modeling of rotary kilns and application to limestone calcination

Modeling of Rotary Kilnsand Application to Limestone Calcination

Uwe Küssel1 Dirk Abel1 Matthias Schumacher2 Martin Weng2

1RWTH Aachen University, Institute of Automatic ControlSteinbachstraße 54A, D-52074 Aachen

2Aixprocess, Process and Fluid EngineeringAlfonsstrasse 44, D-52070 Aachen

Abstract

This paper presents the one dimensional modeling ofrotary kilns used for energy intensive production pro-cesses. Raw material is fed into an inclined rotatingkiln and heated by counter current gas flow. Chemicalreactions take place in the bed of raw material as wellas in the gas phase. Heat and mass transfer betweenthe bed and the gas phase are implemented. Also theheat transfer to the environment is taken into account.As a benchmark, the process of limestone calcinationis chosen. Results are compared with computationalfluid dynamic simulations.

Keywords: CaCO3, calcination, CFD comparison,kilns, limestone, rotary kilns, simulation

1 Introduction

Unhydrated lime is used as a raw material for manyproducts in chemical industry. The limestone calci-nation, as an energy intensive production process forunhydrated lime, is often performed in continuouslyoperating rotary kilns. Until today, the process is man-ually operated and despite existing approaches the useof automatic control is very uncommon. Due to the hotand dusty atmosphere inside the drum, thermodynamicstates used as controlled variables by an expert systemare hardly measurable in a reliable way. In heat drivenchemical production processes such as limestone pro-duction measured data like a temperature as one ther-modynamic variable of the process (often most easilyto measure) is not sufficient to estimate the chemicalrate of degradation of CaCO3. To overcome this prob-lem dynamic physical and chemical models can be ap-plied to predict the behavior of dependent measures.By comparing the results of the modeling to currentplant measurements the states of independent variables

become available to close the control loop. To be ap-plicable to an expert system, the very complex modelof the process has to be capable of real-time operationanyway and thus, several assumptions and simplifica-tions have to be done.

As a first step to the automatic control of continu-ously operating rotary kilns, a detailed model of thisprocess is developed. The model abstracts from re-ality by assuming one dimensional (1-D) counter cur-rent flow of the raw material phase (bed phase) and thegas phase. The bed and gas phase are surrounded bya combination of isolating refractory and steel shells.Two reactions are implemented, one for the productionof heat and one for the calcination itself. Methane isoxidized in the gas phase in order to supply the neces-sary energy to the process and limestone is calcinatedin the bed phase consuming energy due to an endother-mic degradation process. Heat and mass transfer takeplace between the counter current flows and the envi-ronment. The paper is structured as follows: In chapter2 the abstraction to 1-D counter current flow is shown.Additionally, the mechanisms of reactions and heattransfer are described. In chapter 3 the computationalresults with Dymola are analyzed in detail. For vali-dation, the results are compared to computational fluiddynamics (CFD) simulations in chapter 4. Chapter 5concludes the paper with an outlook of future investi-gation.

2 Modeling of rotary kilns

The rotary kiln is modeled using a 1-D approach. Theflows of gas and bed phase are counter current. Therotary kiln itself consists of an isolation and a steelshell. This abstraction is depicted in Figure 1.

Proceedings 7th Modelica Conference, Como, Italy, Sep. 20-22, 2009

© The Modelica Association, 2009 814 DOI: 10.3384/ecp09430084

Figure 1: Rotary kiln with 1-D balance element

2.1 Modeling of the gas phase

The gas phase model is based on the DynamicPipemodel of the Modelica fluid library [1]. It is extendedby dynamically changing cross sectional areas due tobed heights. Replaceable models of radiative and con-vectional heat transfer are integrated and will be dis-cussed in section 2.6. In addition, the gas phase isequipped with a replaceable chemical reaction modelin order to cover the oxidation of mixed gaseous hy-drocarbons (i.e. in this case Methane only), details arecovered in section 2.5.

The balancing equations with a dynamic momen-tum balance are formulated in [2]. Using a finite vol-ume approximation and setting the momentum bal-ance to be static, the equations (1)-(3), correspondingto a single slice used in the DynamicPipe model, arederived. To avoid obscurity, additional equations cov-ering multi-component media are not given in this for-mulation.

dmi

dt= mi+ 1

2+ mi− 1

2+ ⋅ ⋅ ⋅ (1)

0 =m2

i+ 12

Ai+ 12

pi+ 12

−m2

i− 12

Ai− 12

pi− 12

(2)

+Ai

(pi+ 1

2− pi− 1

2

)−FFFV −Aiρigδ z

dUi

dt= Hi+ 1

2+ Hi− 1

2(3)

+viAi

(pi− 1

2− pi+ 1

2

)+ ⋅ ⋅ ⋅

for slice i = 1, . . . ,n

Source terms for heat, namely radiational and con-vectional contributions, are added to the right handside (RHS) of the energy balance in equation (3). Masstransfer between bed and gas phase due to degradationof CaCO3 (releases CO2) and changes in the compo-sition of the gas phase due to the oxidation of gaseous

hydrocarbons are added to the RHS of the mass bal-ance in equation (1). Including the heat of formationof all components implicitly adds the contribution ofchemical reactions to the energy balance while onlyconsidering mass balance changes. For the longitudi-nal gas flow and the heat transfer standard connectorsare used. For the gaseous exchange between gas andbed signal oriented connectors for each direction aredesigned using the same exchange medium (O2, CO,CO2, H2O).

All cross sectional areas, and hence correspondingvolumes, in these equations are dynamically changeddue to changes in bed height. Therefore, the informa-tion of the bed’s cross sectional area is transmitted viainput output relation to the gas phase. Finally, dataon gas phase properties are provided for other compo-nents by an output connector.

2.2 Modeling of the bed phase

The bed phase is modeled by mass and energy bal-ances.

dmi

dt= mi+ 1

2+ mi− 1

2+ ⋅ ⋅ ⋅ (4)

with mi+ 12= ρiVi+ 1

2

dUi

dt= Hi+ 1

2+ Hi− 1

2+ ⋅ ⋅ ⋅ (5)

Heat and mass transfer is included similarly to gasphase modelling via source terms to the RHS of thebalance equations. The transport of material throughthe rotary kiln is specified by equation (6), which iscommonly known as Kramers equation [5].

Vi+ 12=

43

πωR3(

tanα

sinβ− dhi

dxcotβ

)(2

hi

R− h2

i

R2

) 32

(6)The volume flow rate is a function of the rotation

frequency ω , the inner radius of the pipe R, the inclina-tion of the kiln α , the materials angle of repose β , theheight of material h and the corresponding gradient dh

dx .This differential equation in terms of the height is sim-plified by rearranging and approximating the heightand the corresponding gradient with the equations (7)to (9).

hi = R− (Rcos(ϕi/2)) (7)dhi

dx= (R/2)sin(ϕi/2)

dϕi

dx(8)

dϕi

dx≈ (ϕi+1−ϕi)/(L/n) (9)


© The Modelica Association, 2009 815

The mid point angle of the bed phase is denoted byϕ , the length of the rotary kiln by L and n is the numberof slices in the rotary kiln. All geometric details forgas and bed phase are calculated using the mid pointangle. The calculation of ϕi = f (Ai) is presented insection 2.4.

2.3 Modeling of the shells

The isolation and steel shells are modeled by an en-ergy balance for the corresponding material volumeresulting from the 1-D balancing elements. Heat trans-fer, and hence the temperature profile, is realized usingFourier’s relation for heat conduction in solid material.In principle, the shells are structured as grids consist-ing of heat capacitors and thermal conductors likewisemodeled in the modelica standard package. Heat trans-fer is possible in two directions, namely longitudinallyand transversely to the flow direction in the rotary kiln.Geometric and material properties are parameters ofthe model. Standard heat connectors are used.

2.4 Mid point angle approximation

All geometric properties for gas and bed phase caneasily be calculated using the mid point angle ϕ of thebed phase. Nevertheless, the angle has to be calculatedfrom the cross sectional area of the bed phase, whichis a direct result of the mass balance in every bed sliceof the rotary kiln. This is shown in equation (10).

Ai = (mi/ρi)/(L/n) (10)

The relation between the cross sectional area Ai ofa single slice and the mid point angle ϕi is implicitlygiven with the equations (11)-(12).

0 = −P+(ϕi− sinϕi) (11)

P = 2Ai/R2 (12)

In order to avoid additional nonlinear equations, therelationship given with equation (11) is numericallysolved for ϕ in a range of P between 1.25 ⋅ 10−5 and2π . The corresponding pairs are then used for a leastsquare fit in order to find a good approximation forϕ = f (P). The function ϕ = f (P) is given with equa-tion (13).

ϕ = a0 log(P)+a1 (1/P)+a2P12

+a3P+a4P2 +a5P3 +a6P4 (13)

+a7P5 +a8P6 +a9

The error between the approximation and originaldata pairs is given in Figure 2.

Figure 2: Approximation error for ϕ = f (P)

The adapted relationship ϕ = f (P) is implementedas a function and integrated in both the gas and bedphase in order to calculate the mid point angle andsubsequently all geometric characteristics of the rotarykiln.

2.5 Mechanism of chemical reactions

The replaceable chemical reaction model is designedas a reactant limited elementary reaction using an Ar-rhenius type approach for the reaction kinetics. Thereaction kinetics approach is shown with the equation(14).

k = B ⋅T n ⋅ e−EaR⋅T (14)

The preexponential coefficient B, the activation en-ergy Ea and n are free parameters which will be usedto fit the model to CFD simulation data. Generallyspeaking, this fit is necessary since, on the one hand,no reliable chemical reaction data is available for sucha set up of coupled ideal reactors and, on the otherhand, the model is not able to cope with local condi-tions due to low resolution and the lack of adequatemodels. For example, the oxidation of mixed gaseoushydrocarbons (i.e. in this case CH4 only) is mass trans-fer limited and therefore, an ideal mixed reactor needsto be adapted using the averaged chemical reaction ki-netics.

The rate of degradation (massflow) for each com-ponent is calculated using the relationship given withequation (15).



m j = kV λ jM j

k=1

∑l

Cλkk (15)

In this relationship, the velocity of reaction k is cou-pled with the volume of the reaction element V , themolar mass M and the stoichiometric cofficient λ foreach component (index j over all components). Theapproach is reactant limited assuming an elementaryreaction order. Hence, the molar density C to thepower of the stoichiometric coefficient λ sums up overall reactants k of a reaction.

For the bed phase, the degradation of CaCO3 is im-plemented. The chemical reaction is given with equa-tion (16).

CaCO3 =⇒CaO+CO2 (16)

Energy is chemically provided by the combustion ofCH4, equation (17) holds.

CH4 +2O2 =⇒CO2 +2H2O (17)

In principle, various reactions are possible, as longas the defined medium covers all components and thestoichiometric coefficients are defined.

2.6 Mechanisms of heat transfer

For the heat transfer between the gas and bed phaseas well as the isolation shell convectional and radia-tional mechanisms are implemented. For convectionalheat transfer between the gas and its corresponding ex-change partner, the heat transfer coefficient α is de-pendent on the Reynolds number Re, the Prandtl num-ber Pr and the Nusselt number Nu. The general con-vectional heat transfer equation in terms of α is shownwith equation (18).

Qconv 1↔2 = α12A12 (T1−T2) (18)

Various heat transfer models for the gas phase solidinteraction are implemented in the Modelica fluidlibrary [1]. Additionally, two relationships for Nusseltnumbers are given in [10]. The equations are shownwith (19) and (20).

Nu =ξ/8(Re−1000)Pr

1+12.7√

ξ/8(Pr2/3

) [1+(

Dh

L

) 23](19)

ξ = (1.82 ⋅ log10(Re)−1.64)−2 (20)

2300 < Re < 106, Dh/L < 1

Within small deviations in the range of Pr,0.5 < Pr < 1.5, the simplified equation (21) can beused.

Nu = 0.0214(Re0.8−100

)Pr0.4

[1+(

Dh

L

) 23](21)

All the models calculate α in a similar range from8−10 W/m2K.

Convectional heat transfer between the bed phaseand the isolation is also realized with the heat trans-fer coefficient α and equation (18). α is calculatedfrom various process parameters using two differentapproaches which are described in detail in [8]. Typi-cal values are said to be 50≤ α ≤ 200 W/m2K

Also, models with constant α are possible tochoose. The heat transfer models are designed to bereplaceable in order to enable the choice between dif-ferent heat transfer mechanisms as described above.

Radiation between the bed, the gas and the isolationis modeled using equation (22).

Qrad 1↔2 = ε12A12σ(T 4

1 −T 42)

(22)

The referenced area for radiational heat transfer be-tween transfer object 1 and 2 is given with A12. Theemissivity coefficient ε12 relates the visibilty betweenarea A12 and A21 and the emissivity of correspondingobjects. There are three emissivity coefficients to becalculated, namely wall→ bed (wb), wall→ gas (wg)and bed → gas (bg). The formulas for calculatingthese coefficients are given with equation (23) to (26).

εwb =εwεb (1− εg)

U(23)

εwg =εwεg (1+Φ(1− εg)(1− εb))

U(24)

εbg =εbεg (1+Φ(1− εg)(1− εw))

U(25)

U = 1− (1− εg)(1− εw)

(1−Φ(1− (1− εb)(1− εg))) (26)

The variable Φ is defined as the ratio between thefree bed area (surface) and the free isolation area. De-tails about the derivation can be found in [4]. Thevalues of emissivity are almost constant over length xand temperature T with εwb = 0.184, εwg = 0.695 andεbg = 0.615.



3 Computational results

The model is designed and numerically integratedwithin the Dymola modeling environment. The set upis depicted in the Figure 3.

Figure 3: Dymola model of a rotary kiln

The black and the grey objects denote the steel andisolation shell, respectively, with different geometricand material parameters. Inside the pipe, there iscounter current flow of the gas phase (blue element)and the bed phase (limestone material, grey element).Different mechansims for heat and mass transfer aswell as chemical reactions are chosen as describedearlier in this paper. Further components, e.g. crustof semi liquefied limestone, can be added but are notmodeled in this contribution.

The calcination process (degradation of CaCO3) isshown in Figure 4.

The system is initialized at 273.15 K and atmo-spheric pressure (time [s]: 0-3000). In a next step, thesystem is brought to the operating point by increasingtemperature of the incoming mass flows of the bed andthe gas phase (time [s]: 3000-13000). This procedureis followed by the intial increase of the combustiongas massflow (time [s]: 13000-250000, massflow step[kg/s]: 0.1-1.2692). It is clear to see that the rate ofCaCO3 degradation intensifies as the temperature in-creases. A second step to the combustion gas massflowis applied after 300000 seconds (massflow step [kg/s]:1.2692-2.5392). Again, the degradation of CaCO3 in-creases. The increase of degradation, while applyingthese steps to the combustion gas flow, is due to the

Figure 4: Degradation of CaCO3 through calcination

increase of temperature and the endothermic characterof the calcination reaction. The increase of tempera-ture for the main components of the rotary kiln (steel,isolation, gas and bed phase) is depicted in Figure 5

Figure 5: Temperature of steel, isolation, bed and gasphase

While the gas phase (red) responds extremely fastto the step in combustion gas massflow, the bed phase(yellow) is slower. The isolation (turquoise) and steel(blue) shell are even slower in their step response. Thedifferent time constants of the process can be recog-nized by an exemplary inspection of Figure 6 to 7.

It is easy to observe the small time constant of thegas response lying in the range of 10-200 seconds.

For the isolation shell, the time constant of reponselies in the range of 20000-30000 seconds. This ex-plains the stiffness of the system and the necessity ofstiff numerical solvers for simulations. Furthermore,these time constants correspond to the known timeconstants from process industry, which implies that



Figure 6: Temperature response of gas phase due tocombustion gas step

Figure 7: Temperature response of isolation due tocombustion gas step

the dynamical behaviour of the model reliably rep-resents the calcination process. Although the steadystate values of the operating point also correspond tothe known values from process industry, this modelingapproach is justified even more by comparing its val-ues to CFD simulation results in the following chapter.

4 Comparison to CFD simulations

Computational fluid dynamics (CFD) is a widely ac-cepted tool for the detailed description of gaseouscombustion phenomena occurring within a rotary kiln[6],[3]. Unfortunately, it does neither allow for themodeling of transport of the solid bed nor for the theo-retical description of the chemical reactions therein. Inthe current work, different sub-models have been inte-grated in the commercial CFD code Fluent in order tomodel the dynamics of the granular flow of the lime-

stone particles and the coupling of gas and solid phase.Since this work mainly focuses on the 1-D model ofthe limestone calcination process, only a short sum-mary of the models used in the CFD simulations willbe given here.

4.1 Introduction of the CFD rotary kilnmodel

The three dimensional computational domain of thefreeboard in the kiln is bounded by the refractory andthe surface of the solid bed. The methane burner ex-tends into the kiln on one end of the drum (Figure 8).

Figure 8: 3-D computational domain of the limestonerotary kiln

Steady state conservation equations of the com-pressible gas flow are solved considering the realiz-able k-ε-model for turbulent effects in the gas phase.Transport of four separate species (O2, CH4, CO2 andH2O) is calculated explicitly in the gas phase, whilethe fifth one (N2) sums to unity. Combustion ratesof methane oxidization are assumed to be limited bythe mixing of turbulent eddies and thus, the eddy-dissipation model is used to predict reaction rates ofthe volumetric reactions in the gas phase. Energytransport phenomena include conduction, convectionand radiation (P-1 model), while the latter plays themajor role in rotary kiln processes. Absorption of thegas mixture is mainly affected by the product con-stituents of the gas (CO2 and H2O). Therefore thewsggm-cell-based model is applied to calculate the lo-cal absorption coefficient of the gas mixture. A sig-nificant amount of energy discharges into the environ-ment. Conduction driven heat transfer through the re-fractory is being calculated explicitly by applying acomputational grid to this region also. On the outer



surface of the kiln two heat transfer mechanisms areconsidered: convection and radiation.

Thermal coupling between gas and solid phase is re-alized by setting a temperature profile on the bed sur-face. For this purpose mass, species and energy con-servation equations within the particulate solid bed aresolved by implementing a mathematical submodel forthe solid bed. Since it has recently been proven, thataxial mixing can be neglected in industrial rotary kilnprocesses, transport of the solid bed can be simplifiedby assuming a plug flow [9]. Additionally the bed isassumed to be well mixed locally in any given crosssection.

Limestone calcination can be modeled as a shrink-ing core process with surface reaction control accord-ing to equation (27) [7].

dmCaCO3

dt=−k0 exp

(− EA

RTp

)⋅4π r2

p Np MCaCO3

(27)Herein rp and Np represent the mean particle ra-

dius and the total number of limestone particles, re-spectively. CO2 released by the calcination reaction isassumed to be transported instantaneously to the hotflow by neglecting any transport resistance in the solidbed. It is released in the computational space of thehot gas flow by adding mass and species sources in thecells adjacent to the bed surface.

In Figure 9 the contour plot of the local gas tem-perature on the center plane is shown as an exemplaryresult of the CFD simulations.

Figure 9: Contour plot of the local gas temperature onthe center plane in [K]

In order to justify the 1-D abstraction of the processmodeled within the Dymola environment, the compu-tational results are compared to the highly resolute re-sults of the CFD simulations. For this purpose, volumebased average values ΘV, j of the CFD simulation dataare calculated for a discrete number of slices in the gasphase. Due to the strongly anisotropic flow field in thevicinity of the burner mass and velocity weighted av-erage has to be applied for the potential variables. Thisis shown in equation (28).

ΘV, j =∑Ncells

Θi ρi Ai vi,ax

∑Ncellsρi Ai vi,ax

(28)

In equation (28), Vi as the volume of each singlecell inside the discrete slice and vi,ax as the local axialvelocity of the gas mixture are used to calculate thevolume based average of slice j for each scalar Θ.

Since plug flow has been assumed in the clinker bed,equation (28) can be simplified to the volume weightedaverage for all potential variables in the solid phase asgiven in equation (29).

ΘsV, j =

∑NcellsΘiVi

∑NcellsVi

(29)

In contrast, flow variables such as reaction ratesneed to be integrated within each single control vol-ume in the gas and in the solid domain, respectively.For these data equation (30) is valid.

ΘV, j = ∑Ncells

Θi (30)

4.2 Comparison

Geometrical parameters and boundary conditions arechosen to be equal in both simulation environments.In addition, the free chemical reaction parameters(B,n,Ea) for adapting the model are fitted to CFD sim-ulation data by applying a least square fit using equa-tion (15). Therefore, the CFD simulation data are con-centrated in larger 1-D cells by applying the above de-scribed weighting functions. After model adaption vialeast square fit, a Dymola simulation to steady state isperformed. The simulated data from the Dymola simu-lation environment are then compared to the weighted,concentrated CFD simulation data. The essential val-ues of the process are compared. This includes tem-perature profile of gas and bed phase, molar densitiesof O2 and CH4 in the gas phase as well as molar den-sity of CaCO3 in the bed phase (controlled variable forfuture model predictive control).

Figure 10 shows the temperature profiles of the gasphase for Dymola and CFD simulation.

In the next figure (Figure 11), the consumption ofO2 and CH4 is depicted.

The figures show a similar behaviour of the gasphase in both simulation environments. For the errore holds e < 2%. On first inspection, this seems to bea good result. Nevertheless, the more relevant data forintended controlling of the rotary kiln process is thetemperature and the concentration of components in



Figure 10: Comparison of gas phase temperature

Figure 11: Comparison of gas phase molar density ofO2 and CH4

the bed phase. Figure 12 shows the temperature of thebed phase.

Despite the different scaling of the graph, for the er-ror e holds e < 3%. The next figure (Figure 13) showsthe degradation of CaCO3 in the bed phase using themolar density as depicted variable. The maximum er-ror for the molar density of CaCO3 is e = 6.6%. Al-though this value is slightly higher than the previouserrors, the 1-D modeling approach is successfully ap-plied. Various alternative values of the process werecompared, yielding to the same outcome. The mainadvantage of the 1-D modeling approach is the pos-siblity of faster simulations while deviations are keptsmall enough in the scope of robustness in terms of ob-server based model predictive control. While the simu-lation until convergence in the CFD environment takesup to several days, the simulation of the Dymola modeltakes seconds to minutes depending on the change ofinput variables. Another enormous advantage of the 1-

Figure 12: Comparison of bed phase temperature

Figure 13: Comparison of bed phase molar density ofCaCO3

D modeling approach is the use of the 1st principles forphysical abstraction. Since the identified data basedmodels are only valid in the range of measured data,the nonlinear 1-D model of the rotary kiln will have awider range of validation. Furthermore, the simulateddata sets are always open to physical interpretation andhence, are easier to check for plausibility.

5 Outlook

In a first step, the complex counter current flow pro-cess of rotary kilns is modeled and applied to the lime-stone degradation. First results show reasonable be-haviour of the process physics. The comparison toCFD simulation data confirms these results. The es-sential process parameters are compared and the errorsare small enough to allow for application in observerbased model predictive control application. In addi-



tion, the modeling approach has a lower computationalburden and results in linearizations which are capableof real-time application in an expert system.

For the future, details in both models will be refinedin order to get even better results. Furthermore, themodel is going to be enhanced with a particle burnerand applied to the chemically more complex cementproduction process. The task of automatic least squarefit for the free chemical parameters of the model willbe enhanced in order to cover the more complex ce-ment production process. A detailed report on bothtopics will soon be published. Alongside with the en-hanced model, linearizations of the nonlinear model indesired operating points will be derived. Using theselinearizations, an observer for immeasurable processvalues will be established. Furthermore, a model pre-dictive control will be designed in order to hold a de-sired operating point of the plant.

References

[1] F. Casella, H. Tummescheit, and M. Otter.Modelica fluid librarywww.modelica.org/libraries/modelica_fluid/releases/1.0, 2009.

[2] H. Elmqvist, H. Tummescheit, and M. Otter.Object-oriented modeling of thermo-fluid sys-tems. Modelica Association, November 2003.

[3] M. Georgallis, P. Nowak, M. Salcudean, andI.S. Gartshore. Modelling the rotary lime kiln.Canadian Journal of Chemical Engineering,83(2):212–223, 2005.

[4] R. Jeschar, R. Alt, and E. Specht. Grundlagender Wärmeübertragung. Viola-Jescher Verlag,1990.

[5] H. Kramers and P. Croockewit. The passageof granular solids through inclined rotary kilns.Chemical Engineering Science, 1(6):259–265,1952.

[6] F. Marias, H. Roustan, and A. Pichat. Modellingof a rotary kiln for the pyrolysis of aluminiumwaste. Chemical Engineering Science, 60:4609–4622, 2005.

[7] K.S. Mujumdar, K.V. Ganesh, S.B. Kulkarni,and V.V. Ranade. Rotary cement kiln simulator(rocks): Integrated modeling of pre-heater, cal-ciner, kiln and clinker cooler. Chemical Engi-neering Science, 62:2590–2607, 2007.

[8] A. Queck. Untersuchung des gas- und wand-seitigen Wärmetransportes in die Schüttung vonDrehrohröfen. PhD thesis, Otto-von-Guericke-Universität Magdeburg, 2002.

[9] R.G. Sheritt, J. Chaouki, A. Mehrotra, and L. Be-hie. Axial dispersion in the three-dimensionalmixing of particles in a rotating drum reactor.Chemical Engineering Science, 58(2):401–415,2003.

[10] VDI-Gesellschaft Verfahrenstechnik undChemieingeniuerwesen, editor. VDI-Wärmeatlas. Springer, 8th edition, 1997.

6 Acknowledgement

The authors gratefully thank the Federal Ministryof Education and Research for funding BMBF 3257MoProOpt. Furthermore, we highly appreciatethe supervision by the Project Management AgencyForschungszentrum Karlsruhe (PTKA).



modeling of rotary kilns and application to limestone calcination

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