of SO2 and COS, rSO2 and rCOS, are the molar

Figure 3. Evolutions of the gas products from the decomposition of CaSO4 at various reaction temperatures and under 10% CO atmosphere: (a) SO2; (b) COS; and (c) CO2.

ratios of the SO2 and COS produced respectively per second to the total amount of CaSO4 introduced to the TGA reactor. The gas produced during the reaction process just would lead to a maximum of 0.1% increase in the gas flux, so the gas flux at the exit of the TGA reactor is assumed to be constant. Thus, the emission rates of SO2 and COS are calculated based on the calibration profiles (as shown in Figure 2), as follows ! ABSO2 , t 80 103 1 rSO2 ¼ ð1Þ NCaSO4 , TGA 52:5 22:4 5416



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Figure 3 and Figure 4 illustrate the evolutions of the gas products from the parallel reactions of CaSO4 with CO at varied reaction temperature and under varied CO concentration, respectively. Within the temperature range of 850 to 900 C and under 10% CO concentration, the reduction of CaSO4 to CaO was eliminated due to the low temperatures, and there was no sulfur-derived gas such as SO2 to release during the reaction process. However, at the higher reaction temperatures (9501050 C), the CaSO4 reduction processes were accompanied by the COS formation because of the release of SO2 and extra CO used in the higher temperatures of TGA tests.26 When the SO2 was released from the process of CaSO4 reduction, SO2 reacted with CO and was converted to COS via the following way θ SO2 þ 3CO f 2CO2 þ COS ΔH298 ¼ 300:4kJ=mol

ðR4Þ

Thus, the entire release of SO2 could be determined by the COS release in this study. As shown in Figure 3 and Figure 4, the COS emission was dominant, and the emissions of both SO2 and COS were suppressed by the increased CO concentration but aggravated with the rising reaction temperature. The higher the temperature, the more the SO2 was formed via the side reaction of CaSO4 with CO (R3). Moreover, the SO2 generated further reacted with CO via reaction R4, resulting in the level of COS release increasing as the reaction temperature rose. On the whole, the level of the sulfur emission indicated that the mole fraction of CaO product in the solid residue presented an increasing trend with the increase in the reaction temperature. 3.2. Characteristics of CaSO4 Conversion. Based on mass balance, the conversion of CaSO4 to either sole CaS or both CaS and CaO in the reduction experiments carried out in the TGAFTIR was evaluated by the equation below XCaSO4 ¼ XCaO þ XCaS

¼

ðMCaS MCaO Þ m0 m0 mt MCaSO4 MCaSO4 MCaS MCaSO4

Z

Z

t

rSO2 dtþ !

0

!

t

rCOS dt 0

m0

ð3Þ with Z

t

XCaO ¼ 0

! Z t rSO2 dtþ rCOS dt

ð4Þ

0

and Figure 4. Evolutions of the gas products from the decomposition of CaSO4 at 950 C and under various CO concentrations: (a) SO2; (b) COS; and (c) CO2.

rCOS ¼

1 NCaSO4 , TGA

ABCOS, t 80 103 257:1 22:4

XCaS ¼

!

MCaSO4 MCaS MCaSO4

Z

Z

t

rSO2 dtþ !

0

!

t

rCOS dt 0

m0

ð5Þ

ð2Þ

where ABSO2,t and ABCOS,t are the absorbances of SO2 and COS at the reaction time t, and NCaSO4,TGA is the mole amount of CaSO4 introduced to the TGA reactor. The cumulative amount of the gaseous product is an integral result of the emission rate.

ðMCaSO4 MCaO Þ m0 m0 mt MCaSO4

where XCaO and XCaS are the conversions of CaSO4 to CaO and CaS, respectively, m0 is the weight of the CaSO4 particles at the beginning of the reduction stage, mt is the weight of the sample at a time t, rSO2 and rCOS are the emission rates of SO2 and COS, and MCaSO4, MCaS, and MCaO are the molecular weights of CaSO4, CaS, and CaO, respectively. 5417



Figure 5. Conversiontime data for the decomposition of CaSO4: (a) at various reaction temperatures and under 10% CO concentration and (b) at 950 C and under various CO concentrations. Solid lines with symbols: experimental data. Short dot lines with symbols: model predictions with eq 22 from the nucleation and growth model, where the decomposition of CaSO4 to both CaS and CaO are considered.

Figure 5 shows the conversiontime profiles of the CaSO4 decomposition under various CO concentrations (5-28%) and at various reaction temperatures (850-1050 C). An increase in the reaction temperature and the concentration of CO reactant accelerated the overall reaction rate. Additionally, when the reaction temperature exceeded 950 C, there was a reaction course shift from the single reaction R1 to the parallel reactions R1 and R3, which would give a rise in the overall reaction rate. Nevertheless, the rise in the growth rate of the overall reaction rate tended to decrease as soon as the reaction temperature was over 1000 C. This was probably due to the sintering of CaSO4 particles at 1050 C. As far as the reaction rate was concerned, high reaction temperatures and CO concentrations were favorable for the reductive decomposition of CaSO4, and as it is shown in the results above, an increase in the concentration of CO reactant suppressed the sulfide emissions of SO2 and COS, while increasing the reaction temperature aggravated the sulfide emissions and reduced the desirable product CaS. Currently, the chemical reactions for the kinetic modeling are focused on the following section. The operation condition considering the reaction rate and sulfur control should be determined in the future work.

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4. MODEL AND DISCUSSION As stated above, both of the two kinetic models, the nucleation and growth model and the spherical unreacted-core shrinking model, have been used to describe the reaction mechanism of CaSO4 reaction with CO under isothermal conditions. However, for the reaction of fine solid particles, the process of nucleation is more important and may control the reaction over the entire duration, and the nucleation and growth kinetics would be more favorable. For instance, Kim and Sohn40 found that among a number of different rate equations such as the shrinking-core expression, the nucleation and growth kinetics proved to yield the best results for the H2 reduction of the CaSO4 powder to CaS. In the present kinetic study, the nucleation and growth model is applied to describe the mechanism of the finely sized CaSO4 particles with the gas CO, and the CO reduction of CaSO4 particles to simultaneous CaS and CaO are investigated in terms of the selectivity based on the nucleation and growth model under isothermal conditions. The model parameters are calculated by using the TGA data combined with the FTIR quantitative data. 4.1. Nucleation and Growth Model. Grain nucleation and growth are important phenomena in the heterogeneous chemical reaction process with a new solid phase formation, where the reaction interfaces increase until growing nuclei overlap extensively and then decrease. The nucleation and growth model, which was proposed and developed by Johnson and Mehl,50 Avrami,5153 Prout and Tompkins,54 and Erofe’ev,55 has been used widely in the TGA kinetic measurements for the analysis of the solid-state reactions, especially the finely sized solid particles with a gas.40,5658 The profiles of the transformations in solid reactants as a function of the reaction time are often shown to follow a characteristic S-shape. According to this model, the solid-state reactions proceed with the nuclei formation and subsequent nuclei growth. At the beginning of the reaction, there is an induction period for the forming of the nuclei of the new phase. Subsequently, the reaction progress then continues with the nucleation and the growth of the already formed nuclei. During the intermediate period, the nuclei, which consume the old phase, grow into particles; meanwhile, new nuclei continue to form in the remaining parent phase. This in turn results in the transformation being rapid. As soon as the transformation comes to complete approximately, there is little untransformed material for the nuclei to form in and the productions of new particles become slow. Furthermore, the particles already existing begin to touch one another, forming a boundary where the growth stops. The overall transformation in the solid reactant is determined by the relative rates of the nucleation and nuclei growth and the concentration of the potential nucleus-forming sites as well. Most of the solid-state reactions start by forming nuclei at the surface of the solid. As the reaction progresses, these nuclei grow in size and new ones are formed. Eventually, they overlap one another and cover the whole surface, thus forming what has been called the reaction interface in a shrinking-core system. When the ratio of surface to volume of the solid is small or the reaction temperature is high, the time spent for the nucleation is only a small portion of the total reaction time, and thus nucleation is not important. However, for the reaction of fine solid particles, nucleation is more important and may control the reaction over the entire duration.5658 The rate expression for the nucleation and growth kinetics of the solid-state transformations of one phase to another at a constant temperature can be represented by the Johnson-Mehl5418



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Avrami (JMA) equation (so-called Avrami-Erofe’ev equation), which is written as 1 X ¼ ekt

n

ð6Þ

where X is the solid conversion, k and n are the Avrami constants, and k is considered as the apparent rate constant which depends partly on the nucleation rate and the growth rate of the nuclei grain, and n is known as the Avrami exponent. 4.2. Rate Equations for Parallel Reactions of CaSO4CO. Based on the previous kinetic work,5053,59,60 the nucleation and growth rate equations for the solid transformations of CaSO4 into both CaS and CaO (in the range of CaSO4 conversion degree 0.1 e XCaSO4 e 0.5) are derived in the following, with the simplifications and assumptions being made: a The parallel solidgas reactions of CaSO4 with CO are controlled by the new phase nuclei formation and growth. b Nucleation occurs randomly and homogeneously over the entire untransformed volume. c The transformed particles (both CaS nuclei and CaO nuclei) are spherical. d The respective nucleation rates of CaS and CaO nuclei are constant, and the respective radial growth rates of the transformed particles are constant and do not depend on the extent of transformation. Thus, the transformations of CaSO4 into both CaS and CaO are assumed to proceed by 3 3 and NCaO the nucleation of new particles at the rates NCaS 3 3 per unit volume and then grow at the rates GCaS and GCaO into spherical particles, respectively. e The CaS and CaO nuclei only stop growing when they impinge upon one another. 4.2.1. Nucleations. During the time interval τ to τþdτ, the numbers of CaS nuclei and CaO nuclei that appear in the sample of volume V, NCaS and NCaO, will be given respectively by 3

Ni ¼ V Ni dτ ði ¼ Cas, CaOÞ

ð7Þ

4.2.2. Growths of CaS Nuclei and CaO Nuclei. The concept of an expanding volume is applied for model derivation. The expanding volume is the volume of the new phase that would form if the entire sample is still untransformed, and the expansion rate of the new nuclei is the increment of the expanding volumes per unit time and per unit sample volume V. The growths of CaS and CaO nuclei are isotropic, constant, and unhindered by previously transformed material. Thus, the CaS nuclei and CaO nuclei, which are nucleated between the time interval τ and τþdτ, will grow into their respective spheres 3 (tτ) and G 3 of radius GCaS CaO(tτ) at the time t. As a result, the corresponding theoretical expanding volumes of CaS and CaO nuclei at the time t due to particles that nucleated between times τ and τþdτ will be dVτe, i ¼

3 4π 3 Gi ðt τÞV Ni dτ ði ¼ Cas, CaOÞ 3

Thus, the expansion rates of CaS nuclei and CaO at the time t are defined as follows e ,CaS and rVe nuclei rVCaS CaO,CaO

ð8Þ

rVie , i ¼

Vie ¼

0

t

3 3 4π π Gi ðt τÞV Ni dτ ¼ Gi V Ni t 4 ði ¼ Cas, CaOÞ 3 3 ð9Þ 3

3

ð10Þ

4.2.3. Selectivity. The selectivity S is the ratio of the flux of the desired product CaS to that of the side product CaO. With the assumption of the new phase nuclei formation and growth control in the kinetic model, the selectivity S is defined as the expansion rate ratio of CaS nuclei to that of CaO nuclei and can be calculated as follows dnCaS 3 3 rV e , CaS GCaS NCaS ¼ 3 S ¼ dt ¼ CaS 3 dnCaO e rVCaO , CaO GCaO NCaO dt

ð11Þ

where nCaS and nCaO are the mole amounts of CaS and CaO formed, respectively. Thus, for a given reaction temperature, the value of the selectivity S defined in the present study is a constant. 4.2.4. Rate Expressions. In eq 9, the expansion volume becomes infinite with time. However, the growths of the new phases (both CaS and CaO phases) can only proceed in the untransformed volume. It indicates that just a fraction of the expansion volume is valid. Since the nucleation occurs randomly, the virtual expansion volume either VCaS or VCaO, which is formed during each time increment, will be proportional to the volume fraction of untransformed. Thus dVi ¼

ðV VCaS VCaO Þ e dVi ði ¼ Cas, CaOÞ V

ð12Þ

And, based on eq 12, it is inferred that e dVCaS dVCaS ¼ ¼S e dVCaO dVCaO

ð13Þ

With the integration of eq 13 from time [0, t], it gives 1 VCaO ¼ VCaS S

ð15Þ

Substituting eq 15 into eq 12 with i = CaS gives dVCaS V

1

VCaS V

¼ 1 1þ S

e dVCaS V

ð16Þ

Upon integration eq 16 and considering the initial states VCaS = 0 and VCaO = 0 3 VCaS 1 1 π 3 GCaS NCaS t 4 ð17Þ 1þ ¼ 1þ ln 1 S S 3 V

Integrating eq 8 between τ = 0 and τ = t gives the expanding volume Vie, which is formed from the start of the transformation until the reaction time t Z

1 dVie 4π 3 3 3 Gi Ni t ði ¼ Cas, CaOÞ ¼ V dt 3

The volume fractions of the products CaS and CaO in the sample are represented as XCaS = (VCaS)/(V) and XCaO = (VCaO)/(V). In the present work, the XCaS and XCaO are also treated as the mole fractions of products CaS and CaO in the CaSO4 reactant. Thus, rearranging eq 17 with the formula 5419


Industrial & Engineering Chemistry Research XCaS = (VCaS)/(V) gives

XCaS ¼

1e

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Table 1. Values of (1 þ 1/S) at Different Reaction Temperatures and CO Concentrations

3 1 π 3 GCaS NCaS t 4 1þ S 3

1þ

ð18Þ

1 S

Then substituting eq 18 into eq 15 gives 3 1 π 3 GCaS NCaS t 4 1þ S 3 1 1e XCaO ¼ XCaS ¼ S 1þS

ð19Þ

Equations 18 and 19 can be abbreviated to the more familiar form of the Johnson-Mehl-Avrami (JMA) equation and then give the fractions of transformed materials after a hold time at the given temperature for the transformations of CaSO4 into both CaS and CaO 1 n kCaS 1 þ t n S 1e 1 eðkCaS þ kCaO Þt ¼ XCaS ¼ ð20Þ 1 kCaO 1þ 1þ S kCaS 1 ekCaO ð1 þ SÞt 1 eðkCaS þ kCaO Þt ¼ ¼ kCaS ð1 þ SÞ 1þ kCaO n

XCaO

n

XCaSO4 ¼ XCaS þ XCaO ¼ 1 ekCaS ð1 þ SÞt 1

¼ 1 ekt

n

850

10%

1

900 950

10% 10%

1 1.136

1000

10%

1.412

1050

10%

4.044

950

5%

1.303

950

6%

1.213

950

18%

1.073

950

28%

1.050

kin, i ¼ Ai eEai =ðRTÞ ði ¼ CaS, CaOÞ

ð24Þ

where Eai is the activation energy, Ai is the frequency factor, R is the universal gas constant, and T is the absolute temperature. Eai may also be assessed from the logarithmic form of eq 24 ln kin, i ¼ ln Ai Eai =ðRTÞ

ð25Þ

from the slope of the ln kin,i versus 1/T plot. 4.3. Kinetic Parameter Calculations. 4.3.1. Calculation Procedure. Equation 22 is rewritten as the double-logarithmic form 1 lnð lnð1 XCaSO4 ÞÞ ¼ ln kCaS þ ln 1 þ þ n ln t S

n

ð26Þ ð22Þ

where k = kCaS þ kCaO. 4.2.5. Interpretation of Avrami Constants. Originally, n is a parameter connected with the mechanism of a reaction, and n is held to have an integer value or noninteger value which reflects the nature of the transformation of interest.61,62 For instance, in the derivation of present study on the solid transformations of CaSO4 into both CaS and CaO, the value of 4 represents the case where the nucleation rates of both CaS and CaO nuclei are constant and the subsequent growth of each nucleated particle is of three dimensions. However, it has become customary to regard the value of n as an adjustable parameter that may be either nonintegral or integral, which is obtained by the fitting method, and the value of n leads to equations with no obvious physical significance in previous study.40 In this work, the value of the Avrami exponent n is treated in the same way. The parameter ki (i = CaS, CaO) depends partly on both the nucleation rate and the growth rate, and ki is temperature dependent. Moreover, ki perhaps depends on the concentrations of gas reactants for a gassolid reaction. For the reactions of CaSO4 with CO, the dependence of the rate constant ki (i = CaS, CaO) on the reaction temperature T and the concentration of CO reactant is presented by the equation ki ¼ kin, i ð fCO Þli

CO concentration [-]

where kin,i is the intrinsic rate constant, fCO is the concentration of CO reactant, and li is the reaction order for the formation of species i. kin,i is considered to be described by the Arrhenius equation

ð21Þ

where kCaS and kCaO are the rate constants for the transformations of CaSO4 into CaS and CaO, respectively, and kCaS = (π)/(3) 3 N3 , k 3 3 GCaS CaS CaO = (π)/(3)GCaONCaO, S = (kCaS)/(kCaO), and n = 4. Eventually, the entire CaSO4 transformation is expressed as

(1 þ 1/S) [-]

temperature [C]

ð23Þ

Thus, a plot of ln(ln(1XCaSO4)) versus ln t would be linear with n as the slope and ln kCaS þ ln(1þ(1)/(S)) would act as the intercept for ln t = 0. Under the condition of known S, the values of kCaS and then kCaO can be obtained. Currently, the value of the selectivity S at the reaction time t could be measured based on the experimental data and by the formula S= (dnCaS)/(dt)/(dnCaO)/(dt). However, the value of the selectivity measured was not a constant for a given reaction temperature but varied with the reaction time. To simplify the calculation procedure on ki, the average of the selectivity in the specified solid-conversion-interval (0.1 e XCaSO4 e 0.5), S, was substituted into eq 26. Moreover, in terms of the selectivity S, when the parallel reactions are quite inclined to and even only involve reaction R1 to generate CaS, the value of S begins to grow and approach infinity as a limit so that limSf¥(1þ1/S) = 1. Thus, eq 26 can be used to describe the transformations of CaSO4 into either CaS or both CaS and CaO, whether just the single reaction R1 or the parallel reactions R1 and R3 take place in the reaction process. 4.3.2. Calculations of Selectivity and Avrami Exponent. Based on the TGA and FTIR data, the values of (1 þ 1/S) in the range of CaSO4 conversion degree 0.1 e XCaSO4 e 0.5 are calculated and demonstrated in Table 1, which would be subsequently substituted into eq 26. According to eq 26, the conversion function-time plots of the isothermal experimental data on the reductive decomposition of CaSO4 at various reaction temperatures and under various CO 5420



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Figure 8. Dependence of the reaction rate constant kCaO on the concentration of CO.

Figure 6. Plots of ln(ln(1XCaSO4)) as a function of reaction time for the reaction: (a) at various reaction temperatures and under 10% CO concentration and (b) at 950 C and under various CO concentrations. Solid lines with symbols: experimental data. Short dot lines: linear fit data with eq 26 and n = 1.63.

Figure 7. Dependence of the reaction rate constant kCaS on the concentration of CO.

concentrations are given in Figure 6. The conversion functiontime curves are fit by the linear plots, respectively, and these fit

Figure 9. Arrhenius plots of the rate constants kin,CaS and kin,CaO.

curves to the experimental data at varied reaction temperatures are approximately parallel and with the slopes varying between 1.86 and 1.47 for the CaSO4 particles. The mean value of n is 1.63. Thus, with eq 26 and n = 1.63, the linear fit data are also demonstrated in Figure 6. 4.3.3. Kinetic Parameter Calculations and Analysis. The values of kCaS obtained from the intercepts in Figure 6 and kCaO obtained subsequently from the equation S = kCaS/kCaO are plotted in Figure 7 and Figure 8 against the CO concentration for the reductions of CaSO4 to CaS and CaO, respectively. As shown in Figure 7, a straight line through the origin is obtained for the reduction of CaSO4 to CaS via reaction R1, which indicates a first-order reaction with respect to the concentration of CO reactant. While for the reduction of CaSO4 to CaO via reaction R3, the reaction order lCaO is 0.19, as shown in Figure 8. The values of the intrinsic rate constants, kin,CaS and kin,CaO, were obtained from eq 23 at various reaction temperatures (8501050 C), and the Arrhenius plots of the kinetic rate constants kin,CaS and kin,CaO are illustrated Figure 9. When the reaction temperature is below 1000 C, the logarithmic forms of the kinetic rate constants kin,CaS demonstrate a good linear relationship with the reaction temperature 1/T. Nevertheless, the value 5421



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Table 2. Kinetic Parameters for the Parallel Reactions of CaSO4 with CO reaction

reaction order

temperature [C]

Ea [kJ 3 mol1]

A [s1.63]

correlation coefficient

R1

1

850-1000

187.0 ( 10. 1

7191

0.997

R3

0.19

950-1050

427.7 ( 6.3

2.9881 1012

0.999

of ln kin,CaS at 1050 C deviates evidently from the tendency. This is probably due to the melting and sintering of CaSO4 at the high reaction temperature. So the experimental point at 1050 C is excluded from Arrhenius plot of ln kin,CaS ln t. From the results of Arrhenius plots, the estimated apparent activation energies EaCaS and EaCaO and the frequency factors ACaS and ACaO are obtained and listed in Table 2. As demonstrated in Table 2, the activation energies are 187.0 kJ/mol for the reduction of CaSO4 to CaS and 427.7 kJ/mol for the reduction of CaSO4 to CaO with the 95% confidence limits. In parallel reactions, higher reaction temperatures favor the reaction with larger activation energy, while higher concentrations of the gas reactants are in favor for the reaction with larger reaction order. Currently, the values of the kinetic parameters illustrated in Table 2 confirm that a high reaction temperature and a low CO concentration should give a rise in the sulfur emission from the parallel reactions of CaSO4 with CO. 4.4. Simulation Results and Discussion. With these fundamental kinetic parameters, the CO reduction of CaSO4 to either sole CaS or both CaS and CaO (XCaS and XCaO), and the CaSO4 conversion (XCaSO4) at varied reaction temperatures and under varied CO concentration were simulated with eqs 20 - 22 from the nucleation and growth model and shown in the curves (as shown in short dot lines with symbols) in Figures 5, 10, and 11. On a whole, the model simulated well the experimental conversion data in the range of CaSO4 conversion degree 0.1 e XCaSO4 e 0.5. For the reductions at 950 C and under varied CO concentration, evident deviations occurred for CaO formation XCaO (as shown in Figure 11b) when the CO concentration exceeded 10%. These deviations may be due to the big relative tolerance caused by measuring the extremely small amount of sulfide emissions (SO2 and COS) and the proceeding of the side reaction R4. While for the reduction at 10% CO concentration and at varied reaction temperature, the maximum deviation occurred at the high reaction temperature of 1050 C for both CaS formation XCaS (as shown in Figure 10a) and CaSO4 conversion XCaSO4 (as shown in Figure 5a). At 1050 C, the deviations of the predicted values from the experimental data are probably ascribed to the melting and sintering of CaSO4 particles as well as CaS particles. The melting points of pure components CaSO4, CaS, and CaO are 1350, 2450, and 2580 C.6365 The corresponding theoretical sintering temperatures (so-called the Tamman temperature) are approximately 0.4-0.5 times of their respective melting points. The CaSO4 melts at a lower temperature than its reduction products CaS and CaO. The melting and sintering of CaSO4 particles would be aggravated with the increased reaction temperature and would result in a decrease in the reactivity of CaSO4 with CO (involving both the formation rates of CaS and CaO). In the present work, a severe sintering may take place at 1050 C in the TGA-FTIR run and cause an evident decrease in the reactivity of CaSO4 with CO. As a consequence, both CaSO4 conversion XCaSO4 and CaS formation XCaS in the test were much slower than those predicted by the model, as shown in Figures 5a and 10a.

Figure 10. CaS and CaO formation curves for the parallel reactions of CaSO4 with 10% CO at various reaction temperatures. Solid lines with symbols: experimental data. Short dot lines with symbols: model predictions with eqs 20 and 21 from the nucleation and growth model.

By contrast, the CaSO4 and its product CaS would melt into a mixed liquid phase and then further react via the solidsolid reaction R5 above 890 C,6668 resulting in an increase in CaO formation. This positive effect on enhanced CaO formation rate may be offset by the decrease in the reactivity of CaSO4 with CO (R3) during the entire reaction process. As a result, the rate of CaO formation remained almost the same as the reaction temperature increased 3 1 θ ¼ 263:5kJ=mol CaSO4 þ CaS f CaO þ SO2 ΔH298 4 4 ðR5Þ

The reaction time was calculated by using the nucleation and growth model for the parallel reactions. In the range of CaSO4 conversion degree 0.1 e XCaSO4 e 0.5, the residual error (RE) in the nucleation and growth model for the solid component i at the 5422



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Figure 11. CaS and CaO formation curves for the parallel reactions of CaSO4 with CO at 950 C and under various CO concentrations. Solid lines with symbols: experimental data. Short dot lines with symbols: model predictions with eqs 20 and 21 from the nucleation and growth model.

reaction temperature T and under the CO concentration fCO can be calculated as follows REi, T, f CO ðXCaSO4 Þ ¼

tðXi Þ t 0 ðXi Þ ði ¼ CaS, CaO, CaSO4 Þ tðXi Þ

ð27Þ 0

where t(Xi) is the experimental time, and t (Xi) is the calculated reaction time with CaSO4 conversion of XCaSO4. The mean residual error (MRE) for the solid component i at the reaction temperature T, MREi, T, fCO, is the mean value of the absolute error function |REi, T,fCO(XCaSO4)| within the CaSO4 conversion interval [0.1, 0.5], and it is defined by Z MREi, T, f CO ¼

0:5 0:1

REi, T, f CO ðXCaSO4 ÞdXCaSO4 Z 0:5 dXCaSO4 0:1

ði ¼ CaS, CaO, CaSO4 Þ

ð28Þ

Figure 12. Distributions of the residual errors in the nucleation and growth model for the parallel reactions of CaSO4 with 10% CO at various reaction temperatures: (a) CaS formation; (b) CaO formation; and (c) CaSO4 conversion.

The parameter MREi,T,fCO is a measure of the discrepancy between the experimental data and the predicted values from the model. In a previous study,26 the suitable reaction temperature of a fuel reactor in a CLC system should be between 900 and 950 C, so the temperature range of interest would vary from 850 to 1000 C. Thus, the mean value of MREi,T,fCO within the temperature range of 5423



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Table 3. Mean Residual Errors of Both MREi,T and MMREi for Reactions at 10% CO Concentration MREi, T

i

850

900

950

1000

1050

MMREi

C

C

C

C

C

(850-1000 C)

CaS

0.036

0.043

0.047

0.094

0.304

0.055

CaO CaSO4

0.036

0.043

0.041 0.034

0.142 0.022

0.191 0.252

0.092 0.034

Table 4. Mean Residual Errors of Both MREi,fCO and MMREi for Reactions at 950 C MREi,fCO i

5%

6%

10%

18%

28%

MMREi (5-28%)

CaS

0.048

0.125

0.047

0.064

0.099

0.077

CaO

0.188

0.199

0.041

0.457

0.752

0.327

CaSO4

0.075

0.068

0.034

0.0950

0.138

0.082

and MMRECaO, 10% ¼

Figure 13. Distributions of the residual errors in the nucleation and growth model for the parallel reactions of CaSO4 with CO at 950 C and under various CO concentrations: (a) CaS formation; (b) CaO formation; and (c) CaSO4 conversion.

interest (850-1000 C) and at 10% CO concentration, MMREi, is calculated as

MMREi, 10% ¼

1 3 MREi, 850 þ 50n, 10% ði ¼ CaS, CaSO4 Þ 4 n¼0

∑

ð29Þ

1 3 MREi, 850 þ 50n, 10% 2 n¼2

∑

ð30Þ

And the mean values of MREi,T,fCO for reactions at 950 C and under varied CO concentration are also calculated similarly. A small MMREi indicates a tight fit of the model to the experimental data. Figure 12 and Figure 13 show the variations of the residual errors with the CaSO4 conversion XCaSO4 (in the range of solid conversion degree 0.1 e XCaSO4 e 0.5) at various reaction temperatures and under various CO concentrations, respectively. It is inferred that for the reduction of CaSO4 with 10% CO and in the temperature range of interest (850-1000 C), the residual errors REi,T,10% (i = CaS, CaO, and CaSO4) caused by the nucleation and growth model were probably below 0.15 and distributed regularly and uniformly on both sides of the X-axis, resulting in the mean residual errors of both MREi,T,10% and MMREi,10% also no more than 0.15, as indicated in Table 3. For the reactions at 950 C and under varied CO concentration, the residual errors occurred for CaO formation XCaO are large, as shown in Figure 13 and Table 4. As stated above, this may be due to the big relative tolerance caused by measuring the extremely small amount of sulfide emissions (SO2 and COS) and the proceeding of the side reaction R4. However, the mean residual errors of MRE and MMRE occurred for both CaS formation and CaSO4 conversion at 950 C and under 528% CO concentrations are just below 0.15. The error analysis demonstrates that the nucleation and growth model is feasible for describing the reaction mechanism of the CaSO4 oxygen carrier with CO.

5. CONCLUSIONS The reduction of the CaSO4 oxygen carrier by CO in a CLC process has been investigated in a Thermogravimetric Analyzer coupled with Fourier Transform Infrared spectrum (TGAFTIR), and the instantaneous evolutions of SO2 and COS were monitored by the FTIR quantitative analysis. The effects of the reaction temperature and the concentration of CO reactant on 5424


Industrial & Engineering Chemistry Research the reaction rates and the product distributions are discussed. The parallel reactions R1 and R3 of CaSO4 with CO are investigated in terms of the selectivity based on the nucleation and growth model under isothermal conditions, in the range of solid conversion degree 0.1 e XCaSO4 e 0.5. Some interesting results can be achieved as follows: • The reduction of CaSO4 by CO was a complex process, with the products of either sole CaS or both CaS and CaO depending on the reaction temperature as well as the concentration of CO reactant. The increases in the reaction temperature and CO concentration enhance the reaction rate, while the SO2 and COS emissions are aggravated with the increased reaction temperature but suppressed by the rising CO concentration. • The experimental data on the parallel reactions of CaSO4 with CO could be well treated by the nucleation and growth model with the new phase nuclei formation and growth control mechanism. According to the fit results, the apparent activation energies are 187.0 kJ/mol for the reduction of CaSO4 to CaS and 427.7 kJ/mol for the reduction of CaSO4 to CaO with the 95% confidence limits, and the reduction of CaSO4 to CaS is first order with respect to CO concentration and the reduction to CaO of order 0.19. The values of the kinetic parameters confirm that a high reaction temperature and a low CO concentration should give a rise in the sulfur emission from the parallel reactions of CaSO4 with CO.

’ AUTHOR INFORMATION Corresponding Author

*Phone: þ86-25-83795598. Fax: þ86-25-83793452. E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (50976023, 51061130535). ’ NOMENCLATURE ABi,t: absorbance of the ith gaseous species (i = SO2, COS) at the reaction time t [-] Ai: frequency factor [sn] Eai: apparent activation energy [kJ 3 mol1] fCO: concentration of CO reactant [mole 3 mol1] G·i: radial growth rate of the ith nuclei (i = CaS, CaO) [m 3 s1] k: apparent rate constant [sn] ki: rate constant for the transformation of CaSO4 into the ith species [sn] kin,i: intrinsic rate constant for the transformation of CaSO4 into the ith species [sn] m0: weight of the CaSO4 particles at the beginning of the reduction stage [g] mt: weight of the sample at a time t [g] Mi: molecular weights of the ith solid species (i = CaSO4, CaS, CaO) [g 3 mol1] MRE: mean value of the absolute error function |RE| [-] MMRE: mean value of MRE [-] n: Avrami exponent [-] ni: mole amount of the ith product (i = CaS, CaO) [mol] · Ni: nucleation rate of the ith nuclei (i = CaS, CaO)

ARTICLE

Ni: number of the ith nuclei (i = CaS, CaO) NCaSO4,TGA: mole amount of CaSO4 introduced to the TGA reactor [mol] ri: emission rate of the ith species (i = SO2, COS) [mol 3 molCaSO41 3 s1] rVCaSe,CaS: theoretical expansion rate of the ith nuclei (i = CaS, CaO) at the time t [s1] R: universal gas constant [J 3 K1 3 mol1] REi, T: residual error in the model for the solid component i at the reaction temperature T [-] S: selectivity [-] S: average of the selectivity [-] t: reaction time [s] t0 : calculated reaction time [s] T: absolute temperature [K] V: sample volume [cm3] Vi: virtual expansion volume [m3] Vie: theoretical expanding volume [m3] X: solid conversion [-] XCaSO4: CaSO4 conversion [-] Xi: volume fraction or mole fraction of the ith product (i = CaS, CaO) in the CaSO4 sample [-]

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Kinetic Model for Parallel Reactions of CaSO4 with CO in Chemical

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