Kinetics of Magnetite (Fe3O4) Oxidation to Hematite (Fe2O3) in Air for

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Kinetics of Magnetite (Fe3O4) Oxidation to Hematite (Fe2O3) in Air for Chemical Looping Combustion Esmail R. Monazam,‡ Ronald W. Breault,*,† and Ranjani Siriwardane† †

National Energy Technology Laboratory, U.S. Department of Energy, 3610 Collins Ferry Road, Morgantown, West Virginia 26507-0880, United States ‡ REM Engineering Services, PLLC, 3537 Collins Ferry Road, Morgantown, West Virginia 26505, United States ABSTRACT: Thermogravimetric analysis (TGA) of magnetite (Fe3O4) oxidation was conducted at temperatures ranging from 750 to 900 °C over 10 oxidation cycles. Oxidation experiments were carried out in a continuous stream of air for period of 30 min. The oxidized magnetite (Fe3O4), which resulted in formation of hematite (Fe2O3), was then reduced by using continuous stream of CO (5% and 10%) with N2 balance. The rate of oxidation was determined by the oxygen weight gain. Analysis of the data indicated that the oxidation behavior followed a two-stage process. The initial oxidation, which was very fast, took place in 2 min and was described using nucleation and growth processes with a low activation energy of about 4.21 ± 0.45 kJ/mol. As the reaction developed within the surface, oxygen transport through the product layer become the rate-controlling step with activation energy of 53.58 ± 3.56 kJ/mol.

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INTRODUCTION The major source of greenhouse gas emissions that appears to be causing global warming and climate change is CO2 from fossil fuel combustion.1 According to the IPCC (The Intergovernmental Panel on Climate Change) report, the global temperature will rise approximately 2−4 °C by doubling the preindustrial CO2 concentration in the atmosphere.1 Among available technology and strategies to achieve stabilization of the atmospheric carbon dioxide concentration at an acceptable level, chemical looping combustion (CLC) has been identified as a promising technology to reduce CO2 capture cost from power plant.2 Chemical looping combustion (CLC) is a novel technology for energy production that shows great potential to integrate CO2 capture with lower energy penalties than with current technologies. In the CLC process, the fuel is oxidized to CO2 and H2O by oxygen carrier particles such as metal oxides instead of being taken directly from air.3 The reduced oxygen carrier is then oxidized in air producing N2 and depleted oxygen. The reduction of the oxygen carrier is often endothermic, while the oxidation of the oxygen carrier is strongly exothermic. A literature study indicated that metal oxides such as NiO, CuO, Mn2O3, and Fe2O3 were potential candidates as oxygen carriers for CLC systems.4−7 However, low-cost oxygen carrier is desired because some metal oxide may suffer from deactivation, agglomeration, and elutriation.8 Recently, lowcost natural minerals such as hematite have attracted significant interest.9−11 Monazam et al.9−11 had studied the kinetics of the reduction of hematite (Fe2O3) using CH4 and CO as the reducing agent as an oxygen carrier in the CLC process. Their results indicated that iron-based oxygen carrier is promising for CLC technology. Mattisson et al.12 had studied the feasibility of using natural hematite as an oxygen carrier in the CLC process. It was found that the overall reaction rate during the reduction period was significantly affected by the time the hematite had been exposed to methane. Ishida et al.13 had studied the © 2014 American Chemical Society

application of Fe2O3 as an oxygen carrier for the CLC system using hydrogen as a reducing agent. Their results indicated that, as compared to nickel and cobalt oxides, iron oxide was relatively inexpensive and environmentally safe. However, the experimental data of magnetite (Fe3O4) oxidation to hematite (Fe2O3) with air are rare and limited. Most of the previous work on magnetite oxidation has been carried out on pellets because of their industrial importance.14,15 Zeterstrom16 studied the oxidation of batches of pellets made from taconite concentrates at different temperatures. According to his study, the oxidation process is characterized by two distinct rate periods, an initial high rate followed by a significantly lower one. Edström15 studied the oxidation of magnetite pellets in air as well as in oxygen at a single temperature of 1230 °C. The material after reaction was observed to have both oxidized and nonreacted sections. It was concluded that the reaction was mass transfer (diffusion) controlled within the lattice Papanastassiou and Bitsianes17 found that when single magnetite pellet was oxidized in the intermediate temperature range (600−900 °C), it generally follows a complex mechanism in which the zone of reaction extends across the entire pellet section. Chemical reaction and mass transfer steps participate in parallel fashion as the controlling mechanism, and the process is best described by the spherical fixed packed bed (SFPB) model.17 Most of the previous studies on the rate of oxidation were obtained by measuring the oxidation depth of penetration, that is, the layer thickness of the oxidized material. Therefore, to determine the rate of oxidation, one should measure the scale thickness after different intervals of oxidation time. Such a Received: Revised: Accepted: Published: 13320

April 14, 2014 August 4, 2014 August 7, 2014 August 7, 2014 dx.doi.org/10.1021/ie501536s | Ind. Eng. Chem. Res. 2014, 53, 13320−13328

Industrial & Engineering Chemistry Research

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these conditions with no mass transfer or mixing issues has been described by Monazam et al.9−11 previously. The sample temperature was maintained isothermally for 20 min prior to the reduction and oxidation cycles. The reduction−oxidation cycles were conducted within the temperature range 750−900 °C for 10 cycles, using 5%, 10%, and 20% CO concentrations in N2 for the reduction segment and air for oxidation segment at a total flow rate of 100 cm3/min. Reduction reaction times were set at 45 min, and oxidation reaction times were 30 min for all experiments. The system was flushed with ultrahigh pure nitrogen for 10 min before and after each reaction segment. The concentrations of CO2, H2O, CO, and O2 from the exit gas stream of the reactor were analyzed using a mass spectrometer. The mass spectrometer is manufactured by Pfeiffer Omnistar GSD-301. The UHP grade CO, used for the reduction cycle, was obtained from Matheson Trigas. The N2/ O2 (air) used for the oxidation cycle was obtained from Butler Gas Products Co. Inc.

procedure has been time-consuming and has been reported to be not very accurate.18 However, the rate of oxidation can be determined with high accuracy from gravimetric measurements, which is used in the present study. In the present study, the oxidation kinetics of magnetite (Fe3O4) to hematite with air is investigated.

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EXPERIMENTAL SECTION Thermogravimetric Analysis (TGA) Apparatus. A sketch of the reactor unit, a TA model 2050 thermo gravimetric analyzer, is shown in Figure 1. Thermogravimetric reduction

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RESULTS AND DISCUSSION Figure 3 illustrates the weight change of cyclic reduction of hematite using 10% CO and N2 balance, and oxidation of

Figure 1. Schematic layout of the laboratory setup reactor.

tests were carried out with commercial hematite particles originating from Wabush Mine, Canada. For the chemical analysis of the hematite particle, refer to Monazam et al.9 The hematite content of the material was 94%, and the raw material was crushed in a lab to 100−300 μm with an average size of 200 μm. A sample was placed on the pan (5 mm deep and 10 mm diameter), which was centered in the gas inlet and exit ports. The sweep gas was introduced from the top to keep the balance electronics in an inert environment. A typical TGA experimental data on weight change during reduction/oxidation cyclic tests at a given temperature is illustrated in Figure 2. For a typical test, about 60 mg of the hematite sample was heated in a quartz bowl at a heating rate of 10 °C/min under N2 gas at a flow rate of 100 cm3/min. The detailed analysis for selecting

Figure 3. Weight change for isothermal formation of Fe3O4−FeO and hematite at different temperatures for 10% CO reduction and for 5% at 800 °C.

reduced hematite by using air versus time under isothermal conditions at three different temperatures (750, 800, and 900 °C). It was observed that the reduction of hematite in the presence of CO produced Fe3O4−FeO mixtures at all temperatures. We have previously reported kinetic analysis for reduction of hematite with CO.11 Therefore, the objective of this Article is thus to understand the kinetic parameters of the oxidation reactions of reduced hematite using air. The degree of oxidation conversion (X) is calculated from the weight analysis according to the following equation: X=

m (t ) − m 0 m f − m0

(1)

where m(t) is the instantaneous weight of the solid during the exposure to air. Parameters m0 and mf are initial and final weights of the sorbent, respectively. In this study, to simplify the analysis, the oxidation conversion was normalized using a measured weight increase of 3.3%, which is equivalent to conversion of magnetite (Fe3O4) to hematite (Fe2O3).

Figure 2. Typical mass and temperature measurement for hematite particle of 200 μm using 10% CO for reduction and air for oxidation reactions. 13321

dx.doi.org/10.1021/ie501536s | Ind. Eng. Chem. Res. 2014, 53, 13320−13328


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Therefore, the initial weight was considered as the weight of Fe3O4 (corresponds to 3.3 wt % of Fe2O3 + mineral in hematite) and final weight as the weight of hematite. Oxidation of magnetite to hematite takes place according to the following reaction: 4Fe3O4 + O2 → 6Fe2O3

(2)

[ΔH800°C = −481.7 kJ/mol, ΔG800°C = − 163.7 kJ/mol]

The reaction is exothermic, and may take place at room temperature; however, the kinetic rate of the oxidation process is quite slow at low temperature.14 The kinetic analysis is necessary to fully understand the reaction sequence and design the reactors. Figure 4 illustrates the extent of oxidation as a function of time obtained at different temperatures. The results reveal that

Figure 5. Oxygen consumed during oxidation of magnetite as a function of time.

Figure 4. Conversion TGA data (symbols) and parallel process reaction model data (solid lines) of magnetite (formed by reduction of hematite with 10% CO) during oxidation with air at different temperatures.

the degree of oxidation initially proceeds rapidly, after which only a gradual increase in oxidation rate was observed until the completion of tests. The variation in oxidation conversion of magnetite with temperature was more significant after 1.5 min. When the temperature was raised from 750 to 800 °C, the conversion was raised from 64% to 70%. By increasing the temperature to 850 °C, the conversion increases further to 81% and then to 86% at 900 °C. These results suggest that the rate of oxidation is highly dependent on the temperatures. Figure 5 illustrates the O2 gas concentration (as measured by mass spectrometer) as a function of time at different temperatures (750−900 °C). The data in Figure 5 also show that during the oxidation, there was more oxygen consumed as temperatures increased, which resulted in more conversion at given time. Figure 6 shows the CO2 gas concentration as a function of time at different temperatures (750−900 °C). The data in Figure 6 also indicate that during the oxidation phase, after air was introduced into the reactor, there was no production of CO2 in the reactor outlet gases. This indicated that there was no or little carbon deposited during the reduction phase.

Figure 6. CO2 gas analysis at the outlet for the reduction of hematite (Fe2O3) with 10% CO and oxidation with air at different temperatures.

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KINETIC MODELS In most of the previous work, it is reported that the rate of oxidation of metal obeys the parabolic rate constant.14,15 In oxidation process, parabolic kinetics occurs when the weight gain or oxide growth per area of sample is proportional to the square root of time as ΔW = kt 1/2 (3) A where ΔW is the weight gain, A is the sample surface area, and t is the oxidation time. Thus, when oxidation follows the parabolic rate law, a plot of the weight gain per unit surface area versus square root of time is a straight line, the slope of which gives the value of the parabolic rate constant, k. Monsen et al.14 proposed the following parabolic rate equation for spherical particle in terms of conversion, X, as ⎡ 2 ⎤ y = ⎢1 − (1 − X )2/3 + X ⎥ = kt ⎣ (4) 3 ⎦ 13322



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where dX/dt represents the kinetic rate, t is the time, T is the temperature, X is the extent of conversion, and f(X) is a mathematical function that depends on the kinetic model used (see Table 1). In eq 5, k is the rate constant, which is given as

Equation 4 assumes that the oxidation does not contribute to volume change. The parabolic rate law was then fitted to the present experimental results, assuming spherical particles, and the results are shown in Figure 7. The results as illustrated by

⎛ −E ⎞ ⎟ k = A exp⎜ ⎝ RT ⎠

(6)

For reaction kinetics under isothermal conditions, eq 5 can be analytically integrated to yield: g (X ) =

X

dX = kt f (X )

(7)

where g(X) is an integral mathematical expression related to a mechanism of solid-phase reactions. Therefore, the values of kinetic rate constant k can be determined at different temperatures from the slope of the straight line obtained by plotting g(X) against time. This value can be subsequently inserted in the Arrhenius equation together with the corresponding temperature value to yield activation energy and pre-exponential factor values from the slope and intercept of regression straight line. As illustrated by Figure 8, only one of the expressions (no. 10) listed in Table 1, which corresponds to the second-order kinetic model, provided straight lines, except for the initial 90 s. This may indicate that the magnetite oxidation rate follows second-order kinetics law for the whole time period after 90 s as

Figure 7. Data computed using parabolic rate law model at different temperatures, assuming spheres (eq 4).

Figure 7 show that “y” versus “t” does not produce straight lines with the current data, indicating that the oxidation does not follow the parabolic rate law. More recently, many articles also have been devoted to the kinetic analysis of experimental data using the following rate equation: dX = kf (X ) dt

∫0

dX = k(1 − X )2 dt

(8)

The pre-exponential and activation energy then can be obtained by plotting ln k (k’s were obtained from Figure 8) versus T−1 as illustrated in Figure 9. Therefore, the temperature

(5)

Table 1. Basic Kinetic Models and Properties of f(X) and g(X) Functions no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

f(X)

kinetic model power law

contraction model zero order 2-D 3-D kinetics-order models first order 3/2 order second order third order nucleation model n = 1.5 n=2 n=3 n=4 diffusion model 1-D 2-D 3-D (Jander) 3-D (Grinstling)

g(X)

4X3/4 3X2/3 2X1/2 2/3X−1/2

X1/4 X1/3 X1/2 X3/2

1 2(1 − X)1/2 3(1 − X)2/3

X [1 − (1 − X)1/2] [1 − (1 − X)1/3]

(1 (1 (1 (1

− − − −

−ln(1 − X) 2[(1 − X)−1/2 − 1] (1 − X)−1 − 1 1/2[(1 − X)−2 − 1]

X) X)3/2 X)2 X)3

3/2(1 − X)[−ln(1 − X)]1/3 2(1 − X)[−ln(1 − X)]1/2 3(1 − X)[−ln(1 − X)]2/3 4(1 − X)[−ln(1 − X)]3/4

[−ln(1 [−ln(1 [−ln(1 [−ln(1

1/(2X) 1/[−ln(1 − X)] (3/2)(1 − X)2/3[1 − (1 − X)1/3] (3/2)[(1 − X)−1/3 − 1]

X2 (1 − X) ln(1 − X) + X [1 − (1 − X)1/3]2 (1 − 2X/3) − (1 − X)2/3

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− − − −

X)]2/3 X)]1/2 X)]1/3 X)]1/4



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Figure 10. Comparison of predicted data (solid lines) on conversion as a function of time, using second-order kinetic model and experimental data (symbol) at different temperatures.

Figure 8. Examination of linear relationship based on second-order reaction model.

dependence of the rate constants (for time >90 s) can be expressed by the following equation: k(min−1) = 76 880 exp(− 11 532/T )

rate-controlling mechanism. It is possible that for the initial 90 s, other mechanisms such as nucleation/growth may be controlling the rate. Because the second-order kinetic model did not completely describe the conversion data, other approaches to define the kinetics were considered as follows. For a gas/solid reaction system, the reaction rate is generally controlled by one of the following steps as considered in the shrinking core model:19 diffusion of gases through the gas film, diffusion of the reactants to the reaction site, the chemical reaction at the surface of the solid particles, and diffusion of products away from reaction site. The rate of the process would be controlled by the slowest of these sequential steps. Oxidation of mineral metal usually initiates at the surface. As soon as the surface is oxidized, further oxidation will only occur if: (1) metal atoms diffuse through the oxide layer to the surface to react with oxygen at the air/oxide interface or (2) oxygen diffuses through the oxide layer to react with the metal at the metal/oxide interface. Application of shrinking core model for the current data is described below. For the reaction of A(gas) + B(solid) → product, if the gas diffusion through the initial gas film is the rate-controlling step, eq 11 can be applied as

(9)

Figure 9. Arrhenius plot for oxidation of magnetite to hematite based on second-order kinetic reaction model.

tX = τgasX The activation energy was found to be 95.88 kJ/mol. Monsen et al.15 obtained an activation energy of 100 kJ/mol for magnetite oxidation, using a spherical particle in the temperature range of 600−850 °C, which is comparable to 95.88 kJ/ mol in this study. However, their studies did not consider the nonlinear portion of initial period. The comparison of the experimental conversion data, X, for magnetite oxidation and conversion computed using the second-order kinetics model as presented by following equation (integration of eq 8): X=

kt kt + 1

(11)

Generally, gas diffusion is rarely the rate-controlling step. If diffusion through the product solid layer is the ratecontrolling step, eq 12 can be applied as tX = τdif [1 − 3(1 − X )2/3 + 2(1 − X )]

(12)

If chemical reaction at the surface is rate controlling, eq 13 can be applied as tX = τch[1 − (1 − X )1/3 ]

(13)

where τgas, τdif, and τch are the times required for complete conversion due to gas diffusion, diffusion through the product layer, and chemical reaction, respectively. To quantify the effect of temperature on the oxidation rate, the experimental conversion time for each reaction temperature was compared to the ideal chemical reaction (eq 13) and product diffusion control (eq 12) models. However, the conversion−time data did not fit either model (see Figure

(10)

is illustrated in Figure 10 at different temperatures. The model and experimental data agreed well, except for the initial period of about 90 s at all temperatures. This may indicate that for the initial period of the reaction, the second-order model is not the 13324



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11), indicating that the oxidation reaction cannot be described by the shrinking core model.

Figure 12. Typical curve fitting of experimental oxidation data to series and parallel reaction models at 850 °C.

mechanism is well represented by a nucleation model. Therefore, for the observed values, n1 = 1.67 represents the nucleation process, and n2 = 0.57 defines the diffusion control11 in this parallel process. The values of n1 and n2 as a function of temperature indicate that n1 increases linearly with increase of temperature, as n2 decreases with increase of temperature as follows:

Figure 11. Comparison of experimental magnetite−hematite conversion data to data based on shrinking core model (diffusion and reaction control).

From these results, it can be observed that the oxidation of magnetite may follow multistep kinetics. Therefore, a simple multistep process that may involve in parallel or in series was used to describe the current conversion kinetics.9 Parallel process can be defined by eq 14 as n1 n2 Xt = w1(1 − e−a1t ) + w2(1 − e−a2t ) X∞ (14)

n1 = 0.0016 × T (K) − 0.103

and n2 = −0.0005 × T (K) + 1.171

(17)

The comparison of the experimental conversion data (X) and the conversion based on parallel model as presented in eq 14 is also illustrated in Figures 4 and 13 at different temperatures. It should be noted the final mass (mf) corresponding to a conversion value of 1 was considered as mass of hematite. The model data and experimental data agree over the entire conversion time with overall variance (R2) greater than 99.9%. When fitting nonlinear equations with a large number of parameters, it is prudent to consider how sensitive the trend is

Series process can be defined by eq 15 as ⎛ ⎞ ⎛ ⎞ Xt 1 1 = w1⎜ n1 ⎟ + w2 ⎜ n2 ⎟ − a t − a t 1 ⎝1 − e ⎠ X∞ ⎝1 − e 2 ⎠

(16)

(15)

Equations 14 and 15 correspond to two different nucleation or growth processes occurring in parallel or series, with the relative importance of each manifested by the value of the weight factors w1 and w2 where w1 + w2 = 1.9 As illustrated by Figure 12, results from the reaction model with process in series were not comparable with the experimental data. However, the data from the reaction model with parallel process were very compatible with the experimental data as is also shown in Figure 12. Therefore, in this study, reaction model in parallel was used for analysis of oxidation of magnetite using air. For a given temperature, values of X∞, w1, a1, a2, n1, and n2 were determined by curve fitting the rate data of Figure 4 with the parameters in eq 14 using TABLECURVE available from Statistical Package for the Social Sciences. The values of n1 and n2 define the type of reaction mechanism for the process. The values determined for the shape parameters, n1, range from 1.4 to 1.8 for all of the temperatures, with an average value of n1 of 1.67 ± 0.15 (95% CL). The values determined for the shape parameters, n2, range from 0.52 to 0.63 for all of the temperatures; the average value of n2 was 0.57 ± 0.0.04 (95% CL) for the current study. Generally, when n < 1, the mechanism is diffusion-controlled; when n is close to 1, the mechanism approaches first-order kinetic controlled, that is, kinetic controlled mechanism, and when n is close to 2, the

Figure 13. Comparison of experimental conversion data (symbol) of magnetite (formed by reduction of hematite with 5% CO) during oxidation with air at different temperatures and results from parallel process model (solid lines). 13325



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to the choice of input parameters, and whether equally good fits could be achieved with different sets of parameters. Indeed, it was found that the unknown parameters did not vary with different initial choices. The data in Figures 4 and 13 also show that the rate of oxidation of magnetite increases as the reaction temperature is increased. The parallel process, P1 and P2, which correspond to nucleation and diffusion, represent two processes of reactions occurring simultaneously, but with different time dependence. The comparison of the P1 and P2 of the parallel model data is illustrated in Figure 14. The curve P1, which represents process

where k is the oxidation rate constant, A is the frequency factor, R is the gas constant, and T is the absolute temperature. The linear regression of the experimental data of ln k against 1/T determines E/R. A plot of ln k versus 1/T for oxidation of magnetite for both P1 and P2 is shown in Figure 14 at different reaction temperatures. The apparent activation energies for both reactions P1 and P2 were estimated to be 4.21 ± 0.45 and 53.58 ± 3.56 kJ/mol, respectively. The low activation energy in process P1 could be due to the formation of highly porous thin oxide layers at the surface. In the analysis above, the Arrhenius pre-exponential term “A” is found to be a function of the reducing gas used prior to oxidation as shown in Figure 15. As shown in Figure 3, with

Figure 14. Three predicted curves of conversion as a function of time during isothermal reaction of magnetite with air. Curve P1 is a single Avrami equation; curve P2 is a single diffusion equation.

1, has a faster time response than process 2 (curve P2), and curve 3 is the sum of the two processes P1 and P2. As time progresses, processes 1 and 2 reach steady state at different degrees of oxidation. That is, if process 1 alone were contributing to the bulk reaction, at long times the degree of oxidation would be the product of w1 and X∞. With both processes contributing, the degree of oxidation at long times is the product of (w1 + w2) and X∞. Figure 14 illustrates that in the initial portion of the reaction, the time dependence of the total process, curves (P1 + P2), is dominated by process P1. At long times, the total reaction (P1 + P2) is dominated by process P2. Hence, process 2 will have little influence on the initial part of the oxidation process. The two parallel processes obtained from the analysis can be described as follows: The fast nucleation and growth of the product layer dominates initially, while the oxygen diffusion through the oxide layer formed dominates the later part of the reaction. The effects of reaction temperature on the conversion of each process (P1 and P2) during the 30 min reduction are shown in Figure 14. The data indicate that the reaction rates of process P1 increase with increasing temperature. However, the reaction rates of process P2 decrease with increasing temperature; this is due to an increasing oxide thickness during process P1, which acts as a stronger diffusion barrier. To determine the rate-controlling mechanism, the value of apparent activation energy was calculated from the Arrhenius equation as a function of the Avrami kinetic constant (a):

k = a1/ n = A e−E / RT

Figure 15. Temperature dependence of the reaction rates, k1 and k2 (min−1), for two process reactions.

10% CO at all of the temperatures, the reduction to FeO can be achieved with 5% CO, with primarily Fe3O4 obtained. Because the oxidation initiates with different states of iron, the values of “A” for oxidation may vary with the CO concentration used for reduction. It is also known that hematite undergoes significant morphological changes during cyclic reduction/oxidation reactions.20 The grain size grows and dense clusters form during the reduction of Fe3O4 to FeO and Fe. This contributes to the decrease in surface area for the reduction reactions. The experiment in which the hematite was reduced by 10% CO is more reduced as compared to the 5% CO (Figure 3). The value of “A” for the reduction test with 10% CO is 1.76 (min−1) and

(18) 13326



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for reduction tests with 5% CO is 2.26 (min−1). Taking the ratio of these values to assess the surface area effect shows that there is an apparent 25% reduction in the rate for the 10% case as compared to 5% case. This is consistent with the finding of Breault and Monazam,20 which shows that the cycling can cause up to 75% reduction in surface area. Papanastassious and Bitsianes17 reported an activation energy of 10.5 kJ/mol for the initial period of the oxidation of magnetite in the temperature range of 420−1200 °C. They indicated that the low activation energy of 10.5 kJ/mol is of the same order of magnitude as that for mass transport processes in the bulk gas phase. Therefore, it was concluded that the controlling step is that of diffusion through the gaseous boundary layer. However, our studies indicate that this low activation energy could be due to the nucleation and growth process that dominates the reaction initially. The values of weight factor, w1, of nucleation/growth contribution indicate that as temperature increases, the value of w1 increases linearly. A linear fit to the functionality gave a R2 of greater than 95%. Combining all of the values of w1 for different temperatures, the following equation is obtained: w1 = 0.0018 × T (K) − 1.4

Figure 16. Effect of reaction temperature on the rate of oxidation of magnetite with air.

900 °C for a period of 30 min. Experimental results suggested that the oxidation of magnetite occurs in two stages. The initial oxidation took place in about 2 min and was controlled by nucleation and growth process with a low activation energy of about 4.21 ± 0.45 kJ/mol. The conversion corresponding to initial oxidation was increased with increasing temperature, reaching ∼80% at 900 °C. As the reaction progressed beyond the surface, diffusion through the porous oxide layer become the rate-controlling step with an activation energy of 53.58 ± 3.56 kJ/mol. The conversion during the diffusion control decreased as temperature was increased possibly due to the increased thickness of the oxidized layer.

(19)

and w2 = 1 − w1

(20)

An expression for the reaction rate, dX/dt, can be derived by differentiating eq 14 with respect to t, at constant temperature, as follows: dX1 dt

=n1a11/ n1(w1X∞

(1 − 1/ n1) ⎛ ⎛ X1 ⎞⎞ − X1)⎜⎜ −ln⎜1 − ⎟⎟⎟ w1X∞ ⎠⎠ ⎝ ⎝

P1

■

(21)

and dX 2 dt

=n2a 21/ n2(w2X∞

*Tel.: (304) 285-4486. Fax: (304) 285-4403. E-mail: ronald. [email protected].

(1 − 1/ n2) ⎛ ⎛ X 2 ⎞⎞ − X 2)⎜⎜ −ln⎜1 − ⎟⎟⎟ w2X∞ ⎠⎠ ⎝ ⎝

Notes

P2

The U.S. Department of Energy, NETL, and REM contributions to this Article were prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. The authors declare no competing financial interest.

(22)

Therefore, the total rate is summation of eqs 21 and 22 as dX t dt

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Corresponding Author

= P1 + P2

dX1 dt

+ P1

dX 2 dt

P2

(23)

The rate−time (dX/dt versus t) data obtained at different temperatures (750−900 °C) using eqs 21 and 22 are also shown in Figures 16 for process P1 and P2. As shown in Figure 16, the rate−time curves for P1 show the maximum rate at a time greater than 0, which indicates that P1 is controlled by nucleation and growth. However, as shown in Figure 15, the rate−time curves for P2 show the maximum rate when times equal zero at all temperatures, which indicates that P2 is diffusion controlled. Figure 16 also shows that the value of maximum rate increases with the increasing temperature for P1 and decreases with increasing temperature for P2.

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ACKNOWLEDGMENTS We acknowledge the Department of Energy for funding the research through the office of Fossil Energy’s Gasification Technology and Advanced Research funding programs. Special thanks go to Duane D. Miller, Hanjing Tian, and Thomas

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SUMMARY The oxidation of magnetite experiments was carried out in a continuous stream of air over the temperature range of 750− 13327



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Simonyi of URS Energy & Construction, Inc. for their assistance with experimental work and data.

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REFERENCES

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Kinetics of Magnetite (Fe3O4) Oxidation to Hematite (Fe2O3) in Air for

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