Investigation into the Behavior of Reductive ... - ACS Publications

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Ind. Eng. Chem. Res. 2009, 48, 5624–5632

Investigation into the Behavior of Reductive Decomposition of Calcium Sulfate by Carbon Monoxide in Chemical-Looping Combustion Hongjing Tian and Qingjie Guo* College of Chemical Engineering, Qingdao UniVersity of Science & Technology, Key Laboratory of Clean Chemical Processing Engineering of Shandong ProVince, Qingdao 266042, China

Chemical-looping combustion is a promising technology with no contact between fuel and combustion air, featuring the inherent separation of CO2 and avoidance of nitrogen oxide formation. To some metal oxide oxygen carriers, the high costs and positive hazard to living environment inhibit the application of chemicallooping combustion systems in large scale. In this work, we investigate the possibility of using calcium sulfate as oxygen carrier. The release amount of SO2 was not only due to the reacting temperature but also affected by the partial pressure of CO in the reaction. If the partial pressure of CO in the atmosphere is big enough, the release amount of SO2 or the occurrence of side reactions can be eliminated fully even if the temperature is as high as 1000 °C. The reactivity behavior of the reduction of CaSO4 by CO in the heating process is also studied. The values of activation energy, frequency factor, and linear factor corresponding to five different heating rates are calculated using an accurate kinetics integral expression and a temperature integral approximation with high precision. The most probable mechanism function in the decomposition process is characterized by G(R) ) [-ln(1 - R)]1/2. 1. Introduction The chemical-looping combustion (CLC) concept is based on the split of a conventional combustion of gaseous fuel such as syngas from coal gasification, natural gas, or refinery gas into separate oxidation and reduction reactions. It is a combustion technology where an oxygen carrier is used to transfer oxygen from the combustion air to the fuel and circulate between two interconnected reactors, thus avoiding direct contact between air and fuel. The advantage of having combustion in two reactors compared to conventional combustion in a single stage is that the CO2 is not diluted with nitrogen gas but is almost pure after separation from water without requiring any extra energy demand or costly external equipment for CO2 separation. Although a real process could be either pressurized or atmospheric, a first step is to investigate CLC under atmospheric conditions. Expected temperature range could be at least 800-1200 °C for the fuel and air reactor, although the temperature would be higher in the air reactor when the reaction between reduced oxygen carrier product and oxygen is endothermic. Another advantage of CLC is that NOx formation can be thoroughly eradicated because the oxidation reaction occurs at considerably lower temperature (900 °C) without flame.1,2 Moreover, the efficiency of chemical-looping combustion system is potential. It was reported that an LNG fueled chemical-looping combustion combined cycle system with chemical absorption technology was estimated to achieve a thermal efficiency of 56% until 2025, while the that of an NGCC system with oxyfueling and chemical absorption technologies achieves merely 51% until 2020.3 The selection of oxygen-carrying material is a cornerstone in the industrial application of CLC. The majority of past studies on oxygen carriers concentrated on those metal oxides for CLC with gaseous fuels. Ni-based,4-15 Cu-based,4,7,16-18 Co-based,7,9,19 Fe-based,4,7,11,14,20-22 and Mn-based4,7,20 metal oxides and their metal blends4,17-19 were all investigated to be suitable as oxygen carriers. However, Fe-based oxygen carriers have the disadvantage of their low capacity of carrying oxygen and larger * To whom correspondence should be addressed. E-mail: qingjieguo@ yahoo.cn.

endothermic enthalpy; Cu-based oxygen carriers have the disadvantage of a tendency to agglomerate at lower operation temperatures; Ni-based oxygen carriers have the disadvantage of their potential hazardous effect on people’s living environment. In addition, the costs of all the metal oxides especially the oxides of Co and Mn are too high to be economically viable to use the metal oxides oxygen carriers in large scale in CLC. Because of the various problems associated with each of these metal oxides oxygen carriers, calcium sulfate (CaSO4) is introduced to be used as a new kind of oxygen carrier. The possible reactions in air and fuel reactors are illustrated as reactions R1-R9. First, CaSO4 has a relatively higher oxygen capacity compared with other metal oxides. The oxygen ratio R0, which is defined as R0 ) (mox - mred)/mox, represents the oxygen transport capacity. The value of R0 for CaSO4/calcium sulfide (CaS) is 0.4706, which is much higher than that of many other metal oxides such as CuO/Cu, NiO/Ni, and Fe2O3/Fe3O4. In addition, calcium sulfate is a stable and widespread natural sulfate and phosphogypsum is the main byproduct of phosphoric acid plants, and thus its cost is quite low. In particular, calcium sulfate powder is friendly to peopl e’s living environment without secondary pollutants. Air reactor: CaS + 2O2 f CaSO4, ∆H298θ ) -957.97 kJ/mol (R1)

CaO + 0.5O2(g) + SO2(g) f CaSO4, ∆Hf,298θ ) -503.00 kJ/mol

(R2)

Fuel reactor: CaSO4 + CH4(g) f CaS + CO2(g) + 2H2O(g), ∆H298θ ) 140.24 kJ/mol

(R3)

CaSO4 + 4H2(g) f CaS + 4H2O(g), ∆H298θ ) -24.51 kJ/mol

(R4)

CaSO4 + 4CO(g) f CaS + 4CO2(g), ∆H298θ ) -174.16 kJ/mol

10.1021/ie900089m CCC: $40.75  2009 American Chemical Society Published on Web 05/11/2009

(R5)

Ind. Eng. Chem. Res., Vol. 48, No. 12, 2009

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CaSO4 + CO(g) f CaO + CO2(g) + SO2(g), ∆Hf,298θ ) 210.49 kJ/mol

(R6)

CaSO4 + 4CO(g) ) CaO + COS(g) + 3CO2(g), ∆Hf,298θ ) -76.82 kJ/mol

(R7)

CaS + 3CaSO4 f 4CaO + 4SO2(g), ∆H298θ ) 1054.04 kJ/mol

(R8)

3CO(g) + SO2(g) f 2CO2(g) + COS(g), ∆H298θ ) -299.94 kJ/mol

(R9)

Carbon monoxide (CO) is a major component in gaseous fuels, and therefore it is necessary and significant to investigate the reactivity behavior and determine the kinetic parameters of the reaction between CaSO4 and CO. In reduction of CaSO4 by CO, temperatures greater than 800 °C are required to obtain near-stoichiometric conversions. Diaz-Bossio et al.23 investigated the reductive decomposition of calcium sulfate utilizing both hydrogen and carbon monoxide in a thermogravimetric analyzer. They found the direct reductive products of CaSO4 are pure CaO from 900 to 1180 °C and the reaction was first order with respect to the concentration of either hydrogen or carbon monoxide. Shen et al.24 found that the direct reductive products of CaSO4 by CO or H2 are mixtures of CaO and CaS at temperature from 850 to 1050 °C. The mole fraction of CaS is bigger than that of CaO at temperature lower than 1000 °C. In particular, the direct reductive products of CaSO4 by CO or H2 are almost pure CaS at 900 °C. Song et al.25 investigated the effects of reaction temperature, gas flow rate, sample mass, and particle size on reduction reactions of CaSO4 by CH4 in a laboratory-scale fixed bed reactor. The results show that CaSO4 has a high reduction reactivity and stability in a long-time reduction/oxidation test. However, a significant SO2 formation was observed at a temperature higher than 950 °C. Song et al.26,27 also performed the cyclic test of a natural anhydrite in alternating reducing simulated coal gas and oxidizing conditions at 950 °C in a fluidized bed reactor at atmospheric pressure. They discovered the formation of SO2 and H2S during the reduction process in the cycles, which hugely weakens the recycling ability of CaSO4. However, most previous studies focused on the investigation into the reaction using an isothermal method with some disadvantages compared with the nonisothermal method. Additionally, sulfur release is unavoidable in all experiments with CaSO4 as oxygen carrier. In this work, it is discovered that the partial pressure of CO in CO/CO2/N2 atmosphere is crucial to sulfur release in the chemical-looping combustion system. With some certain partial pressures of CO, the reduction of CaSO4 by CO is carried out without the formation of SO2 and COS, and the fraction of CaS in solid reductive products is more than 0.9 even at the temperature higher than 1000 °C. The experiments in TGA are carried out with both isothermal and nonisothermal methods. Compared with the isothermal method, the thermal analysis using the nonisothermal method is more convenient because the information of some isothermal curves can be replaced by a single nonisothermal curve. Additionally, the isothermal method is actually very difficult to realize, especially at the beginning of the reaction. Therefore, some kinetic parameters including activation energy and frequency factor of the reaction between CaSO4 and CO are determined with the nonisothermal method when the partial pressure of CO is 20 kPa.

Figure 1. Equilibrium composition for the reaction of 1 mol of CaSO4 and 4 mol CO at room pressure (based on the data from ref 28).

Figure 2. Equilibrium composition for the reaction of 1 mol of CaS with 2 mol of O2 at a total pressure of 1 atm (based on the data from ref 28).

2. Thermodynamic Analysis of the Reduction of CaSO4 by CO Chemical reaction thermodynamics analysis is indispensable for the choice of oxygen carrier and evaluation of CO2 purity in product gas. Figure 1 shows the equilibrium amounts of the major species present when 1 mol CaSO4 reacted with 4 mol CO calculated on the principle of the Gibbs free energy minimization (based on the data from ref 28) to prove the feasibility of calcium sulfate as oxygen carrier. It is shown that at temperatures below 950 °C the major solid reductive product will be calcium sulfide and the gaseous reductive product will be dominantly water vapor and carbon dioxide. Note that a highly concentrated CO2 stream will be obtained in the proposed CLC system. The amounts of some other gaseous products including sulfur dioxide (SO2), carbonyl sulfide (COS), and carbon disulfide (CS2) are negligible. The calculated thermodynamic data presented in Figure 2 indicate that the oxidation products indeed are calcium sulfate and the side reactions that produce CaO and SO2 do not occur to appreciable extents below 950 °C. However, Figures 1 and 2 show that increasing the reacting temperature leads to increasing the amount of sulfurous gas products. It is a key issue to prohibit release of byproduct gas especially sulfur dioxide in both air and fuel reactors.

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Figure 3. Variation of Gibbs free energy at equilibrium for oxygen carrier CO as a function of temperature (based on the data from ref 28).

Figure 4. Effect of the ratio of PCO/PCO2 and reacting temperature on the equilibrium of both reactions R5 and R6 (based on the data from ref 28).

From the standard Gibbs free energy changes, the equilibrium constants can be calculated for various reductions of oxygen carrier and various oxidations of reduced oxygen carrier for a

wide range of operating temperatures. Figure 3 shows thermodynamic analysis of the reduction reactions of calcium sulfate along with several typical metal oxide oxygen carriers such as CuO, Fe2O3, CoO, Mn3O4, and NiO. The free energy of reaction is shown versus temperature from 700 to 1300 °C (based on the data from ref 28). It is shown that calcium sulfate is a relatively stable oxygen carrier and its reactivity with CO is near that with NiO. In addition, it is noted that reaction R5 takes precedence over the side reactions R6 and R7 in reduction of CaSO4 by CO at temperature below 1140 °C because the standard Gibbs free energy change of reaction R5 is less than that of side reactions R6 and R7. Therefore, it is critical to prevent the side reactions to the recycling of calcium sulfate in the CLC system. As shown in Figure 4, reactions R5 and R6 can be controlled through the reducing potential of the gas phase represented by the ratio of PCO/PCO2. In the temperature range from 900 to 1000 °C, the sulfur dioxide concentration in the gas phase at equilibrium is limited to below 7 mol %. Higher temperature may lead to more formation of SO2 in gas phase. In this temperature range, the value of log(PCO/PCO2) is between -2.0 and -1.75, and therefore the corresponding value of PCO/PCO2 is between 0.01 and 0.017783. Additionally, the value of PCO/ PCO2 is below 5%. As a result, the amount of COS produced in the reduction of CaSO4 by CO is so small that it can be neglected. That is to say, from 900 to 950 °C, with the concentration of SO2 ranging from 1 to 3%, the product gas with the purity of CO2 more than 96% can be obtained. It must be noted that reaction R5 is a strong exothermic reaction, whereas the side reaction R6 is a strong endothermic reaction. Especially, the changes of standard Gibbs free energy show a slight monotonically increasing trend for the reaction R5 and an obvious monotonically decreasing trend for the reaction R6. Therefore, increasing reacting temperature actually inhibits the exothermic reaction R5 while greatly promoting the endothermic reaction R6. Moreover, it is thermodynamically feasible for reaction R5 to be promoted while reaction R6 is suppressed by keeping the ratio smaller than the crossover value between the two lines for reactions R5 and R6, respectively. It can also been seen that reducing the concentration of sulfur dioxide in gas phase leads to lessening of the crossover temperature between the two lines for reactions R5 and R6, respectively. Figure 5 illustrates an equilibrium gas ratio of PCO2/PCO as a function of both the partial pressure of SO2 and the temperature

Figure 5. (a) 3D phase diagrams for the reduction of calcium sulfate by CO. (b) 2D projection of three curved surfaces on log(PCO2/PCO) - log(PSO2) plane (based on the data from ref 28).


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for the reduction of calcium sulfate. It is indicated that the ratio approaches approximately 1.99526 × 100.3 at the triple point of calcium sulfate, calcium sulfide, and calcium oxide without reciprocal transformation in the temperature range from 700 to 1300 °C. Therefore, CaS is a stable compound when the gas ratio of PCO2/PCO is less than 0.31623 × 10-1.5 and the partial pressure of sulfur dioxide is above 0.001 × 10-3 kPa. Bigger partial pressure of CO and SO2 can promote the trend of conversion of CaSO4 to CaS. Furthermore, a bigger partial pressure of SO2 in reduction should be maintained in the CLC pilot base because of reaction R2. However, the partial pressure of SO2 should be a small value to avoid the corrosion of the reactor and leak of SO2. This problem can be solved by adding a calciner in which some fresh limestone reacts with sulfur dioxide29 while the products of CaSO4 can be used as oxygen carriers later. 3. Reactivity Behavior of the Reduction of CaSO4 by CO The investigation into reactivity behavior and kinetics analysis of the reduction reaction of CaSO4 by CO was determined using a nonisothermal method by a thermogravimetric analyzer (Netzsch STA 409 PC). Five samples of analytically pure calcium sulfate were each weighed at 20.0 ( 0.1 mg using an analytical balance. The samples were heated at 800 °C for 3 h at first to be dehydrated, and then the five samples were heated in simulated atmosphere from 20 to 1200 °C to be reductively decomposed with five different heating rates including 5, 7, 10, 15, and 20 °C/min in a thermogravimetric analyzer. Considering the complicated atmosphere in the fuel reactor composed of at least CO2, CO, and N2, the simulated atmosphere consisted of 40 mol % CO2, 40 mol % N2, and 20 mol % CO. The average particle size of the sample powders was evaluated to be 8.934 µm using a Rise 2000 laser particle size analyzer. In the 40 mol % CO2, 40 mol % N2, and 20 mol % CO atmosphere, calcium sulfate was reductively decomposed by carbon monoxide and the reduction products were calcium sulfide and calcium oxide, illustrated as reactions R5, R6, and R7. Simultaneously, calcium sulfate could react with calcium sulfide quickly, illustrated as reaction R8, because the two solids form a eutectic liquid.23 The relationship between the conversion of calcium sulfate and reacting temperature is shown in Figure 6. It can be seen that a bigger heating rate causes the delay of the initial reacting temperature from 830 °C with heating rate of 5 °C/min to 930 °C with heating rate of 20 °C/min. DTG curves for the reduction of CaSO4 are illustrated in Figure 7. It is observed that the absolute maximum value of the derivative of sample mass of CaSO4 to time is increasing from 3.5%/min with heating rate of 5 °C/min to 11%/min with heating rate of 20 °C/min. As shown in Figure 8, the composition of the reductive products differs with different heating rates smaller than 23 °C/min. It can be seen that the mole fraction of calcium oxide in products increases with increasing heating rate and approaches almost 100% with the heating rate bigger than 23 °C/min. That is because a bigger heating rate leads to higher reacting temperature in the last part of the reaction, which greatly promotes reactions R6 and R8. However, as illustrated in Figure 9, when CaSO4 begins to react with CO at 1100 °C, the composition of reduction products has no relationship with heating rate and the residues are merely calcium oxide. Similarly, the reduction products of the reaction between CaSO4 and CO at 1100 °C are also

Figure 6. Conversion curves of calcium sulfate for five different heating rates in reduction of CaSO4 by CO.

Figure 7. DTG curves of calcium sulfate for five different heating rates in reduction of CaSO4 by CO.

Figure 8. Mole fraction of CaO and CaS in reductive products of the reductive reaction of CaSO4 by CO.

only calcium oxide, as illustrated in Figure 10. It can be explained that at 1100 °C the strong endothermic reactions R6 and R8 are greatly promoted. The reaction rate of reaction

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Figure 9. TG curves of the reductive decomposition of CaSO4 with five heating rates at the CO partial pressure of 20 kPa when CaSO4 begins to react with CO at 1100 °C.

Figure 10. TG curves of the reductive decomposition of CaSO4 by CO at the constant reacting temperature of 1100 °C.

R8 is so fast that the newly produced CaS reacts with fresh CaSO4 immediately. At last no CaS species remains in the solid residues. It is clear that high reacting temperature increases the reaction rate and promotes the conversion of solid reactant in gas-solid reaction. However, as shown in Figures 9 and 10, that high reacting temperature enhances sulfur release in the reaction between CaSO4 and CO. In this work, we found that the release amount of SO2 was not only due to the reacting temperature but also affected by the partial pressure of CO in the reaction. Figure 11 shows that the proportion of solid residues to the initial solid reactants increases monotonically when the partial pressure of CO is increasing from 9 to 50 kPa at the same heating rate of 15 °C/min. If the partial pressure of CO is increasing above 50 kPa, the proportion approximately remains a constant value. It can be deduced that the proportion is 0.5289 when CaSO4 is wholly converted to CaS, while it is 0.4113 when CaSO4 is wholly converted to CaO. Figure 11 implies that the partial pressure of CO higher than 50 kPa inhibits the formation of SO2 because the proportion of solid residues is 0.5315, near the theoretical value 0.5289. Figure 12 shows the reactivity behavior between CaSO4 and CO with four different partial pressures of CO at 1000 °C. Similarly, the proportion of solid residues to the initial solid

Figure 11. TG curves of the reductive decomposition of CaSO4 by CO for the different partial pressures of CO with the same heating rate of 15 °C/ min.

Figure 12. TG curves of the reductive decomposition of CaSO4 by CO for the different partial pressures of CO at 1000 °C.

reactants remains an approximately constant value when the partial pressure of CO is more than 75 kPa. The species in the solid residues can be estimated by XRD spectroscopy, as shown in Figure 13. At the partial pressure of CO over 50 kPa, it is shown that almost no CaO species are left in the residues of CaSO4 reduction. 4. Kinetics Analysis of the Reduction of CaSO4 by CO Considering the occurrence of many reactions including reactions R5, R6, R7, R8, and R9 in a single process, the whole process can be regarded as overall reaction R10. CaSO4 + (4 - 3n)CO f (1 - m - n)CaS + (m + n)CaO + (4 - m - 3n)CO2 + nSO2 + mCOS

(R10)

The reductive decompositions of solids usually assume that the reaction rate is a function of reaction temperature and amount of solid. The equation describing the progress of the reductive decomposition is dR ) kf(R) (11) dt where t is the reaction time, and R is the conversion of CaSO4 at a time. R is defined as R ) (Wi - W)/(Wi - Wr), where W


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Figure 13. XRD characterization of the solid residues after reduction of CaSO4 by CO at 1000 °C with different CO partial pressures. (a) PCO ) 20 kPa. (b) PCO ) 50 kPa. (c) PCO ) 75 kPa.

is the solid weight and subscripts i and r correspond to the initial and residual values, respectively. f(R) is the kinetic function related to the reaction mechanism. k is the rate constant expressed by the Arrhenius equation: E k ) A exp RT

( )

(12)

where E is the activation energy, A is the frequency factor, and R is the universal gas constant. When the reaction meets a linear temperature program (T ) T0 + βt, where β is the heating rate and T0 is the starting temperature), eq 11 becomes dR A E ) exp f(R) (13) dT β RT The kinetic parameters were calculated by the iterative method proposed30 using the approximation with quite high accuracy proposed by Chen and Liu.31 The values of activation energy, frequency factor, and linear factor corresponding to five different heating rates and 30 different reaction mechanism functions are listed in Table 1. The results corresponding to seven screened reaction mechanism functions with good linear factors close to 1 are listed in Table 2. Pan et al.32,33 proposed a double extrapolated method to determine the kinetic mechanism of reductive decomposition of some solid materials. The values of the kinetic parameters

( )

Table 1. Thirty Common Integral Approximations of Kinetics Mechanism Functions No.

function

1 2 3 4, 5 6 7 8 9 10-16

parabolic rule Valensi function G-B function Jander function Jander function anti-Jander function Z-L-T function Mampel rule Avrami-Erofeev function

17-22

Mampel power rule

23-27 28 29 30

Mampel power rule

30 common reaction mechanism function R2 R + (1 - R) ln(1 - R) 1 - 2R/3 - (1 - R)2/3 [1 - (1 - R)1/3]n, n ) 2 1/2 [1 - (1 - R)1/2]1/2 [(1 + R)1/3 - 1]2 [(1 - R)-1/3 - 1]2 -ln(1 - R) [-ln(1 - R)]n, (n ) 2/3, 1/2, 1/3, 4, 1/4, 2, 3) 1 - (1 - R)n, (n ) 1/2, 3, 2, 4, 1, 1/3, 1/4) Rn, (n ) 1, 3/2, 1/2, 1/3, 1/4) (1 - R)-1 (1 - R)-1 - 1 (1 - R)-1/2

with heating rate close to zero including Eβf0 and ln Aβf0for every screened function are solved when the heating rate is extrapolated to zero according to eqs 14 and 15. E ) a1 + b1β + c1β2 + d1β3

(14)

ln A ) a2 + b2 β + c2 β2 + d2 β3

(15)

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Table 2. Kinetics Parameters for Reductive Decomposition of CaSO4 by CO According to Seven Reaction Mechanism Functions with the Value of Linear Factor Close to 1 β ) 5 °C/min

β ) 7 °C/min

-1

β ) 10 °C/min

No.

E (kJ/mol)

ln A (s )

r

E (kJ/mol)

ln A (s )

r

E (kJ/mol)

ln A (s-1)

r

5 6 11 12 14 25 26

216.94 204.85 243.81 156.31 112.71 173.55 109.66

17.88 16.81 21.22 12.38 7.89 13.87 7.39

0.99607 0.99336 0.99825 0.99931 0.99794 0.97984 0.97752

172.26 162.49 193.94 123.05 87.77 137.16 85.40

13.19 12.38 15.98 8.93 5.33 10.07 4.90

0.99379 0.99055 0.99893 0.99959 0.99620 0.97510 0.97142

159.42 150.27 179.74 113.55 80.63 126.54 78.30

12.02 11.28 14.66 8.14 4.81 9.16 4.39

0.99332 0.98998 0.99854 0.99912 0.99564 0.97399 0.96978

β ) 15 °C/min

β ) 20 °C/min

-1

E (kJ/mol)

ln A (s )

r

E (kJ/mol)

ln A (s )

r

E (kJ/mol)

ln A (s-1)

5 6 11 12 14 25 26

144.60 136.40 162.81 102.21 72.10 115.09 70.63

10.61 9.98 13.01 7.14 4.13 8.13 3.80

0.99692 0.99521 0.99879 0.99939 0.99593 0.98378 0.98071

139.07 131.24 156.43 97.88 68.79 110.90 67.75

10.05 9.46 12.33 6.76 3.91 7.75 3.63

0.99860 0.99798 0.99831 0.99987 0.99535 0.98975 0.98762

364.22 384.57 429.89 280.45 205.79 311.60 201.65

33.56 35.51 40.85 25.34 17.51 28.31 16.89

conversion fraction

activation energy (kJ/mol)

Rf0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95

linear factor

280.05 261.66 235.35 216.01 201.78 191.92 185.47 179.03 175.15 171.93 169.73 167.04 165.83 164.16 162.92 161.60 160.12 159.44 158.29 156.11

0.99924 0.99889 0.99872 0.99839 0.99829 0.99887 0.99885 0.99935 0.99972 0.99941 0.99977 0.99926 0.99955 0.99907 0.99888 0.99821 0.99798 0.99863 0.99874

After rearranging eq 16 derived in our previous work,30 we obtained eq 17: G(R) T0 2 Q(u0) exp[-(u0 - u)] T Q(u) 1 T Q(u)

{ ()

2

where Q(u) ) (RT). ln

[∫u∞

-2

x

exp(-x) dx]/[u

-2

{ ()

to zero, ERf0, are determined when the conversion is extrapolated to zero according to eq 18. E ) a3 + b3R + c3R2 + d3R3

(18)

As illustrated in Figure 14, the value of activation energy is reduced with increasing conversion rate. The value of activation energy for the decomposition of the samples unaffected by any reaction can be obtained by extrapolating the conversion rate to zero, and we get ERf0 ) 280.05 kJ/mol. The reaction mechanism function corresponding to the minimal value of the difference between ERf0 and Eβf0 is the most probable mechanism function for reductive decomposition of CaSO4 by CO. It can be found that the most probable function is function 12, G(R) ) [-ln(1 - R)]1/2. Therefore, the reductive decomposition process is likely to be controlled by a nucleation mechanism. Popescu34 proposed a multiple scanning rate method to evaluate the reaction mechanism function without any assumption by analyzing some TG curves with different heating rates, and its results have good reliability. With Popescu’s method, eq 19 can be obtained after rearrangement and integration of eq 11:

E AR βE RT (16)

exp(-u)] and u ) (E)/

β T0 2 Q(u0) T Q(u) 1 exp[-(u0 - u)] T Q(u) 2

}

) ln

-1

β f 0 °C/min

No.

Table 3. Relationship between Activation Energy and Conversion Rate for Decomposition of CaSO4

ln

-1

}

) ln

AR E G(R)E RT (17)

It can be seen from eq 17 that to a fixed value of the conversion of CaSO4, ln(AR/G(R)E) can be seen as a constant. Therefore, the value of activation energy, E, can be achieved directly with eq 17 using an iterative method even though the reaction mechanism function, G(R), is not yet known. The calculated results of the activation energy corresponding to every conversion value from 0.05 to 0.95 are listed in Table 3. The values of the activation energy with conversion of CaSO4 close

Figure 14. Variations of activation energy with conversion fraction of calcium sulfate to calcium sulfide or calcium oxide by carbon monoxide. (The red curve is fitted by the data in Table 3 with the form of eq 17, the data in Table 3 are reflected by these black points.)

Ind. Eng. Chem. Res., Vol. 48, No. 12, 2009 Table 4. Linear Fitting Results of Seven Probable Reaction Mechanism Functions Selected in Table 2 by the Popescu Method T ) 968 °C

T ) 985 °C

T ) 995 °C

No.

linear factor

standard deviation

linear factor

standard deviation

linear factor

standard deviation

5 6 11 12 14 25 26

0.99296 0.99388 0.99058 0.99820 0.99396 0.99554 0.99363

0.01694 0.02006 0.03552 0.00509 0.16063 0.03214 0.11314

0.98969 0.99181 0.98361 0.99847 0.99183 0.99428 0.99088

0.02649 0.03066 0.06706 0.00113 0.17994 0.05632 0.14675

0.98507 0.98950 0.97210 0.99774 0.98758 0.99384 0.98975

0.03699 0.03789 0.12181 0.00202 0.18202 0.05305 0.16685

∫

R2

∫

1 T2 dR ) k(T) dT (19) f(R) β T1 To a certain temperature the integration of ∫TT12 k(T) dT is constant. Therefore, the relationship between G(R) and 1/β is a straight line through zero. The reaction mechanism function corresponding to the best linear relationship is the most probable reaction mechanism function. The relationship between G(R) and 1/β can be determined by eq 19, and the linear fitting results including linear factor and standard deviation are shown in Table 4. The linear factor corresponding to function 12 is closest to 1, and the standard deviation is nearest zero for three random temperatures of 968, 985, and 995 °C, which implies that function 12 is the most probable reacting mechanism function by the Popescu method.34 G(R) )

R1

5. Conclusions (1) CaSO4 may be used as a promising oxygen carrier in thermodynamic analysis for a chemical-looping combustion system. (2) A bigger heating rate causes the delay of the initial reacting temperature from 830 °C with heating rate of 5 °C/min to 930 °C with heating rate of 20 °C/min. The composition of the reductive products differs with different heating rates smaller than 23 °C/min. If the heating rate is bigger than 23 °C/min, the mole fraction of calcium oxide in products approaches almost 100%. (3) The release amount of SO2 was not only due to the reacting temperature but also affected by the partial pressure of CO in the reaction. If the partial pressure of CO is big enough in the reaction, CaSO4 can be wholly converted to CaS even if the temperature is as high as 1000 °C. (4) Kinetic parameters of reductive decomposition without any disturbance from some other reactions, including Eβf0 and ln Aβf0, are determined, and we get ERf0 ) 280.45 kJ/mol and ln Aβf0 ) 25.34 s-1. The most probable reaction mechanism function can be determined as G(R) ) [-ln(1 - R)]1/2 using a nonisothermal method. Acknowledgment The financial support from New Century Excellent Talents in University (NCET-07-0473), Natural Science Foundation of China (20676064, 20876079), and Taishan Mountain Scholar Constructive Engineering Foundation (JS 200510036) is greatly appreciated. Literature Cited (1) Ishida, M.; Jin, H. G. A new advanced power-generation system using chemical-looping combustion. Energy 1994, 19, 415.

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ReceiVed for reView January 19, 2009 ReVised manuscript receiVed April 1, 2009 Accepted April 14, 2009 IE900089M

Investigation into the Behavior of Reductive ... - ACS Publications

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