Latter Stages of the Reduction of NO to N2 on Particles of Fe while

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Latter Stages of the Reduction of NO to N2 on Particles of Fe while Simultaneously Oxidizing Fe to Its Oxides P. S. Fennell,† J. S. Dennis, and A. N. Hayhurst* Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United Kingdom ABSTRACT: The gaseous pollutant, nitric oxide, is produced in almost every combustor but can be converted back to molecular N2 by reacting it with metallic iron in ðIÞ

NO þ Fe f FeO þ 1=2N2

In fuel-rich regions of a combustor, the product, iron oxide, can be chemically reduced to metallic Fe (for subsequent reuse) by, e.g., carbon monoxide in FeO þ CO f Fe þ CO2

ðIIÞ

NO þ CO f 1=2N2 þ CO2

ðIIIÞ

The net reaction of reactions I and II is This paper investigates the latter stages of reaction I in a thermogravimetric balance, where the sample of iron was held in a specially designed bucket to ensure good contact of the gas with iron. In this case, the nearly spherical particles of Fe (initial diameter of 104126 μm) became covered with successive layers of FeO, Fe3O4, and even Fe2O3. Measurements of the rate of reaction I were made for different concentrations of NO in N2 contacting the particles of Fe at fixed temperatures from 500 to 900 °C. At 900 °C, the reaction between NO and Fe proceeded rapidly and completely to Fe2O3 under kinetic control. At lower temperatures, the reaction became controlled by diffusion through the oxide product at progressively lower extents of the reaction. When [NO] in the gas was increased at a fixed temperature, the onset of diffusion control occurred at lower conversions of Fe. In contrast to its early stages of reaction control, the rate of reaction I under diffusion control was found to be independent of the concentration of NO in the gas phase. It is concluded that, in these latter stages, the rate of reaction I is controlled by the diffusion of iron ions through an oxide layer around each particle. It is likely that this involves Fe2þ ions diffusing through FeO, but after Fe has been oxidized to FeO, the rate becomes determined by both Fe2þ and Fe3þ diffusing through Fe3O4. In these cases, the diffusion coefficient varies with the temperature from ∼0.6 10-13 to ∼3 10-11 m2/s from 500 to 900 °C; the associated activation energy exceeds 100 kJ/mol. This study indicates that particles of either Fe or its oxides can be usefully included in a fluidized-bed combustor to remove NOx.

1. INTRODUCTION Allen and Hayhurst1 confirmed that the overall reaction III, which is useful for removing two combustion-generated pollutants of the atmosphere, is catalyzed by surfaces of iron or an iron oxide, as previously concluded by Cowley and Roberts.2 It is clear3,4 that both the pollutants NO and N2O can oxidize metallic iron; the products are innocuous molecular N2, with oxides of Fe covering the metal. Hayhurst and Lawrence4 found that NO produced a “very porous and almost sponge-like” layer of oxide, which contrasted with the “relatively smooth, continuous, and impervious” oxide, when N2O reacts with an iron surface. The role of CO is to chemically reduce the oxides back to metallic iron in reaction II; this can also be performed by H2. Subsequently, Hayhurst and Ninomiya5 studied the kinetics of the conversion of NO to N2 by adding tiny particles of iron to a hot bed of sand fluidized by mixtures of NO and N2; the disappearance of NO from the off-gases enabled the rate of production of N2 to be measured. They found that the reaction occurred in two stages. The first was controlled by the inherent kinetics of the reaction between NO and the external surface of iron; the second was controlled by some diffusional process through the layer of oxide r 2011 American Chemical Society

product covering the iron. One purpose of this paper is to investigate this second stage. Such reactions involving metallic iron, its oxides, and the oxides of nitrogen (NOx) are very important, because they offer a means of converting NOx, produced in the combustion of any fuel, to molecular N2. In fact, Lissiansky et al.6 have demonstrated that the removal of NO from combustion off-gases is a practical proposition using iron additives. However, there are still relatively few published studies of these reactions. Fennell and Hayhurst7 studied the initial kinetics of the reaction of NO with pure iron to yield molecular nitrogen and a mixture of solid oxides of iron (FeO, Fe3O4, and Fe2O3) and found that the initial rate of reaction per unit initial Brunauer-Emmett-Teller (BET) surface area of the iron particles is given by rNO ¼

k1 ½NO f1 þ ðk2 ½NO=k1 Þ1=2 g2

ð1Þ

Received: December 10, 2010 Revised: February 11, 2011 Published: March 11, 2011 1510

dx.doi.org/10.1021/ef101675j | Energy Fuels 2011, 25, 1510–1520

Energy & Fuels Here, k1 and k2 are rate constants, which were measured by Fennell and Hayhurst7 to have activation energies of 22 ( 10 and 56 ( 15 kJ/mol, respectively. Very recently, Grado n and Lasek8 have confirmed eq 1 and also found k1 and k2 to have low activation energies. Equation 1 holds only for the earliest stages of the reaction, when the oxides of iron formed at the surface are so thin that they do not present a diffusional resistance to NO reaching Fe. Thereafter, the progress of the reaction is increasingly influenced by the presence of the layer of the oxide product, which builds up on the exterior of the iron. Hayhurst and Lawrence4 studied the reactions of NO and N2O with iron particles (diameter, 250-300 μm) in a fluidized bed. They found that the oxide, formed when N2O reacts with Fe, acts as a protective scale on the surface of the iron; therefore, the highest measured conversion of Fe to an oxide was only 0.3%. On the other hand, when NO reacts with Fe particles under the same conditions, a conversion of 100% to the oxide Fe2O3 is possible, as noted below. Interestingly, when N2O was reacted with iron in the presence of NO, no protective layer was formed; N2O continued to react with iron until iron had reacted fully to form an oxide. Hayhurst and Lawrence4 surmised that the oxide formed when iron reacts with NO in a fluidized bed is relatively porous, so that both NO and N2O can diffuse through it in the gas phase. Scanning electron micrographs9 confirmed that the oxide is very porous. The measured surface area of iron used in these experiments was 0.169 m2/g prior to the reaction; this is substantially higher than the nominal external surface area of nonporous spheres of iron with the same sieve diameter, thereby indicating that the particles of iron used were, in fact, porous. Most studies of the formation of iron oxides have been concerned with the oxidation of iron by oxygen,10-14 but the morphology of the oxide layer and its mechanism of formation have relevance to the current work. Pilling and Bedworth10 found the oxidation to be governed by the parabolic rate law, (Δm/A)2 = kt, where A is the initial surface area of iron and k is a constant. This law applied when iron wire was oxidized in air or oxygen at 700-1000 °C. They10 recorded seeing a thick outer layer of oxide, with a thinner inner layer of oxide; at sufficiently long reaction times, a hollow center was formed in the wire. The outer surface of the layer of oxide became progressively smoother and less crenellated, when the [O2] was reduced. The mean composition of the oxides was determined to be intermediate between FeO and Fe3O4. Païdassi12,13 found that the oxidation of both FeO to Fe3O4 and Fe3O4 to Fe2O3 obeys the parabolic law and that the oxides formed were dense and free of pores. He also claimed that the direct oxidation of FeO to Fe3O4 in O2 is substantially faster than the growth of Fe3O4 in a scale containing successive layers of FeO, Fe3O4, and Fe2O3. Engell and Wever15 found that the oxide formed when Fe reacts in air at 600-850 °C was dense and free of pores. Above 850 °C, they did not observe discrete layers of FeO, Fe3O4, and Fe2O3; instead, there was one reasonably thick layer of FeO, with a thicker, mixed layer of both Fe3O4 and FeO, followed successively by thin layers of Fe3O4 and Fe2O3. Below 850 °C, they showed that only Fe2þ is expected to be mobile in the w€ustite (FeO) phase. This should lead to the formation of gaps at the Fe/ FeO interface, because of the diffusion of cationic (Fe2þ) vacancies to the boundary. These gaps should start off as single vacancies, which subsequently coalesce to form macroscopic voids. However, Engell and Wever15 found no such voids and explained this by plastic flow of the oxide to maintain adherence between the oxide and the metal. Above 850 °C, they found that

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Figure 1. Schematic diagram of the thermogravimetric balance, the quartz buckets, and the flows of gas.

O2- diffused into the oxide layer; this conclusion came from the fact that platinum markers placed on the outer surface of Fe moved into the middle of the w€ustite layer, when the iron was reacted with air for a long time. Finally, Rahmell and Engell,16 using mixtures of oxygen in argon (with the mole fraction of O2 varied from 1 to 100% at various total pressures), found that, after the reaction had entered the parabolic stage, its rate was independent of the partial pressure of oxygen in the gas phase. Slattery et al.17 and Slattery18 have examined ionic diffusion in the layers of oxides produced by oxidizing Fe. In their model, they assumed that Fe2þ and Fe3þ ions diffuse through a stationary lattice of O2- ions. Also, at the interface between metallic Fe and FeO covering it, the reaction Fe þ 2Fe3þ = 3Fe2þ occurs, in preference to Fe = Fe2þ þ 2e- assumed below. In fact, Slattery’s approach ignores free electrons, and Schweica et al.19 clearly disagree with such a picture. The mechanism of the reaction of NO with iron, once a layer of oxides has been formed, is dealt with below. From the foregoing, studies of the reaction of iron with oxygen in this regime have found that the rate of reaction is nearly independent of [O2]. This needs checking using NO as the oxidant, when there is limited information on the degree of porosity of the resulting oxide and its dependence upon the conditions of the experiment, as well as the size and morphology of the particles of iron used.

2. EXPERIMENTAL SECTION Experiments were performed in an extremely sensitive thermogravimetric balance (TGA, Sartorius 4436 MP8), sensitive to changes of (1 μg. Iron particles (Goodfellow, >99% purity; bulk density, 7870 kg/m3), previously sieved to a very small size (104-126 μm), were carefully 1511

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Figure 3. Electron micrograph of an unreacted iron particle. The white line shown represents 100 μm. The particles had been sieved to 104126 μm.

Figure 2. Three different types of quartz buckets used in the thermogravimetric balance. sprinkled onto a small piece of quartz wool located inside a quartz bucket (inner diameter, 5 mm; outer diameter, 6 mm). A schematic diagram of the balance is shown in Figure 1. The bucket, with the quartz wool already positioned, had previously been weighed (Precisa 290 SCS balance; sensitivity, (0.01 mg). The bucket was weighed again after the addition of the iron particles. In this way, the initial mass of the iron particles, mo, was determined; values of mo ∼ 5 mg were usually used. The initial heating of the sample to the experimental temperature was performed under a steady stream of N2 to avoid any oxidation of the iron. The Fe particles were then reacted with a known mixture of NO and N2, all at a fixed temperature in the range of 500-900 °C. Measured rates of increase in the mass of iron enabled rates of oxidation of Fe to be determined. The bucket containing the iron particles was located in a quartz tube (inner diameter, 15 mm; outer diameter, 16 mm; length, ∼300 mm; see Figure 1) inside the furnace (inner diameter, 20 mm; hot length, ∼200 mm). The temperature was measured using a type K thermocouple, located in the gas stream just below the bucket; further details have been given by Fennell.20 The purpose of the quartz wool was to separate the particles, so that they became isolated and individual entities. Such an arrangement prevented the formation of large clumps of Fe particles before and during the reaction. The bucket was suspended from one arm of the balance. Another similar quartz bucket was used as a counterweight on the other arm of the balance. Three types of bucket, shown in Figure 2, were tested as containers for the iron particles. Each bucket had a handle made from platinum wire (outer diameter, 125 μm). The difference between the three types of buckets was in their bases: one had a solid quartz bottom; one had a sintered, porous quartz bottom; and one had an open bottom. The open-bottomed bucket used a small plug of quartz wool to prevent particles from falling out. The buckets with a solid base gave the poorest contact between gas and the particles of Fe, as evidenced by the measured initial rate of the reaction being up to 25% lower than that measured using a bucket with an open bottom. Their use was accordingly discontinued. There was negligible difference between the rates of reaction measured using the sintered and open-bottomed buckets. It was also found to be important not to use too much iron during an experiment; thus, provided less than 10 mg of Fe was used, the measured initial rate of oxidation per unit mass of Fe was found to be independent of the mass of particles used. Otherwise, at higher loadings,

Figure 4. Normalized increase in mass plotted against time at 700 °C. Particle size, 104-126 μm; mo, ∼5 mg. The concentrations of NO in N2 were as shown; the gas flow was 3 mL/s. the particles of Fe were insufficiently isolated. These findings indicate that care must be taken to not simply put the reacting particles on, e.g., a conventional pan, as previously demonstrated by Yrjas.21 Temperature control was effected by a proportional controller. At first, dry nitrogen was passed through the quartz tube (flow rate, ∼3 mL/ s) for 5 min before the bucket was located in the furnace to ensure no air remained. The system was then left to heat up, with N2 flowing through it; therefore, any moisture on the iron particles would have been expected to evaporate. When the measured temperature and mass had stabilized, nitrogen with a known [NO] (between 0.01 and 10 vol %, with a typical total flow rate of 3 mL/s, as measured at 1 atm using a rotameter) replaced the N2 flowing over the particles. Readings of the increase in their mass were taken every 5 s for at least 100 s but sometimes for as long as 8 h. If the reacted particles were required for BET analysis or microscopic analysis, the furnace was switched off and nitrogen was passed through the system until it had cooled to room temperature. Although it is probable that the particles initially had a very thin layer of iron oxide on their exterior, it was found that if CO (10 vol % in N2) was passed over the particles at elevated temperatures (∼900 °C) prior to the reaction with NO, there was neither a measurable change in mass nor a difference in the initial rate of the reaction. Thus, any such layer of oxide on the raw particles was of no consequence. Particles were also examined by electron microscopy before and after the reaction. A typical unreacted particle is shown in Figure 3. It is 1512


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Figure 5. Normalized increase in mass plotted against time at 700 °C. Particle size, 104-126 μm; mo ∼5 mg; gas flow rate, 3 mL/s.

Figure 6. Rate of mass increase per unit initial mass plotted against the fractional increase in mass for a temperature of 700 °C. Particle size, 104-126 μm; mo, ∼5 mg; total flow rate of gas, 3 mL/s. The concentrations of NO were as shown. immediately apparent that the particles, although approximately spherical on a scale of ∼100 μm, have an extremely rough and crenellated appearance at lower length scales (∼0.5 μm). FeO has a molar volume 1.8 times greater than that of metallic Fe. Thus, it might be expected that FeO, produced in reaction I, would fill any gaps on the surface of a particle, such as that displayed in Figure 3.

3. RESULTS Typical plots of the fractional increase in the mass of a sample of Fe particles versus time are shown in Figures 4 and 5, with the difference between them being that, for Figure 5, the experiments lasted almost 10 h. The measurements in these figures were made at 700 °C. It appears that there are at least two distinct stages to the reaction. Initially, the increase in normalized mass (Δm/mo) is approximately linear in time; this behavior has been studied before.7 After a certain time, which evidently depends upon [NO], there is a fall in the rate of increase in Δm/mo. Interestingly, this drop occurs at lower conversions or Δm/mo with higher [NO]; this might suggest that the layer of oxide product is less permeable to NO, when higher [NO] is used. Another point of interest in Figure 4 is that, even with a very low [NO], the rate of increase in mass during the latter stages appears to be the same

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as at higher [NO]; therefore, the curves become almost parallel, suggesting that the order with respect to NO becomes eventually zero in this second stage. However, the plot in Figure 5 for the lower [NO] actually “overtakes” that for the higher [NO], given sufficient time. This indicates that the nature of a reacting particle and properties of the oxide layer, such as its porosity and permeability, might depend upon the conditions of the experiment, particularly [NO]. This is discussed in detail below. The rate of increase of Δm/mo at a particular time was obtained by dividing the average value of Δm/mo, as measured from t - 25 to t þ 25 s minus the average of Δm/mo obtained from t - 20 to t þ 30 s, by 5. Figure 6 shows the results plotted against Δm/mo. It is now clear that the rates of increase of Δm/ mo, when the concentration of NO varies from 0.1 to 9.51 vol %, become very similar and interestingly independent of [NO] for Δm/mo > 0.24. This is an important finding and clear confirmation that the reaction becomes ultimately of zeroth order in NO. At Δm/mo < 0.24, it is clear from Figure 6 that the normalized rate depends upon Δm/mo and [NO]. However, for Δm/mo = 0.15 and [NO] ranging from 0.1 to 9.51 vol %, i.e., again an increase by nearly 2 orders of magnitude, the rate of increase in Δm/mo varies by only a factor of 2-3. Of course, the rate of increase would have been expected to be proportional to [NO] and, therefore, much more strongly depend upon [NO] if gasphase diffusion through a porous oxide was rate-controlling. The indications are thus that, at 700 °C for Δm/mo > 0.24, the reaction is most likely controlled by diffusion of, e.g., ions in the solid layers of oxides covering the iron particles. At this stage, it is informative to consider the increases in mass, when Fe is converted to its different oxides, FexOy. The fractional increase in mass for complete conversion to this general oxide is Δm/mo = 16/55.847 (y/x). There are three stable oxides of Fe; the approximate increases in mass for complete conversion of Fe to each oxide are given in Table 1. The final values of Δm/mo ∼ 0.38 in Figure 5 indicate that the mean conversion of Fe is roughly to Fe3O4 and certainly beyond FeO. Also, the plots in Figure 6 for a temperature of 700 °C show that zeroth-order behavior is achieved when Δm/mo > 0.24 and ∼84% of Fe has been oxidized to FeO. In addition, Table 1 reveals that, when a mole of Fe is oxidized to Fe2O3, the volume increases by a factor of 15.21/7.10 = 2.14. Finally, Table 1 demonstrates that the successive steps of Fe f FeO f Fe3O4 f Fe2O3 are all exothermic, when Fe is oxidized in air. Figure 7 shows measured values of Δm/mo plotted against time for a variety of [NO] and temperatures. Again, the reaction appears to have an initial linear region, followed by a second curved part, where the rate of reaction is much lower. At the highest temperature of 900 °C, it is clear that, for [NO] = 1 vol %, Δm/mo reaches ∼0.43 in ∼12 min, when, according to Table 1, iron has been fully converted to Fe2O3, mainly in the first stage of reaction, i.e., under kinetic control. According to Figure 7 at 800 °C and [NO] = 1 vol %, the reaction becomes controlled by diffusion at a fractional increase in mass of ∼0.25, when FeO is a major product. At 700 °C, with [NO] again equal to 1 vol %, the onset of diffusion control is at the lower value of Δm/mo ∼ 0.15. However, with the lower [NO] of 0.1 vol % at 700 °C, the reaction becomes diffusion-limited at the higher Δm/mo of ∼0.3. At lower temperatures, these trends continue and reaction becomes diffusion-controlled at progressively lower Δm/mo. It is interesting to note that the experiment at 600 °C and 0.1 vol % [NO] shows a greater degree of curvature at lower conversions than that at 600 °C and 0.05 vol % [NO]. Figure 6 has shown 1513


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Table 1. Properties of the Different Oxides of Iron

species

density (kg/m3)

approximate mole fraction of Fe

fractional increase

volume of oxide

volume of oxide

heat of

in mass on production from Fe (Δm/mo)

per kilomole of Fe (m3/kmol)

per mole of Fe (m3/mol)

formation at 25 °C (kJ/mol)

Fe

7870

1

0

FeO

5600

0.50

0.286

12.82

1.81

-266.3

Fe3O4

5100

0.43

0.382

15.13

2.13

-1118.4

Fe2O3

5250

0.40

0.430

15.21

2.14

-824.2

Figure 7. Measured values of Δm/mo at a variety of [NO], temperatures, and times. All concentrations shown are volume percent. Particle sizes, 104-126 μm; total gas flow rate, 3 mL/s; mo ∼5 mg.

that, at 700 °C, the rate of change of Δm/mo finally becomes independent of [NO]. However, the curve in Figure 7 for 500 °C and 0.05% of NO becomes curved at the very low Δm/mo of ∼0.04. This might be caused by a different oxide being produced at low temperatures or a change in permeability. Of course, alternatively, the smaller conversion required at lower temperatures for diffusion in the solid state to control the reaction at a given [NO] could suggest that the diffusional process has an appreciable activation energy. This is in accordance with the reaction being kinetically controlled at and above 900 °C, as shown in Figure 7. This aspect is discussed below.

4. DISCUSSION 4.1. Models. Figures 4-7 make it clear that there is a drop in the rate of reaction at larger conversions of Fe. Possible explanations include the following: (1) The reduction in rate is due to the lower surface area of the Fe/FeO phase boundary at higher conversions. A chemical reaction at this boundary controls the overall rate. (2) The rate-controlling step is diffusion of gaseous NO through pores in the outer layers of oxide, through which there is either molecular or Knudsen diffusion. (3) By analogy with the oxidation of Fe in hot air, the rate-controlling step is solid-state diffusion through the oxide, driven by a concentration gradient in Fe ions. Models 1 and 2 can be discarded, because they require the rate of reaction in these latter stages to depend upon [NO] in the gas phase. Figure 6 shows that this is not the case, particularly when Δm/mo exceeds 0.24. Model 3 must accordingly be examined further. The following assumptions can be made. The Fe particles are spherical, with a shrinking core of unreacted Fe.

7.10

1

0

Figure 8. Main reactions, oxides, and diffusing species in the reaction NO þ Fe f 1/2N2 þ FexOy. The thicknesses of the different oxide layers are not to scale.

Around the shrinking core is a growing layer of FeO (w€ustite), which actually varies in composition from Fe0.95O to Fe0.88O at 1000 °C. On the very exterior are thin layers of Fe3O4 and nonporous Fe2O3. Figure 8 is a schematic diagram of a section of an oxidizing particle of iron. The reactions occurring at each phase boundary are also shown. This figure is based on that by Birks et al.14 for the oxidation of Fe in O2. At this stage, any bulk movement of the oxide layers, caused by the changes in the molar volume noted in Table 1, is ignored. At the exterior of the particle, NO dissociatively adsorbs while reacting with free electrons to produce O2- ions. The resulting nitrogen atoms recombine and, therefore, yield gaseous N2 in the overall reaction NO þ 2e- ¼ 1=2N2 þ O2-

ðIVÞ

which is shown in Figure 8. At the other extreme at the inner Fe/ FeO boundary, Fe ionizes to form Fe2þ and free electrons in Fe ¼ Fe2þ þ 2e-

ðVÞ

Both species Fe2þ and e- diffuse outward through the thickish layer of FeO. At the Fe3O4/FeO boundary, some Fe2þ in effect forms more FeO via the rapid equilibrium: Fe2þ þ 2e- þ Fe3O4 = 4FeO. In fact, at every phase boundary in Figure 8, there is a fast chemical equilibrium; such a situation ensures that the overall rate of reaction between NO and Fe is controlled by some slower, diffusional process. In addition, some Fe2þ ions will jump from FeO into the Fe3O4 phase, where they can ionize further to form Fe3þ and more free electrons. Then, both Fe3þ and Fe2þ diffuse outward through Fe3O4 to produce more Fe3O4 at the 1514


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Fe2O3/Fe3O4 phase boundary, as shown in Figure 8. The highest oxide, Fe2O3, can be produced in various regions, via 2Fe3þ þ 3O2- ¼ Fe2 O3

ðVIÞ

It may be that Fe2O3 forms at the boundary between the gas phase and Fe2O3. On the other hand, O2- ions might diffuse inward through Fe2O3 and form Fe2O3 in the fast equilibrium (reaction VI) at the boundary between Fe3O4 and Fe2O3. For simplicity, it will be assumed that, until all the Fe has oxidized, the Fe3O4 and Fe2O3 layers are relatively thin compared to the layer of FeO, as was found by Kubaschewski and Hopkins.22 Furthermore, it is assumed that there is an excess of O2- ions on the Fe3O4 side of the phase boundary with FeO. Looking at the initial stages of diffusion control, it is likely that the rate of oxidation will be controlled by the rate of diffusion of Fe2þ through the relatively thick layer of FeO and will be driven by the difference in the mole fractions of Fe2þ at the boundaries between Fe and FeO and also FeO and Fe3O4. Free electrons move very rapidly to maintain charge neutrality, as assumed in Wagner’s model.23 The mole fractions of Fe at the inner and outer boundaries of the layer of FeO are assumed to be 1 and approximately 0.5, as measured from the phase diagram by Hauffe.11 4.2. Diffusion within FeO. An iron particle will now be modeled as having a shrinking core of unreacted iron, with a radius rc. Layers of oxides, as in Figure 8, separate the Fe core from the surrounding gas containing NO. The much greater mobility of defects (Fe2þ vacancies and electron holes) in FeO causes this layer to be much thicker14 than those of Fe3O4 and Fe2O3. Thus, during much of the second stage of reaction, FeO is being produced in the overall reaction Fe2þ þ O2- f FeO; therefore, the increase in mass is 16 g/mol of iron reacted. A simple shrinking-core model will slightly overestimate the conversion to FeO, because some of the iron oxidizes to Fe3O4 and Fe2O3; this model will therefore underestimate rc. Because FeO has a greater molar volume than Fe, the outer radius, a, of the particle will increase with conversion (from an initial value of ao). The increase in mass is assumed to be that for a shrinking core, therefore Δm ¼

4 16:0FFe πðao 3 - rc 3 Þ 3 55:84

ð2Þ

The outer radius of the particle, a, can also be estimated from the analogous expression 4 16:0FFeO ð1 - εFeO Þ Δm ¼ πða3 - rc 3 Þ 3 71:84

ð3Þ

Figure 9. Plot to check eq 11 and measure the diffusivity, DFe2þ, for an assumed value of zero for εFeO and particle size of 104-126 μm. The temperature and [NO] were as shown on the plot.

at a radius r, with rc e r e a. In eq 5, xFe2þ is the local mole fraction of Fe2þ ions in the FeO, CT is the total concentration of ions in the FeO phase, and DFe2þ is the diffusivity of Fe2þ in FeO. The approximation has been made in eq 5 that the driving force for diffusion is the gradient of mole fractions rather than the gradient of chemical activities. Finally, the factor of 1 - εFeO is necessary, because the voids reduce the effective area available for the diffusion of Fe2þ. Table 1 shows that, if 1 mol of Fe moves into the FeO phase, it leaves a gap of 7.1 10-6 m3, which can only be filled by 7.1/12.83 = 0.55 mol of FeO. This suggests that, for each mole of Fe ionized to form Fe2þ, only 0.45 mol of Fe2þ actually diffuses outward from a control volume originally on the Fe/FeO boundary. The total rate of reaction of one particle is Q ¼ 4πr 2 NFe2þ in mol/s. Rearranging eqs 5 and 6 and integrating yields Z a Z xa Q dr ¼ dxFe2þ 4πDFe2þ CT ð1 - εFeO Þ rc r 2 xrc

4 πao 3 FFe 3

ð4Þ

Thus, while the reaction is controlled by ions diffusing through FeO, it can be modeled as involving the equilibria (IV) at the exterior of a particle and (V) at the shrinking core. The result is that, for every Fe2þ ion created at the inner surface, an O2- is created at the exterior of the particle. Adding reactions IV and V leads to the overall reaction being reaction I. Also, Fick’s law states that the flux of Fe2þ ions through the layer of FeO is N

Fe2þ

¼ -D

Fe2þ

dx 2þ CT ð1 - εFeO Þ Fe dr

ð7Þ

where xrc and xa are the mole fractions of Fe2þ at the Fe/FeO and FeO/Fe3O4 boundaries, respectively. This integrates to

with εFeO being the voidage fraction of the layer of FeO and FFeO being the skeletal density of FeO. The initial mass of a particle is mo ¼

ð6Þ

Q

1 1 ¼ 4πCT DFe2þ ð1 - εFeO Þðxa - xrc Þ rc a

ð8Þ

At any moment, the rate of increase of mass of the reacting sample is dm=dt ¼ 16:0QNp mo

ð9Þ

where Np is the number of particles in unit mass of unreacted, raw Fe. Integration of eq 9 yields Z

ð5Þ

t 0

1515

16:0Q dt ¼

Δm mo Np

ð10Þ


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Figure 10. Same plot as Figure 9 but for 600 °C. Again, the particle size was 104-126 μm; values of [NO] were as shown on the plot.

In these equations, a is calculated throughout the course of the reaction from eqs 2-4. Eliminating Q leads to Z t Δm 64ðFFeO 1000ÞπDFe2þ ð1 - εFeO Þðxa - xrc Þ ¼ dt 1 1 mo Np 0 71:84 rc a ð11Þ This can be numerically integrated, given knowledge (from eqs 4 to 6) of rc and a as functions of time. Of course, if gaps open up between the oxide and the metal, the bulk density of FeO will be different, as will the area available for Fe2þ to diffuse. Equation 11 can be checked by plotting the measurements as f(Δm) = (71.84Δm)/(64πmoNpFFeO(xa - xrc)(1 - εFeO)) R against t0[(1/rc) - (1/a)]-1dt, whose slope is expected to be DFe2þ(1 - εFeO). Figure 9 shows such a plot for the results in Figures 7 and 8 for experiments at 700 and 800 °C. Of course, the plots in Figure 9 do not pass through the origin, because of the effects of the early stages, when the reaction is kinetically controlled. Even so, there is reasonable linearity evident in Figure 9. The gradient of the line of best fit for the experiment at 800 °C is DFe2þ = 1.5 10-12 m2/s, assuming εFeO = 0. Likewise, with the same assumption, the plots at 700 °C yield DFe2þ = 8.6 10-13, 1.1 10-12, and 8.6 10-13 m2/s, with values of R2 of 0.99, 0.995, and 0.999 for the experiments with [NO] = 9.51, 0.4, and 0.3 vol %, respectively. The measurements included in Figure 9 are those for 0.15 e Δm/mo < 0.286; for these values, Figure 6 shows that d(Δm/mo)/dt is only a function of Δm/mo rather than [NO] in the gas phase. Figure 4 confirms that the measurements in Figure 9 were made over a reasonably long period of time; e.g., the measurements presented for 0.4 vol % of NO were made over a period of 1600 s. It is clear from Figure 9 that the plots for 700 °C are approximately parallel and that the plot for 800 °C has a higher gradient. It was noted above in Figure 7 that measurements at 900 °C indicated that the initial reaction of Fe to FeO was kinetically controlled. Consequently, experiments at 900 °C are not considered. Figure 10 plots the same functions but for experiments at 600 °C. Assuming again that εFeO = 0, the diffusivities obtained for Fe2þ ions from Figure 10 are 1.5

10-13 and 1.6 10-13 m2/s, with corresponding values of R2 of 0.98 and 0.99 for 0.05 and 0.1 vol % NO, respectively. All of the diffusivities derived from such plots are shown in Table 2. Each value of DFe2þ is an average of at least five different measurements over a range of [NO]. Also shown in Table 2 are the values of DFe2þ, obtained if the values of εFeO quoted by Hayhurst and Ninomiya5 are assumed. These values are 0.22, 0.42, and 0.60 for experiments at 700, 800, and 900 °C, respectively. Below 700 °C, no voidage has been assumed. This is a reasonable assumption, because the rate of growth of the oxide layers might be expected to be slow enough for the oxide to be reasonably coherent. In any case, when deriving DFe2þ, εFeO appears as 1 - εFeO; therefore, changes in the assumed value of εFeO do not make a big difference in the measured value of DFe2þ, provided that εFeO is close to zero. Of course, for the mechanism proposed above to be feasible, the rate of reaction at a particular temperature and also the derived diffusivity must be a function of only Δm/mo within the diffusion-controlled regime. Figure 11 shows that the derived DFe2þ is indeed independent of Δm/mo in the latter stages of the reaction, when Δm/mo > 0.15. For the experiments at 800 °C, it is also clear that the measured DFe2þ is much more variable than for experiments at 700 °C. This is probably because the experiment at 800 °C took place over a much shorter time scale, yielding a shorter time within the diffusionlimited regime; the explanation derives from the fact (established below) that the diffusional processes measured here have a larger activation energy than the initial rates measured during the regime limited by the surface reaction kinetics. One result is a greater variability in the measured diffusivities. Values of DFe2þ obtained from plots such as Figure 11 are similar to those from Figures 9 and 10. Of course, it is clear from Figure 11 that there is an error of at least (25% in each determination of DFe2þ; hence, the requirement for repeated experiments. It was also noted in section 3 and Figure 5 that a plot of Δm/mo against time for a lower [NO] might actually overtake that for a higher [NO], after a sufficiently long period of time. One explanation for this phenomenon is that a slower reaction would lead to a more cohesive oxide layer (i.e., containing fewer voids), because the growing oxide layer would have more time to plastically deform and fill in a void, while it was formed at the Fe/FeO interface. In contrast to the situation where pores lead to the surface of a particle, for a continuous layer with solid-state diffusion being rate-limiting, the less porous the particle, the faster the overall rate of reaction in the diffusionlimited regime. Such phenomena have been observed in reacting systems of similar geometry, such as the hydration of lime,26 where the observed characteristics (such as the resistance to attrition) of the growing hydroxide layer are strongly related to the chemical and thermal environment experienced by the particles. 4.3. Diffusion within Fe3O4. An analysis similar to the one above is possible for when diffusion of the ions Fe2þ and Fe3þ in Fe3O4 controls the overall rate of reaction. Such a situation will occur when the particle has been converted almost entirely to FeO; i.e., the fractional weight increase exceeds 0.286. Then, the rate-determining step has become the diffusion of ions through Fe3O4. It is accordingly assumed that Fe2þ ions cross from the inner layer of FeO into the surrounding Fe3O4 phase. Some Fe2þ ions ionize further to Fe3þ, but some Fe2þ ions diffuse through Fe3O4 to form more Fe3O4 at the Fe3O4/Fe2O3 phase boundary. 1516


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Table 2. Comparison of Values of DFe2þ or DFenþ Derived Here with the Results from Others DFe2þ (1013, m2 s-1)17 DFe2þ DFe2þ T (°C) (1013, m2 s-1)24 (1013, m2 s-1)5

from kexp

from k

DFe2þ (1013, m2 s-1)10

DFe2þ or DFenþ (1013, m2 s-1) (this work)

Armco Armco electrolytic DFe2þ or DFenþ DFe2þ or DFenþ in O2 in air in O2 (1013, m2 s-1)25 (1013, m2 s-1)12

with voidage

no voidage

1.1 7.9 39

1.1 5.6 16

0.6 1.2

0.6 1.2

2.5 6.0 230

1.7 4.2 84

Fe f FeO 600 700 800 900 1000

36 155 400

9.1 25 77

4 38 170

2.7 43 190

36 190 810

20 91 380

3.2 19 120

0.20 2.4 29 48

4.9 43 180

FeO f Fe3O4 500 550 600 700 800 900

1 10 40

Figure 11. Plot of measured values of DFe2þ against Δm/mo for the experiments shown in Figure 9. The temperatures and [NO] were as shown; zero voidage has been assumed.

In this case, the final expression obtained is Δm mo Np Z ¼ 0

t

12 ð77:17 - 71:84ÞðFFe3 O4 1000ÞπDFenþ ð1 - εFe3 O4 Þðxa - xrc Þ dt 1 1 231:52 rc a

ð12Þ nþ

This expression arises because the number of moles of Fe per gram of Fe3O4 is 3 103FFe3O4/231.52, and each mole of Fenþ moving from FeO into and through Fe3O4 and forming Fe3O4 at the Fe3O4/Fe2O3 border leads to an increase of 77.17 - 71.84 g/ mol in the mass of the particle. It is assumed that all Fe in the particle has become FeO prior to this. Of course, in this expression, rc and a are the inner and outer radii of a layer of Fe3O4 growing on FeO; also, xrc and xa are the corresponding mole fractions of Fe ions at the inner and outer radii. In addition, DFenþ refers to the combined diffusivity of Fe2þ and Fe3þ moving through Fe3O4. The value of Δm is of course now the fractional increase in mass going from FeO to Fe3O4. The value of εFe3O4

Figure 12. Plot of ln DFe2þ against 1/T, assuming either the voidage was zero (lower line) or that it varied (upper line). The gradient of a plot gives the activation energy for the diffusion of Fe2þ ions in FeO.

has been assumed to be the same as that for the formation of FeO. Plotting eq 12 in a form similar to Figures 9 and 10 gives the values for diffusivity for Fenþ presented in Table 2. Below 570 °C, only Fe3O4 is stable, which is why no measurements of DFe2þ were made below 600 °C. Consequently, only values of DFenþ are presented in Table 2 for temperatures below 570 °C. In this case, the mass increase per mole of diffusing Fenþ is 20 g, and the corresponding difference in mole fraction of Fe at the Fe/ Fe3O4 and Fe3O4/Fe2O3 phase boundaries is 1 - 0.42. 4.4. Activation Energies. Solid-state diffusion is an activated process; therefore, a plot of ln DFe2þ or ln DFenþ against 1/T should be a straight line, with a gradient of -E/R, where E is the activation energy. Figures 12 and 13 are such plots, for DFe2þ and DFenþ, respectively, making two different possible assumptions about porosity: either that the porosity is zero or increases with 1517


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Figure 14. Section of two particles (initial diameter, 104-126 μm), which had been reacted with 1% NO in N2 for 300 s at 900 °C. The scale bar shown is 100 μm in length. The white area at the center of one particle is unreacted iron. The exteriors of the two particles have been highlighted; also lines indicate the four locations at which the thickness of the oxide layer was measured. Figure 13. Plot of ln DFenþ against 1/T, again assuming the voidage was zero (solid line) or that it varied (broken line). The gradient of this plot gives the activation energy for the diffusion of Fenþ ions through Fe3O4 during the latter stages of the reaction.

an increasing temperature in the manner observed by Hayhurst and Ninomiya.5 Looking at Figures 12 and 13, it is clear that the measurements are fitted reasonably well by straight lines. In fact, DFe2þ and DFenþ are given by the following equations: DFe2þ ¼ 3:1 10-7 expð - 110 ( 50 kJ=mol=RTÞ m2 =s ðno porosityÞ

ð13Þ

DFe2þ ¼ 2:5 10-5 expð - 141 ( 60 kJ=mol=RTÞ m2 =s ðchanging porosityÞ

ð14Þ

DFe2þ ¼ 2:7 10-8 expð - 86 ( 40 kJ=mol=RTÞ m2 =s ðno porosityÞ

ð15Þ

DFenþ ¼ 3:9 10-7 expð - 104 ( 20 kJ=mol=RTÞ m2 =s ðchanging porosityÞ 2

ð16Þ

Values of R for plots of ln DFe2þ against 1/T are 0.71, 0.8, 0.8, and 0.82 for eqs 13-16, respectively. Thus, a better fit is obtained by assuming the voidages measured by Hayhurst and Ninomiya.5 This is reasonable and has the advantage that εFeO is not derived from simply fitting these measurements, although it is clear that there is substantial room for improvement in measuring εFeO for the oxide produced in the thermogravimetric balance. Equations 14 and 16 and their activation energies are consequently preferable to eqs 13 and 15. The resulting activation energies are now seen to be much larger than those for k1 and k2. This explains, at least partly, why, at 500 °C, the onset of diffusion control occurs at low conversions with small [NO], but at higher temperatures, diffusion becomes rate-controlling only at larger [NO]. In fact, at 900 °C, the reaction proceeds almost entirely under kinetic control. 4.5. Comparison to Literature Values for Oxidation of Fe in Air or Oxygen. Table 2 compares the results derived here to those from the literature. It is clear that the results presented here

are broadly in line with values from the literature. Some previous workers did not report diffusivities; for such studies, a diffusivity has been calculated from, e.g., reported values of k, the constant of proportionality in the parabolic scaling law, Δm/A = (kt)1/2, assuming zero porosity of the oxide layer, the particular geometry, and the same diffusing species and mole fractions at the extremities of the oxide region. In fact, this comparison checks that the measured rates of mass increase are similar rather than implying any check of the model. It is clear that the diffusivities derived here (i.e., comparing values of DFe2þ from this work for “no porosity” to those derived by others) are similar to those from previous investigations, which importantly used a totally different oxidizing gas. 4.6. Microscopic Observations of Reacted Particles. Some particles of Fe, which had been oxidized by NO in the thermogravimetric balance were set in epoxy and then sectioned20 using an automatic machine (Struers Secotom-10). This sliced the particles without damaging them. One such section is shown in Figure 14, for a particle which had been reacted with 1% NO at 900 °C for 300 s. The main feature to note is the clearly apparent shrinking core of iron in the center of the particle. However, it appears that the oxide visible does not all come from the single particle whose iron core is marked. Hence, there are two areas of oxide marked. It is apparent that modeling the particle as a sphere, with a spherical shrinking core of iron within it, is a big (although necessary) simplification, even at this late stage in the reaction. From the measured mass change, the value of Δm/mo should be ∼0.24 for this particle. The voidage of the particles can be estimated by measuring a variety of radii for the core of iron in Figure 14. Knowing the approximate value of Δm/mo, an estimate of the initial value of ao can be obtained from eqs 2 and 3, while measuring rc from Figure 14. The thicknesses measured for the oxide layer were 30, 24, 30, and 48 μm. Values for rc were 27, 25, 20, and 40 μm. These values led to a value of 60 μm for ao and, consequently, a value of 0.1 for the voidage. However, the large errors inherent in measuring a thickness for the oxide, as well as rc and Δm/mo, and especially in assuming the particles to be spheres indicate that this value for the voidage has a very large error associated with it. The main error, which is the assumption that the particles are spheres, would lead to an 1518


Energy & Fuels overestimate of the voidage, because if they were any other shape, the surface area, upon which the oxide layer was growing, would be higher. This results in a lower thickness of oxide required to give the same value of Δm/mo. Such measurements on a variety of different particles after being reacted under the same conditions indicated20 a voidage between 0 and 0.4. It is worth noting that both Hayhurst and Ninomiya5 and Hayhurst and Lawrence4 found that the outer layer of oxide formed in the reaction between NO and Fe was so porous that gas-phase diffusion initially occurred through the layer of oxide. The porosities of particles formed here were measured20 to be substantially lower than those derived by Hayhurst and Ninomiya5 from work in a fluidized bed. A tentative explanation for the differences observed between the reaction in a fluidized bed and a thermogravimetric balance is that a weakly adhesive, thin, nonporous, outer layer of oxide forms in both reactors. However, attrition in the fluidized bed causes this thin, dense layer to be continually removed, opening up the inner, more openly structured FeO and Fe3O4 to gaseous diffusion. Herein lies an advantage of using Fe-based particles to reduce emissions of NOx from fluidized-bed combustors. In the fuel-rich regions of such a bed, where, e.g., coal or biomass enters, any Fe-containing particles will be reduced by H2, CO, the lower hydrocarbons, and even NH3 to metallic Fe. Usually a fluidized-bed combustor also has oxygen-rich regions, where metallic Fe is oxidized (to one of its oxides) by O2, NO, N2O, and even radicals, such as OH. Such a situation facilitates the removal of NO and CO in reaction III. All of this can be achieved by adding to the bed, e.g., particles of Fe, its oxides, or even iron ore or red sand, rich in iron.

5. CONCLUSIONS The latter stages of the oxidation of iron with NO have been studied and modeled. It has been confirmed that the rate of oxidation of iron by NO becomes independent of [NO], once a sufficiently thick layer of oxide has built up on the surface of iron. The rate of oxidation is well-described by a mechanism involving diffusion of ions through a layer of product, initially assuming a shrinking core of Fe but later one of FeO. Values of diffusivities of Fe ions through FeO and Fe3O4 were derived. These were found to be close to the values obtained by others. Values were measured for the diffusivities of Fe2þ ions through FeO and for Fenþ ions through Fe3O4, formed toward the end of the reaction of the particles. These fitted well to the expressions -5 expð - 141 ( 40 kJ=mol=RTÞ m2 =s DFe2þ ¼ 2:5þ2:5 -1:3 10 -7 DFenþ ¼ 3:9þ4 expð - 104 ( 20 kJ=mol=RTÞ m2 =s -2 10

These activation energies are larger than that for k1 for reaction I, causing the final stages (involving ionic diffusion through a layer of product) to be kinetically controlled at higher temperatures of 900 °C or above. The use of particles of Fe or its oxides in fluidized-bed combustors is discussed briefly.

’ AUTHOR INFORMATION Corresponding Author

*Telephone: þ44-(0)1223-334790. Fax: þ44-(0)1223-334796. E-mail: [email protected]. Present Addresses †

Department of Chemical Engineering and Chemical Technology, Imperial College, London SW7 2AZ, U.K.

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’ NOMENCLATURE a = outer radius of a particle, initially Fe, after oxidizing for a time t (m) ao = initial radius of a particle of Fe (m) A = surface area of reacting particles of Fe (m2) CT = total number of moles per unit volume (mol m-3) DFe2þ = diffusivity of Fe2þ in FeO (m2 s-1) DFenþ = combined diffusivity of Fe2þ and Fe3þ through Fe3O4 (m2 s-1) E = activation energy (kJ mol-1) k = rate constant in parabolic rate law (g2 m-4 s-1) mo = initial mass of Fe (g) Δm = increase in mass of particles of Fe (g) NFe2þ = flux of Fe2þ (mol m-2 s-1) NO2- = flux of O2- in FeO (mol m-2 s-1) Np = number of particles per gram of raw Fe particles (g-1) Q = molar rate of the reaction of one particle (mol s-1) rc = radius of a shrinking core of Fe or FeO in a particle originally consisting of Fe or FeO (m) t = time (s) T = temperature (K) [X] = concentration of any gas X (mol m-3) ΔxFe2þ = difference in the mole fraction of Fe2þ at Fe/FeO and Fe3O4 phase boundaries xX = mole fraction of any species X Greek Symbols

ε = voidage in a particle FX = density of any species X (kg m-3)

’ REFERENCES (1) Allen, D.; Hayhurst, A. N. Proceedings of the Institute of Energy’s 5th International Fluidized Combustion Conference; Adam Hilger: Bristol, U.K., 1991; pp 221-230. (2) Cowley, L. T.; Roberts, P. T. Proceedings of the Fluidised Combustion Conference, Energy Research Institute, University of Cape Town: Cape Town, South Africa, 1981; Vol. 2 (issue 5.3), pp 443-462. (3) Hayhurst, A. N.; Lawrence, A. D. Proceedings of the 45th Canadian Chemical Engineering Conference; Quebec, Canada, Oct 1518, 1995; p 512. (4) Hayhurst, A. N.; Lawrence, A. D. Combust. Flame 1997, 110, 351–365. (5) Hayhurst, A. N.; Ninomiya, Y. Chem. Eng. Sci. 1998, 53, 1481–1489. (6) Lissiansky, V. V.; Maly, P. M.; Zamansky, V. M.; Gardiner, W. C. Ind. Eng. Chem. Res. 2001, 40, 3287–3293. (7) Fennell, P. S.; Hayhurst, A. N. Proc. Combust. Inst. 2002, 29, 2179–2185. (8) Grado n, B.; Lasek, J. Fuel 2010, 89, 3505–3509. (9) Lawrence, A. D. Ph.D. Dissertation, University of Cambridge, Cambridge, U.K., 1993. (10) Pilling, N. B.; Bedworth, R. E. J. Inst. Met. 1923, 29, 529–591. (11) Hauffe, K. Metalloberflaeche 1954, 7, 98–103. (12) Païdassi, J. Acta Metall. 1958, 6, 184–194. (13) Païdassi, J. Acta Metall. 1958, 6, 219–221. (14) Birks, N.; Meier, G. H.; Pettit, F. S. High Temperature Oxidation of Metals, 2nd ed.; Cambridge University Press: Cambridge, U.K., 2006. (15) Engell, H.-J.; Wever, F. Acta Metall. 1957, 5, 695–702. (16) Rahmel, A.; Engell, H.-J. Arch. Eisenhuettenwes. 1959, 30, 743–746. (17) Slattery, J. C.; Peng, K. Y.; Gadalla, A. M.; Gadalla, N. Ind. Eng. Chem. Res. 1995, 34, 3405–3410. (18) Slattery, J. C. Advanced Transport Phenomena; Cambridge University Press: Cambridge, U.K., 1999; p 545. 1519


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(19) Schweica, W.; Hoser, A.; Martin, M.; Carlson, A. E. Phys. Rev. B: Condens. Matter Mater. Phys. 1995, 51 (22), No. 15771. (20) Fennell, P. S. Ph.D. Dissertation, University of Cambridge, Cambridge, U.K., 2004. (21) Yrjas, P. Academic Dissertation, Åbo Akademi, Turku, Finland, 1996. (22) Kubachewski, O.; Hopkins, B. E. Oxidation of Metals and Alloys, 2nd ed.; Butterworths: London, U.K., 1962; pp 104-112. (23) Wagner, C. Atom Movements; American Society for Metals: Materials Park, OH, 1951; pp 153-171. (24) Himmel, L.; Mehl, R. F.; Birchenall, C. E. Trans. Am. Inst. Min., Metall. Pet. Eng. 1953, 197, 827–843. (25) Smeltzer, W. W. Acta Metall. 1960, 8, 377–383. (26) Blamey, J.; Paterson, N. P. M.; Dugwell, D. R.; Stevenson, P. S.; Fennell, P. S. Proc. Combust. Inst. 2011, 33, 2673–2681.

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Latter Stages of the Reduction of NO to N2 on Particles of Fe while

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