Modelling and parametric studies of direct reduction reactor

Abstract

This paper presents the development of a mathematical model to describe the direct reduction of iron oxides in a shaft furnace. The concept of the shrinking core model was adopted. A pellet model was developed for the direct reduced iron using three consecutive reaction schemes, while the furnace was modelled as a one-dimensional steady state moving bed reactor. The combined pellet–reactor model was used to determine the profiles of compositions and temperature of gas and solid. The resulting boundary value problem was solved using the orthogonal collocation method. Validation of the model against data from a local iron/steel plant showed satisfactory results. A sensitivity analysis was carried out for the effects of key operating parameters, such as bustle gas temperature, ratio of gas/solid feedrates and reductant/oxidant ratio. Useful profiles were compiled to illustrate the results of the sensitivity analysis. These results may serve as guidelines for further optimisation studies of the unit.

List of symbols

a _p

surface area per unit volume/m⁻¹

A _i

fitting kinetic parameters

c ₁

reactant (H₂ or CO) concentration at haematite/magnetite interface/mol m⁻³

c _1,p

product (H₂O or CO₂) concentration at the haematite/magnetite interface/mol m⁻³

c ₂

reactant (H₂ or CO) concentration at the magnetite/wüstite interface/mol m⁻³

c _2,p

product (H₂O or CO₂) concentration at the magnetite/wüstite interface/mol m⁻³

c ₃

reactant (H₂ or CO) concentration at the wüstite/Fe interface/mol m⁻³

c _3,p

product (H₂O or CO₂) concentration at the wüstite/Fe interface/mol m⁻³

c ₄

reactant (H₂ or CO) concentration at the external pellet surface/mol m⁻³

c _4,p

product (H₂O or CO₂) concentration at the external pellet surface/mol m⁻³

c ₅

bulk phase gas reactant (H₂ or CO) concentration/mol m⁻³

c _5,p

bulk phase gas product (H₂O or CO₂) concentration/mol m⁻³

C _c

moles of carbon/mole of iron

C _CO

concentration of carbon monoxide along the reactor/mol m⁻³

concentration of haematite in the pellets along the reactor/mol m⁻³

concentration of hydrogen along the reactor/mol m⁻³

C _pg

heat capacity of the gas/J mol⁻¹ °C⁻¹

C _ps

heat capacity of the solid/J mol⁻¹ °C⁻¹

d _t

reduction furnace diameter/m

D ^Fe

effective diffusion coefficient for the reducing gas in the Fe phase/m² s⁻¹

D ^m

effective diffusion coefficient for the reducing gas in the magnetite phase/m² s⁻¹

D ^w

effective diffusion coefficient for the reducing gas in the wüstite phase/m² s⁻¹

effective diffusion coefficient for the product gas in the Fe phase/m² s⁻¹

effective diffusion coefficient for the product gas in the magnetite phase/m² s⁻¹

effective diffusion coefficient for the product gas in the wüstite phase/m² s⁻¹

gas molar flux/mol m⁻² s⁻¹

G _s

solid molar flux/mol m⁻² s⁻¹

heat transfer coefficient between the gas and solid/J m⁻² °C⁻¹

k _g

mass transfer coefficient between bulk reactant gas and the surface of the particle/m s⁻¹

k _g,p

mass transfer coefficient between bulk product gas and the surface of the particle/m s⁻¹

k ₁

reaction rate constant at the haematite/magnetite interface/m s⁻¹

k ₂

reaction rate constant at the magnetite/wüstite interface/m s⁻¹

k ₃

reaction rate constant at the wüstite/Fe interface/m s⁻¹

K ₁

equilibrium constant for the reduction reaction at the haematite/magnetite interface

K ₂

equilibrium constant for the reduction reaction at the magnetite/wüstite interface

K ₃

equilibrium constant for the reduction reaction at the wüstite/Fe interface

reactor height/m

P _i

partial pressure of component i/N m⁻²

r ₁

effective radius of interface between haematite and magnetite in the pellet/m

r ₂

effective radius of interface between magnetite and wüstite in the pellet/m

r ₃

effective radius of interface between wüstite and Fe in the pellet/m

r ₄, r _p

pellet radius/m

R ₁

resistance of the interfacial reaction at the haematite/magnetite layer/s m⁻³

R ₂

resistance of the interfacial reaction at the magnetite/wüstite layer/s m⁻³

R ₃

resistance of the interfacial reaction at the wüstite/Fe layer/s m⁻³

R ^F

gas film resistance for the gaseous reactant/s m⁻³

gas film resistance for the gaseous product/s m⁻³

R ^Fe

resistance of the intraparticle diffusion of the gaseous reactant in the Fe layer/s m⁻³

resistance of the intraparticle diffusion of the gaseous product in the Fe layer/s m⁻³

R ^m

resistance of the intraparticle diffusion of the gaseous reactant in the magnetite layer/s m⁻³

resistance of the intraparticle diffusion of the gaseous product in the magnetite layer/s m⁻³

R ^w

resistance of the intraparticle diffusion of the gaseous reactant in the wüstite layer/s m⁻³

resistance of the intraparticle diffusion of the gaseous product in the wüstite layer/s m⁻³

T _g

gas temperature along the reactor/^oC

T _s

solid temperature along the reactor/^oC

u _g

gas velocity/m s⁻¹

u _s

solid velocity/m s⁻¹

V _Fe

volume of the iron layer/m³

reduction rate at the haematite/magnetite interface/mol s⁻¹

x _CO

moles of carbon monoxide consumed at the haematite/magnetite interface/mol s⁻¹

moles of hydrogen consumed at the haematite/magnetite interface/mol s⁻¹

reduction rate at the magnetite/wüstite interface/mol s⁻¹

y _CO

moles of carbon monoxide consumed at the magnetite/wüstite interface/mol s⁻¹

moles of hydrogen consumed at the magnetite/wüstite interface/mol s⁻¹

reduction rate at the wüstite/Fe interface/mol s⁻¹

axial coordinate/m

z _CO

moles of carbon monoxide consumed at the wüstite/Fe interface/mol s⁻¹

moles of hydrogen consumed at the wüstite/Fe interface/mol s⁻¹

ΔH _i

heat of reaction for reaction i/J mol⁻¹

ϵ _b

bed bulk porosity

ϵ _h

porosity of the haematite

φ ^h–m

oxygen atoms reacting/mole of haematite converted to magnetite = 0·333

φ ^m–w

oxygen atoms reacting/mole of hematite to convert magnetite to wüstite = 0·555

φ ^w–Fe

oxygen atoms reacting/mole of hematite to convert wüstite to iron = 2·112

ρ _Fe

molar density of iron/mol m⁻³

ρ _g

average molar density of reducing gases/mol m⁻³

ρ _h

molar density of haematite/mol m⁻³

dimensionless axial coordinate

Introduction

The direct reduction process has gained growing importance in recent decades as a source of metallic units for electric arc furnaces. The world production of direct reduced iron (DRI) has grown from near zero in 1970 to 68·5 million tonnes in 2008.1 Midrex technology is the most important one and has ∼58% of the world DRI production.1 The main reactor (i.e. the shaft furnace) in the technology is a moving bed reactor.

The modelling and simulation of the direct reduction process are important objectives since the iron/steel industry is known to be one of the most energy intensive industries. Modelling is, however, a challenging task since there are a number of material and energy flows that interact in unpredictable ways. Early studies of moving gas–solid bed reactors were carried out in the 1950s.2,3 These studies used simple linear models to obtain the dependence of reaction rates on solid temperature in order to solve analytically the reactor model. The validity of these solutions is limited to a narrow range of temperatures. Schaefer et al. 4 carried out a study of the steady state behaviour of the reactor and showed the existence of multiple steady states. Yoon et al. 5 developed a model for a Lurgi type reactor used in the carbon gasification. The authors used the shrinking core model for solid particles while assuming identical temperatures in solid and gas phases. Amundson and Arri6 re-examined the same model while considering different temperatures in both phases. Arce et al.,7 on the other hand, developed a model for a countercurrent moving bed reactor using a shrinking core model for the pellet and a heterogeneous model for the reactor. Rao and Pichestapong8 developed a model for a moving bed reactor by considering that the controlling step is the mass transfer of gaseous reactants in the product solid layer. Takenaka et al. 9 developed a reactor model in which the reduction rate equations were derived from a three-interface model and involved both mass and heat balances. The model rate parameters were determined according to a parameter fitting method. Negri et al. 10 carried out a comparison between one- and three-interface pellet models in the direct reduction of haematite in a moving bed reactor. Parisi and Laborde11 used an unreacted shrinking core model as a basis to model a counter current gas–solid reactor but assumed that haematite is reduced to iron irreversibly. This is an oversimplification since the most difficult reduction step is the one from wüstite to iron, which is highly reversible. The effects of various operating parameters on the performance of the reduction reactor were studied by several authors.12,13 The most important parameters seemed to be the reduction gas temperature and composition. By raising the reducing gas temperature, the gas ratio (H₂/CO) necessary to obtain the desired degree of reduction is lowered. Recently, Nouri et al. 14 used the grain model with product layer resistance to simulate the direct reduction reactor. The model considered intergrain diffusion of the porous haematite pellet as well as product layer (sponge iron) diffusion around each grain. Similar to the work of Parisi and Labrode,11 the authors assumed the reduction of haematite to proceed directly and irreversibly to iron.

In this work, we present the derivation and numerical simulations of a model that describes the direct reduction of iron oxides in the reactor. The concept of the shrinking core model8,13 was adopted. A mathematical formulation was obtained that defines the mass flux of the reactant gas in terms of bulk gas phase and pellet properties. A complete pellet model was developed for the DRI using three consecutive reaction schemes. Afterwards, a one-dimensional non-isothermal moving bed reactor model was derived for the furnace. Unlike the previous work, both the kinetics of steam reforming of methane and carburisation are included in the model. Moreover, all the reduction reactions are assumed to be reversible, which is more reminiscent of the actual behaviour in the reactor. The method of orthogonal collocation is successfully applied to the solution of the resulting boundary value problem. This numerical method is known to be efficient in handling moderately steep solution profiles. The simulations were validated against data obtained from a local iron/steel plant. A sensitivity analysis of the effect of key operating parameters was also carried out.

Iron oxide reduction

Three consecutive reactions are considered for the reduction of iron oxide ore (haematite). The reduction reactions by hydrogen are represented as follows.

Haematite reduction to magnetite (1) Magnetite reduction to wüstite (2) Wüstite reduction to iron (3) In the case of reduction by CO, the three reactions are as follows.

Haematite reduction to magnetite (4) Magnetite reduction to wüstite (5) Wüstite reduction to iron (6) Unlike previous works,11,14 all the reactions are assumed to be reversible. This is specifically the case for the most difficult reduction step from wüstite to iron, which is highly reversible.

Pellet model

The three consecutive reactions were used to develop a pellet model based on the shrinking core scheme. The following assumptions were made:

quasi-steady state assumption

ii.

the reduction reactions are assumed to take place on three sharp interfaces: the first between iron and wüstite, the second between wüstite and magnetite and the third between magnetite and haematite

iii.

the gas diffusivities between the different layers are the same for the reducing gases and are calculated based on bulk gas conditions (a more rigorous model that assumes that gas diffusivities change with composition from one layer to another would complicate unnecessarily the model)

iv.

the water gas shift reaction takes place only close to the top gas exit and is modelled as suggested by Negri et al. 15

there is no volume change during the reduction. The reduction process occurs at three advancing interfaces inside the haematite particle (Fig. 1), which proceeds through the following steps:

vi.

transport of gas reactant from the bulk gas phase to the outer surface of the solid

diffusion of gas through the porous layer (Fe) to the iron/wüstite interface

a portion of the gas reacts with wüstite to form iron and gaseous products

the balance of the reactant gas diffuses through the porous wüstite layer to the wüstite/magnetite interface

a portion of the diffusing gas in the previous step reacts with magnetite to form wüstite and gaseous products

the balance of the reactant gas diffuses through the porous magnetite layer to the magnetite/haematite interface (unreacted core oxide)

chemical reaction of the gas with haematite to produce magnetite and gaseous products

outward transport of the gaseous products follows an opposite pattern.

Figure 1.

Schematic representation of three-interface pellet mode

Each step offers resistance to the overall reduction, which is determined by summing up the rates of reduction of the three interfaces. The rate of moving for each interface is determined in terms of rate constants for surface reactions and bulk gas conditions. The key assumption in the model is the quasi-steady state approximation, i.e. the mass flux of the reactant diffusing towards an interface is equal to the amount of the gas reacted plus the remaining amount that diffuses to the following interface. The diffusion of the gaseous product is related to the reactant by the stoichiometric ratio, which is 1∶1 for both hydrogen and carbon monoxide.

In our derivation, subscripts 1–5 are used to indicate the haematite/magnetite, magnetite/wüstite, wüstite/Fe, Fe/boundary layer and boundary layer/bulk interfaces, as shown in Fig. 1. The reaction rate Ω_j of the reducing gas at the pellet interface j is expressed in the following form (7) where k _j is the rate constant at interface j, r _j is the radius, c _j is the concentration of the reducing gas, c _j,p is the concentration of the product gas and K _j is the equilibrium constant of the reduction reaction. For the two reducing gases (H₂ and CO), we have a total of six rate equations. Let x, y and z be the reaction rates of one reducing gas (e.g. hydrogen) with haematite (layer 1), magnetite (layer 2) and wüstite (layer 3) respectively. The rates are defined by (8) where R _j is the resistance of the interfacial reaction and is equal to 1/(k _j r _j ²). The rates x, y and z are related to Ω_j simply by (9) The reduction rate in the first layer (magnetite/haematite) can also be expressed in terms of the resistances of the intraparticle diffusion of the reactant R ^m and the product in the magnetite region (10) where (11) where D ^m and are the effective diffusion coefficients of the reducing gas and the product gas respectively.

Similarly, the reduction rate in the second layer (wüstite/magnetite) is expressed in terms of the reduction rate in the first layer and the resistances of the intraparticle diffusion of the reactant and product in the wüstite region, i.e. (12) where (13) The reduction rate at the outside interface (Fe/wüstite) is given in terms of the reduction rates at the first and second interfaces and the resistances of the intraparticle diffusion of the reactant and product in the Fe region, i.e. (14) where (15) Finally, the mass flux of the reactant and product in the gas film is given by (16) where R ^F and are the gas film resistances for the reactant and product respectively. They are given by (17) Equation (10) can be rewritten in the following forms (18) (19) (20) Equation (18) corresponds to the inward reactant diffusion in the magnetite layer, equation (19) corresponds to the reaction at the magnetite/haematite interface, while equation (20) corresponds to the outward product diffusion through the magnetite layer. Similar interpretations can be written for the other layers.

Reactor model

A moving bed model was developed for the DRI reactor. The following assumptions were used:

steady state operation

ii.

both gas and solid streams move in plug flow with no radial temperature or concentration gradients, i.e. one-dimensional model

iii.

ideal gas behaviour for the reducing gases

iv.

spherical pellets with equal size and with constant voidage of packing

heat transfer from the reactor wall to the surrounding is through an effective convective heat transfer coefficient.

Mass balance – solid phase

In the first step, mass balance equations are written for iron oxides in the interface positions as particles move down through the reactor. The changes in iron oxides along the bed are represented in terms of the variation in the radii of the shrinking interfaces for the three layers. For the magnetite/haematite interface, the change in the haematite concentration is defined as the oxygen fraction consumed during the reduction at this interface.

Considering a volume of element (π/4)d _t ² Z, the change in the haematite concentration in the pellets of this element, in terms of the interface radius, can be expressed as follows (21) The number of moles of haematite consumed in this element is related to the reaction rates by the following balance equation (22) In this equation, we use the stoichiometric ratio: one atom of oxygen is removed from the pellet for each mole of hydrogen or carbon monoxide reacted. The parameter φ ^h−m is simply the relation between the consumed oxygen atoms and the reduced haematite molecules. and x _CO indicate reaction rates with respect to H₂ and CO respectively, u _s is the solid velocity and ϵ _b is the bed bulk porosity.

Introducing the dimensionless reactor height (23) The balance equation for the haematite concentration in terms of the interface radius can be rewritten as a differential equation (24) The molar flux for the solids is given by (25) where ρ _h and ϵ _h are the density and porosity of the haematite. Thus, equation (24) can be rewritten for the radius r ₁ of the magnetite/haematite interface as follows (26) Similar equations can be written for the wüstite/magnetite and Fe/wüstite layers, i.e. (27) (28) For these equations, the initial conditions are given by (29)

Mass balance – gas phase

Two mass balance equations are written for the reducing gases: one for hydrogen and the other for carbon monoxide. The hydrogen molar balance in the element (π/4)d _t ² Z is given by (30) The mass flux of hydrogen is related to the reduction rates at all the interfaces by the following relation (31) The mass balance equation for hydrogen can be rewritten as follows (32) Simply, this equation relates the change in hydrogen concentration along the bed with the amount of hydrogen used to reduce the three types of iron oxides. The gas mass velocity is defined as follows (33) Thus, equation (32) can be rewritten as follows (34) A similar equation can be derived for CO (35) with the following boundary conditions (36)

Energy balance – solid phase

The differential heat balance for solid relates the change in solid temperature along the bed with the heat transferred from the gas phase into the solid phase and the heat generated or consumed by the reduction reactions (37) where T _g and T _s are the gas and solid temperatures respectively along the reactor. The solid energy balance equation can be rewritten as follows (38) With the boundary conditions (39) H _R defines the heat generated or consumed by the reduction reactions, and it is given by (40) with ΔH _i being the heat of reaction for reaction R _i (i = 1–6).

The heat capacity of the solid is given by (41) where the subscripts h, m and w denote haematite, magnetite and wüstite respectively.

Energy balance – gas phase

The heat balance for the gas phase is written as follows (42)

Model modification to account for steam reforming and carburisation

In this part, we include the effect of the other side reactions that could occur in the reduction reactor. All these reactions are assumed to take place on the iron layer. These reactions are the following.

Steam reforming reaction16 (43) The rate equation for this reaction is given by (44) and in the reverse reaction (45) Methane decomposition reaction17 (46) The rate equation is (47) where a _c is the carbon activity.

Carbon monoxide disproportionation18 (48) The reaction rate equation is (49) Carbon monoxide reduction by hydrogen18 (50) (51) The subscripts m, d, c and r denote steam reforming, methane decomposition, carbon monoxide disproportionation and carbon monoxide reduction by hydrogenation, respectively. The parameters A _i (i = 1, 6) appearing in the reaction rates are used as tuning parameters to fit industrial data. Reactions involving carbon and iron to form carbides were not included in the model due to the scarcity of information.

The reactor model includes two additional mass balances in the gas phase: one for methane consumption (52) and the second one for carbon formation (53) The gas balance equations (equations (34) and (35)) for hydrogen and carbon monoxide are modified to the following forms (54) (55) where the rate r _m is such that r _m = r _mf when r _mf>0 and r _m = r _mb otherwise.

The carbon activity a _c is based on the formula given by Chipman19 (56) where C is atom C/atom Fe.

The solid differential heat balance equation (38) is also modified to include the heat of all side reactions (57)

Kinetics

The kinetics used in this work are those developed by Tsay et al. 20,21

For hydrogen production, the kinetic rate constants are (58) (59) (60) For the reduction of carbon monoxide, the kinetic rate constants are (61) (62) (63)

Assumptions for transition and cooling zones

The main role of the transition zone is to carburise the product iron, which saves energy in the subsequent refining in the electrical arc furnace. As to the cooling zone, its main role is to cool down the product iron. The gas temperature profiles in the transition and cooling zones are very steep because the flowrate of gas is small while that of the solid is large, resulting in a large temperature increase. The solution of the models for both transition and cooling zones may lead to difficulties in convergence because of the severe steepness of the profiles. For this purpose, we made a simple analysis to approximate the events taking place in the transition zone. We assumed that 95% of the methane in the transition zone decomposes into carbon and hydrogen and that 5% of the hydrogen is used in the further reduction of iron oxides. As to the cooling zone, the methane decomposition is very minor and could be neglected.

Numerical methodology

The method of orthogonal collocation is used to solve the boundary value problem. The main advantage of this technique is its adequate representation of the model with minimum number of variables and its capability of solving moderately steep profiles. It is known that the solid temperature rises quickly as it enters the reactor from about ambient temperature to reaction temperature. Afterwards, the solid temperature changes slowly past the entry zone. Soliman22 developed a spline collocation method that is suitable for this kind of problems. The method is based mainly on subdividing the domain into zones in which the profile is fitted by a spline polynomial. For the boundary between the zones, proper continuous conditions are imposed. Thus, we can have the first spline point that divides the temperature profile into a fast and slow changing zone. Then, we have two consecutive zones representing the points at which two of the three moving fronts reach the centre of the iron ore pellet. Moreover, in order to obtain an adequate initial guess for the problem, we start by solving a simple problem whose solution is known. For our case, a reactor with zero length will have the boundary conditions as its solution. This solution is used as an initial guess for a reactor with a small length δ _l. The solution of this problem is the initial guess for a problem with a reactor of length 2δ _l. These iterations are continued until the required reactor length is recovered. This elementary length δ _l is used as an adjustable parameter when convergence problems are encountered.

Results and discussion

The numerical simulations were carried out using the design and operating parameters shown in Table 1. These parameters are associated with a local iron/steel plant. In the start of the simulations, we study the selection of the number of collocation points needed for the numerical simulation. Figure 2 shows the effect of collocation points on the calculated profiles of gas temperature. When the number of collocation points is 4, some oscillations could be seen in the profile. Increasing the number of collocation points to 6 yields a smooth profile, while further increase to 7 does not yield any improvement. Therefore, the number of collocation points chosen in the computations is 6. It can be seen from Fig. 2 that since the gas is fed countercurrently to solid, the gas temperatures decreases starting from the dimensionless distance of 1 (bustle gas) to the dimensionless distance of 0 (top gas). This decrease is due to the endothermic nature of the reaction and to the fact that the solid is fed at colder temperature. Figure 3 shows the profile of the solid temperature. The profile is quite close to that of the gas temperature. Table 2, on the other hand, shows the results of the validation against plant data. Only dry gas composition is available for validation. The sampling is carried out in the real plant after the scrubber, i.e. at low temperatures. The results of the table show overall satisfactory agreement, in consideration that measurements errors are quite possible.

Figure 2.

Effect of collocation points on gas temperature profile

Figure 3.

Profile of solid temperature for collocation point number of 6

Table 1.

Nominal and design parameters of reactor

Parameter	Value
Diameter/m	5·5
Height/m	9·1
Gas flowrate/N m³ h⁻¹	192197
Inlet composition/%
CH₄	5·6
CO₂	0·9
H₂O	3·9
CO	30·7
H₂	56·5
N₂	2·3
Inlet temperature/K	1249
Inlet haematite flowrate/t h⁻¹	180
Gas/solid ratio	1068
Flowrate of gangue (SiO₂)/t h⁻¹	8
Iron ore pellets radius/m	0·012
Porosity	0·2

Table 2.

Comparison between plant data and model results at exit conditions for top gas dry analysis

Parameter value/%	Plant data	Model predictions
H₂	47·8	51·6
CO	24·4	26·1
CO₂	22·3	19·4
CH₄	3·0	0·9
N₂	2·4	2·0

Figure 4 shows the effect of some operating parameters on the profile of the gas temperature. The figure shows that for an increase in the bustle gas flowrate (from a ratio of 1068∶1100), the gas temperature starts from the same values at the bustle gas side (dimensionless distance of 1) but then yields larger values of gas temperature compared to the base case. This is due to the fact that a smaller residence time causes less endothermic reduction, and for the same heat input, the increase in the flowrate causes a less decrease in temperature drop, which means a larger gas temperature compared to the base case. A decrease, on the other hand, in bustle gas temperature (from 1249 to 1204 K) causes evidently a decrease in gas temperature. A decrease in methane fraction (from 5·6 to 3·6%) causes less reforming and less decrease in temperature drop, causing an increase in gas temperature compared with the base case.

Figure 4.

Effect of some operating parameters on profile of gas temperature

Figure 5 shows that a decrease in the ratio of H₂/CO (from 1·84 to 1·45) causes a less decrease in temperature drop and, hence, an increase in the gas temperature. The reason is that the reduction by carbon monoxide is less endothermic than by hydrogen. This causes excess heat and therefore less temperature drop. Figure 5 also shows that a decrease in the reductant/oxidant ratio (H₂+CO)/(H₂O+CO₂) causes a less temperature drop because of less availability of reducing gases.

Figure 5.

Effect of some operating parameters on profile of gas temperature

The profiles of the thickness of the different layers with the distance are shown in Fig. 6. It can be seen that the third layer of FeO is the controlling step as it decays much slower than the layers of Fe₂O₃ (layer 1) and Fe₃O₄ (layer 2). The effect of some operating parameters on the thickness of the layers is shown in Figs. 7 and 8. This effect is similar for the three layers, so only the first layer is chosen for the simulations. It can be seen from Fig. 7 that an increase in the bustle gas flowrate results in more reduction, which results in the layer to decay quicker than the base case. The decrease in the bustle gas temperature induces less reduction so the layer decays much slower. A decrease in the ratio of H₂/CO, on the other hand, yields larger temperature and therefore more reduction, causing the layer to decay quickly. Figure 8 shows that a decrease in the reductant/oxidant ratio causes less reduction and therefore less temperature drop, resulting in high temperatures. This results in a faster decay of the layer. A decrease, on the other hand, in methane mole fraction can be seen to decrease the temperature drop, so it has a similar effect to the increase in reductant/oxidant ratio.

Figure 6.

Profile of thickness layers

Figure 7.

Effect of some operating parameters on profile of thickness layer

Figure 8.

Effect of some operating parameters on profile of thickness layer

Having studied the variations of the local profiles, we show the simulations for the overall performance of the reactor. Figures 9–^{Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17} 18 show the effects of key operating parameters on the metallisation degree and carbon content. Figures 9 and 10 show the effect of a change in bustle gas temperature. The decrease in this temperature causes a reduction in the gas temperature, and this leads to less reduction and therefore less metallisation. A decrease in bustle gas temperature, for instance from 1300 to 1200 K, decreases the metallisation degree from 98·3 to 86·6%. Figure 10 shows the effect on carbon content. Carbon comes primarily from methane and then from CO. A larger gas temperature causes more decomposition and therefore more carbon content. It can be seen that a decrease in bustle gas temperature from 1300 to 1200 K decreases the carbon content from 0·62 to 0·22%.

Figure 9.

Effect of bustle gas temperature on metallisation

Figure 10.

Effect of bustle gas temperature on carbon content

Figure 11.

Effect of H₂/CO on metallisation

Figure 12.

Effect of H₂/CO on carbon content

Figure 13.

Effect of (H₂+CO)/(H₂O+CO₂) on metallisation

Figure 14.

Effect of (H₂+CO)/(H₂O+CO₂) on carbon content

Figure 15.

Effect of methane feed percentage on metallisation

Figure 16.

Effect of methane feed percentage on carbon content

Figure 17.

Effect of gas flowrate/solid rate on metallisation

Figure 18.

Effect of gas flowrate/solid rate on carbon content

Figures 11 and 12 show the effect of the ratio H₂/CO. Generally, this ratio is constrained between 1·2 and 2 to avoid carbon deposition. The decrease in the reductant ratio leads to better metallisation because carbon monoxide is a better reductant than hydrogen as the overall reaction of CO is exothermic and the temperature therefore remains high. The decrease in the ratio H₂/CO also means more CO and therefore more reduction and more carbon formation. A decrease, for instance, in the ratio of H₂/CO from 2 to 1·3 leads to an increase in the metallisation degree from 93·3 to 96·7% and an increase in the carbon content from 0·35 to 0·57%. Figures 13 and 14 show the effect of the reductant/oxidant ratio. Similarly to the H₂/CO ratio, the reductant/oxidant ratio is generally constrained between 10 and 14. The decrease in this ratio evidently reduces the degree of metallisation because there are less available reducing gases. The carbon content also decreased because of the decrease in CO. For instance, a decrease in the reductant/oxidant ratio from 14 to 10 leads to a decrease in the metallisation degree from 93·5 to 91·7% and a reduction in the carbon content from 0·36 to 0·26%. Figures 15 and 16 show the effect of methane mole fraction. The decrease in mole fraction reduces the metallisation because it leads to less reforming. The carbon content has decreased because of less methane decomposition. For instance, a decrease in the methane mole fraction from 9 to 2·5% reduces the metallisation degree from 98·7 to 87·6% and also the carbon content from 0·62 to 0·28%. Finally, Figs. 17 and 18 show the effect of the ratio of gas to solid feedrates. The increase in this ratio leads to more reducing gases, i.e. hydrogen and carbon monoxide, and therefore to more metallisation. This also yields more decomposition of methane and therefore more carbon content. An increase, for instance, in the ratio of gas to solid feedrate from 950 to 1200 leads to the increase in the metallisation degree from 86 to 98·7% and also an increase in the carbon content from 0·28 to 0·53%.

Conclusions

A detailed model based on shrinking core pellet was developed for a direct reduction reactor. The models for the transition and cooling zones were approximated by simple algebraic equations since a detailed model in these zones would result in too steep profiles (and stiff problems), while a small extent of methane decomposition takes place in the transition zone and even less in the cooling zone. The model was solved using a spline collocation method for the base case to obtain local profiles of temperature and layers thicknesses and was subsequently used for a sensitivity analysis of the effect of reactor operating parameters. Satisfactory results were obtained when the model was validated against gas dry compositions, the only data available from a local plant. The effects of model parameters on the metallisation degree and carbon content permitted the construction of useful plots showing the effects of bustle gas temperature, reductant ratio, reductant/oxidant ratio, methane mole fraction as well as the ratio of gas/solid feedrates. The results of the sensitivity analysis may be helpful in further optimisation studies of the unit.

Footnotes

Acknowledgements

This work was made possible by a generous grant from the National Plan for Science and Technology (project no. 08-ENE337-2).

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