Energy & Fuels 2008, 22, 3915–3921
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Investigation into Decomposition Behavior of CaSO4 in Chemical-Looping Combustion Hongjing Tian,† Qingjie Guo,*,† and Jing Chang‡ College of Chemical Engineering, Qingdao UniVersity of Science and Technology, Key Laboratory of Clean Chemical Processing Engineering of Shandong ProVince, Qingdao 266042, China, and Resources and EnVironment College, Qingdao Agricultural UniVersity, Qingdao 266109, China ReceiVed April 10, 2008. ReVised Manuscript ReceiVed August 6, 2008
Chemical-looping combustion (CLC) is a promising technology to combine the energy-use situation in China and CO2 zero emission in situ, which allows for CO2 sequestration by efficient ways and without nitrogen oxide (NOx) formation. An oxygen carrier with good performance is one of the key issues of the CLC process. Calcium sulfate has proven to be a kind of new oxygen carrier with sufficient reactivities in reduction and oxidation reactions, with enough ability for carrying oxygen and no secondary pollution. The decomposition mechanism of calcium sulfate with an average particle size of 8.934 µm in a different simulated atmosphere in CLC is investigated using a simultaneous thermal analyzer at five different heating rates. In an inert atmosphere, the relationship between activation energy and conversion fraction of calcium sulfate is obtained without the introduction of the reaction mechanism function. The values of activation energy, frequency factor, and linear factor corresponding to 5 different heating rates and 30 different common reaction mechanism functions, respectively, are calculated using an accurate kinetics integral expression and a temperature integral approximation with high precision. Kinetic parameters of the decomposition reaction without any disturbance of other reactions, including Eβf0 and ln Aβf0, are determined by extrapolating the heating rate to zero. Additionally, the relationship between the activation energy of decomposition and conversion rate is found using the double-extrapolated method. The activation energy at the start of the decomposition reaction, ERf0, is also evaluated by extrapolating the conversion rate to zero. Whe Eβf0 and ERf0 are compared, the most likely mechanism function in the decomposition process is characterized by the Avrami-Erofeev equation and the reaction is dominated by the nucleation rate. The Avrami-Erofeev equation is also evaluated on the basis of the most likely mechanism function by the Popescu method.
1. Introduction Earth’s climate is experiencing a tremendous change characterized by global warming. In December 2007, Bali declaration, of significant importance to reduce the emission of greenhouse gas especially for the emission of carbon dioxide, was issued at the United Nations Climate Change Conference. Chemical-looping combustion (CLC) is a promising technology to promote reduction of CO2 emission because CO2 can be separated from produced gas directly without any extra energy consumption and separating apparatus. CLC also shows its advantage in system thermal efficiency that the irreversible exergy reduction in CLC is less than that in conventional combustion of fuel because of the two-step use of heat in the CLC system. The selection of an oxygen carrier is a key issue in the application of CLC. A common oxygen carrier such as metal oxides of Fe,1-3 Ni,3-7 and Cu8-10 as well as some metal blends are expensive, which may cause secondary pollutions in the case * To whom correspondence should be addressed. E-mail: qingjieguo@ yahoo.cn. † Qingdao University of Science and Technology. ‡ Qingdao Agricultural University. (1) Mattisson, T.; Johansson, M.; Lyngfelt, A. Multicycle reduction and oxidation of different types of iron oxide particlessApplication to chemicallooping combustion. Energy Fuels 2004, 18 (3), 628–637. (2) Cho, P.; Mattisson, T.; Lyngfelt, A. Comparison of iron-, nickel-, copper- and manganese-based oxygen carriers for chemical-looping combustion. Fuel 2004, 83 (9), 1215–1225.
of some heavy metal elements being dissipated into the atmosphere. Recently, some sulfates, such as CaSO4, SrSO4, and BaSO4, are considered as new oxygen carriers. Their direct reduction products are CaS, SrS, and BaS, respectively, when they react with syngas, methane, or even some solid fuels in an appropriate temperature range, while the reduction products can (3) Johansson, M.; Mattisson, T.; Lyngfelt, A. Creating a synergy effect by using mixed oxides of iron and nickel oxides in the combustion of methane in a chemical-looping combustion reactor. Energy Fuels 2006, 20 (6), 2399–2407. (4) Ishida, M.; Yamamoto, M.; Ohba, T. Experimental results of chemical-looping combustion with NiO/NiAl2O4 particle circulation at 1200 °C. Energy ConVers. Manage. 2002, 43 (9-12), 1469–1478. (5) Jin, H.; Okamoto, T.; Ishida, M. Development of a novel chemicallooping combustion: Synthesis of a looping material with a double metal oxide of CoO-NiO. Energy Fuels 1998, 12 (6), 1272–1277. (6) Mattisson, T.; Jardnas, A.; Lyngfelt, A. Reactivity of some metal oxides supported on alumina with alternating methane and oxygenapplication for chemical-looping combustion. Energy Fuels 2003, 17 (3), 643–651. (7) Jin, H.; Okamoto, T.; Ishida, M. Development of a novel chemicallooping combustion: Synthesis of a solid looping material of NiO/NiAl2O4. Ind. Eng. Chem. Res. 1999, 38 (1), 126–132. (8) De Diego, L. F.; Garcia-Labiano, F.; Adanez, J.; Gayan, P.; Abad, A.; Corbella, B. M.; Palacios, J. M. Development of Cu-based oxygen carriers for chemical-looping combustion. Fuel 2004, 83 (13), 1749–1757. (9) Corbella, B. M.; De Diego, L.; Garcia, F.; Adanez, J.; Palacios, J. M. The performance in a fixed bed reactor of copper-based oxides on titania as oxygen carriers for chemical looping combustion of methane. Energy Fuels 2005, 19 (2), 433–441. (10) Adanez, J.; Gayan, P.; Celaya, J.; de Diego, L. F.; Garcia-Labiano, F.; Abad, A. Chemical looping combustion in a 10 kWth prototype using a CuO/Al2O3 oxygen carrier: Effect of operating conditions on methane combustion. Ind. Eng. Chem. Res. 2006, 45 (17), 6075–6080.
10.1021/ef800508w CCC: $40.75 2008 American Chemical Society Published on Web 09/13/2008
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also be directly oxidized to CaSO4, SrSO4, and BaSO4 by oxygen.11 In addition, the ability of calcium sulfate to carry oxygen is high, and it can be produced with low cost because it exists widely in nature. The oxidation and reduction reactions of calcium sulfate in a chemical-looping combustor for solid fuels, such as coal and biomass, are illustrated in eqs 1-4. In the air reactor, CaS + 2O2 T CaSO4,
∆Hθ298 ) -957.97 kJ/mol
(1)
In the fuel reactor, CaSO4 + CH4 T CaS + CO2 + 2H2O(l),
∆Hθ298 ) 67.46 kJ/mol (2)
CaSO4 + 4H2 T CaS + 4H2O(l),
∆Hθ298 ) -185.56 kJ/mol (3)
CaSO4 + 4CO T CaS + 4CO2,
∆Hθ298 ) -174.16 kJ/mol (4)
However, at high temperature, calcium sulfate can be decomposed according to eq 5; therefore, it is a key issue to prevent the decomposition of calcium sulfate and emission of produced sulfer oxide. CaSO4 T CaO + SO2 + 0.5O2,
∆Hθ298 ) 50.30 kJ/mol (5)
This is a complicated reversible reaction. Calcium sulfate is decomposed into calcium oxide, sulfur dioxide, and oxygen if the partial pressure of sulfur dioxide is lower than the equilibrium partial pressure, while calcium oxide is transformed to calcium sulfate if the partial pressure of sulfur dioxide becomes higher than the equilibrium partial pressure. The total reaction is controlled by reaction temperatures and the partial pressure of sulfur dioxide. The reaction rate is very slow when temperature is lower than 1473.15 K, even no sulfur dioxide exits in the atmosphere. Therefore, the mechanism and kinetics parameters of the decomposition of calcium sulfate are of great significance in CLC. Felix and Dirk12 investigated the kinetic of bassanite (calcium sulfate hemi-hydrate) dissolution and gypsum (calcium sulfate dihydrate) precipitation and obtained an apparent activation energy that indicates a diffusion-controlled dissolution mechanism. Vasilije and Borislav13 presented a model in which the reduction between the produced CaSO4 and CO and thermal decomposition of the produced CaSO4 were incorporated, for the process of inherent sulfur capture in coal particles during combustion in a fluidized bed. Furthermore, Tarelho and Matos14 pointed out that limestone addition is suitable for in situ SO2 removal during atmospheric bubbling fluidized bed combustion and the reductive decomposition of CaSO4 could be responsible for the low efficiency of SO2 removal by limestone. In 1993, Kamphuis and Potma15 examined the reductive decomposition (11) Cao, Y.; Pan, W. P. Investigation of chemical looping combustion by solid fuels. 1. Process analysis. Energy Fuels 2006, 20 (5), 1836–1844. (12) Felix, B.; Dirk, B. Bassanite (CaSO4 · 0.5H2O) dissolution and gypsum (CaSO4 · 2H2O) precipitation in the presence of cellulose ethers. J. Cryst. Growth 2001, 233 (4), 837–845. (13) Vasilije, M.; Borislav, G.; Davor, L. Modeling of inherent SO2 capture in coal particles during combustion in fluidized bed. Chem. Eng. Sci. 2006, 61 (5), 1676–1685. (14) Tarelho, L. A. C.; Matos, M. A. A.; Pereira, F. J. M. A. The influence of operational parameters on SO2 removal by limestone during fluidised bed coal combustion. Fuel Process. Technol. 2005, 86 (12), 1385– 1401. (15) Kamphuis, B.; Potma, A. W.; Prins, W.; Van Swaaij, W. P. M. The reductive decomposition of calcium sulphate. I. Kinetics of the apparent solid-solid reaction. Chem. Eng. Sci. 1993, 48 (1), 105–116.
of CaSO4 or, equivalently, the apparent solid-solid reaction between CaS and CaSO4 and found it takes place when a mixture of these compounds is heated at the temperature above 1373.15 K using an inert atmosphere. CLC is a promising technology to combine fuel combustion and pure CO2 production. Unfortunately, little information is available where calcium sulfate is used as the oxygen carrier in a CLC process. One of the key issues of the application of calcium sulfate as a new oxygen carrier is the inhibition of its decomposition at high temperatures. Therefore, it is important to investigate the decomposition behavior of calcium sulfate in simulated atmospheres in CLC and the kinetic parameters and mechanism in thermal decomposition of calcium sulfate. Cai et al.16 proposed a new temperature integral approximate formula using the pattern search method. The new approximate formula is much simpler but gives more accurate values of the temperature integral than some other formulas. Chen and his co-workers17 derived a new approximation with a higher accuracy for temperature integral of similar form with the approximation proposed by Cai et al. from a new procedure. Orfao18 gave a critical review of the known approximations and established a clear ranking. Moreover, he proposed a “novel” and excellent expression that can approximate very accurately the temperature integral, and then, correct values of the activation energy are obtained. Pan et al.19,20 proposed a double-extrapolated method to determine the kinetic mechanism of thermal decomposition of solid materials. He thought in a thermal field with a certain heating rate that the heat conduction of the sample itself results in the temperature differences between the sample surface and surrounding gas and even two different parts of the sample itself. Therefore, the samples are at a thermal non-equilibrium throughout the heating process, which causes the errors between the calculated value and the true value in thermal equilibrium. When the heating rate is close to zero, the errors approach zero obviously and the calculated kinetic parameters reflect the real mechanism of thermal decomposition of calcium sulfate. Additionally, Pan et al. thought kinetic parameters change regularly with the conversion rate. Consequently, the kinetic parameters are more precise if the conversion rate of the sample approaches zero and all side reactions can be avoided. Popescu21 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 a good reliability. In this paper, thermal gravimetric analysis (Netzsch STA 409 PC) in a microreactor is used to determine the decomposition mechanism of calcium sulfate through analyzing the weight of the mixture as a function of time and temperature. An accurate kinetics integral expression and the double-extrapolated method (16) Cai, J.; Yao, F.; Yi, W.; He, F. New temperature integral approximation for nonisothermal kinetics. AIChE J. 2006, 52 (4), 1554– 1557. (17) Chen, H.; Liu, N. New procedure for derivation of approximations for temperature integral. AIChE J. 2006, 52 (12), 4181–4185. (18) Orfao, J. J. M. Review and evaluation of the approximations to the temperature integral. AIChE J. 2007, 53 (11), 2905–2915. (19) Pan, Y. X.; Guan, X. Y.; Feng, Z. Y.; Li, X. Y. A new method determining mechanism function of solid state reactionsThe non-isothermal kinetic of dehydration of nickle(II) oxalate dihydrate in solid state. Chin. J. Inorg. Chem. 1999, 15 (2), 247–251. (20) Pan, Y. X.; Guan, X. Y.; Feng, Z. Y.; Li, X. Y. Study on the kinetic mechanism of the dehydration process of FeC2O4 · 2H2O using double extrapolation. Acta Phys.-Chim. Sin. 1998, 14 (12), 1088–1093. (21) Popescu, C. Integral method to analyze the kinetics of heterogeneous reactions under non-iso-thermal conditions: A variant on the OzawaFlynn-Wall method. Thermochim. Acta 1996, 285 (2), 309–323.
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dR ) kf(R) dt
(6)
where t is the reaction time and R is the degree of conversion. R is defined as R ) (Wi - W)/(Wi - Wr), where W is the solid weight and the 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
( RTE )
k ) A exp -
(7)
where E is the activation energy, A the frequency factor, and R 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 6 becomes
dR A E ) exp f(R) dT β RT
( )
Figure 1. Particle size distribution graph of the fresh calcium sulfate sample. Table 1. 30 Common Integral Approximations of the Kinetics Mechanism Function number
function
reaction mechanism function
1 2 3 4 and 5 6 7 8 9 10-16
Parabolic rule Valensi function G-B function Jander function Jander function anti-Jander function Z-L-T funtion Mample rule Avrami-Erofeev function Mampel power rule Mampel power rule
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
17-22 23-27 28 29 30
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
are carried out to calculate the kinetic parameters of decomposition and evaluate its mechanism. 2. Experimental Details and Data Processing Method 2.1. Preperation of Calcium Sulfate Samples. Five samples were weighted 20.0 ( 0.1 mg, respectively, using an analytical balance. The analytically pure calcium sulfate powders are heated at 1073.15 K for 3 h at first to be dehydrated, and then the five samples are heated in different simulated atmospheres from 298.15 to 1628.15 K to be decomposed at five different heating rates, including 5, 7, 10, 15, and 20 K/min, respectively, in a Netzsch STA 409 PC thermal analyzer. The atmospheres in CLC are very complicated and are composed of at least CO2, CO, and N2 in the reduction reactor and at least N2 and O2 in the oxidation reactor. Therefore, the composition of the simulated atmosphere is 40 mol % CO2, 40 mol % N2, and 20 mol % CO in the reduction reactor and 79 mol % N2 and 21 mol % O2 in the oxidation reactor. To investigate the thermal decomposition mechanism of calcium sulfate, its decomposition in a pure nitrogen atmosphere is also carried out. The particle size distribution of the sample powders is illustrated as Figure 1, and its average diameter is evaluated to be 8.934 µm using a Rise 2000 laser particle size analyzer. 2.2. Data Processing Method. The decomposition reactions of solids are usually assumed that the decomposition rate is a function of the reaction temperature and amount of solid. If only a single reaction is involved, the equation describing the progress of the decomposition is
(8)
For the interpretation of experimental data by the integral method, it is necessary to integrate the differential equation. After separation of variables and integration, eq 8 leads to
G(R) )
A β
[∫ exp(- RTE )dT - ∫
T0
T
0
0
( RTE )dT]
exp -
(9)
After rearrangement and simplification, eq 9 can be transformed to a linear form
ln
E G(R) AR ) ln T0 2 Q(u0) βE RT exp[-(u0 - u)] T Q(u) 1 T Q(u) (10) 2
{ ()
}
where Q(u) ) (∫u∞x-2 exp(-x)dx)/(u-2 exp(-u)) and u ) E/RT. Q(u) is chosen to be the approximation proposed by Chen and Liu17 with quite high accuracy
Q(u) )
3u2 + 16u + 4 3u2 + 22u + 30
(11)
The kinetic parameters are calculated by the iterative method. The value of activation energy, frequency factor, and linear factor corresponding to 5 different heating rates and 30 different reaction mechanism functions, respectively, are listed in Table 1, whose results are indicated in Table 2. Some reaction mechanism functions with good linear relation are screened corresponding to the value of linear factor, r, close to 1. The values of Eβf0 and ln Aβf0 for every screened function are solved when the heating rate is extrapolated to zero according to eqs 12 and 13.
E ) a2 + b2β + c2β2 + d2β3
(12)
ln A ) a3 + b3β + c3β2 + d3β3
(13)
The value of activation energy, E, can be achieved directly using the Flynn-Wall-Ozawa method, even though the reaction mechanism function, G(R), is not yet known. Vyazovkin22 thought the Flyn-Wall-Ozawa method is applicable when eq 14 is satisfied.
E g 13 RT
(14)
After rearrangement and integration of eq 6, we obtain21
G(R) )
∫
R2
R1
1 dR ) f(R) β
∫
T2
T1
k(T)dT
(15)
(22) Vyazovkin, S.; Dollimore, D. J. Linear and nonlinear procedures in isoconversional computations of the activation energy of non-isothermal reactions in solids. J. Chem. Inf. Model. 1996, 36 (1), 42–45.
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Table 2. Kinetcs Parameters for Decomposition of Calcium Sulfate in a Nitrogen Atmosphere According to 30 Reaction Mechanism Functions number
E (kJ/mol)
1 2 3 4 7 15 24
798.16 825.48 835.13 854.46 758.12 883.90 592.26
β ) 5 K/min
β ) 7 K/min
(s-1)
(s-1)
ln A
55.93 57.44 56.71 58.26 50.49 62.83 40.76
r
E (kJ/mol)
0.99990 0.99941 0.99953 0.99971 0.99826 0.99988 0.99895
781.82 825.48 835.13 854.46 758.12 883.90 592.26
β ) 15 K/min number
E (kJ/mol)
1 2 3 4 7 15 24
751.33 777.07 786.17 804.38 713.59 832.12 557.03
ln A
54.67 57.44 56.71 58.26 50.49 62.83 40.76
r
E (kJ/mol)
ln A (s-1)
r
0.99905 0.99941 0.99953 0.99971 0.99826 0.99988 0.99895
781.82 825.48 835.13 854.46 758.12 883.90 592.26
54.67 57.44 56.71 58.26 50.49 62.83 40.76
0.99905 0.99941 0.99953 0.99971 0.99826 0.99988 0.99895
β ) 20 K/min
(s-1)
52.39 53.74 52.96 54.40 47.17 58.80 38.36
ln A
β ) 10 K/min
r
E (kJ/mol)
0.99910 0.99948 0.99959 0.99974 0.99846 0.99987 0.99908
751.33 777.07 786.17 804.38 713.59 832.12 557.03
To a certain temperature, the integration of ∫T1ˆT2k(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 likely reaction mechanism function.
ln A
(s-1)
52.39 53.74 52.96 54.40 47.17 58.80 38.36
βf0 r
Eβf0 (kJ/mol)
ln Aβf0 (s-1)
0.99910 0.99948 0.99959 0.99974 0.99846 0.99987 0.99908
917.43 930.63 941.45 963.10 855.09 991.77 668.75
64.03 65.85 65.20 66.92 58.11 71.84 46.54
conversion and reaction rate of calcium sulfate in its decomposition. As shown in Figure 5, the conversion and reaction rate of calcium sulfate is highest in 10 mol % O2 atmosphere and smallest in 21 mol % O2 atmosphere.
3. Results and Discussion In the inert atmosphere, the relationship between the weight of the calcium sulfate sample and temperature is shown in the TG curve illustrated as Figure 2. As shown in Figures 2 and 3, when the temperature is below 1473.15 K, all five samples are quite stable without decomposition. Then, the samples begin to decompose slowly when the temperature reaches 1500.15 K and accelerates to decompose when the temperature exceeds 1523.15 K. When the temperature is close to 1613.15 K, the reaction rate reaches it peak. In 79 mol % N2 and 21 mol % O2 atmosphere, the initial temperature of decomposition of calcium sulfate is slightly higher than that in inert atmosphere and the reaction rate is far below that in inert atmosphere. As show in Figure 4, when the reaction temperature approaches 1623.15 K, merely 52.51% of calcium sulfate has decomposed at the heating rate of 5 K/min, with the fastest reaction rate in five different heating rates. The presence of oxygen greatly inhibits the decomposition of calcium sulfate. The molar percentage of oxygen also affects the
Figure 3. DTG curve of decomposition of calcium sulfate at five heating rates.
Figure 2. TG curve of decomposition of calcium sulfate at five heating rates.
Figure 4. Conversion curve of decomposition of calcium sulfate at five heating rates in 79 mol % N2 and 21 mol % O2 atmosphere.
CaSO4 in Chemical-Looping Combustion
Figure 5. Conversion curve of decomposition of calcium sulfate sample at three different mole fractions of oxygen in atmosphere.
Energy & Fuels, Vol. 22, No. 6, 2008 3919
Figure 7. Mole fraction of CaO and CaS in reductive products of the reaction between calcium sulfate and carbon monoxide.
Figure 6. TG curve of decomposition of calcium sulfate at five heating rates in 40 mol % CO2, 40 mol % N2, and 20 mol % CO atmosphere.
Figure 8. TG curve of decomposition of calcium sulfate at five heating rates when calcium sulfate begins to react with carbon monoxide at 1373.15 K.
In the 40 mol % CO2, 40 mol % N2, and 20 mol % CO atmosphere, calcium sulfate is reductively decomposed by carbon monoxide and the reduction product is calcium sulfide. Simultaneously, calcium sulfate can react with calcium sulfide quickly, illustrated as eq 16, because the two solids form a eutectic liquid.23
illustrated in Figure 8. Similarly, the reduction product of the reaction between calcium sulfate and carbon monoxide at a constant temperature of 1373.15 K is also merely calcium oxide, as illustrated in Figure 9. Consequently, it can be seen that the reaction between calcium sulfate and carbon monoxide is illustrated as eq 17, when the initial reaction temperature is above 1373.15 K.
CaS + 3CaSO4 f 4CaO + 4SO2,
∆Hθ298 ) 1054.04 kJ/mol (16)
As shown in Figure 6, the initial temperature of reductive decomposition is about 1123.15 K and the whole reaction time between calcium sulfate and carbon monoxide is smaller than 40 min. The reductive products differ with different heating rates smaller than 23 K/min. The relationship between the mole fractions of calcium oxide and calcium sulfide and the heating rates are illustrated in Figure 7. The mole fraction of calcium oxide in products becomes bigger with the increasing of heating rates and approaches 100% with the heating rate bigger than 23 K/min. When calcium sulfate begins to react with carbon monoxide at 1373.15 K at five different heating rates, respectively, the reduction product is merely calcium oxide, as (23) Davies, N. H.; Hayhurst, A. N. On the formation of liquid melts of CaSO4 and their mportance in the absorption of SO2 by CaO. Combust. Flame 1996, 106 (3), 359–362.
CaSO4 + CO f CaO + CO2 + SO2,
∆Hθ298 ) 220.04 kJ/mol (17)
To investigate the decomposition behavior of calcium sulfate better in CLC, its decomposition mechanism and kinetics parameters in a pure nitrogen atmosphere are also studied. The value of the reaction mechanism function, G(R), is fixed for a certain conversion rate. The values of activation energy of decomposition of calcium sulfate for all conversion rates and all reaction mechanism functions are calculated and tabulated in Table 3. The value of activation energy reduces when the conversion rate increases, and it reaches a minimum value when the conversion rate increases to 40%, as illustrated in Figure 10. 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 obtain ERf0 ) 992.15 kJ/mol.
3920 Energy & Fuels, Vol. 22, No. 6, 2008
Tian et al. Table 4. Linear Fitting Results of Six Probable Reaction Mechanism Functions Selected in Table 2 T ) 1578.15 K
Figure 9. TG curve of decomposition of calcium sulfate at a constant reaction temperature of 1373.15 K. Table 3. Relationship between Activation Energy and Conversion Rate for Decomposition of Calcium Sulfate conversion rate (%)
activated energy (kJ/mol)
linear factor
5 10 15 20 25 30 35 40
917.76 862.43 817.83 785.71 768.34 754.51 742.92 739.50
0.99972 0.99930 0.99976 0.99989 0.99958 0.99969 0.99941 0.99948
After substitution of the minimum of activation energy and maximum of temperature into eq 14, we obtain ER ) 0.4/(RTmax) ) 52.89 . 13. Therefore, it is proven that the Flynn-Wall-Ozawa method is applicable in decomposition of calcium sulfate. The reaction mechanism function corresponding to the minimal value of difference between ERf0 and Eβf0 is the most likely mechanism function for decomposition of calcium sulfate. It can be found that the most likely function is function 15, G(R) ) [-ln(1 - R)]2, and therefore, the decomposition process is likely to be controlled by the nucleation mechanism. It is concluded that the nucleation rate of products controls the decomposition of solid reactants when the reacting temperature exceeds 1423.15 K and the conversion rate of calcium sulfate is lower than 40%.
Figure 10. Variations of the activation energy with the conversion rate of calcium sulfate in decomposition.
T ) 1613.15 K
number of funtion in Tables 1 and 2
linear factor
standard deviation
linear factor
standard deviation
1 2 3 4 7 15 24
0.99667 0.99275 0.99347 0.99780 0.99300 0.99870 0.99650
0.00425 0.00073 0.00374 0.00432 0.00024 0.00243 0.00417
0.99704 0.99153 0.99507 0.99638 0.99258 0.99913 0.99752
0.00466 0.00041 0.00226 0.00340 0.00046 0.00541 0.00343
The relationship between G(R) and 1/β can be determined by eq 15, and the linear fitting results including linear factor and standard deviation are shown in Table 4. The linear factor corresponding to the Avrami-Erofeev equation is closest to 1, and the standard deviation is near zero for both random temperatures of 1578.15 and 1613.15 K, which implies that the Avrami-Erofeev equation is the most likely reacting mechanism function by the Popescu method.21 The shape and morphology of both the fresh and reacted calcium sulfate particles are studied using the scanning electron microscope (SEM). Figure 11 shows the surface morphology of the fresh calcium sulfate sample. It is observed that the particles are stripy and grainy. Their surfaces are quite rough, but the pore is not found on the surface of an individual grain. When the temperature increases to 1628.15 K, the surface morphology of the calcium sulfate is shown in Figure 12. The sintering behavior between different grains can be observed, causing many large particle agglomerates. Some unreacting samples are featured by irregular shape. This can be explained that, at high temperatures, the ions at equilibrium positions of the lattice structure leave their primary position and move randomly through the interface of contacted grains. When the grains melt, they tend to a state with minimal surface area and minimal surface energy, forming many aggregations, including a lot of crystalline grains, grain boundaries, and pores. As shown in Figure 12, most of the samples have decomposed partly. As the reaction initiates, in the early period of the reaction, some active points appear in the surface of reactants and the decomposition occurred from the active points first. Then, the products of the solid phase in adjacent active points accumulate to some nucleus of the new material phase. The nucleus becomes bigger slowly, and therefore, the interfaces
Figure 11. SEM image for the samples of fresh calcium sulfate at 298.15 K in a nitrogen atmosphere.
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Energy & Fuels, Vol. 22, No. 6, 2008 3921
Figure 12. SEM image for the samples of calcium sulfate at 1623.15 K in a nitrogen atmosphere.
between the unreacted molecules and the nucleus become larger gradually. The produced gas diffuse through the layers of calcium oxide production thickened gradually. 4. Conclusions The subsequent conclusions can be drawn from this study: (1) In the inert atmosphere, when the temperature is below 1473.15 K, all five samples are quite stable and have not decomposed yet. Then, the samples begin to decompose slowly when the temperature reaches 1500.15 K and accelerate to decompose when the temperature exceeds 1523.15 K. When the temperature is close to 1613.15 K, the reaction rate reaches its peak. (2) In 79 mol % N2 and 21 mol % O2 atmosphere, the initial temperature of decomposition of calcium sulfate is slightly higher than that in an inert atmosphere and the reaction rate is far below that in an inert atmosphere. The presence of oxygen greatly inhibits the decomposition of calcium sulfate. The molar percentage of oxygen also affects the conversion and reaction rate of calcium sulfate in its decomposition. (3) In the 40 mol % CO2, 40 mol % N2, and 20 mol % CO atmosphere, calcium sulfate is reductively decomposed by carbon monoxide. The initial temperature of reductive decomposition is about 1123.15 K, and the whole reaction time between calcium sulfate and carbon monoxide is smaller than 40 min. The mole fraction of
calcium oxide in products becomes greater with the increase of heating rates and approaches 100% with the heating rate bigger than 23 K/min. When calcium sulfate begins to react with carbon monoxide at 1373.15 K at five different heating rates, respectively, the reduct product is merely calcium oxide. Similarly, the reduct product is also merely calcium oxide at a constant reaction temperature of 1373.15 K. (4) Kinetic parameters of the decomposition reaction without any disturbance form some other reactions, including Eβf0 and ln Aβf0, are determined. The activation energy of the decomposition reaction at the beginning of the reaction is also figured out, and we obtain ERf0 ) 992.15 kJ/mol. When Eβf0 and ERf0 are compared, the most likely mechanism function in the decomposition process is characterized by the Avrami-Erofeev equation and the reaction is dominated by the nucleation rate. The Avrami-Erofeev equation is also evaluated to be the most likely mechanism function by the Popescu method. Acknowledgment. The financial support from the New Century Excellent Talents in University (NCET-07-0473), Natural Science Foundation of China (20676064), and Taishan Mountain Scholar Constructive Engineering Foundation (JS 200510036) is greatly appreciated. EF800508W
