Model Matematic La Reducerea Directa in Cuptoare Rotative

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Mathematical Modeling of Pneumatic Char Injection in aDirect Reduction Rotary Kiln

V. RAMAKRISHNAN and P.S.T. SAI

A one-dimensional steady-state mathematical model is proposed for direct reduction process in rotarykilns akin to the SL/RN process. The model takes into account pneumatic coal char injection from

the discharge end of the kiln to supplement the heat availability. The model is based on material andenergy conservation principles, and the empirical equations for kinetics and heat transfer are obtainedfrom the literature. Predictions are carried out for both iron oxide reduction and ilmenite beneficiationprocesses. Improvement in the performance was predicted with pneumatic char injection.

I. INTRODUCTION and to the kiln and compared to a simple resistive networkmodel. They also developed models to determine the temper-DIRECTreduction processes are widely known alterna-ature distribution in the wall of a rotary kiln[6] and heat flow

tives for the blast furnace route to iron manufacture. Directin the flame zone of a direct-fired rotary kiln. [7] Barr et

reduction processes in rotary kilns are also used for theal.[8,9] proposed a model for rotary kiln heat transfer that

beneficiation of low-quality iron ores and ilmenite. A biblio-accounts for the interaction of all the transport paths and

graphic survey of the direct reduction processes for ironprocesses. They applied a ray tracing technique to derive

ore reduction has been complied by The Metals Societycoefficients for radiative heat transfer in the kiln freeboard(London),[1] which gives information on the various pro-and extended the finite difference model into the contacting

cesses that are of academic and industrial significance.bed material in order to calculate the exchange between the

In direct reduction rotary kilns, the solid reductant servescovered wall and the bed.

the purpose of both fuel and reducing agent. Heat is suppliedPneumatic char (or coal fines in some cases) injection is

to the charge by the hot freeboard gas flowing countercurrentbeing carried out in the present day direct reduction opera-

to the solids through convection, radiation, and also regener-tions in rotary kiln.[10] This generally serves two purposes.

atively through the walls. Heat is generated in the freeboardOne, in providing heat to the freeboard gas by oxidation

by the combustion of CO released from the bed. The desiredand, two, in increasing the carbon content in the bed and

temperature is attained by the controlled addition of themaintaining a reducing atmosphere in the bed. Coal/char

combustion air along the length of the kiln. A number ofinjection rate, char particle size, and angle of injection pipe

fans are installed on the shell of the kiln, which supply theare the parameters that characterize the direct reduction pro-

necessary process air via the so-called air tubes or via aircess. A commercial process for ilmenite beneficiation using

injecting nozzles in the feed zone of the rotary kiln.direct reduction in rotary kilns in Western Australia[10] uses

Direct reduction processes for iron ore reduction in rotary pneumatic coal injection to supply the additional heatkilns have been modeled by Wingfield et al.,[2] Venkates-required in the reduction zone.waran and Brimacombe,[3] and Mukhopadhyay et al.[4] Of

Coal char injection involves the storage of particles inthese models, the former is for gaseous reductant, while thean unsealed silo continuously supplied with material. Theother two are for coal-based direct reduction process.particles are released from the silo by a rotary air lock feederThe model proposed by Venkateswaran and Brima-into a high velocity air stream of the injector system. Aircombe[3] is a comprehensive and yet simple model. Inspite offrom a supply source is allowed to expand to the systemthe simplifying assumptions made in the kinetics, dispersion,pressure through a variable nozzle to achieve desired flowand heat transfer, the model calls for the solution of a bound-rates. The particles are carried through the ducting by theary value problem of 12 first-order differential equations.air stream to a suitable outlet in the kiln where it is let outMore rigorous modeling work on the direct reduction processas a free jet. The particles reach the bed tracing an approxi-has not been reported.mate path of a projectile falling under the influence ofMany mathematical models have been proposed for opera-gravity.tions in rotary kilns with heat transfer to the solids bed.

Pneumatic injection of the coal/char particles is achieved

Goroget al.

[5]

studied the radiative heat transfer between a by utilizing the kinetic energy or flow momentum of airnongray freeboard gas and the interior surfaces of a rotaryused for injection, using either more air at low velocities orkiln by evaluating the fundamental radiative exchange inte-less air at high velocities. The dynamics of the injectedgrals to develop a model for the net heat flux to the solidsparticles and air flow requirements are reported by Bis-was,[11] who deals with the design requirements of the coalinjector for the coal-based direct reduction process in rotaryV. RAMAKRISHNAN, Graduate Student, formerly with the Department

of Chemical Engineering, Indian Institute of Technology, is withthe Depart- kilns. No published literature, which will predict the influ-ment of Chemical Engineering, University of Connecticut, Storrs, CT ence of coal char injection on the performance, is available06269-3222. P.S.T. SAI, Associate Professor, is with the Department of

on the modeling of the process.Chemical Engineering, Indian Institute of Technology, Madras-600 036,

A number of mathematical models for combustion of coalIndia.Manuscript submitted July 9, 1998. char particles have been developed, vary depending upon

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 30B, OCTOBER 1999969


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C (1/2)O2 CO [2]

The reaction rates for the two char-gas reactions as reportedby Caram and Amundson[13] are used in the present workand they are

For Char-O2 reaction,

R1 k1C1s [3]

For the Char-CO2 reaction,

R2 k2C2s [4]Fig. 1Coal char particle undergoing combustion.

where

k1 3.007 105 e(17,966/Tp) [5]

the simplifying assumptions used in each case. The models andof significance are the ones developed by Yagi and Kunii,[12]

k2 4.1 109 e(29,790/Tp) [6]Caram and Amundson,[13] and Essenhigh.[14] Caram and

Amundson have compared various models and have dis- The reaction rate at the surface equals the mass-transfer ratecussed the shortcomings of each. and for the two reacting gases

In the present study, an attempt is made to develop asimple and yet comprehensive model of direct reduction

R1 k1km1

0.5k1 km1C1 [7]

process with pneumatic injection of char so as to retain themathematical tractability. A mathematical model for charcombustion inside the kiln is formulated based on shrinking

R2

k2km2

k2 km2 C2 [8]core principle and is integrated with the direct reduction

process along with the particle dynamic equations. Thus,The mass-transfer coefficient through the boundary film

the model takes into account the influence of kinetics, heataround the carbon particle, km , can be calculated using thetransfer, and operating variables such as air distribution andexpression given by Ranz and Marshall.[15]

pneumatic char injection on the performance of the process.

NNu km dp f

Dvf 2.0 0.6(NSc)

1/3(NRem)1/2 [9]

II. MODELING OF COAL CHAR COMBUSTION

The mass conservation equation for the particle isAs proposed here, to integrate the mathematical model forcoal char combustion with the model of the direct reduction ddp

dt

2

P(R1 R2)Nc [10]process, certain simplifying assumptions are made, which

makes it adaptable within reasonable margins of error. Theyare as follows: The heat balance equation for the particle is

(1) Pneumatically injected char particles are divided into dHP

dt d2P{hp(TG TP) [GG(T

4G T

4P)

[11]different size ranges and particles of each size rangeare lumped.

SP(T4S T

4P) WP(T

4W T

4P)]}(2) The particles are assumed to be spherical and are charac-

terized by the mean size (diameter) of the size range. On simplification, the preceding equation reduces to(3) Both O2 and CO2react at the char surface to give CO.(4) The freeboard gas in the kiln around the particle as a dTP

dt

6

pdPCP{hp(TG TP) [GG(T

4G T

4P)whole is lumped (across the cross section), and the vol-

ume of the gas film is assumed to be insignificant in SP(T

4S T

4P) WP(T

4W T

4P)] [12]comparison to the bulk volume.

(5) The combustion of the CO is assumed to occur in the (HB)R1 (HR)R2}freeboard gas. This assumption is reasonable consider-

The convective heat-transfer coefficient for the heat transfering the fact that the gas film is assumed to be small,between the coal char particle and the freeboard gas, hp ,and at high temperatures at which the reaction takes

can be calculated by following the heat-transfer analogousplace, CO is generally observed to be the main productof Eq. [9], as reported by Ranz and Marshall:at low O2 partial pressures.

(6) The resistance due to the ash layer that forms on theNu

hpdp

k(f) 2.0 0.6 (NPr)

1/3 (NRem)1/2 [13]char particle is assumed to be very small considering

the particle velocities in the kiln.(7) The products of the reaction freely diffuse out of the The preceding equations are coupled with the particle

gas film surrounding the char particle. dynamic equations given by Biswas,[11] as presented in theAppendix, and are used in the model of the direct reduction

Reactions that occur at the surface of a pneumaticallyprocess. The material and energy balance equations for the

injected char particle shown in Figure 1 aresolid and gas phases as proposed by Venkateswaran andBrimacombe[3] are described in the Appendix. The velocityC CO2 2CO [1]

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of the conveying air is determined from the particle velocity,based upon the particle size and host of other factors. Bis-was[11] has tabulated the expressions for the air conveyingvelocities for different particle sizes. The solution methodemployed in the present study is detailed subsequently.

(1) When integrating the differential equations for the directreduction process from the discharge end, at each pointalong the length of the kiln for a given increment in theindependent variable (distance from the discharge end),

the heat- and mass-transfer rates per unit volume of thekiln are determined;

(2) These are obtained by determining the heat- and mass-transfer rates (for gases O2, CO2, and CO) for a singleparticle in a given size range and multiplying by thenumber of particles per unit volume of the kiln for thesize range, Np , given as follows:

NP 6fiW

2pr21

1

d3Puh[14]

(3) Once the particle reaches the solids bed, or the particlesize reduces to less than 5 pct of its original size, theparticles are no longer assumed to undergo combustion.In the former case, they are assumed to get mixed withthe bed and no corrections are made to the carbon con-centration in the bed as the amount injected is very smallin comparison to the amount of coal in the bed. In thelatter case, the particle is assumed to be carried awaywith the gases. This point varies for the different sizeranges. The integration is then carried out as detailedsubsequently.

III. BOUNDARY CONDITIONS ANDNUMERICAL SOLUTIONS

The model comprised of coupled differential and algebraicequations has to be numerically solved to obtain the predic-

Fig. 2Flow chart for the solution of the mathematical model.tion for a given set of conditions. The boundary conditionsare defined for the solid charge at the feed end and thefreeboard gas at the discharge end. The initial condition for approaches are not better, the previously described methodthe coal particles and the conveying air are defined at the is used.discharge end. This is a two-point boundary problem of first-order differential equations. The solution uses the fourth-

IV. RESULTS AND DISCUSSIONorder RungeKutta methodfor the solution of the differentialequations, and shooting to a fitting point approach was used, The prediction of the mathematical model proposed here

is compared with the experimental data for the ilmenitewherein initial conditions are assumed at either ends, andthe variables are compared at a certain point halfway. The beneficiation process carried out in rotary kilns. The solid

bed temperature and reduction profiles of ilmenite beneficia-error, i.e., sum of square of the normalized differencesbetween the variables, at this point was minimized by chang- tion carried out at The Western Titanium Limited (Capel,

Western Australia) were obtained from Hockin.[10] The bene-ing the initial conditions using the globally convergentNewton Raphson method. ficiation process is based on the direct reduction of iron

oxide content of the ilmenite to metallic iron in a rotary kilnThe flow chart is shown in Figure 2. The accepted levelof error was fixed as 0.1 pct. This approach of shooting to using a highly volatile coal as both fuel and reductant.

The conditions that were used for the runs for this systema fitting point is essential due to the instability encounteredwhen proceeding from the charge end, while, when proceed- are shown in Table I. Other relevant information such as

the kinetic expressions are given in the Appendix. Owinging from the discharge end, one is left out with only oneinitial condition to match, and hence by proceeding to a to lack of information available on the amounts of coal char

injected and the air distribution used, the predictions havepoint halfway from either end and matching the variables,these problems can be avoided. But one encounters a prob- been made by assuming the amount of coal injected and

choosing an air distribution shown in Figure 3 such that thelem of solving simultaneous equations with seven unknownsand computation of the Jacobian at each step to choose predictions reasonably agree with the experimental observa-

tions. Though one cannot claim this as a properconfirmation,the direction and step to minimize the error. As alternative



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Table I. Input Parameters for the Ilmenite BeneficiationProcess

Kiln characteristicsLength of the kiln, m 45Degree of fill, pct 18Outer shell diameter, m 3.5Inner shell diameter, m 3.4Inner diameter of outer refractory, m 3.16Inner diameter of inner refractory, m 2.59

Input characteristics

Ilmenite feed rate, tons/annum 53,225Coal feed rate, tons/annum 19,054Pneumatic coal injection rate, tons/annum 1710Initial particle velocity, m/s 63.2Solid to air ratio 3.25

Composition of charge, pctPreoxidized Ilmenite CoalTiO2 53.5 Fixed carbon 42.1FeO 0.6 Moisture 25.0Fe2O3 44.7 Volatiles 27.4MnO 1.3 Ash 4.8

Fig. 4Comparison of experimental and predicted solids bed temperatureSulfur 0.7and degree of reduction of ilmenite.

Size distribution of pneumatically injected coalchar particles, pct

12.70 mm 0.012.70 mm 6.35 mm 4.56.35 mm 3.34 mm 43.03.34 mm 1.40 mm 21.01.40 mm 1.00 mm 27.51.00 mm 4.0

Fig. 5Temperature distribution for direct reduction of ilmenite.

variation of partial pressure and degree of reduction areshown in Figure 6. The general trends are the same as theones one would expect in a direct reduction process. In orderto make some comparisons regarding the influence of coalinjection, a run was carried out without coal char injection.

Fig. 3Air distribution used for the ilmenite beneficiation process. The comparison of solids bed temperature and the degreeof reduction is shown in Figure 7. It is seen that the lowerheat availability results in lower solid temperature and hencelower degree of reduction.it definitely indicates that the model predictions may not be

off by a large margin, and the model will be helpful in giving In order to show the ease of adaptability of the model fordifferent systems, the influence of coal char injection is alsoat least a rough idea of the performance where no results

exist. The comparisons are shown in Figure 4. studied for iron oxide system. For the present study, thesame process conditions as used by Venkateswaran andThe variation of the solid, gas, wall, and shell temperatures

along the length of the kiln is shown in Figure 5, and the Brimacombe[3] for iron oxide reduction are considered to be



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Table II. Input Parameters for the Iron OxideReduction Process

Kiln characteristicsKiln length, m 30Inner radius of the kiln, m 1.05Outer radius of inner refractory, m 1.28Outer radius of outer refractory, m 1.33Outer shell radius, m 1.36Thermal conductivity of the inner 0.0031

refractory, cal cm1 s1 K1

Thermal conductivity of the outer 0.0005refractory, cal cm1 s1 K1

Input characteristicsOre feed rate, tons/day 174Coal feed rate, tons/day 118Air feed rate, m3/ton ore 1645.3Natural gas rate, m3/ton ore 21.2Inlet charge temperature, K 298

composition, pct

Ore CoalHematite 95.5 Fixed carbon 42.0

Fig. 6Partial pressure and reduction profiles for direct reduction of Moisture 1.4 Moisture 31.0ilmenite. Gangue 3.1 Volatiles 16.7

Ash 10.0

Sulfur content 0.3

Iron concentration in bed, g/cm3 0.763Carbon concentration in bed, g/cm3 0.275Oxide pellet reducibility, cm3 g1 3.143 103

s1

Coal reactivity, cm3 g1 s1 51.9 1016

Table III. Air Distribution Used for the Iron OxideReduction Process

Distance from the Charge End, mAir rate, m3/ms 0 to 4 4 to 19 19 to 26 26 to 30

0.1 0.14 0.10 0.00

shown in Figure 8 through 10, respectively. As for the ilmen-ite reduction predictions, it was seen that the solid and gastemperatureswere higherand hence a higherdegree of reduc-

Fig. 7Comparison of solids bed temperature and reduction profiles for tion was predicted. It was also predicted that with coal chardirect reduction of ilmenite with and without char injection. injection, the ratio of the reduction to preheat zone length

was increased, which would be an indication of the betterutilization of the rotary kiln. The variation in oxygen partialpressure indicated that more air than required was presentin the case without coal char injection and hence dilutiona meaningful comparison. The conditions that are common

for all studies carried out with this system are shown in of temperature and poor performance resulted.Table II. The air profile used here is given in Table III.

A run was carried out without natural gas or coal charV. CONCLUSIONS

injection and subsequently a run was carried out with coalinjection, and the data used in relation to coal injection were A mathematical model for the direct reduction process

with coal char injection has been proposed, and coal charas follows:solid to air ratio 1.0, particle velocity 45 m/s, rate injection predicted improved performance of the direct

reduction process. The uncertainty involved in the rangeof char injection 0.174 kg/s, and primary air from dis-charge end 0.1467 m3/s. of pneumatically injected particles had a bearing on the

predictions. It can be improved by determining the averageThe comparison of solid and gas temperatures, degree ofreduction, and oxygen partial pressure for the two cases is range empirically for given kiln geometry and particle size.



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Fig. 8Comparison of solids bed and freeboard gas temperature distribu-tion for direct reduction of iron oxide with and without char injection.

Fig. 10Comparison of oxygen partialpressure profile for directreductionof iron oxide with and without char injection.

Dvf diffusivity of O2 in the freeboard gas, m2/s

EB , ER activation energies for Boudouard and reductionreactions, respectively, cal/gmol

fi weight fraction of the ith size rangeF degree of reductiong acceleration of gravity, m/s2

G mass flow rate of the freeboard gas, kg/sGgi, Gsi mass flux of the ith component in the gas and

solid phases, respectively, kg/m2shp heat-transfer coefficient between coal char parti-

cles and the freeboard gas, kcal/m2sKhcws heat transfer coefficient for covered wall to sol-

ids (across area A3), kcal/ms2sKhgsc heat-transfer coefficient for convection from gas

to solid (across area A2), kcal/m2sK

hgsr heat-transfer coefficient for radiation from gasto solid (across area A2), kcal/m

2sK

hgwc heat-transfer coefficient for convection from gasto wall (across area A1), kcal/m

2sK

hgwr heat-transfer coefficient for radiation from gasFig. 9Comparison of reduction profile for direct reduction of iron oxide to wall (across area A1), kcal/ms

2sK

with and without char injection.hsh heat-transfer coefficient for heat loss from wall

to ambience (across area A4), kcal/m2sK

hssc heat-transfer coefficient for convection lossNOTATIONfrom shell, kcal/m2sK

hssr heat-transfer coefficient for radiation loss froma acceleration, m/s2

A cross-sectional area of the kiln, m2 shell, kcal/m2sKhwsr heat-transfer coefficient from wall to exposedA1, A2, areas as shown in Fig A1, m

2

A3, A4 solids (across area A2), kcal/m2sK

H enthalpy flux, kcal/m2sAp reducibility of ore, cm3/gs

C1, C2 concentrations of O2 and CO2 in the bulk, respec- HC reactivity of coal, cm3/gs

Hp enthalpy of the particle, kcaltively, kmol/m3

C1s, C2s concentrations of O2 and CO2 at the surface of k(f) average thermal conductivity of the freeboardgas, W/mKthe char particle, respectively, kmol/m3

Cp Specific heat capacity, kcal/kgK k1, k2 reaction rate constants for char-O2and char-CO2reactions, respectively, m/sdp diameter of the char particle, m

D diameter of the kiln, m ka thermal conductivity of ambient air, kcal/msK



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kI, kO thermal conductivities of inner and outer refrac- G standard free energy change, cal/mol viscosity of air, kg/mstory in kiln lining respectively, kcal/msK

KB , KR equilibrium constants for Boudouard and reduc- v kinematic viscosity of air, m2/s

tion reactions, respectivelySubscriptskm1, km2 mass-transfer coefficients of O2and CO2in the

a ambient airgas film, respectively, m/sB boudouard reactionMC, MFe concentrations of carbon and iron in the charge,G freeboard gasrespectively, g/cm3 chargeh horizontalN rotational speed of the kiln, s1

p char particleNC molecular weight of char particle

R reduction reactionNGr grashof number ( D32g(Tsh TG)/2)S solids bedNNu nusselt numbersh shellNP number of particle per unit volume of the kilnt at time tNPr prandtl number ( Cp/ka)t t at time t tNRem modified Reynolds number ( uhpdP/)t, t t between tand t t time intervalNRew rotational Reynolds number ( ND

2/)v verticalNSc schmidt number ( v/Dvf)W kiln wallPBCO equilibrium partial pressure of CO for Boudou-

ard reaction, atmPCO2 bulk partial pressure of CO2 in the bed, atmPBCO2 equilibrium partial pressure of CO2for Boudou- APPENDIX

ard reaction, atm A. Material and Energy BalancesPRCO2 equilibrium partial pressure of CO2 for reduction

In a direct reduction of a metal oxide with carbon in areaction, atmrotary kiln, the reactions are given by the followingQwg heat-transfer rate from wall to gas, kcal/sequations:Qwl heat loss from wall to ambience, kcal/s

Qws heat-transfer rate from wall to solids, kcal/sMexOy(s) CO (g) MexOy1(s) CO2(g) [A1]qcg, qcs rate of consumption of heat in gas and solid

phases, respectively, kcal/m3s CO2(g) C (s) 2CO (g) [A2]qgg, qgs rate of generation of heat in gas and solid phases,

respectively, kcal/m3s The material and energy balances for solid and gas phasesrgi, rci rate of generation and consumption of the com- over an infinitesimally small cylindrical element along the

ponent i, respectively, kg/m3s length of the kiln at a distance x from the charge end arer1 inner radius of the kiln, m as follows.r2, r3 outer radius of the inner and outer refractory,

1. Material balance equationsrespectively, mFor solids,r4 outer radius of the kiln shell, m

R gas constant, 1.987 cal/molKR1, R2 rate of char-O2and char-CO2 reactions, respec- dGsi

dx rgi rci 0 [A3]

tively, kmol/m2sRB , RR rate of Boudouard and reduction reactions,

where i denotes the components such as coal and ore.respectively, kmol/m2sFor gases,S displacement, m

T temperature, Ku velocity of the char particle, m/s

dGgj

dx rgj rcj 0 [A4]

ur relative velocity between the particle and the air,m/s

Here, j stands for gases such as CO, CO2, O2, N2, H2,va velocity of air for pneumatic char injection, m/sand CH4.vx velocity at a horizontal location x, m/s

x distance from charge end of the kiln, m 2. Heat balance equationsxd distance from discharge end of the kiln, m For solids,W rate of char injection, kg/s

dHS

dx qgs qcs 0 [A5]Greek Symbols

G absorptivity of the freeboard gas coefficient of thermal expansion of air, K1 For gases, decceleration rate, m/s2

emissivity dHg

dx qgg qcg 0 [A6]f volume fraction of the gas film around the

char particle density, kg/m3 For the kiln wall, stephanBoltzmann constant, kcal/m2sK4

Qwg Qws Qwl 0 [A7]H standard enthalpy change, cal/mol



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0.9 and 1.0, respectively. The emissivity and absorptivitydata for different concentrations of CO2 and H2O areobtained from Perry and Green,[16] and a regression fit isused to calculate the emissivity and absorptivity of the free-board gas. All the physical properties of the gases are com-puted by taking the weighted average using the mole fractionof the components. The experimental data reported by Ven-kateswaran and Brimacombe[3] for drying and volatilizationof coal are fitted to a polynomial expression and are used.

B. Kinetic Expressions Used for the IlmeniteBeneficiation Process

The reaction scheme is

C CO2 2CO

FeTiO3 CO FeTiO2 CO2

The rate expression for the Boudouard reaction is given by

RB MCHCeEB/RTS

PCO2 PBCO2

RTS[A17]

and that for the reduction reaction is given by

RR MFeAP F(1 F) eER/RTS

PRCO2 PCO2

RTS[A18]

Fig. A1Cross section of the kiln showing heat flow processes and thecorresponding areas (Venkateswaran and Brimacombe[3]). The equilibrium partial pressure of CO2 for the Boudouard

reaction and the reduction reaction can be evaluated using

KB eGB/RTS e(40,800/RTS41.7/R)

[A19]To determine the heat fluxes at different positions in thekiln, the kiln internal surface is divided into various zones,as shown by the cross section of the kiln in Figure A1. The

(PBCO)2

PBCO2

(1 PBCO2)2

PBCO2heat-transfer coefficients for various modes of heat transferbetween solids, gases, and kiln are as follows:

KR eGR/RTS e(2890/RTS7.82/R)

[A20]hgsr

(gT4g gT

4S)

(Tg TS) [A8]

PBCO2

PBCO

PBCO2

1 PBCO2hgsc 2.63(10

3)(G/A)0.067 [A9]

C. Kinetic Expressions Used for the Iron Oxidehgwr

(gT4g gT

4W)

(Tg TW) [A10]

Reduction Process

The reaction scheme ishgwc 2.63(103)(G/A)0.067 [A11]

C CO2 2COhwsr

WS(T4W T

4S)

(TW TS) [A12]

Fe2O3 3CO 2Fe 3CO2

The empirical first-order rate expression for the reductionhcws 5hgsc [A13]reaction as proposed by Von Bogdandy and Engell[17] isas follows:

hsh 1

2r4 r2 r1k1(r1 r2)

[A14]RR 4.48(10

2

) eER/RTSAP(1 F)MFe

PRCO2 PCO2

PRCO2 r3 r2k0(r3 r2) 1

2r4(hssc hssr)

1

[A21]

where The rate expression for the Boudouard reaction is the sameas that for the ilmenite beneficiation process (Eq. [A17]).

hsscD

ka 0.11[(0.5N2Rew NGr) NPr]

0.35 [A15]

D. Particle Dynamic Equations

hssrsh(T

4sh T

4a)

Tsh Ta[A16] The air mixed with coal particles upon leaving the outlet

of the injector is assumed to expand as a turbulent free jet.The longitudinal distribution of velocity along the centralThe emissivities of the kiln wall and solid bed are taken as



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line in the stabilized zone obtained from Perry and Green[16] REFERENCESis given as follows:

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vx

va 2.28 dpxd

0.5

for 5 xd

dp 2000 [A22]

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[ah]t,tt [ur]

2t

2 gdp[A27] 10. H.W. Hockin:Proc. 101st Annual Meeting AIME, TMS, Warrendale,

PA, 1972, pp. 209-31.

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[uv]2t

2 gdp[A28]

12. S. Yagi and D. Kunii:Proc. 5th Int. Symp. on Combustion, Reinhold,New York, NY, 1955, pp. 231-39.[ur]t [uh]t [vh]t [A29]

13. H.S. Caram and N.R. Amundson: Ind. Eng. Chem. Fund., 1977, vol.16 (2), pp. 171-81.

[vh]t

va for [Sh]t

15 dp[A30]

14. R.H. Essenhigh: in Coal Conversion Technology, C.Y. Wen and E.Stanley Ley, eds., Addison-Wesley Publishing Company, Inc., Read-

[vh]t 2.28va dp[Sh]t0.5

for [Sh]t 15 dp ing, MA, 1979, pp. 171-304.15. W.R. Ranz and W.R. Marshall, Jr.: Chem. Eng. Prog., 1977, vol. 48,

pp. 141-46. 0.137 for dp 3.00 mm16. R.H. Perry and Don Green:Perrys Chemical Engineering Handbook,

6th ed., McGraw-Hill Publications, New York, NY, 1984. 0.220 fordp 1.00 mm [A31]17. L.Von Bogdandy and H.J.Engell: TheReduction of Iron Ores, Spinger-

Verlag, Berlin, 1971, pp. 286-310. 0.270 fordp 1.00 mm


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Model Matematic La Reducerea Directa in Cuptoare Rotative