ISSN 0967-0912, Steel in Translation, 2008, Vol. 38, No. 6, pp. 421–423. © Allerton Press, Inc., 2008.Original Russian Text © V.M. Abzalov, V.I. Klein, B.P. Yur’ev, 2008, published in “Izvestiya VUZ. Chernaya Metallurgiya,” 2008, No. 6, pp. 7–9.

421

The oxidation of magnetite in pellets is a complexheterogeneous phenomenon, consisting of numerousparallel processes. Almost all of these are activationalprocesses. As a rule, they cannot be isolated orobserved experimentally. Therefore, despite extensiveresearch, it is still difficult to describe the basic laws ofmagnetite oxidation in pellet roasting. Nevertheless,most researchers describe this process as a sequence ofstages: 1) external mass transfer of oxygen from the gasflux to the pellet surface; 2) diffusional transfer of oxy-gen molecules through the pellet pores to the surface ofthe magnetite grains; 3) reaction at the phase boundary;4) diffusion of reagent ions in the lattice due to thechemical potential gradient.

Since these stages occur in sequence, the rate of thewhole process is determined by the rate of the sloweststage.

In practice and in laboratory simulations, pelletroasting is characterized by a turbulent gas flow, inwhich the mass transfer is determined by convectivediffusion, including molecular and molar transfer.Therefore, the external diffusional drag is small in com-parison with the internal drag, and may be neglected.

Thus, magnetite oxidation is limited either by inter-nal diffusion (diffusional conditions) or by the reactionkinetics (kinetic diffusion). Formal description of thereaction kinetics, corresponding to the Arrhenius law, isnot very difficult. It is considerably more difficult todescribe the diffusional behavior. We consider thisproblem in the present work.

For the subsequent analysis, we make two assump-tions: the raw pellets are characterized by open poresthroughout their volume; and the magnetite particles(grains) are in point contact. Thus, the surface of all theparticles is open, and there is an adequate pore surface.The ratio of the pore-channel diameter (

d

pc

) to the meanparticle diameter (

d

p

) is determined by the pellet poros-ity

ε

Internal diffusion consists of a series of parallel pro-cesses: I) molecular (free) diffusion in pores whoseradius is large in comparison with the mean free pathlength of the gas molecules; II) Knudsen (capillary) dif-

dpc

dp------

23--- ε

1 ε–-----------.=

fusion in pores whose diameter is less than the meanfree path length of the molecules; III) activated (sur-face) diffusion by adsorbed molecules along the porewalls; IV) diffusion in the solid state through the layerof reaction products (hematite) that forms. Since thesediffusion processes occur in parallel, the one that makesthe greatest contribution to the total process will bedominant.

Activated diffusion may be neglected on account ofits slowness and small contribution to the overall diffu-sion process. Diffusion in the solid state may also beneglected. That leaves molecular diffusion and Knud-sen diffusion, whose contribution depends on the rangeof pore sizes.

Division of pores into macrocapillaries (radius

r

pc

>10

–7

m) and microcapillaries (

r

pc

< 10

–7

m) was sug-gested in [1]. This distinction was linked to differentmechanisms of gas transfer in these capillaries. In prac-tice, there is no such sharp transition from one type ofdiffusion to another. Rather, there is an intermediaterange of pores in which a distinctive transfer mecha-nism operates.

Pores were divided into three categories as a func-tion of their radius in [2]: macropores, for which

r

pc

>2

×

10

–6

m; intermediate pores (mesopores), for which2

×

10

–6

>

r

pc

> 1.5

×

10

–7

m; and micropores, for which

r

pc

< 1.5

×

10

–9

m. This classification applies to sorbentsand catalysts characterized by a specific pore surface of10

3

–10

5

m

2

/kg and porosity 0.4–0.5.Note that any classification is somewhat arbitrary

and depends on the chosen model of the porous body.The selection of a classification system depends onmethods of investigating the pore structure [3]. It ismore helpful to base the classification on the possibilityof describing gas transport in the pore space. From thisperspective, the diffusion mechanisms in the pores ofpellets with a specific surface of 130–200 m

2

/kg may bebetter described by the following categories:macropores, for which

r

pc

> 10

–5

m; mesopores, forwhich 10

–5

≥

r

pc

≥

10

–7

m; and micropores, for which

r

pc

< 10

–7

m. This classification corresponds to valuesof the Knudsen number

Λ

characterizing different dif-fusion mechanisms in the pore grain [4]. We employ theKnudsen number

Λ

=

d

pc

/

λ

(where

d

pc

is the pore diam-eter and

λ

is the free path length of the molecules) for

Oxygen Diffusion in Pores of Iron-Ore Pellets

V. M. Abzalov, V. I. Klein, and B. P. Yur’ev

Pervouralsk Branch, Ural State Technical University–Ural Polytechnic Institute

DOI:

10.3103/S0967091208060016

422

STEEL IN TRANSLATION

Vol. 38

No. 6

2008

ABZALOV et al.

the diffusion of oxygen in pores over a temperaturerange 400–900

°

C, with a free path length of around 2

×

10

–7

m. Then, for macropores, the free-diffusion coeffi-cient may be used when

Λ

> 100; for mesopores, theeffective diffusion coefficient may be used when 100

≥

Λ

≥

1; and for micropores, the diffusion mechanismchanges to molecular flow, with

Λ

< 1.In the initial pellet, the mean pore diameter is less

than the macropore diameter but greater than the meso-pore diameter: it is (9–14)

×

10

–6

m. The Knudsen num-ber

Λ

= 45–70 also indicates that an intermediate diffu-sion mechanism operates in these pores.

For most of the pores in roasted pellets, the radius isbetween 5

×

10

–6

and 1

×

10

–7

m. In other words, meso-pores predominate in the roasted pellet, with only smallquantities of macropores and micropores. The meanpore diameter in the roasted pellets is around 1.5

×

10

−

6

m. Thus, on transition from the initial pellet to theroasted pellet, the mean pore size declines by a factorof 5–10.

The rate of free diffusion depends on the mutual-diffusion coefficient

D

of oxygen and nitrogen [5]. Atconstant pressure,

D

depends on the temperature asfollows [6]

(1)

here

T

is the temperature, K;

δ

N

and

δ

O

are the diame-ters of the nitrogen and oxygen molecules, 0.1 nm;

P

isthe total pressure, Pa;

M

N

and

M

O

are the molecularmasses of nitrogen and oxygen.

D 853.195T1.5

δN δO+( )P---------------------------

MN MO+MNMO

---------------------- m2/s;=

Substituting the values of

M

i

and

δ

i

into Eq. (1), wefind that

(2)

The mechanism of diffusional transfer in mesoporesof a capillary-porous body such as the pellet has certaindistinctive features. The skeleton of the porous body (inparticular, its structure) has a considerable influence onthe mass transfer. The diffusion coefficient declineswith increase in the number and size of the particlesthat lie in the path of the diffusional flux [4]. Diffusionis also subject to the retarding influence of the capillarywalls. For the capillaries of the raw pore, whose diam-eter is 45–70 times the free path length of the oxygenmolecules, the walls have little influence on the gas dif-fusion. The porosity and twist of the capillaries willinfluence the effective diffusion coefficient (

D

ef

).In the transition region, the effective diffusion coef-

ficient may be used [3]

(3)

where

ς

= 1/

k

t

is the labyrinth factor, depending on thetwist of the pore channels;

k

t

is the twist coefficient.For the pellets, on average, when

ε

= 0.3 and

ς

= 1/4,the effective diffusion coefficient is

(4)

In steady conditions, the diffusional flux (diffusionrate)

v

is as follows, according to Fick’s first law

(5)

here

F

is the cross-sectional area of the pellet, m

2

;

r

pe

isthe pellet radius, m;

C

0

and

C

r

are the oxygen concen-trations in the heat-carrier gas and at the reaction sur-face, mole/m

3

.For a pellet in isothermal conditions, at constant

pressure, the diffusional flux is

(6)

For a pellet whose radius is 0.65

×

10–2 m

(7)

and for atmospheric oxygen

(8)

The molecular-flow coefficient Dm may be foundfrom the approximate Knudsen formula

(9)

D 4.269 10 4– T1.5/P m2/s.×=

Def Dες,=

Def 0.075D.=

v FDdCdx-------–=

= 0.03πrpe2 D

C0 Cr–

22.41 10 3– rpe×------------------------------------P

T--- mole/s;

ν 0.03πrpeDC0 Cr–

22.41 10 3–×----------------------------- mole/s.=

ν 36.43 10 7– D C0 Cr–( ) mole/s,×=

ν 7.65 10 7– D mole/s.×=

Dm23---rpc.eq

8RTπMO----------- m2/s,=

0.9

673

2.5

1073

2.1

1.7

1.3

0.5873 1273 1473

Temperature, K

Diffusion rate, m2/s

D × 104

D ef × 10

5

Dm × 106

Fig. 1. Influence of temperature on the diffusion coefficientof oxygen in the pellet (at atmospheric pressure): D × 104 isthe free-diffusion coefficient; Def × 105 is the effective dif-

fusion coefficient; Dm × 106 is the molecular flow coeffi-cient.

STEEL IN TRANSLATION Vol. 38 No. 6 2008

OXYGEN DIFFUSION IN PORES OF IRON-ORE PELLETS 423

where rpc.eq is the equivalent pore radius, cm; R =8.314 J/K mole is the gas constant.

Substituting the known values into Eq. (9), weobtain

(10)

Since molecular flow applies to pores whose radiusis less than 10–7 m, we may write

(11)

The molecular flow rate vm is [5]

(12)

where l is the capillary length, m.Then, for the pellets

(13)

and hence the molecular flow rate declines as the tem-perature rises, on account of the increase in the freepath length.

The mechanisms of free diffusion, effective diffu-sion in the porous material, and molecular flow appearin the sequence corresponding to the diffusion coeffi-cients of oxygen calculated for the pore structure of the

Dm 0.54rpc.eqT1/2.=

Dm 0.54 10 7– T1/2.×=

vm 0.02Frpc.eqP

2πMORT---------------------------

C0 Cr–l

-----------------,=

vm 9.67 10 11– PT 1/2– ,×=

initial pellet (Fig. 1). The slope of the curves, whichindicates the influence of the temperature on the diffu-sion coefficient, declines on passing from free diffusionto molecular flow. The diffusion rate of oxygen in thepellet pores also reflects the influence of the tempera-ture (Fig. 2).

Pores at the boundary of macropores and mesoporespredominate in the initial pellet, whereas mesoporespredominate in the roasted pellet. We may then assumethat, in the oxidation of magnetite on pellet heating, thediffusion rate must be calculated on the basis of theeffective diffusion coefficient, which depends on thepore structure of the pellet. Note that the macroporesare characterized by free diffusion, which does notdepend on the pore structure, while the micropores arecharacterized by molecular diffusion. Since these typesof diffusion have little influence on oxygen transport inthe pellet pores, however, they may be neglected.

CONCLUSIONS

Pores have been classified in terms of the character-istics of gas transport in the pore space, which is relatedto different diffusion mechanisms in the porous pellet.For the pore structure of the initial pellet, mechanismsof free diffusion, effective diffusion, and molecularflow are employed. The results may be used in mass-transfer calculations and in studying diffusional pro-cesses in porous bodies, with the determination of theeffective diffusion coefficient of oxygen to the reactionfront.

REFERENCES1. Lykov, A.V., Yavlenie perenosa v kapillyarno-poristykh

telakh (Transport Phenomena in Capillary-Porous Bod-ies), Moscow: Gostekhizdat, 1954.

2. von Bogdandy, L. and Engel, H.J., The Reduction of IronOres, New York: Springer, 1971.

3. Karnaukhov, A.L., Metody issledovaniya vysokodisper-snykh i poristykh tel (Methods of Investigating HighlyDisperse and Porous Bodies), Moscow: Izd. AN SSSR,1958.

4. Aksel’rud, G.A. and Al’tshuler, M.A., Vvedenie v kapil-lyarno-khimicheskuyu tekhnologiyu (Introduction toCapillary-Chemical Technology), Moscow: Khimiya,1983.

5. Statnikov, B.Sh., Bratchikov, S.G., and Yur’ev, B.P., Izv.Vyssh. Uchebn. Zaved., Chern. Metall., 1972, no. 6,pp. 42–45; no. 8, pp. 42–45.

6. Shkodin, K.K., Sb. nauchnykh trudov LPI (Proceedingsof Leningrad Polytechnic Institute), Leningrad: Metal-lurgiya, 1964, issue 225, pp. 34–53.

0.6

673

1.8

1073

1.4

1.0

0.2873 1273 1473

ν × 104

ν ef × 105

Temperature, K

Diffusion rate, m2/s

νm × 106

Fig. 2. Influence of temperature on the diffusion rate of oxy-gen in the pellet (at atmospheric pressure): v × 104 is thefree-diffusion rate; vef × 105 is the effective diffusion rate;

vm × 106 is the molecular flow rate.