modelling and optimization of a rotary kiln direct ... · modelling and optimization of a rotary...

IntroductionRotary kilns are used for a range of mineralprocessing operations. Kilns range in size from2–6 m in diameter and can be 50–225 m longwith an operating mass of up to 3000 t. Two ofthe most common applications are cementproduction and sponge iron production. Hatchuses a proprietary one-dimensional kiln modelto evaluate designs for clients (Haywood et al.,2009). This tool has been utilized for a varietyof pyrometallurgical applications includingferrovanadium, nickel carbonate, nickellaterite, iron ore reduction, and spodumene(lithium) production. In this paper the directreduction of iron ore to sponge iron is used asan example.

The model incorporates a large number ofvariables covering, amongst others: feedproperties and rates, combustion options, kilnoperating information (speed and fill level),blower locations and flow rates, and theenvironmental conditions. Owing to the highlevel of detail included in the model, a largenumber of variables may influence the resultsand it becomes challenging to find optimaldesigns through trial and error. Numericaloptimization techniques are ideally suited toautomate the calculations and allow theanalyst to investigate a large number ofscenarios and goal functions.

The first part of the paper presents anoverview of the kiln modelling method. Thesecond part shows how the process isautomated and combined with a numericaloptimization scheme. The result is a powerfulapproach to kiln operational optimization.Illustrative examples are included for the caseof iron ore reduction in a generic rotary kiln.

Rotary kiln modelKiln modelling consists of two steps. Firstly,an Excel®-based calculation is used todetermine the kiln bed profile and residencetime based on specific operating conditionsand the kiln configuration. This is followed bya calculation of the kiln operating character-istics with a FORTRAN program based on aone-dimensional model of the kiln’s mass andenergy transfer.

The FORTRAN model provides informationon the solids and gas temperature evolutionalong the kiln, as well as a prediction of thereduction profile and off-gas composition. Thebed profile and residence time from the Excelcalculation form part of the input required bythe FORTRAN program. The program allowscomparison of results for a variety of geometricand operating conditions, including bedprofiles, mass flow through the kiln, residencetime, air profiles, ore and coal composition,and others parameters (a total of 108 inputvariables were defined for the example in thispaper).

In the case of a generic iron ore reductionkiln (Figure 1), Table I provides an overviewof the parameters (and ranges) that areconsidered.

Modelling and optimization of a rotarykiln direct reduction processby H.P. Kritzinger* and T.C. Kingsley*

SynopsisRotary kilns are used for a variety of mineral processing operations. Hatchmakes use of a kiln model developed from first principles to evaluatedesigns for its clients. This tool has been applied to a variety of pyrometal-lurgical applications, including ferrovanadium, nickel carbonate, nickellaterite, iron ore reduction, and spodumene (lithium) production.

This paper illustrates the application of numerical optimizationtechniques in combination with the kiln model in the interrogation of ageneric iron ore reduction process. The fundamental modelling conceptsare explained, followed by a description of the optimization approach. Theresults show how the combination of the two methods, with moderncomputing power, can generate a large number of viable design andoperating candidates.

Keywordsdirect reduction, DR process, rotary kiln, modelling, numericaloptimization.

* Hatch Goba, South Africa.© The Southern African Institute of Mining and

Metallurgy, 2015. ISSN 2225-6253. This paperwas first presented at the, PyrometallurgicalModelling Principles and Practices, 4–5 August2014, Emperors Palace Hotel Casino ConventionResort, Johannesburg.

419The Journal of The Southern African Institute of Mining and Metallurgy VOLUME 115 MAY 2015 ▲

Modelling and optimization of a rotary kiln direct reduction process

Kiln residence time and fill levelKiln residence time and fill level affect the progress ofchemical reactions, as well as the maximum throughput for arotary kiln. This is determined by (i) the maximum flow rateof the proposed burden through a kiln, and (ii) the residencetime at temperatures that would allow sufficient reduction totake place.

A calculation method was developed that allows for theprediction of the bed profile and residence time in a rotarykiln. The method is based on the principle of granularmovement in a kiln as described by Saeman (1951) and Scottet al. (2008). It assumes the kiln is operating in the rollingregime, the active layer has zero thickness, and the bed islocally flat. The experimental results provided by Scott et al.(2008) were used to validate the calculation method fordifferent kiln and dam configurations. Figure 2 shows anexample of the correlation between the model results andexperimental data.

The method allows for the treatment of a number ofgeometrical parameters related to the kiln, including:

➤ Variations in kiln length, diameter, inclination, androtation speed

➤ Straight or conical inlet and outlet configurations➤ Stepped sections in the shell➤ Conical or cylindrical-shaped dams inside the shell.

The limitations of the model include:➤ No provision for density changes or material loss along

the kiln length➤ Lifters or chain sections cannot be considered➤ The effects of gas velocity are neglected➤ Transient effects in the bed are neglected.

The kiln under investigation does not have lifters or achain section. Based on the good correspondence with experi-mental data, the other limitations in the model were not

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420 MAY 2015 VOLUME 115 The Journal of The Southern African Institute of Mining and Metallurgy

Figure 1 – Schematic of a rotary kiln

Table I

Model inputs used in the evaluation of the kiln performanceDesign parameters Values

Kiln internal diameter 4.34 mKiln length 80 mKiln inclination 1.5°Solids angle of repose 31°

Operating parameters RangeKiln rotational speed 0.25–0.39 r/minBed residence time 6–10 hC/Fe ratio (based on reducible Fe) 0.5 –0.73Combined feed flow rate: cold feed 48.8–54.0 t/hCombined feed flow rate: hot feed 60.6 t/hCombined feed density range 1895–2100 kg/m3

Exit dam height 0.7–1.0 mOff-gas temperatures 640–1210°C

Figure 2 – Comparison of fill level calculation to experimental data

deemed to be critical for calculating bed profiles in the currentinvestigation. Should greater accuracy be required, a discreteelement method simulation of the bed flow would berecommended.

One-dimensional kiln modelThe kiln model applied in this work was developed by Hatchover a number of years and has been used for several rotarykiln projects. It has its roots in a FORTRAN program that wasdeveloped by Venkateswaran (1978) to study the reductionof iron ore. The original software was used to model theoperation of a 35 m pilot kiln at the Stellco company inCanada. A number of enhancements to the originalVenkateswaran code have been added to increase thereliability and fidelity of the model. Examples of theseenhancements include, but are not limited to:

➤ Incorporation of a bed level profile calculation along thelength of the kiln

➤ Improved radiation modelling to account for viewfactors and gas participation at each axial node

➤ Extensive development of a comprehensive materialdatabase

➤ Inclusion of several additional chemical reactionschemes and kinetics (including ferrovanadium, nickelcarbonate, nickel laterite, and spodumene)

➤ Code optimization to improve solution time by takingadvantage of advances in modern compilers.

The kiln model is a one-dimensional finite-volumerepresentation of the governing equations for mass andenergy conservation, which are approximated by integrationover discrete control volumes along the kiln length (i.e. axialslices). The solution of these discrete equations provides thelocal gas and solids temperatures and mass fluxes at eachaxial location along the kiln length.

In the bed phase the reactions may include the removal ofmoisture (free and bound) from the feed material, calcinationof dolomite, as well as the Boudouard and Fe reductionreactions. The moisture removal from the bed is modelledwith Arrhenius rate equations which describe the progress ofthe free and fixed moisture removal. The rate constants formoisture removal have been validated in earlier projects andwere not modified for the presented calculations.

Where dolomite is included in the feed, it is assumed toconsist of CaCO3 only. Calcination occurs according to thereaction:

CaCO3(s) → CaO(s) + CO2(g)The reaction rate is effected through the use of an

Arrhenius rate equation with constants as per previousapplications of the model.

The Boudouard reaction is included as:C(s) + CO2(g) →2CO(g)The reduction reaction is modelled with a single step from

haematite to metallic iron:Fe2O3 + 3CO → 2Fe + 3CO2The rates of the Boudouard and reduction reactions are

prescribed by appropriate rate terms and determine theevolution of species concentrations and energy along the kiln.

The energy required for material heating, endothermicreactions, and heat losses is provided by the combustion ofcoal volatiles and char, combustion of CO gas from theBoudouard reaction, as well as a portion of the lance coal

injected with ambient air at the discharge end of the kiln. Thekiln model solves a comprehensive set of reaction equationsusing a Gibbs free energy minimization technique at theprevailing gas-phase temperature that yields realisticspeciation of the reaction products. The effect of localconditions within the kiln, where thermal effects andchemical reactions in the bed may produce different speciesin the gas phase, is included in the model.

Application of optimizationThe multivariable nature of a kiln operation can make itsomewhat difficult for the analyst to find optimalcombinations of operational or design variables through trialand error. Solution trends can be nonlinear and variablescoupled in their influence on the solution. This calls for amore rigorous exploration of the design space through designof experiments and associated numerical techniques. Due tothe need for the evaluation of a large number of designpoints, these techniques are well suited for use incombination with the one-dimensional kiln code, due to itsrelatively short solution time. LS-Opt software (LSTC) is usedto coordinate the numerical optimization techniques and theautomation of the solution evaluation.

One simple example of the use of this technique is thedetermination of the optimal distribution of secondary airintroduced along the length of the kiln. The objective is toachieve a high level of metallization while respecting upperlimits on the solids bed temperature. The aim of the designexploration is to find a secondary air distribution thatachieves these objectives while keeping the off-gas volumesand temperatures low.

The optimization function formulated here is described asfollows:The objective:

Minimize {f(x)}, the combined blow flow rateConsidering the variables:

Blower rate on each of the 8 blowers, [x1;x8]Coal feed rate, [x9]

Subject to inequality constraints:Max. bed temperature < 1250ºC, {g1(x)}Max. outlet gas temperature < 850ºC, {g2(x)}Metallization > 95%, {g3(x)}Outlet char > 10%w, {g4(x)}

and side constraints:Blower rate on each of the 8 blowers: 1000 < x1;8 <7500 Nm3/h, {g5(x)}Coal feed rate: 5 < x9 < 13 t/h, {g6 (x)}

Results

Kiln model simulationThe base case operation of the kiln was established byrunning the model with the design values for all operatingparameters. The temperatures distributions in the bed,freeboard (gas), inner wall, and outer shell are shown inFigure 3 along the length of the kiln.

The feed material (bed) enters the kiln at ambienttemperature and rapidly heats up due to the hot gas in thefreeboard. At about 10 m into the kiln the volatiles arereleased from the coal, resulting in a local temperature spike


421The Journal of The Southern African Institute of Mining and Metallurgy VOLUME 115 MAY 2015 ▲


due to combustion of the volatiles in the freeboard. At thedischarge end (80 m) the air injected into the kiln is rapidlyheated by the burner. Despite the high freeboard temper-atures, the shell temperature remains at about 200°C due tothe refractory lining on the inside of the kiln.

The progress of mass transfer along the kiln length ispresented in Figure 4. The metallization curve shows the startof metallization at around 20 m into the kiln, where the ore isreaching the required reduction temperatures. The exit valueis 94% of the available Fe in the model (the model considersonly 67% of the total Fe in the feed to take part in thereduction). In terms of the total Fe content in the feed, thisrepresents a conversion of 63% Fe.

The curve representing the percentage bed carbon tracksthe mass of the carbon in the bed in relation to the carbonadded to the kiln feed inlet. The consumption of carbon bythe Boudouard reaction follows the reduction reactionprogress. It is clear that in the present case the bed is notdepleted of carbon when the material reaches the kilndischarge.

Volatiles release occurs rapidly from about 8 m into thekiln and is substantially completed at around the 25 m mark.

The gas composition in the freeboard is shown with gaspartial pressure in Figure 5. The nitrogen partial pressure isplotted on the secondary y-axis and the rest of thecomponents use the primary y-axis. The N2 and CO2 levelsthrough the kiln are appreciably higher than othercomponents.

OptimizationConsidering the costs for a single experiment on a rotary kiln,minimizing the number of physical experiments is always anaim. Through formal design of experiments, this number iskept as low as possible and the most informative combinationof the factors is chosen. In this example, five sequentialdesign domains are considered, with sequential domainreduction. The space-filling point selection requires 83 designpoints per successive design space evaluation. The fullyautomated execution and evaluation of the 416 (83*5 + 1)design points is performed on a 12-core workstation within70 minutes. Quadratic surrogate models are created for eachset of results and provide a means to evaluate sensitivities

and identify good candidate designs. A surrogate model, ormetamodel (Gasevic et al., 2007), is a mathematical modelthat describes the behaviour of a system with respect to itsvariables. In the context of this paper, a quadratic metamodelis trained from the results of the individual analysesperformed. This can be considered in much the same way asa quadratic trendline is fitted through data-points in aspreadsheet. Intuitively, the greater the number of analysesperformed, the greater the confidence one has in the qualityof the fit of the metamodel.

An illustration of this successive domain reduction(Stander et al., 2002) is shown in Figure 6, providing theresults for the relationship between combined blower flowrate, outlet gas temperature, and maximum bed temperature.In the context of the confidence in the area of interest, thedomain reduction ensures that sets of subsequent analysesare concentrated closer to the good candidate designs.

Results can be combined and good candidate designsshown within the complete cloud of results. Figure 7 providespoint cloud plots for metallization with respect to combinedblower flow, outlet gas temperature, and maximum bedtemperature. The best candidate designs are highlighted toshow their position in the cloud of results.

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Figure 3 – Kiln temperature distribution for the base case

Figure 5 – Gas partial pressure (N2 on secondary axis) along the kiln

Figure 4 – Volatiles content, bed carbon and metallization along the kilnfor the base case


The Journal of The Southern African Institute of Mining and Metallurgy VOLUME 115 MAY 2015 423 ▲

Figure 7 – 2D results sets for metallization showing good candidate designs

Figure 6 – 3D results plot showing successive domain reduction around the area of the good design candidates


Figure 8 shows key performance indicators of the bestcandidate designs relative to the base case design. Thepercentage improvement is shown in parentheses. Based onthe spread of results, a preferred design can be selected as atrade-off between the best candidates. The base case designwas based on a blower flow distribution applied from goodkiln rules-of-thumb practice. Without the use of numericaloptimization, this design is likely to have been the chosenoperating condition imposed on the kiln. From the results,case 5.27 provides improvement of all key indicators with asignificant drop in overall gas volume, exit gas temperature,and maximum bed temperature.

ConclusionsThe direct reduction one-dimensional kiln model can bemodified to accommodate any direct reduction process (notjust iron ore), but will require physical test work and baselinecalibration. This is usually part of the process for largeprojects, but was omitted here for brevity. The model allowsevaluation of a comprehensive set of factors that mayinfluence the kiln performance.

A certain class of problem lends itself to formal design ofexperiments and subsequent numerical optimization as anelegant means of design optimization. This paper illustrateshow the one-dimensional kiln model can be coupled to theappropriate numerical tools to yield a powerful tool for kilndesign and optimization. A significant number of designvariables and design objectives (not an intuitive combinationof input variables) can be evaluated in an automated fashion.

Key components of the success of the optimization are theaccuracy of the kiln model and sensible interpretation of themodel outputs. At Hatch the first component is addressed by

working in close collaboration with clients during the modelcalibration phases to ensure model outputs are consistentwith real experience. The second component is covered byensuring that people with actual operating experience on therelevant equipment are included in the design team for theduration of the project.

References

Gasevic, D., Kaviani, N., and Hatala, M. 2007. On metamodelling inmegamodels. MoDELS’07. Proceedings of the 10th InternationalConference on Model Driven Engineering Languages and Systems.Springer-Verlag, Berlin. pp. 91–105.

Haywood, R., Taylor, W., Plikas, N., and Warnica, D. 2009. Enhanced problemsolving; the integration of CFD and other engineering applications. 7thInternational Conference on CFD in the Minerals and Process Industries,CSIRO, Melbourne, Australia, 9-11 December 2009.

Livermore Software Technology Corporation (LSTC). LS-OPT user manual.http://ftp.lstc.com/anonymous/outgoing/trent001/manuals/lsopt/lsopt_50_manual.pdf

Saeman, W.C. 1951. Passage of solids through rotary kilns. ChemicalEngineering Progress, vol. 47. pp. 508-514.

Scott, D.M., Davidson, J.F., Lim, S.-Y., and Spurling, R.J. 2008. Flow ofgranular material through an inclined, rotating cylinder fitted with a dam.Powder Technology, vol. 182. pp. 466-473.

Stander, N. and Craig, K. 2002. On the robustness of a simple domainreduction scheme for simulation-based optimization. EngineeringComputations, vol. 19, no. 4. pp. 431-50.

Venkateswaran, V. 1976. Mathematical model of the SL/RN direct reductionprocess. MSc thesis, Department of Metallurgy, University of BritishColumbia. ◆

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Figure 8 – Results for best candidate designs

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