The Kinetics of Hematite to Magnetite Reduction in Hydrogen-Water and Hydrogen-Water-Nitrogen Mixtures G . Nabi' and W.-K. Lu* Department of Metallurgy and Materials Science, McMaster University, Hamilton, Ontario, Canada
The kinetic studies of this interfacial chemical reaction were carried out with synthetic specimens by the weight-loss method, with negligible interference of mass transport processes for the first time. Rate expressions based on reasonable reaction mechanisms were derived and their validity was checked with the experimental data. The rate equation was found to be quite different from those assumed by many authors. Values of the changes of enthalpies and entropies for the mechanistic steps were calculated from the temperature dependence of the reaction parameters and were found to be consistent with the proposed mechanism.
In hematite reduction to iron, the overall reaction consists of many steps, such as gaseous diffusion through the boundary layer, porous magnetite and wustite scales, and interfacial chemical reactions. The general phenomenological representations, considering the variation of the areas of interfaces with time, have been adequately reviewed by Manning and Philbrook (1969). In these mathematical models, the kinetic parameters, diffusivities, and rate constants of first-order reactions were assumed to be constants because of a lack of information. The true rate expressions of these interfacial reactions have never been examined independently. Very little difficulty was encountered in fitting these mathematical models to the experimental data because there are several adjustable parameters. For the same reason, the correctness of the assumed rate expressions has never been tested. However, it is known that the interfacial chemical reaction is not an elementary step but consists of at least chemisorption, surface reaction, and desorption. The present work was designed to investigate the kinetics and the mechanism of interfacial reactions between hematite and hydrogenwater vapor mixtures. To simplify the system a single interfacial reaction, reducing hematite (FezO3) to magnetite (FesO4), was chosen. To avoid the complication arising from diffusion through the magnetite layer, only the initial rates were measured and analyzed. The thermodynamics of this system have been well established. Preparation of Specimens Specimens made from chemical reagents are preferred over those made from natural minerals because of their high purity and simple geometric shape, such as spheres. Ferric oxide supplied by Atomergic Chemicals Co., New York, N. Y., was used as the starting material (chemical analysis: 99.76% FezO3, 0.013% Mn, 0.002% Cu, 0.004% Zn, 0.07% substances not precipitated by NHIOH, 0.1% sulfate, 0.01% phosphate, and 0.002% nitrate). Handrolled spheres were heated three times at 750, 900, and 1000°C in air for 1 hr in each case. After each firing, the spheres were dipped in a thick hematite slurry and evacuated to facilitate the filling of void space and rolled in a ball mill with hematite powder to improve their spherical shape. The final sintering was carried out in the following way. The specimens were placed in high-purity alumina boats,
' Pakistan Steel Mills Corp., Ltd.. Karachi, Pakistan
smoothed with Fez03 powder, and sintered in tubular furnaces with free circulation of air. The temperature was raised to 1050°C in 3 hr and then increased at the rate of 100"C/hr to the desired temperature. After sintering for the required length of time, the furnace was slowly cooled a t the rate of 80"Cfhr down to 850°C; then the power was turned off. As expected, the reactivity of the specimens, in terms of weight loss under identical experimental conditions, was influenced by the conditions of the final sintering process as shown in Figure 1. The decrease in reactivity of hematite when the sintering temperature was raised from 1100 to 1200°C was found to be due to sintering and grain growth; therefore, a sealed and smooth surface resulted, which was observed metallographically by Nabi (1970) and by Nabi and Lu (1973). The increase in reactivity as the sintering temperature was raised beyond 1200°C was concluded by Nabi (1970) to be due to the further deviation from stoichiometry, based on the influences on sintering time at 1350°C and the cooling rates after sintering. The density of spheres was determined, based on the Archemedes principle in distilled water with a microbalance. These are listed in Table I. It was observed by cleaving the specimens sintered at or above 1200°C that the outer portion of the specimen was pore free, but small isolated pores existed near the center of the specimen. The standard conditions chosen for the preparation of specimens for the present work, for good reproducibility of reactivity, were 1200°C as the final sintering temperature and 5 hr as the sintering time. All specimens used were spheres weighing 2.78 g ( & 2 5 mg). Apparatus. A simplified schematic diagram of the equipment is shown in Figure 2. It consists of arrangements for preparation of H2-H20 reducing gas mixtures, a reaction furnace and a Cahn RH2500 microbalance. The present method for the preparation of Hz-HzO mixtures by partial combustion of Hz with 0 2 is an improved form of the procedure described by Nabi and Lu (1968). The reactant gases and the specimen were heated to reaction temperature in a noninductively would Kanthal furnace. The specimen was suspended from the left arm of the microbalance into the reaction tube. Two hand-made platinum chains were used. The specimen basket was a quartz ring which was a little smaller in diameter than the specimen. The specimen rested on small gold rings attached to the quartz ring so as to give negligible contact area and minimum hindrance to the flow of gases. The specimen was also in contact with the suspension chain, which in turn was grounded through the balance weighing assembly. Ind. Eng. Chem., Fundam.,Vol. 13, No.4, 1974
311
TLUE OF REaKTlON = 90 MIN.
Table I. Density of Specimens (g/cm3) Sintered at Various Temperatures for Different Lengths of Time
~
Temp, "C
_1
1100
1150
1200 1250 1300 TEMPERATURE, C '
1350
1400
Figure 1 . Surface reactivity us. sintering temperature for constant sintering time, 5 hr.
24-2
n
r'
Z
-
2
6
-+ I
Figure 2. Schematic diagram of the apparatus: 1, microflow control valves at the hydrogen-oxygen-nitrogen cyclinders; 2, absorption and purification system; 3, bubblers; 4, long inclined Utube monometers; 5 , absorption tubes; 6, absorption and flame arresting unit on hydrogen line; 7, single inlet double exit valves; 8, bubble flow meter; 9, oxygen-hydrogen combustion unit; 10, low-temperature furnace; 11, stop valves; 12, stop valves; 13, iron-constantan thermocouples; 14, high-temperature heating tapes; 15, nitrogen from purification and measurement unit; 16, nitrogen inlet valve; 17, specimen temperature measurement thermocouple; 18, quartz beads packing; 19, specimen; 20, threezone noninductively wound furnace, on a vertically sliding platform; 21, detachable hook; 22, specimen inlet hole; 23, aluminum joint with O-rings; 24, nitrogen from purification and measurement unit; 25, microbalance; 26, microbalance control and recording; 27, low-temperature heating tapes; 28, three-way valve; 29, gas exit; 30, cooling water; 31, HzO vapor condensor; 32, condensate outlet; 33, unburnt H2 temperature measurement.
Experimental Considerations. The kinetic experiments were carried out in the temperature range from 650 to 800°C and in the composition range of gas mixtures such that magnetite is the only solid product. The lower limit of temperature was chosen to avoid having nucleation of magnetite to disturb the uniformity of the reaction over the surface of the specimen. The higher limit of temperature is due to the fact that fast reaction would reduce the accuracy of the measurement of the initial rate. The flow rate of 360 ml (STP)/min at atmospheric pressure, in a reaction tube of 1.8-cm inside diameter, with a pellet about 1 cm diameter, is high enough to assume that gaseous diffusion through the boundary layer has a negligible effect on the observed rates. If the overall rate of reaction is controlled by convective mass transfer in the gaseous phase, the rate in terms of weight loss would be 13.6 mg/ cm2 min at 800°C with P H 2 / P H z 0 = 0.05, and 71 mg/cm2 min at 800°C with P H 2 / P H 2 0 = 0.35. These calculated values reported by Nabi (1970), are more than 100 times 312
Ind. Eng. Chem., Fundarn., Vol. 13,No. 4, 1974
Time, h r
1350
1 5 10 15 20
5.18 5.18 5.17 5.21 5.20
1300
1250
1200
1150
1100
5.19
5.17
5.19
5.15
5.05
higher than the actual observed rates under the given conditions. This type of calculation has been tested and found to be valid under similar conditions (Nabi and Lu, 1968). It should also be pointed out that the supply of reductant, hydrogen, was adequate so that the gas composition around the specimen was very similar to that at the inlet. This can be illustrated by showing the extent of conversion in the gaseous phase at different temperatures. Based on the values of equilibrium constants and the maximum measured weight-loss rates, the extent of conversion of hydrogen after passing through the reaction chamber was about 0.17Y0,0.42%, 0.75%, and 1.2%, or less, for the cases at 650, 700, 750, and 800"C, respectively. The uncertainty in the adjustment of the reducing gas ratio may be up to &2%. The major souce of variation in the results may be the surface area and the nature of the specimen surface, the precise reproducibility of which is difficult. By careful surface preparation, the difference in the reaction time for initial 4% reduction from hematite to magnetite may vary within *lo% for specimens of similar density values. Blank runs with inert specimens were performed for each set of experimental conditions. This was done to determine loss in weight from buoyancy and aerodynamic forces, effects of top blown gases, and adsorption or desorption of gases on the specimen or suspension systems. These corrections were applied to the actual weight of the specimen. The transition time in changing from one gas atmosphere to another was observed to be less than 30 sec by heat conduction measurement. The specific rate in terms of weight loss per unit area per unit time is the value of dwldt (which may be obtained graphically from recording charts) divided by the area of the interface between hematite and magnetite. This area, which varies with time, may be calculated according to the expression A = A, (1 2 /3
go)
where A0 and AWo are the initial surface area and the weight loss for the complete conversion for a particular specimen, respectively. All measured rates reported in this work were obtained before 6% completion was reached, and in most cases before 2% completion. The calculated thickness of the porous magnetite layer was less than 0.1 mm. It is considered that such thin porous layers do not form a significant diffusional barrier for gases. This point will be discussed further in the next section. A very detailed description of the apparatus and experimental considerations of this work has been given by Nabi (1970). Experimental Results Figure 3 shows the reaction rate us. partial pressures of hydrogen for binary gas mixtures at four different temper-
4
4 *
__. ann
Figure 3. Reaction rates at various temperatures in Hz-HzO
mixtures. 0 251
/"'
1
I
012
I
016
P 'u' 2 (alms
)
1 020
I 028
O6
-
t
-1
0 5-
P i
I
024
Figure 5. Reaction rates in binary and ternary gas mixtures at 750°C.
I
0 201
I
008
8 0 0 'C
w 030
a 02-
p"z +PH$
il/ P
"20--01I+N,
0
IP
X
lP,2/P,q021+N~
-
A I PH,/PH,e 0 3 I+ \ 01
PHL,otrns
atures. Figures 4-6 show the reaction rates in binary and ternary gas mixtures us. partial pressure of hydrogen for three different temperatures. The hydrogen-water vapor ratios were fixed, but their partial pressures were varied by the introduction of nitrogen. In the case of ternary gases a t 700°C (see Figure 4) the reaction rate increases with the partial pressure of hydrogen, first very slowly, then increases rapidly, and slowly again. With ternary mixtures the reaction rate depends on the PH2/PH20ratio, and is always greater than the rate for the binary mixtures at the same partial pressure of hydrogen. Retardation effects due to gaseous diffusion through the porous magnetite layer would cause the specific rate to decrease with an increase in time. It has been observed by many authors, e.g., Nabi and Lu (1968), that during hematite to magnetite transformation the volume of the specimen increases by 25-3070 due to directional growth of magnetite. Hence, the magnetite layer is very porous. Parallel to the gaseous diffusion through the void space in the magnetite layer, solid-state diffusion across the product layer would also take place. However, the diffusivities of cations and anion in magnetite over the temperature range concerned are 10-11 cm2/sec or smaller. It is reasonable to suggest that the mass transfer across the product layer is mainly by gaseous diffusion. The diffusion effects were not observed at 750 and 800°C until about 3040% reduction had occurred. At 650 and 700°C the diffusion effect appears at about 6-1570 reduction, depending on the composition of the reducing gases.
-
004
000
012
016
020
024
028
032
Reaction Mechanism a n d R a t e Expression In principle, the rate expressions which describe the interfacial chemical reaction should consist of all the three steps, namely, adsorption, surface reaction, and desorption. Of course, each step should be considered to be reversible; hence there are two kinetic parameters to be determined experimentally. It is feasible, as shown by Happel (1968) and by Nakhmanovich, et al. (1963), to derive the rate expressions including all the three steps but they would involve six constants. However, they may not be evaluated uniquely based on present data. The simplified approach which is employed here involves the assumption that one of these steps is rate controlling, but the other two are intrinsically capable of going much faster than the rate-controlling step. However, the actual rates of these steps and the rate of the overall reaction are governed by that of the slowest step. By comparing the rate expressions obtained this way with the experimental data, the identification of the single controlling step would be possible. In general, of course, the present work is not an exception; it is possible that there is more than one mechanism which suggests a rate expression to be consistent with the same kinetic data. Four mechanisms, which are different in the types of adsorbed species and in the way the water molecules are formed, were considered in this study. The first two of the four mechanisms to be proposed considered the chemisorption of hydrogen molecules to be nondissociative. The difference between these two mechanisms is that the adInd. Eng. Chem., Fundam., Vol. 13, No. 4,1974
313
0010-
+
?
0007-
A -04 A -03 x -02 0 -01
0001 01
05
03 PNt
07
09
I
The chemical equations of the other mechanisms are listed in Appendix B.
IO
IOfrTS )
Figure 7 . Calculation for the adsorption equilibrium constant for
nitrogen.
Mathematical Analysis of the Experimental Data The rate expressions developed in the previous section were changed to a linear form. For example, eq 2 was changed to the following form
where (5)
K = k,KaLS/2
or where
I/Tald
I("
Figure 8. Effect of temperature on hematite reduction at various hydrogen, water, vapor partial pressures.
sorbed species are hydrogen and water molecules in one, and hydrogen molecules and oxygen atoms in the other. In the other two mechanisms, hydroxyl groups, as the result of dissociative adsorption of hydrogen, and water molecules are the adsorbed species. The difference between these two mechanisms is that in one, the adsorbed water molecules are formed as the result of a reaction between the adsorbed hydroxyl groups, and in the other, as a result of a reaction between hydroxyl groups and the hydrogen gas. Only the last mechanism will be discussed in detail here. A hydrogen molecule may dissociate into two hydrogen atoms during adsorption or after adsorption on a lattice site, with the formation of two hydroxyl ions. Another hydrogen molecule can split into two hydrogen atoms. It may or may not use the cation site as an intermediate for adsorption and dissociation. These hydrogen atoms may join with hydroxyl ions forming water molecules. The following simple steps may represent the course of the chemical reaction H,(g) + Os-Os = HO*-HO* HO*-HO*
+
(adsorption)
H,(g) = H20*-H20* (surface reaction)
HzO* = H,O(g)
+
s (desorption)
where * indicates the adsorbed species, 0,-0, and s are the dual oxygen sites and single site on the hematite surface, respectively. The following rate expressions to one of each rate-controlling step of the above sequence are obtained (see Appendix A) 314
Ind. Eng. Chem., Fundam., Vol. 13, No. 4 , 1974
The terms involving the reverse reaction were neglected because of the large value of the equilibrium constant. Under the experimental conditions in this study, K, has a value of the order of 104; r, was measured experimentally. The rate equations for all four mechanisms are written in a form which is linear in terms of the unknown constants A, B, and C. Following Hougen and Watson (1967), these constants were evaluated by the least-squares method with matrices inversion solution of the simultaneous equations using a CDC 6400 computer. The constants A , B, and C should be positive, as rate constants and equilibrium constants cannot have negative values. Nabi (1970) reported that the only rate expression which satisfies this requirement is eq 4, and hence this will be accepted as the best approximation describing the overall reaction of hematite to magnetite reduction in Hz-HzO or Hz-HzO-Nz mixtures.
Results of the Mathematical Analysis and Discussion In eq 2, the rate is expressed as the number of oxygen atoms removed from hematite/(sec cmz). On the other hand, the experimental values shown in Figures 3 to 6 have the units of mg loss in weight/(min cm2). The conversion factor, K O is 9.6 x lo5 divided by Avogadro's number. Therefore, eq 4 may be rewritten as -PH2 =-
1/ 2
+
1
rex,
where = FsKa, F, = ks(SL/2)Ko, and shown in Figures 3 to 6. Then eq 8 becomes Rex, = A
$.
BPH2'l2
+
IlePH20
Zt/Z rexp
(8)
are values
CPH~O
(9 )
where Rexp, A, B , and C are defined by eq 8 and 9. The constants A, B, and C in eq 9 were evaluated by the least-squares method with matrices inversion solution of the simultaneous equation. The calculated results
Table 11. Values of the Rate and Equilibrium Constants
1.17 2.8 5.8 17.1
923 973 1023 1073
25.8 17.5 10.8 5.4
2.3 1.48 1.36 1.33
0.08 0.087 0.078
Table 111. Calculated Values of Changes of Enthalpies, Entropies, and Free Energies a t 1073°K Adsorption of H,
Surface reaction
Desorption of HzO
AH," = -22.0 kcal/mol A S = - 16.5 eu AF," = -4.8 kcal/mol
AH,* = 33 kcal/mol AS ,* = - 15 eu
AHd' = -6.5 kcal/mol A S d " = -5.4 eu AF," = -0.7 kcal/mol
AF,* = 50 kcal/mol
based on the data obtained by using binary Hz-HzO mixtures are listed in Table 11. The values of A , B, and C in eq 9 were found to be slightly different for the data obtained with ternary gas mixtures. Naturally, this is due to the existence of nitrogen. I t is considered that the possibility of nitrogen forming strong chemical bonds with oxygen, iron, or hydrogen would be very small, under the conditions investigated. Therefore, the likely effect is that the surface is partly occupied by adsorbed nitrogen, with or without dissociation. The total number of sites should be equal to the sum of C, CHO*, CH,O* and CN,(see Appendix A).The equivalent of eq 9 with ternary reducing gas is of the following form
Rexl,(ternary)- (A
+ BPH2"2 +
CPH20) = DP,
2
(10) Using the values of A , B, and C obtained previously, eq 10 was found to be adequate as shown in Figure 7. The values of the equilibrium constants for molecular adsorption of nitrogen are listed in Table 11. The temperature dependence of the rate constant, k , , may be given, according to transition-state theory, as
k
kT
(
- - eh m - -
s -
RT
loss of three translational degrees of freedom of the hydrogen molecule in the gas phase. The values of the free energy and enthalpy of activation for surface reactions are found to be reasonable. Both adsorption and surface reactions involve the disappearance of a hydrogen molecule; the entropy change of these steps is comparable, as it should be. The small values of the changes of enthalpy, entropy, and free energy for the desorption of water vapor suggests physical adsorption. In analyzing the data, nitrogen was assumed to be a diluent and appears to be so.
Acknowledgments The authors wish to acknowledge financial assistance from the National Research Council of Canada in the form of a research grant to W.-K. Lu, and the Canadian International Development Agency in the form of a Scholarship Award to G. Nabi. Helpful suggestions and constructive criticism from Professors J. s. Kirkaldy and R. B. Anderson are also gratefully acknowledged. Appendix A When the surface reaction is rate controlling, the equilibrium relationships for adsorption and desorption are
R
A plot of log ( F , / T ) against 1/T is shown in Figure 8. The value of the enthalpy of activation may be calculated from the slope of this plot and intercept gives the combined factor
I t is obvious that the value of AS,* depends on how we choose the constants. k and h are the Boltzmann and Planck constants, respectively; KO = 9.6 x 105/N, N is Avogadro's number; S = 6, the coordination number for a close-packed plane. For a hematite surface L may be taken as having a value of 1.29 x 1015 cm-2. The enthalpy, entropy, and free energy of activation and the corresponding quantities for equilibrium steps are listed in Table 111. The various values of the enthalpy and entropy changes listed in Table I11 agree well with the proposed mechanism. The enthalpy change of adsorption for hydrogen, according to Hayward and Trapnell (1964), is within the range usually given for chemisorption. The idea of dissociation of hydrogen into atoms is further supported by the values of entropy change which may be attributed to the
Applying mass-action law, the rate
In obtaining (A3) the relaticnship between the concentration of dual sites Cl-, and that of single sites C, c1-i
=
s 2 -c 2L
has been applied. Substituting (Al) and (A2) for CHO*and CH,O*in (A3)
By definition
L =
cs
$- C H O *
+
CH2O*
(A5)
From (AI), (A2), and (A5) Ind. Eng. Chem., Fundam.,Vol. 13, N o . 4 , 1974
315
L = c,(1
(&PH2)1/2+ K,pH2,)
(A6)
By eliminating C, between (A4) and (A6)
Y -
'
-
k$aSL(PH22
2[1
R = gas constant (cal/deg-mol)
-PH~o~/K~~) + ( K a P H 2 ) 1 / +2 K ~ H ~ O ] '
+ 0,
= H,*O,
(adsorption)
H2*0, = HzO* (surface reaction) HzO* = HzO(g) + s (desorption) 2. Hydrogen molecules and oxygen atoms as adsorbed species. As suggested by McKewan (1962, 1965), the desorption of water vapor is assumed to be very fast.
H,*O, = H,O*
(surface reaction)
3. Two adsorbed hydroxyl groups forming a water molecule Hz(g)
+ 0,
- 0, = HO*- H0* (adsorption)
HO*-HO* = H,O*-s
(surface reaction)
H 2 0 * = H,O(g) + s (desorption)
Nomenclature A = area of gas/solid surface of hematite specimen Ci = concentration of adsorbed species i (no./cm2) h = Planck's constant, 6.625 X 10-a4 J sec k = Boltzmann constant, 1.38 X 10-23 J/"K k,k' = forward and reverse reaction rate constants (with subscripts)
K = equilibrium constant
316
M*-M* = adsorbed species M, on dual sites
N = Avogadro's number (6.022 x 1023 molecules/mol) P H ~ P, H ~ = O partial pressure of hydrogen and water
Appendix B 1.Hydrogen and water molecules as adsorbed species Hz(g)
KO = conversion coefficient L = total number of sites (no./cm2) M* = adsorbed species M
I n d . Eng. Chem., F u n d a m . , Vol. 13, No. 4 , 1974
vapor, atm
r = reaction rate (mg/cm2-min) A S = entropychange AH = enthalpychange A F = free energy change S = coordination number for close packed plane s = single site
Subscripts 0 = initialvalue a = adsorption s = surfacereaction d = desorption Superscripts * = activatedstate 0 = standardstate
Literature Cited Happel. J., J. Res. Inst. Catal., 16 (No. 1 ) . 305 (1968). Hayward, D. O., Trapnell, B. M. W., "Chemisorption," Butterworths, London, 1964. Hougen, 0. A.. Watson, K. M., "Chemical Process Principles," Part I l l , p 902, Wiley, New York, N. Y.. 1967. Manning, F. S., Philbrook. W. 0.. "Blast Furnace: Theory and Practice," p 853, J. H. Strassburger, Ed., Gordon and Breach, New York, N. Y., 1969. McKewan. W. M.. Trans. Met. SOC..A I M € . 224, 387 (1962). McKewan. W. M., "SteelrnakinQ: The Chiprnan Conference." p 141, J. F. Elliott, Ed., The M.I.T. Press, Cambridge, Mass., 1965. Nabi, G., Lu, W.-K.. Trans. Met. Soc., AIME, 242, 2471 (1968). Nabi. G., Ph.D. Thesis, McMaster University, Hamilton, Ont., Canada, 1970. Nabi, G., Lu. W.-K., J. lron Steel Inst., 211, 429 (1973). Nakhmanovich. M. L., Morozov, N. M.. Buadze, L. G., Temkin, M. I . , Dokl. Phys. Chem., 148, 782 (1963).
Received for review J a n u a r y 15, 1973 Accepted M a y 13,1974
