Numerical Calculations of Spray Roasting Reactors of the Steel Industry with Special Emphasis on Fe2O3-Particle Formation

Research Article

Numerical Calculations of Spray RoastingReactors of the Steel Industry with SpecialEmphasis on Fe2O3-Particle Formation

This work presents numerical calculations for the lay-out of spray roasting reac-tors for the steel industry. In these reactors, a pickling liquor based on water andHCl containing FeCl2 is regenerated in a combustor leading to the formation ofFe2O3 particles. For the lay-out of these reactors, detailed knowledge of the flowand temperature field, the associated gas phase reactions, and especially, of theformation of the Fe2O3 particles is required. An extended particle formationmodel is presented which is based on earlier work. Finally, results for an indus-trial spray roasting reactor are given showing the potential of the numerical toolsdeveloped for the improvement of the technical lay-out of such thermal reactors.

Keywords: Modeling, Particle formation, Particles, Spray roasting reactors

Received: June 19, 2007; accepted: July 22, 2007

DOI: 10.1002/ceat.200700231

1 Introduction

Pickling liquor is an aggressive fluid based on hydrochloricacid (HCl) and therefore is often applied in cleaning proce-dures of metals, for example hot rolled steel panels. It is awashing liquid to remove surface oxide films. In the course ofthe process, metal ions and solids accumulate in the picklingsolution so that either the renewal of the solution, the separa-tion of the solids or the recycling of the pickling fluid is neces-sary.

The first step of the acid regeneration with the intention toseparate the iron chloride from the pickling liquor takes placein spray roasting reactors. These reactors contain natural gasfired burners which generate hot combustion gases. Fig. 1illustrates the circulation of the waste liquid and shows themost important steps of the regeneration process. After thecleaning procedure of the metal sheets, the pickling liquormainly consists of FeCl2 and H2O and is collected in a reser-voir. Afterwards, this waste liquid is fed into a thermal reactorvia injection nozzles to separate the iron chloride from thesolution. The burner is fired with natural gas in order to evap-orate the liquid water fraction and to initiate a chemical roast-ing process. Finally, the fresh acid leaves the reactor and upperoutlet. It is liquified and fed back into the pickling line.

Fig. 2 shows the lay-out of spray roasting reactors which arecurrently applied in industrial facilities. These reactors mainly

consist of an empty cylindrical tower lined with refractory ce-ramic material. The bottom is conical ensuring the flow ofprocessed iron oxide to the outlet. The metal chloride solutionis sprayed through pressure nozzles into the upper part of thereactor, so the droplets descend in the reactor, dry up and be-come pyrohydrolyzed. Typical droplet diameters required areabout 100 to 150 lm. One to four burner chambers (usuallythree), which charge the interior with hot combustion gases,are mounted tangentially outside of the reactor, thus produc-ing a rotating flow. The inlet speed of the combustion gases isadjusted to the diameter of the reactor ensuring thorough mix-ture of particles and hot gases. The droplets produced by thenozzles are caught by this flow and are intensively mixed withthe atmosphere in the reactor. The temperature profile showsvery intense gradients in the chamber, so that the amount offuel is adjusted to obtain a specific temperature in the roastgas outlet.

The gross exothermic chemical reaction taking place is givenby Eq. (1).

4 FeCl2 + 4 H2O + O2 → 2 Fe2O3 + 8 HCl + 55 kJ (1)

In addition to the release of the desired HCl gas, Fe2O3 par-ticles are generated which are important by-products for sever-al applications. Although the spray roasting process has beenused on an industrial scale for several years, details of the par-ticle formation are still unknown. To simulate reactors on anindustrial level, a simplified model for the Fe2O3 particle for-mation is required. In earlier papers, a model was presented[1, 2] and an extended version of this model has been imple-mented into a numerical CFD code. The code now allows to

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.com

Marcus Beck1

Siegmar Wirtz1

Viktor Scherer1

Frank Bärhold2

1 Ruhr-University Bochum,Department of Energy PlantTechnology, Universitätsstr.150, Building IB 3/127, D-44780 Bochum, Germany.

2 Andritz AG,Eibesbrunnergasse 20,A-1121 Vienna, Austria.

–Correspondence: Dipl. Phys. M. Beck ([email protected]), Ruhr-University Bochum, Department of Energy Plant Technology, Uni-versitätsstr. 150, Building IB 3/127, D-44780 Bochum, Germany.

Chem. Eng. Technol. 2007, 30, No. 10, 1347–1354 1347

simulate the most important steps during particle formationlike the determination of characteristic time scales for the dif-ferent formation stages, like water evaporation, FeCl2 con-sumption or Fe2O3 formation, and the chemical reactions gov-erning the heat balance in a spray roasting reactor. Note that atthis step, details of particle morphology formation are not ofinterest and therefore are not modeled.

2 Theoretical Background

First the FeCl2 solution is injected into the reactor. At first, adroplet behaves like a pure water droplet; it is heated until theevaporation temperature is reached. Afterwards, the waterfraction begins to evaporate, leading to the formation of a con-centration gradient of the dissolved FeCl2 within the dropletand a size reduction. This process continues until a criticalconcentration of FeCl2 is reached on the droplet surface,

exactly a mass fraction of 0.64, corresponding to theconcentration of FeCl2 in the tetrahydrate, FeCl2·4H2O. When this critical concentration is reached, theshrinking of the droplet stops. The droplet is heatedup again and the remaining crystal water evaporates.When the crystal water, 4 H2O, is consumed (∼ 538 K)the chemical reaction commences [3].

From there on, the development critically dependson the surrounding gas atmosphere and its tempera-ture. The ideal process was already stated in Eq. (1),which can be specified in more detail by:

4 FeCl2 + 4 H2O → 4 FeO + 8 HCl – 508 kJ (2)4 FeO + O2 → 2 Fe2O3 + 563 kJ (3)4 FeCl2 + 4 H2O + O2 → 2 Fe2O3 + 8 HCl + 55 kJ (4)

In addition to the shown reactions of the ideal pro-cess, Eqs. (2–4), there are many more reactions possiblewith respect to the driving substance, FeCl2. Most ofthem are insignificant for spray roasting reactors andrequire specific atmospheric and temperature condi-tions. Fig. 3 shows the known reactants for FeCl2 based

on the current state of research. The primary reactants, H2O andO2, are indicated by the thick arrow and are the focus of thiswork. More detailed information of the required boundary con-ditions for each minor reaction can be found in Gmelin [4].

For the ideal roasting process, a water vapor to oxygen ratiogreater than 4 is required; otherwise excess oxygen remainsafter consumption of the vapor, leading to several side reac-tions [4] and the formation of undesired by-products. Whichsubstances are formed depends on the temperature and gasspecies concentration, mainly Cl2, H2 and Fe2Cl6. Eqs. (5–10)show the individual reactions of FeCl2, H2O and O2.

3 FeCl2 + 3 H2O → 3 FeO + 6 HCl – 382 kJ (5)3 FeO + H2O → Fe3O4 + H2 + 63 kJ (6)3 FeCl2 + 4 H2O → Fe3O4 + 6 HCl + H2 – 318 kJ (7)

12 FeCl2 + 3 O2 → 2 Fe2O3 + 4 Fe2Cl6+ 167 kJ (8)4 Fe2Cl6 + 2 Fe2O3 + 6 O2 → 6 Fe2O3 + 12 Cl2 + 684 kJ (9)12 FeCl2 + 9 O2 → 6 Fe2O3 + 12 Cl2 + 851 kJ (10)


Figure 1. Typical circulation process of the pickling liquid.

Figure 2. Lay-out of a typical spray roasting reactor.

Figure 3. Possible reactants for FeCl2.

1348 M. Beck et al. Chem. Eng. Technol. 2007, 30, No. 10, 1347–1354

For the formation of hematite Fe2O3, the temperatureshould not exceed approximately 900 K with a surroundingwater vapor to oxygen ratio of at least 4 to 1 (ideal reaction).In industrial reactors, these conditions usually exist and there-fore kinetic modelling can be reduced to Eqs. (2–4). Forfurther processing of the generated particles as feedstock, alarge specific surface is required which exponentially decreaseswith increasing temperature. During the formation of Fe2O3, asolid hull is formed, leading to an over-pressure in the remain-ing interior liquid. In the final formation stages, the remaininginterior liquid evaporates and escapes through the surface,leaving a hollow sphere with a porous structure.

Summarizing, four important steps can be identified whichmust be described for a detailed modeling of the formationprocess:– Excess water fraction vaporizes until the critical concentra-

tion is reached on the droplet surface.– Shrinking process stops and crystal water evaporates until

pure FeCl2 is present on the surface.– Chemical reaction is initiated under energy consumption,

leading to the formation of several intermediates. Mean-while, a solid hull is formed.

– Remaining liquid in the particle interior cracks through thesolid hull due to over-pressure, leaving the end-product(under ideal circumstances, hematite Fe2O3) with a poroussurface.

3 Numerical Modeling

In section 2, it was shown that several separate stages have tobe considered in order to model the roasting process correctly.In particular, the process temperature, water vapor, and oxy-gen concentration of the particles are important for the chemi-cal reaction. There is no way to measure these parameters inindustrial reactors, which is why the information has to be ex-tracted from numerical simulations. Next to an increased cal-culation effort for modeling the entire intermediate reactions,most of the required parameters, e.g. kinetic data, are still un-known. The focus is the development of a reaction model,which is capable of handling large particle numbers withinacceptable calculation times, including the most importantsteps of the formation process. The first calculations of the for-mation process were performed in a previous work based on alaboratory reactor [1, 2]. The formation of the hollow sphereand the processes in the particle interior were neglected in thecurrent model and the chemical conversion reduced to themain formation stages:– Excess water evaporates from the droplets until the critical

concentration of FeCl2 is reached on the surface. The dropletshrinks during this process.

– The FeCl2 fraction of the particle undergoes a chemical con-version according to Eq. (1) until it is fully consumed andFe2O3 is generated while the particle radius remains con-stant.Heating until evaporation temperature (373 K) is calculated

by a simple unsteady heat balance for the individual droplets.When the particle reaches 373 K, evaporation and the develop-

ment of a concentration gradient of the dissolved FeCl2 withinthe particle is initiated.

The diameter shrinking rate and thus the mass loss resultingfrom the evaporation rate is calculated by:

d

dtdp � � 4k

qpcp�∞dp�1 � 0�23

��Re

� � ln 1 � cp�∞�T∞ � Tp�h

� �(11)

Here cp�∞ is the specific heat capacity of the gas and h, the la-tent heat of water1).

For the particle formation process, it is crucial to knowwhen the critical concentration of FeCl2 (mass fraction, 0.64)is reached on the droplet surface. Therefore, the developmentof the concentration gradient is calculated using the model ofBrenn [4], who presents an analytical solution of the diffusionequation on a spherical domain with its surface shrinking line-arly with time. The solution is given as a series expansion inconfluent hypergeometric functions and is valid for arbitraryratios of the shrinking rates of the surface of the sphere. Themass fraction, Y, of the dissolved FeCl2 as a function of radiusand time is then given by:

Y s� n� � ��

j

Cj 1 � as� ��kj Mk kj�3

2�� a

4Gn2

� �(12)

where s represents a dimensionless time, n the dimensionlessradius, a the dimensionless shrinking rate, G the dimensionlessdiffusion coefficient, and kj specific eigenvalues of the givenproblem. Mk is a specific Kummer function [5] in the form ofa series expansion. Cj are expansion coefficients which are alsoto be calculated by using the Kummer functions. Details of thismodel are presented in [4].

Important initial conditions for this model are the initial di-ameter, d0, the initial mass fraction of the dissolved FeCl2, theshrinking rate, �a, of the droplet and the binary diffusion coeffi-cient, DFeCl2-H2O, of iron chloride and water.

The initial diameter, d0, and the initial mass fraction of thedissolved FeCl2 are known at the beginning of the process. Theshrinking rate, �a, has to be estimated since it is dependent ontime and thus varies during the residence time. A good estima-tion can be derived by calculating the shrinking process of apure water droplet in a hot atmosphere. For the boundaryconditions of the investigated spray roasting reactor, a dropletwith d0 = 100 lm shrinks with approximately 1.1 · 10–8 m2/s.

The binary diffusion coefficient, DFeCl2-H2O, of the mixtureis also unknown, but can be estimated with proven methods,e.g. the Wilke-Chang [6] or the Hayduk-Minhas [7] correla-tion, leading to approximately 1.8 · 10–9 m2/s at a temperatureof 293 K.

When the critical concentration is reached, shrinking of theparticle stops and the particle temperature increases. As soonas 538 K is reached, the Fe2O3 formation starts. This forma-tion is controlled by two main processes, the kinetic reactionat the particle surface and the gas diffusion of the requiredcomponents, H2O and O2, towards the particle surface.


–1) List of symbols at the end of the paper.

Chem. Eng. Technol. 2007, 30, No. 10, 1347–1354 Modeling 1349

At the current state of research, there is only limited data onthe chemical kinetics available. Vilcu [8] presented kinetic dataof the anhydrous FeCl2 reaction at high temperatures. His ex-periments showed values of the reaction rate constant, kkin,H2O

for three temperatures – 853 K, 873 K, and 893 K – which leadto approximations of the activation energy, Ea,H2O (∼121 kJ/mol), and the Arrhenius factor, k0,H2O (2080 mol m–3s–1 kg–1)according to the Arrhenius equation:

kkin � k0 exp � Ea

RT

� �(13)

Furthermore Rollason [9] presented kinetic data of the FeOreaction with oxygen. His numerical calculations showed val-ues of the activation energy, Ea,O2 = 3.78 kJ/mol, and of thepre-exponential factor, k0,O2 = 1.427 · 108 m3/(mol s)–1 forEq. (3). Thus, all required kinetic parameters for the idealroasting process are determined.

The diffusion of H2O and O2 towards the surface can be cal-culated with:

kdiff �2MFeCl2

D

dRT(14)

where D denotes the gas diffusion coefficient, MFeCl2 the molarmass of FeCl2, and d the current particle diameter.

The combined influence of Eq. (2) is modeled by an effec-tive rate constant, keff,H2O, according to:

keff �H2O � 11

kkin�H2O

� 1

kdiff �H2O

(15)

Combining the kinetic and diffusion terms according toEq. (15), the FeCl2 consumption rate was modeled by:

d

dtmFeCl2 � �p d2 keff �H2O nf �H2O ptot (16)

The partial pressure for the primary reaction gas, H2O, wassubstituted with its mole fraction, nf;H2O, and the totalpressure, ptot. Simultaneously, with the FeCl2-mass decrease,FeO is generated which is calculated by:

�mFeO � �nFeCl2MFeO (17)

Eq. (17) states that for each consumed mole of FeCl2, onemole FeO is generated. Hence, the source terms for the masstransfer of HCl and H2O with the gas phase were modeledaccording to:

Mass Transfer HCl: �mHCl � �nHCl MHCl�f Dt (18)

Mass Transfer H2O: �mH2O � � 1

2�nHCl MH2O

�f Dt (19)

where �nHCl denotes the current mole flow rate of HCl, �f theparticle flow rate, and Dt the time step.

As soon as FeO is formed in the particle, the second reac-tion, Eq. (3), with oxygen is initiated whose effective reactionrate constant corresponds to Eq. (15) and reads:

keff �O2� 1

1

kkin�O2

� 1

kdiff �O2

(20)

The FeO-mass, which was generated by Eq. (17), decreasesafterwards according to:

d

dtmFeO � �p d2 keff �O2

nf �O2ptot (21)

whereas the end-product Fe2O3 is generated by

�mFe2O2� 1

2�nFeO MFe2O2

(22)

The Fe2O3 formation leads to an O2 consumption on theparticle surface and reads as:

Mass Transfer O2: �mO2� � 1

4�nFeO MO2

�f Dt (23)

The particle formation model described above was inte-grated into FLUENT using a User-Defined-Function. To simu-late the geometry of the spray roasting reactor, a mesh consist-ing of 350000 hexahedron cells was generated. The appropriategas resulting from the combustion of methane and air entersthe reactor at three tangentially mounted burners.

4 Results

Computing the reaction rate constants, kkin,H2O and kdiff,H2O,according to Eq. (13) for the significant temperature range fordifferent particle diameters, it becomes clear that at low tem-peratures up to 830 K, the kinetic values kkin,H2O are relativelysmall compared to the diffusive values, kdiff,H2O, so kinetic pro-cesses dominate the reaction in this temperature range. Abovethis limit, the kinetic rate constant denotes an immenseincrease due to its exponential temperature dependence.Consequently, the surrounding particle atmosphere can nolonger provide a sufficient flow of water vapor via diffusionfor the surface reaction so that the FeO formation is nowdominated by diffusion processes to the particle.

Compared to the reaction rate constants with water vapor,there is a completely different progression for O2. Due to theassumed values of Rollason [9], the kinetic processes are extra-ordinarily fast and exceed the diffusion by twelve orders ofmagnitude. Hence, the conversion of FeO to the end-product,Fe2O3 (see Eq. (3)), is controlled by the diffusion of O2

towards the particle surface at all times.The shown particle formation model was applied to simula-

tions of a standard “Andritz-Ruthner” reactor which was de-signed for flow rates of the pickling liquor of about 9500 L/h.A droplet spectrum ranging from 30 to 170 lm was injectedinto four nozzles, with initial velocities from 6 to 10 m/s.Furthermore, these reactors have a typical spray angle of45 degrees.

Fig. 4 shows the calculated temperature distribution in thespray roasting reactor. The hottest regions are located at theburners, where flame zones with temperatures of approxi-mately 2000 K are formed. Due to the tangentially mountedburners, a ring with temperatures of 2000 to 2300 K is formedalong the walls, which falls rapidly with increasing distance to



the burners. At the center of the reactor, they drop to 1300 K.The leakage air entering at the bottom with 298 K forms a coldregion, whereas the temperature increases again in the direc-tion of the burners. In the regions of the rotating stream aboveand below the burners, there are areas with higher tempera-tures of about 450 to 600 K, since the eddies affect the streamdirection of the entering gases. At the location of the injectionnozzles (second cut from above), there are low temperatures incomparison with 350 K since at this place the main evapora-tion of the droplet water fraction takes place, consuming heat.The temperatures increase again towards the reactor wall dueto exothermic iron oxide production.

Another important result of the calculations is the locationof the main iron oxide conversion. Fig. 5 shows the sourceterm distribution of HCl and points out the primary regionsof the chemical reaction. The diagram shows the generatedHCl mass per second fed into the gas phase in a range of 0 to10–4 kg/s. A significant part of the reaction takes place in the

upper part of the reactor, with HCl outputs above 0.1 g/s. Be-low this location, the FeCl2 conversion is negligibly small, sothat most of the particles are fully roasted when they reach thehot regions of the reactor near the flame. This leads to goodparticle surface conditions. Since the nozzles are located at theinjection plane, the particles cover a distance of about 2.7 muntil the reaction is initiated. The figure demonstrates the mo-tivation to use CFD, since it is impossible to detect the particleformation regions experimentally.

Fig. 6 exemplarily shows the calculated particle trajectoriesfor initial diameters of 33 and 130 lm. After the injection, thedroplets are forced on a circular path due to the tangentiallymounted burners and the resulting gas stream profile. The leftimage demonstrates that larger particles (≥ 100 lm) leave thereactor at the lower outlet, with a maximum residence time of14 to 20 seconds, depending on the initial diameter. Smallerparticles, as indicated by the image on the right, are stronglyaffected by the lifting force and thus escape the reactor at theupper gas outlet to a large part.

The diagrams shown above give satisfying information onthe temperature behavior and HCl output of the gas phase. Inaddition, the particle behavior regarding the required time forthe different reaction phases and the corresponding speciesconcentration along their trajectories is important. Fig. 7shows the gas concentrations of the relevant species, H2O andO2, at the particle surface along their flight path for the first10 seconds. A total of 100 particles were plotted for statisticalanalysis. These concentrations directly affect the conversionand specify the dominating reaction according to Eqs. (2–10).Within all the size ranges shown, the H2O concentration is wellabove the O2 concentration and exceeds the required water va-por-oxygen ratio of 4 for the ideal reaction. However, there is aminimum concentration of O2 necessary for the further reac-tion of the intermediates. The concentrations in the diagramshow a very large spectrum which does not matter in the caseof H2O, since its concentration is high enough for all particlesto initiate the reaction. In the case of O2, whose concentrationis comparatively small, there is the possibility that the supplyis insufficient for some particles. This leads to a “wet” roasting


Figure 4. Temperature distribution of the spray roasting reactor.

Figure 5. HCl source terms of the spray roasting reactor.Figure 6. Particle trajectories for the initial diameter, d0 = 130 lm(left) and d0 = 33lm (right).


and, thus, the formation of other products according toEq. (7), like magnetite Fe3O4 and H2.

Fig. 8 shows the development of the FeCl2 particle mass. Assoon as this mass becomes zero, the HCl output stops and thefirst endothermic reaction, Eq. (2), ends. According to Fig. 5,this first conversion occurs at a height of 12.1 m for most ofthe particles. The statistical distribution illustrates that the re-quired conversion time of FeCl2 is different and depends onthe particle diameter. Larger particles show fewer fluctuationsin the mass decrease than smaller particles. The product, whichis formed during this process, critically depends on the currentsurrounding concentration of water vapor. Most of the linesshow a straight continuous decrease of the FeCl2 mass, whichindicates a sufficient supply of the required water vapor for the

entire reaction time. However, compared to the majority, a fewparticles – especially smaller ones – need a very long time(∼ 5 s) until all the FeCl2 is consumed in which they show acascaded decrease of the FeCl2 mass. This cascaded decreaseindicates unwanted reactions, since a reaction only takes placeif the water vapor supply is sufficient according to the imple-mented model (see Section 3). Under real conditions, the reac-tion would advance with a “dry” roasting process, in this caseunder the formation of the products seen in Eqs. (7–10).However, most of the FeCl2 mass development shows satisfy-ing characteristics and indicates normal (ideal) roasting, whichdemonstrates that modeling only the ideal reaction for the in-dustrial reactors is justified. A minor percentage (∼ 0.1 %) ofthe particles do not fully convert FeCl2 mass before they leavethe reactor as the curve decrease stops before the zero-point isreached. This behavior corresponds to the observations of in-dustrial spray roasting reactors which show that ejected parti-cles still have a chloride fraction in the magnitude of 0.05 to0.15 %.

For the particle formation and hence the final product, thetemperature development is also important. Fig. 4 alreadyindicated the temperature distribution of the entire reactor.Corresponding to this contour plot, Fig. 9 shows the statisticaltemperature distributions for the particles. After the evapora-tion of the water fraction, which can be seen at the horizontaltemperature distribution in the first second, the temperaturerapidly increases. The greatest increase is indicated by largeparticles since they reach the hottest regions of the reactor,near the burners, faster. Their maximum temperature is atapproximately 1400 K, while some of them reach even highervalues. With decreasing initial diameter, the average maximumtemperature is lower since they stay in the upper part of the re-actor considerably longer due to their bigger lifting force asalready indicated by Fig 6. Consequently, the chance of leavingthe reactor at the upper HCl outlet is high according to thestream behavior inside the reactor. The calculations showedthat about 14 % of all particles leave the reactor at the upper


Figure 7. H2O and O2 gas concentrations along the particle tra-jectory for four initial diameters.

Figure 8. Particle mass of FeCl2 of four initial diameters.Figure 9. Particle temperature distribution for four initial dia-meters.


outlet. Separating this percentage in classes according to size,the escape rate is 26 % for d0 = 33 lm, 18 % for d0 = 75 lm,7 % for d0 = 130 lm, and 5 % for d0 = 170 lm. To ensurea maximized particle surface, the conversion should befinished in the first seconds, otherwise the particles reach un-wanted temperature ranges leading to small specific surfaces.Based on the previous diagrams, the roasting process isfinished after four seconds for most particles, avoiding such aneffect.

Including all effects described above, a temporal estimationof the most important particle formation stages can be done.Fig. 10 summarizes the estimated values for each modeledparticle state for different initial diameters. The time neededfor the first inert heating to 373 K and the following evapo-ration of the water fraction can be estimated without anybigger errors, since these stages are finished nearly simul-taneously for all initial particle diameters. This is indicated bythe profiles of Fig. 9 which show a similar curve progression atthe beginning for each particle size range. As expected,larger particles need more time to heat up due to the increasedinitial mass. Furthermore, they have a bigger volatile fractionand, thus, reach the critical FeCl2 concentration on the surfacelater.

The third state (2. Inert Heating) represents the heating pro-cess up to 538 K, where the last crystal water evaporates. Dueto the turbulent particle trajectories in the spray roasting reac-tor, the temporal evolution of this state fluctuates extremelyfor each particle so that the given time in Fig. 10 is only an ar-ithmetic mean value. After evaporation of the volatile massfraction, the reaction is initiated which is represented by the“Reaction” time. This final state includes the entire conversiontime to the end-product (FeCl2 → FeO → Fe2O3) and againfluctuates for each particle. In this case, the estimated meanvalue of the reaction time is higher for small particle diame-ters, since the FeCl2 conversion to the end product in these sizeclasses are statistically spread over a wider time scale, which isindicated by Fig. 8. Most of the smaller particles remain in theupper part of the reactor for a long time, where the particletemperature increases to 538 K (start of the reaction) occurs ata slow rate.

5 Summary

The intention of the current work was the development of anumerical model appropriate for the design of industrial sprayroasting reactors, which was tested on a widely used reactor,the “Andritz-Ruthner 10000” type.

The process was modeled in such a way that at first the par-ticle water fraction evaporates until the critical concentrationof FeCl2 is reached at the particle surface. Afterwards, the reac-tion of FeCl2 to Fe2O3 is initiated consuming water vapor andoxygen and generating hydrochloric acid in parallel. Kineticdata from the literature are used to describe this dominatingchemical reaction in spray roasting reactors. An effective rateconstant was used considering kinetic and diffusion rates. Thecurrent model is adequate to simulate large particle numbersin industrial spray roasting reactors, in which individual char-acteristics like the morphology are of secondary interest. Itdoes not include the formation of the hollow sphere and theprocesses in the particle interior. However, the most importantinformation for the thermal and fluid dynamic lay-out of anindustrial reactor can be obtained which corresponds to thelimited experimental data. This information is the location ofthe FeCl2 conversion, HCl production, and Fe2O3 formationwhich influence the temperature field in the reactor. Also, theresidence time and gas phase requirements for the formationof the favored product Fe2O3 can be specified and, hence, canbe considered in the reactor design.

Symbols used

A [m2] surface�a [m2/s] shrinking ratea [–] dimensionless shrinking ratecp�∞ [J/(kg K)] specific heat capacityc [mol/m3] concentrationCj [–] expansion coefficientsd [m] diameterD [m2/s] diffusion coefficientEa [J/mol] activation energy�f [L/s] particle flow rateh [J/kg] latent heatG [–] dimensionless diffusion

coefficientk0 [vary] Arrhenius factork [vary] reaction rate constantk [–] air ratiok [W/(m K)] thermal conductivitykj [–] eigenvalues�m [kg/s] mass flow rate

m [kg] massMk [–] Kumme’s functionM [kg/mol] molar mass�n [mol/s] mole flow ratenf [–] mole fractionp [Pa] pressureq [kg/m3] densityR [J/(mol K)] gas constantRe [–] Reynolds number


Figure 10. Average elapsed time until full conversion to ironoxide.


s [–] dimensionless timeDt [s] time stepT [K] temperaturev [m/s] velocityn [–] dimensionless radiusY [–] mass fraction

References

[1] M. Beck, V. Scherer, S. Wirtz, Chem. Eng. Technol. 2007,30 (6), 790. DOI: 10.1002/ceat.200600393

[2] M. Beck, V. Scherer, S. Wirtz, Chem. Eng. Technol. 2005,28 (6), 659. DOI: 10.1002/ceat.200407130

[3] R. J. Meyer, Gmelins Handbuch der anorganischen Chemie.,8th ed., Verlag Chemie GmbH, Berlin 1932.

[4] G. Brenn, Chem. Eng. Technol. 2004, 27 (12), 1252.DOI: 10.1002/ceat.200407025

[5] M. Abramowitz, I. A. Stegun, Handbook of MathematicalFunctions, Dover Publications, New York 1972.

[6] C. R. Wilke, P. Chang, AICHE J. 1981, 1, 264.[7] W. Hayduk, W. S. Minhas, Can. J. Chem. Eng. 1982, 60, 295.[8] R. Vilcu, T. Coseac, D. Oancea, Revue Roumaine de Chimie

1997, 42 (2), 93.[9] R. J. Rollason, J. M. C. Plane, Chem. Phys. 2000, 2, 2335.



Documents

Numerical Calculations of Spray Roasting Reactors of the Steel Industry with Special Emphasis on Fe2O3-Particle Formation