PROBLEM OF PROCESS INGENEERING

Chemical Engineering Journal 104 (2004) 35–43

Modeling of counter current moving bed gas-solid reactor used in direct reduction of iron ore

Daniel R. Parisi∗, Miguel A. Laborde Departamento de Ingenier´ıa Quı́mica, Facultad de Ingenier´ıa, Universidad de Buenos Aires, Pabell´on de Industrias,

Ciudad Universitaria, 1428 Buenos Aires, Argentina

Received 11 November 2003; received in revised form 6 August 2004; accepted 9 August 2004

Abstract

In this work, the shaft furnace reactor of the MIDREX® process is simulated. This is a counter current gas-solid reactor, which transforms iron ore pellets into sponge iron.

Simultaneous mass and energy balance along the reactor leads to a set of ordinary differential equation with two points boundary conditions. The iron ore reduction kinetics was modelated with the unreacted shrinking core model. Solving the ODE system allows to know the c

tion ( e used for d ©

K

1

g t f n o f

w [ a m v p

m

dy- lance dy-

tor same nking

but

ctor d the oth

. c- he nsfer con- olid is tive

1 d

oncentration and temperature profiles of all species within the reactor. The model was able to satisfactorily reproduce the data of two MIDREX® plants: Siderca (ARGENTINA) and Gilmore Steel Corpora

U.S.A.). Also, it was used to explore the performance of the reactor under different operating conditions. This capacity could b esign and control purpose. 2004 Elsevier B.V. All rights reserved.

eywords: Shaft furnace simulation; Gas-solid reactor; Moving bed; Direct reduction.

. Introduction

Direct reduction of iron ore is today’s major process for enerating metallic iron, necessary in the iron and steel indus-

ry. World production of direct reduce iron (DRI) has grown rom near zero in 1970 to 45.1 Mt in 2002. MIDREX® Tech- ology is the most important one, responsible for the 66.6% f the world total DRI production. Its main reactor (the shaft

urnace) is a moving bed reactor. The first studies related to moving bed solid-gas reactors

ere performed by Munro and Amundson[1], Amundson 2] and Siegmund et al.[3]. In these works, the authors used linear function of the solid temperature in order to approxi- ate the reaction rate and to obtain analytical solutions. The

alidity of this solution is limited to a narrow range of tem- eratures.

∗ Corresponding author. Tel.: +54 11 4576 3240; fax: +54 11 4576 3241. E-mail addresses:[email protected] (D.R. Parisi),

[email protected] (M.A. Laborde).

Schaefer et al.[4] studied the heat generation in a stea state reactor. They used a step function for the heat ba and the results show the existence of multiplicity of stea states.

Yoon et al.[5] developed a model for a Lurgi type reac used in the carbon gasification. They considered the temperature in both phases (solid and gas) and the shri unreacted core model for the solid particle.

Amundson and Arri[6] analyzed the same system considering different temperatures in both phases.

Arce et al.[7] studied a countercurrent moving bed rea using a heterogeneous model for the reactor design an shrinking core model for the solid particle. They applied b models to an irreversible first order exothermic reaction

Rao and Pichestapong[8] developed a model for a rea tor in which the reduction of iron mineral is carried out. T model considers that the controlling step is the mass tra of the gaseous reactants in the product solid layer. The centration of the gaseous species on the interface gas-s that of the equilibrium and it was evaluated using an itera

385-8947/$ – see front matter © 2004 Elsevier B.V. All rights reserved. oi:10.1016/j.cej.2004.08.001

36 D.R. Parisi, M.A. Laborde / Chemical Engineering Journal 104 (2004) 35–43

Nomenclature

Ap pellet external area (cm 2)

C reactor gas concentration (mol/cm3) D effective diffusion coefficient (cm2/s) Gm molar flow (mol/cm

2 s) H reaction enthalpy (cal/mol) h global heat transfer coefficient (pellets/gas)

(cal/s/cm2/K) k kinetics constant of the surface reaction (cm/s) kg external mass transfer coefficient (cm/s) L reduction zone length (cm) Mw molecular weight np number of pellets per unit volume (1/cm

3) R reaction rate (mol/cm3s) R̂ reaction rate per pellet (mol/s) r0 external radius of the pellet (cm) rc radius of the unreacted core (cm) T temperature (◦C) u gas velocity (cm/s) X extent of reaction/extent of reactant conversion

(mol/cm3) z space variable inside the reactor (cm)

Subscripts atm atmosphere i ith reaction in reactor inlet j jth reactant (gas or solid) n gaseous reactant rs reactive solid (Fe2O3) ps product solid (Fe) sol solid g gas

Greek letters α stoichiometric coefficient ρ density of the solid reactant (g/cm3)

method. As a consequence, the problem cannot be solved in terms of differential equations system. In this paper, the heat balance is avoided since the authors assumed a linear function of the temperature with the reactor length.

The aim of this work is to model and simulate a solid-gas countercurrent moving bed reactor in which the reduction of iron ore pellets is performed using CO and H2 as reducing gases.

In order to do that, mass and energy balance are taken into account simultaneously. This leads to a set of ordinary differential equation with two point boundary conditions.

The model is validated with data from two industrial plants. Also, it is used to explore the performance of the reactor under different operating conditions.

Fig. 1. Shaft furnace geometry.

1.1. Shaft furnace of the MIDREX® process

The main function of the shaft furnace is to generate sponge iron from iron ore. The solids flow downwards by gravity and the reducing gases flow upwards in counter cur- rent, while the corresponding chemical transformations oc- cur. Fig. 1 shows a scheme of the reactor.

As it can be observed, the furnace consists of a vertical cylindrical container, with a conic lower zone. The inner wall is covered with insulating materials resistant to erosion.

The reducing gases enter by the middle zone of the reactor through the bustle, which consists of a channel with approx- imately 70 nozzles that direct the gas towards the center of the solid bed.

Immediately underneath, the upper burdenfeeders are lo- cated. Following in descendent order one can found: the wind boxes (which take the cooling gas that circulates around the lower conical zone of the reactor), cooling gas distrib- utor or (“inverted Christmas tree”), which besides to inject cooling gases has the function to support most of the bed weight.

Gases going out from the shaft furnace are recycled into another reactor: the Reformer. This is a fixed bed catalytic reactor, which transforms the process gas (with addition of natural gas) into reducing gas again.

2

l- l

nre- ade

( film ith

. The model

In order to model the MIDREX® shaft furnace, the fo owing approximations are considered:

(a) The iron ore pellet consumption is governed by the u acted shrinking core model. This aproximation was m by several authors, see for instance[8,9].

b) Mass and heat transfer resistances through the around the solid particle are negligible comparing w

D.R. Parisi, M.A. Laborde / Chemical Engineering Journal 104 (2004) 35–43 37

diffusional resistance inside the porous solid (kg � D/2/r0).

(c) Only steady-state operating conditions will be consid- ered.

(d) Plug flow is assumed for gas and solid phase.

Due to high gas flow rate in the reactor, turbulence regime is reached. Under this situation, inertial effects are predom- inanant. So it will not be considered neither axial nor radial dispersion[10].

For the solid phase this hypothesis was verified through a previous work[11]. Distinct element method simulations (DEM) were performed in order to study the granular bed dynamics of a typical MIDREX® shaft furnace.

Only the global direct reduction reactions are taken into account. The area of interest is the reduction zone of the reactor. Carburization reaction will not be considered as they occur in the lower zone.

The reaction system studied is the following:

1 3 Fe2O3 (s) + H2 (g) = 23 Fe (s)+ H2O (g) (R1) 1 3 Fe2O3 (s) + CO (g) = 23 Fe (s)+ CO2 (g) (R2) It must be noted that the water gas shift reaction (WGSR) is a linearly dependent reaction with reactions R1 and R2 (In fact, R1 − R2 = WGSR). The WGSR is a very important reaction i en as o , it is t

tion a

C

f - c

ase,

X

X

a

X

C t the c unit o the u E

r

w f p r w .

The origin of coordinates is placed at the top of the reactor (seeFig. 1).

Under the above assumptions (a)–(d), the mass and energy balances for a steady-state counter current moving bed reactor can be stated as:

• Gas phase

u dX1 dz

+ npR̂1(X1, X3) = 0 (6)

u dX2 dz

+ npR̂2(X2, X3) = 0 (7) dTg dz

− npAph(Tsol − Tg) GmgCpg(X1, X2, Tg)

= 0 (8)

• Solid phase

usol dX3 dz

+ np(R̂1(X1, X3) + R̂2(X2, X3)) = 0 (9)

dTsol dz

− np Gmsol(X3)Cpsol(X3, Tsol)

× [ Aph(Tsol − Tg) −

∑ i

∆Hi(Tsol)R̂i(Xi, X3, Tsol)

]

= 0 (10)

dict hat dary

the c n by:

R

w on r

R

I sible k it- u m.

t e

G

n the reductor reactor studied. So even it was not chos ne of the linearly independent reactions of the system

aken into account implicitly, in the present analysis. The extent of reaction is defined in terms of concentra

s:

j = C0j + ∑

i

α i jXi (1)

or each speciesj and whereαij is the stoichiometric coeffi ient.

From definition (1), it can be wrote for the gaseous ph

1 = C0H2 − CH2 (2)

2 = C0CO − CCO (3) nd for the solid phase,

rs = X1 + X2 = 3(C0Fe2O3 − CFe2O3) ≡ X3 (4) onsidering the unreacted shrinking core model and tha oncentration of reactive solid must be measured per f reactor volume, it is possible to relate the radius of nreacted core (rc) with the solid conversion (X3) through q. (5),

c = (

r 3 0 −

X3 Mw

np4πρ

)1/3 (5)

herer0 is the external radius of the pellet,np the number o ellets per unit reactor volume,Mw andρ are the molecula eight and the density of the reactive solid, respectively

with the following boundary conditions:

X1(z = L) = 0, X2(z = L) = 0, X3(z = 0) = 0, Tg(z = L) = T ing , Ts(z = 0) = Tatm (11)

The problem is solved making an attempt to pre X1, X2 andTg at z = 0 (shaft furnace gas outlet) so t after solving the equations system (6)–(10) the boun conditions atz = L are satisfied,X1(z = L) = X2(z = L) = 0 y Tg(z = L) = T ing . The shrinking core model is used for the solid pellet;

orresponding reaction rate expression per pellet is give

ˆ = −4πr 2 c Cn

(1/kn + rc/Dn − r2c /r0Dn) (12)

heren = 1,2 denotes H2 and CO, respectively. The reacti ate per unit volume of reactor (R) is obtain through

= npR̂ (13) t must be noted that this model is based on an irrever inetics, which limits the validity of the simulation in the s ations in which the gas composition is far from equilibriu

The solid molar flow (Gmsol) is a function ofX3, related o shrinking core radius byEq. (5), such asGmsol can be valuated using expression (14):

msol(rc) = GLmsol [1/2 rc

3ρrs/Mwrs + (r03 − rc3)ρps/Mwps] [rc3ρrs/Mwrs + (r03 − rc3)ρps/Mwps]

(14)

38 D.R. Parisi, M.A. Laborde / Chemical Engineering Journal 104 (2004) 35–43

The solid specific heat was calculated using:

Cps = [crsp ρrsrc

3 + cpsp ρps(r30 − r3c )] [ρrsr3c + ρps(r30 − r3c )]

(15)

This expression considers theCp weighted average of reactive solid (rs) and product solid (ps) for any state of transformation given by the unreacted radius (rc). Heat transfer coefficient (h) is obtained from Chilton and Colburn correlation, used for fixed bed reactors (neglecting the resistance in the gaseous film),

h = 1〈Cp〉Gmg Pr

2/3 (16)

wherePr is the Prandtl number. Values of reaction enthalpies (�H) and specific heats (Cp)

were taken from NIST (http://webbook.nist.gov/chemistry/). The kinetics and diffusion parameters take as reference

those that were obtained from experiments performed in a laboratory gas-solid fixed bed reactor[12] at 900◦C with SAMARCO pellets.

Kinetics coefficients follow Arrhenius law. Activation en- ergies were obtained from literature. For the R1 reaction, Ea1/Rg = −179.14 corresponding to McKewan[13] and for the reaction R2,Ea2/Rg = −342.43 reported by Bohnenkamp a

plant d llets.

ith t

nd- a licit R pair [

3

lues w vel o res, A gon, U

3

re- d plant i

dur- i

and h n i

in T 10)

Table 1 Operating conditions of Siderca plant

Gas Gas flow rate 1 40 000 Nm3/h

Inlet composition (atz = L) H2 52.9% CO 34.7% H2O 5.17% CO2 2.47% CH4 + N2 4.65% Inlet temperature 957◦C (1230 K)

Solid Production (Fe) 100 t/h Mineral pellet density 3.4 g/cm3

Sponge iron density 3.1 g/cm3

Pellet ratio (r0) 0.5 cm np 0.99 pellets/cm

3

Reactor Reaction zone length 1000 cm Diameter 488 cm

was solved numerically obtaining the profiles shown in Figs. 2 and 3.

It can be seen that the two extents of reaction are very similar, in the same way as reaction rates even when the H2 concentration is greater than that of CO. This indicates that the different concentrations used in the reducing gas allow that both reducing gases act simultaneously throughout the entire reactor, removing the same amounts of oxygen. Also it is clear that the CO is a better reducer than the H2 since with smaller concentrations of CO similar reaction rates are achieved.

The fact that reaction rate R2 is greater than R1 near the gases outlet (low temperature) is a consequence of the acti- vation energies values (Ea2 is two times greater thanEa1). This causes that the difference between both reaction rates is more sensible to the temperature than to the concentrations.

In the sameFig. 2, it can also be appreciated that molar fractions of gases (reactive and products) evolve monotoni- cally within the reactor, and that the temperatures of the gases and solids tend to be uniform asz grows.

Fig. 3 shows that the whole reactor length is used effi- ciently for the transformation of the solid, which in fact is incomplete (94% of metallization). This situation is prefer- able to one in which the solid is transformed completely be- fore arriving to the solid outlet, in this case, the residence t ction w y of t

T K oeffi- c

k k D D h

nd Riecke[14]. Pre-exponential values were fitted using the available

ata in each case, depending on the different types of pe The dependency of the effective diffusion coefficients w

emperature is taken asDi ∼ T1.75 [15]. The differential equations system (6)–(10) with bou

ry conditions (11) is solved numerically using an exp unge–Kutta method based on the Dormand–Prince

16].

. Results and discussion

The model was validated comparing the estimated va ith values of exit gas composition and metallization le f two MIDREX® plants: Siderca (Campana, Buenos Ai rgentina) and Gilmore Steel Corporation (Portland, Ore .S.A.).

.1. Siderca MIDREX® plant

In this section the model will be used to simulate the uction zone of the shaft furnace belonging to Siderca

n Campana, Buenos Aires, Argentina. Table 1summarizes the operating conditions recorder

ng 2 h of an arbitrary day. The values of kinetics constants, diffusion coefficients

eat transfer coefficient (h) used in the simulation are show n Table 2.

With the values and operating conditions given ables 1 and 2, the differential equations system (6)–(

ime would be greater than the necessary and the produ ould be lower than the maximum production capacit

he plant.

able 2 inetics constants, effective diffusion coefficients and heat transfer c ient used in the simulation of the Siderca shaft furnace

1 0.225 exp (−14700/82.06/T) cm/s 2 0.650 exp (−28100/82.06/T) cm/s 1 1.467× 10−6 × T1.75 cm2/s 2 3.828× 10−7 × T1.75 cm2/s

4 × 104 cal/cm2/s/K

D.R. Parisi, M.A. Laborde / Chemical Engineering Journal 104 (2004) 35–43 39

Fig. 2. Profiles of many variables along the reduction zone of the Siderca shaft furnace.

In addition, the simulation allows to predict the outlet com- position of gases (atz = 0) as it is shown inTable 3.

Data fromTable 3was obtained directly from instruments in the plant. The predictions of the model agree satisfactorily with this data, within the experimental error.

phase

3.2. Gilmore MIDREX® plant

Rao y Pichestapong[8] published data from another MIDREX® plant, the Gilmore Steel Corporation Plant in Portland, Oregon, U.S.A.

Fig. 3. Profiles of variables related to the solid

along the reduction zone of the Siderca shaft furnace.

40 D.R. Parisi, M.A. Laborde / Chemical Engineering Journal 104 (2004) 35–43

Table 3 Comparison of the Siderca Plant data with model predictions

SIDERCA data (dry base) (%)

MODEL data (dry base) (%)

Outlet gas composition (z = 0) H2 49.0± 2 48.19 CO 23.6± 1 24.15 H2O – – CO2 21.3± 1.2 21.90 CH4 + N2 6.1 ± 0.8 5.76

Metallization 93.7± 1 93.8

Table 4 Operating conditions of gilmore plant

Gas Gas flow rate 53863 Nm3/h

Inlet composition (atz = L) H2 52.58% CO 29.97% H2O 4.65% CO2 4.80% CH4 + N2 8.10% Pressure 1.4 atm

Solid Production (Fe) 26.4 t/h Mineral pellet density 4.7 g/cm3

Sponge iron density 3.2 g/cm3

Pellet ratio (r0) 0.55 cm np 0.64 pellets/cm

3

Reactor Reaction zone length 975 cm Reactor diameter 426 cm

The model was also applied to this plant. The operating conditions are shown inTable 4.

Regarding the gas flow rate per ton of sponge iron pro- duced, it can be noted that these operating conditions are less efficient that those of Siderca.

This difference is due to, at least, two factors. First, the apparent density of iron ore pellets is greater in the case of Gilmore Plant. Second, the concentration of CO in the reduc- ing gas is lower.

As in the previous section the differential equations sys- tem (6)–(10) was solved numerically, but with the values and operating conditions given inTables 4 and 5

These values are similar to those inTable 2. The kinetics and effective diffusive parameters were adjusted in order to fit the plant data. A natural reason for this difference is that the type of pellet and the operating conditions are different.

Table 5 Kinetics constants, effective diffusion coefficients and heat transfer coeffi- cient used in the simulation of the Gilmore shaft furnace.

k1 0.114 exp (−14700/82.06/T) cm/s k2 0.283 exp (−28100/82.06/T) cm/s D1 1.467× 10−6 × T1.75 cm2/s D2 1.276× 10−7 × T1.75 cm2/s h 1 × 10−4 cal/cm2/s/K

Table 6 Comparison of gilmore data with model predictions

GILMORE data (%) MODEL data (%)

Outlet gas composition (z = 0) H2 37.0 36.7 CO 18.9 18.5 H2O 21.2 20.5 CO2 14.3 16.1 CH4 + N2 8.6 8.2 Metallization (z = L) 93 92.8

The coefficienth was calculated fromEq. (16). Fig. 4 shows the evolution of several variables along the

reaction zone of the shaft furnace. In this case (D2 is lower than in the previous case and there are different operating conditions) it can be observed that the reaction rate R1 is smaller than R2 near to the gases outlet (z = 0), where iron ore pellets are fresh (rc ≈ r0) because the pre-exponential factork02 is greater thank01.

However, whenrc begins to be small, the reaction rate is controlled by the diffusional resistance in the ash layer and, in consequence, R2 results lower than R1.

In Table 6the model prediction of the Gilmore plant data [8] are compared.

Also in this case the model reproduced the data satisfac- torily.

4. Analysis of alternative operating conditions

In this section the model will be used to simulate the be- havior of the Siderca shaft furnace in extreme operating con- ditions that are not used normally.

4.1. Production versus metallization

rsion o te of t

ary- i tion t hich p clear t cal c gas c

nce t t this w uc- t

tion a

n is r t/h). A uld f

The relation between the production and the conve f the solid, assuming the same composition and flow ra

he reducing gas (Table 1), is analyzed. To maintain constant the composition of gases while v

ng the production is not a simple task, due to the recircula hat exist between the shaft furnace and the reformer, w roduces the reducing gases. For that reason, it must be

hat the validity of this study is limited to the hypotheti ase in which the same characteristics of the reducing an be maintained.

If it is desired to increase the metallization, the reside ime of pellets inside the reactor must be increased. Bu ould decrease the production. Alternatively, if the prod

ion increases the metallization decreases. Results of the simulations varying the wished produc

re shown inTable 7. It can be observed that if a complete metallizatio

eached, the production would be lower by a 30% (70 lso if the production increases, the metallization level wo

all bellow the level required by the steel mill (92%).

D.R. Parisi, M.A. Laborde / Chemical Engineering Journal 104 (2004) 35–43 41

Fig. 4. Profiles of many variables along the reduction zone of the Gilmore shaft furnace.

Table 7 Variation of the metallization for different productions. The flow rate and the composition of the reducing gas are those ofTable 1

Production Fe (t/h) Metallization (%)

50 100 70 100 80 99.2 90 97.5

100 93.8 110 91.5

In a normal operation, the plant produces 100 t/h with 94% of metallization (superior to the acceptable minimum of 92%). In this case, the whole reactor is used efficiently (seeFig. 3). Nevertheless, the production could be slightly increased before reaching a metallization of 92%.

Fig. 5shows the evolution of different variables within the reactor in the case in which the complete conversion of the solid is reached. This situation also serves to test the validity of the model when the chemical reactions stop because the solid was completely reduced.

It can be observed that beyond 6 m depth approximately, there is no chemical reaction because the solid is already reduced. The reaction takes place near the entrance of the solid and the exit of gases.

4.2. Increase of CO in the reducing gas

As it has been said, the carbon monoxide is a better re- ducer than hydrogen. Consequently some simulations are per-

formed varying the relation H2/CO. This allows analyzing the influences of that relation over the iron production.

Concentration of both reducing gases in the feed is 87.6% (Siderca plant,Table 1). The percentage of each reducing specie (CO and H2) will be varied so that their sum remains constant (87.6%). Molar flows of the other species are not varied. Then we explore how much it is possible to increase the production (maintaining a metallization of 94%) as the proportion of CO increases.Table 8shows the results of sim- ulations.

It is observed, indeed, that when the proportion of CO is increased with respect to the H2, the model predicts a pro- duction increment of approximately 7% between the extreme values studied.

Naturally, the operating conditions of the Reformer reactor (the other main reactor of MIDREX® process which provides the reducing gases) should be changed in order to obtain the desired H2/CO ratio. But for doing this, it is necessary a coupled analysis of both reactors simultaneously. Besides, limitations at the reformer could arise to achieve the studied values.

Table 8 Predicted effect of the CO/H2 relation (in the composition of the reducing gas) over the production of sponge iron in the MIDREX® process

CO% (atz= L, gas i

H2% (atz = L, gas Sponge iron pro-

3 4 4

nlet) inlet) duction (t/h)

4.7 52.9 100 0.0 47.6 104 3.8 43.8 107

42 D.R. Parisi, M.A. Laborde / Chemical Engineering Journal 104 (2004) 35–43

Fig. 5. Profiles of different variables along the reduction zone of the Siderca shaft furnace with a production of 50 t/h.

5. Conclusions

The reduction zone of the shaft furnace of the MIDREX®

direct reduction process was simulated. In order to do this, mass and energy balances were solved for each phase in the countercurrent gas-solid reactor. The resolution of the dif- ferential equations system allows knowing the evolution of several variables throughout the reactor.

The model satisfactorily fit the data from at least two MIDREX® plants (Siderca SA in Argentina and Gilmore Steel Co. in the U.S.). In addition, they allow exploring the be- havior of the reactor for different operating conditions. This could become an important tool for controlling and modify- ing the shaft furnace operating conditions.

The kinetics used in the simulations were found in a labo- ratory scale reactor described in[12]. Also some parameters were slightly adjusted for both different plants in order to fit the avaible plant data and taking into account the different type of iron ore pellets and operation conditions.

The proposed model allowed studying abnormal opera- tion regimes, for example the relation between metallization and production of iron and how the production is affected by the proportion of carbon monoxide used in the reducing gas.

With respect to metallization, it is observed that if it would i uc- t ion), w lant w und 9

Concerning the carbon monoxide, simulations predict that greater it is the CO proportion; greater it will be the pro- duction of iron (maintaining the total gas flow rate and the metallization level fixed). However, an optimization analysis on this subject must be done considering a cou- pled simulation of both reactors: the Shaft Furnace and the Reformer.

Acknowledgements

Authors would like to acknowledge to SIDERCA S.A. for the contribution of plant data, to Francisco Ajargo for useful comments and to José Comas for text revision.

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