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Computers and Chemical Engineering 31 (2007) 1484–1495

A reduced order thermo-chemical model for blastfurnace for real time simulation

Ashish Jindal, Saswati Pujari, P. Sandilya 1, Saibal Ganguly ∗Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India

Received 30 March 2005; received in revised form 4 December 2006; accepted 16 December 2006Available online 7 January 2007

bstract

Real time simulation of process variables for complex industrial processes like the blast furnace is essential and important for better functioningf process industries. This paper emphasizes a reduced order model of the blast furnace for process monitoring, control and optimization. It

escribes the assumptions, formulation and solution methods used in making the simulation model. It shows how reduced order model betters theurrently available higher order models by reducing computation time and achieving greater accuracy. The effects of certain model parametersave also been studied to show the validity of the model.

2007 Elsevier Ltd. All rights reserved.

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neipmroeid

eywords: Real time simulation; Blast furnace; Reduced order

. Introduction

A real time model of any process helps to gain better under-tanding and predictability of the process. Blast furnace is anmportant iron making process unit and is the first step towardshe production of steel. In spite of many years of research, blasturnace continues to exhibit many complexities for most processngineers, since little is known about the physics of the process.his calls for a mathematical analog of the process, which cano real time simulation, thus improving the predictability andexibility of plant operation. Real time reduced order mathe-atical analog of blast furnace for monitoring and optimization

s hardly available in literature.Development of blast furnace models of varying complexities

as been attempted by researchers in the past. One-dimensionalodels have been reported by Muchi (1967), Yagi and Muchi

1970), Omori (1987), and Torssell and Wijk (1992). Many of

hese models require knowledge of product composition bound-ries to start the iterative process. Such models have been foundo be inaccurate when used for monitoring of real life blast

∗ Corresponding author. Tel.: +91 3222 283928; fax: +91 3222 282250.E-mail address: sganguly@che.iitkgp.ernet.in (S. Ganguly).

1 Present address: Cryogenic Engineering Centre, Indian Institute of Technol-gy Kharagpur, Kharagpur 721302, India.

atbBt

cmo

098-1354/$ – see front matter © 2007 Elsevier Ltd. All rights reserved.oi:10.1016/j.compchemeng.2006.12.015

urnaces. Detailed transport phenomena based 2-dimensionalr 3-dimensional models (Viswanathan, Srinivasan, & Lahiri,997, 1998) have been attempted in literature for better under-tanding of steady state blast furnace operation. However, suchodels are extremely CPU time intensive and often extremely

igid for real time plant usage.A blast furnace model may be classified into several segments

amely burden distribution, shaft, raceway, and hearth mod-ls. The present work attempts to model the shaft and racewayndividually. Subsequently, a concentric cylinder approach isroposed to integrate them. In reduced order lumped parameterodeling, the shaft is considered to be a multistage countercur-

ent reactor. Model equations for simulating the shaft consistf integral component mass balance and energy balance aroundach stage. An iterative procedure with a dual loop convergences employed to generate the solution. In raceway modeling, sevenifferential equations comprising of mass and energy balancesre solved to obtain the profile of temperature and composi-ion in raceway zone. These two models have been integratedy dividing the shaft into concentric cylinders along the length.oundary conditions for each of these cylinders are obtained by

he solution of the raceway region.

The reactor models available in literature or in commer-

ial simulators were developed as rigorous steady state offlineodules primarily catering to the petroleum, petrochemical

r the basic chemical industries. Real time simulation using

A. Jindal et al. / Computers and Chemical

Nomenclature

a specific area of particleDb diameter of bellyDh diameter of hearthDT diameter of tuyereDz diameter of cross chapter at z heightDi discrepancy function which is non-zero at initial

guess and tends to zero at convergenceFb flow rate of blast (Nm3/min)Foh total flow rate of gas at tuyere levelFx flow rate in x-directionFy flow rate in y-directionhgs convective heat transfer coefficient between gas

and solidshi,j enthalpy of condensed phase in ith stage for jth

componentH total height of blast furnaceHi,j enthalpy of gaseous phase in ith stage for jth com-

ponent�Hri heat of reaction (J)ki rate constant of ith reaction (kmol/m3)1−n s−1

kfi mass transfer coefficient (m/s)kmi chemical rate constant (m3/kgs)Keffi effective rate constant for ith equationli.j jth component flow rate of condensed phase of ith

stage (kg/h)Ls0 height of throat (m)Ls height of shaft (m)La height of belly (m)P′ total pressure (N/m2)ri,j rate of dissipation of component j at ith

stage(kmol/m3 s)Ri overall reaction rate of equation I (kmol/m3 s)Tb temperature of blast (K)Tgi temperature of gas at ith stage (K)Tsi temperature of solid at ith stage (K)Tso temperature of solid at top (K)Tt temperature of gas at top (K)Twe temperature of cooling waterT1 temperature at tuyere level (K)U overall heat transfer coefficient for cooling

(J/K m2)Vi,j jth component flow rate of gas phase of ith stage

(kg/h)�V differential volume of stage i.WO2 oxygen enrichmentWst steam addition

Greek lettersε void fractionξ integration parameterψ coefficient of heat transfer between gas and cool-

ing waterζ fractional area of effective outflow surface in y-

direction

eaooffdcBbcmsrft

2

2

mmrtli

(wcAm

C

rhif

sstugci

t(

dS

Engineering 31 (2007) 1484–1495 1485

xperimental or plant data requires compensation of input datand synchronization with the process flowsheet, reorganizationf equations based on locations and applications and use ofptimization algorithms with the choice of various objectiveunctions, variable constraints and boundary limits. Provisionor changing model equations, lumping of kinetics or thermo-ynamics, incorporation of novel schemes like the concentricylinder approach are hardly available in available simulators.last furnaces offer a wide range of complexities and cannote substituted by reactor modules developed for general chemi-al engineering applications. Therefore, a reduced order lumpedodel for blast furnace has been attempted in the present work

o as to make the mapping of the process substantially accu-ate, flexible and consuming less computational time for efficientuture usage in the industry with optimizers and advanced con-rol applications.

. Shaft modeling

.1. Overview of the process

Charge fed to the furnace mainly consists of iron ore, coke,anganese ore and limestone. The source of iron is its ore,ainly hematite which contains 50–70% iron. Coke is added for

eduction of iron oxide to iron and to provide heat for combus-ion. Limestone and magnesia affect basicity of slag making itess viscous. Manganese ore is added for its beneficial propertiesn steel making.

Along the periphery of the lower part of the furnace, tuyeres20–25 in number) are provided for feeding preheated air (blast)ith small amount of humidity. The hot blast of air burns the

oke to form CO2, giving a flame temperature of 1800–2000 ◦C.t this high temperature CO2 reacts with carbon to form carbononoxide.

O2 + C = 2CO

Carbon monoxide formed by this reaction is responsible foreduction of ore to iron. The tuyere gas encounters wustite (FeO),ematite (Fe2O3) and magnetite (Fe3O4) (various iron contain-ng ore compounds) as it ascends and reduces them in steps toorm iron.

Along with the pig iron, slag materials are also formed. Thelag can be separated from metal only when it is in the moltentate. Combustion of coke increases temperature of tuyere regiono as high as 2500 ◦C. Slag being lighter than iron, forms thepper layer in the hearth. The burnt tuyere gas rises up andoes out through the outlet at the top. This outgoing gas mainlyonsists of CO, CO2, H2 and N2. The unused CO, in the top gas,s indirectly utilized in pre-heating blast.

Numerous chemical reactions occur in blast furnace. Impor-ant reactions relevant to modeling are listed in Table 1

Davenport & Peacey, 1979; Jindal, 2004).

On basis of the above reactions, the blast furnace can beivided into the following zones (Biswas, 1981; Peters, 1982;asaki, Ono, Suzuki, Okuno, & Yoshizawa, 1977, etc.):

1486 A. Jindal et al. / Computers and Chemical Engineering 31 (2007) 1484–1495

Table 1Important reactions occurring at various parts of the shaft

Serial no. Name of equation Equation Intermediate steps

(I) Indirect reduction of iron ore by CO 13 Fe2O3 + CO → 2

3 Fe + CO2 (a) 3Fe2O3 + CO → 2Fe3O4 + CO2

(b) Fe3O4 + CO → 3FeO + CO2

(c) FeO + CO → Fe + CO2

(II) Solution loss reaction C + CO2 → 2CO(III) Direct reduction of molten wustite FeO + C → Fe + CO(IV) Decomposition of limestone CaCO3 → CaO + CO2

(V) Indirect reduction of iron ore by H213 Fe2O3 + H2 → 2

3 Fe + H2O (a) 3Fe2O3 + H2 → 2Fe3O4 + H2O(b) Fe3O4 + H2 → 3FeO + H2O(c) FeO + H2 → Fe + H2O

(VI) Water-gas reaction C + H2O = CO + H2

( CO +

(

(

(

(

2

coTftb

s

((

((((

(

cTc

1

2

3

4

2

fe1

2

VII) Water-gas-shift reaction

1) Lumpy zone extends from the top of furnace to the pointwhere solution loss reaction starts. At this point temperatureis around 1000 ◦C. Reactions taking place in this zone arereaction numbers (I), (IV), (V) and (VII). This zone is furtherdivided in two sub-zones. Sub-zone 1 is from stock level toshaft sensor level and sub-zone 2 from this point to lowerpart of lumpy zone.

2) Softening zone starts with the end of lumpy zone and con-tinues up to the point where melting point of ore is reached.Reactions (I), (II), (IV)–(VII) take place in this zone. In thiszone temperature of solid varies from 1000 to 1400 ◦C.

3) Once 1000 ◦C temperature is reached melting of ore starts.At this point melting zone begins. This zone ends when totalamount of iron melts down. Reactions (Ia), (II), (IV), (Va),(VI) and (VII) take place in this zone.

4) Above 1400 ◦C there is dripping zone, which extends up tothe tuyere level. In this zone only reaction (III) takes place.

.2. Model formulation

The blast furnace is considered to be a multi-stage counterurrent chemical reactor of N stages. Charge is fed from the topf furnace whereas hot gases are fed at the bottom of furnace.he first to the last stage of the furnace shaft are numbered

rom 1 to n as shown in Fig. 11. Flow rates, compositions andemperature are known at the top for condensed phase and at theottom for gaseous phase.

The following assumptions are made for one-dimensionalteady state modeling of blast furnace:

1) Steady state operation of furnace.2) Axial dispersion of gas and solid is neglected, i.e. both

phases are assumed to move in cylindrical form.

3) No entrapment of the gases in the solid phase.4) Radial distribution of process variables is neglected.5) Voidage of the bed remains constant.6) Temperature of molten material is equal to that of the solid

phase.7) Charge is uniformly mixed, i.e. it is a homogeneous mixture.

ci1

H2O = CO2 + H2

Model equation for simulating the shaft consist of integralomponent mass balance and energy balance around a stage i.he model equations for each stage are further written for eachomponent j.

. Component mass balance for solid phase:

li−1,j − li,j + ri,j(�V ) = D1 (1)

. Component material balance for gaseous phases:

Vi+1,j − Vi,j + ri,j(�V ) = D2 (2)

. Energy balance for solid phase:

comp∑j

hi−1,jli−1,j −comp∑j

hi,jli,j +nreactn∑k

(−�Hrk)Rk(�V )

+hgs(Tgi − Tsi ) = D3 (3)

. Energy balance for gaseous phases:

comp∑j

Hi+1,jVi+1,j −comp∑j

Hi,jVi,j +nreactn∑k

(−�Hrk)Rk(�V )

−hgs(Tgi − Tsi ) − ψ(Tgi − Twe) = D4 (4)

.3. Formulation of lumped kinetic model

The lumped kinetic model of the blast furnace is preparedrom the earlier mentioned reactions by the incorporation offfective rate expressions (Fruehan et al., 2000; Torssell & Wijk,992, etc.).

.3.1. Indirect reduction of iron ore by CO

13 Fe2O3 + CO = 2

3 Fe + CO2

The reduction of iron oxide is assumed to precede topochemi-ally with one interface. In blast furnace conditions, this reactions active up to a temperature of 1400 ◦C (Davenport & Peacey,979; Jindal, 2004).

mical

R

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ao

R

2

strdb

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F

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r

R

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2

C

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R

2

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R

2

C

Ipw

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A. Jindal et al. / Computers and Che

The rate of consumption of carbon monoxide is expressed as:

1 = Keff1YCO (5)

.3.2. Solution-loss reactionThe solution-loss reaction described by the following equa-

ion proceeds in the lower part of a blast furnace:

+ CO2 → 2CO

In blast furnace conditions, this reaction proceeds at temper-tures above 1000 ◦C (Omori, 1987). The rate of consumptionf carbon dioxide is expressed as below:

2 = Keff2YCO2 (6)

.3.3. Direct reduction of molten wustiteThe wustite formed by indirect reduction of iron ore in the

haft region of a blast furnace melts and molten wustite fallshrough the packed bed of lump coke. The wustite may beeduced by solid coke or by dissolved carbon in molten ironuring this molten slag flow according to the reaction describedelow:

eO(l) + C(s) = Fe(l) + CO(g)

eO(l) + C = Fe(l) + CO(g)

The reaction is second order with respect to the concentrationf wustite in the slag.

Under these conditions, the expression for the overall reactionate per unit volume of the bed is:

3 = Keff3C2FeO (7)

This reaction is assumed to proceed in the melting region,hich commences above a temperature of 1400 ◦C (Torssell &ijk, 1992).

.3.4. Decomposition of limestone

The reaction is represented as:

aCO3 = CaO + CO2

In blast furnace condition, this reaction proceeds above aemperature of 1058 ◦K (Muchi, 1967; Torssell & Wijk, 1992).ate of decomposition of limestone can be expressed as:

4 = Keff4 (Y∗CO2

− YCO2 ) (8)

.3.5. Indirect reduction of iron ore by H2

Iron ore is also reduced by H2 in a blast furnace in accordanceith the equation:

13 Fe2O3 + H2 = 2

3 Fe + H2O

The reduction is assumed to precede topochemically with onenterface, and this reaction takes place above 575 ◦C under blast

urnace conditions (Biswas, 1981). The rate of consumption ofydrogen is expressed as below:

5 = Keff5YH2 (9)

sbbe

Engineering 31 (2007) 1484–1495 1487

.3.6. Water-gas reaction

For the water-gas reaction is given by

+ H2O = CO + H2

The chemical reaction is assumed to be irreversible first order.n blast furnace conditions, this reaction proceeds above a tem-erature of 1000 ◦C (Omori, 1987). The rate of consumption ofater can be expressed as below:

6 = Keff6YH2O (10)

.3.7. Water-gas-shift reactionThe water-gas-shift reaction is represented by

O + H2O = CO2 + H2

This reaction may take place in a blast furnace because theas ascending in the furnace consists of CO, CO2, H2, H2Ond N2. In blast furnace, this reaction attains equilibrium abovetemperature of 820 ◦C. Overall reaction rate is expressed as

iven below:

7 = Keff7

(YCOYH2O − YCO2YH2

K7

)(11)

.3.8. Reduction of silica in slagReduction in silica in slag is assumed to proceed in accor-

ance with the equations:

iO2(l) + 2C(s) = Si + 2CO(g)

iO2(l) + 2C = Si + 2CO(g)

It has been established that these reactions proceed in theigh temperature region and their rates are extremely low andhat the overall reaction rate may be expressed approximately byhe following equation based on the assumption that the reactions of irreversible first order with respect to the concentration ofilica in slag:

8 = Keff8CSiO2 (12)

The kinetic rate equations for each component are summa-ized in Table 2. They are further used to formulate the modelquations for heat and mass transfer.

.4. Method of solution

The model equations result in a set of coupled algebraic equa-ions. However, the solution procedure is decoupled by solvingrst the component mass balance equation (for both phases),

o obtain component flow rate, which are subsequently used inhe energy balance equation for both phases to solve for theemperature profile. The final solution is obtained by iterative

tep-wise solution of the component mass balance and energyalance equation. The component mass balance equations haveeen solved by Gauss–Siedel method, while the energy balancequations are solved by a modified Newton–Raphson procedure

1488 A. Jindal et al. / Computers and Chemical Engineering 31 (2007) 1484–1495

Table 2Rates of appearance of each component in the blast furnace

Serial no. Components Equation

1 Fe r1 = −2/3R1 − R3 − 2/3R5 (13)2 Fe2O3 r2 = 1/3R1 + 1/3R5 (14)3 Fe3O4 r3 = 0 (15)4 FeO r4 = R3 (16)5 C r5 = R2 + R3 + R6 + 2R8 (17)6 CaCO3 r6 = R4 (18)7 CaO r7 = −R4 (19)8 SiO2 r8 = R8 (20)9 Si r9 = −R8 (21)

10 MgO r10 = 0 (22)11 MnO r11 = 0 (23)12 Al2O3 r12 = 0 (24)13 TiO2 r13 = 0 (25)14 O2 r14 = 0 (26)15 CO2 r15 = −R1 + R2 − R4 − R7 (27)16 CO r16 = R1 − 2R2 − R3 − R6 + R7 − 2R8 (28)17 H2 r17 = R5 − R6 − R7 (29)11

bp

3

3

jcptta

F

A

F

Tt

F

Iaca

Tzfis

3

C

C

8 H2O r18 = −R5 + R6 + R7 (30)9 N2 r19 = 0 (31)

y “relaxing” the correction using Golden Section search. Thisrocedure has been represented as an algorithm in Fig. 1.

. Raceway modeling

.1. Overview of the process

The raceway zone is assumed to comprise of a cylindricaletting space which has the same diameter as the tuyere. Theombustion zone is assumed to be a bed which includes cokearticles. The molar flow rate of blast is approximately given byhe average flow rate in the conditions before and after combus-ion. Before combustion, the flow rate of gas can be expresseds

O,1 = Fb

[1000(1 +WO2 )

22.4+ Wst

18

](32)

fter the combustion, the flow rate is

O,2 = Fb

{1000[0.79 + 2(0.21 +WO2 )]

22.4+ 2Wst

18+ Woilβh

2

}

(33)

hen, the average flow rate of gas based on the cross-section ofhe hearth reduces to

oh = 2(FO,1 + FO,2)

πD2h

(34)

n regard to the flow rate in the vicinity of the upper bound-ry, the following approximate relationship between the upwardomponent Fy, and the horizontal component Fx, was found at

ny position along the tuyere axis:

Fy

Foh= 2.3 erf

(0.5FxFoh

− 2

)+ 2.9 (35)

C

H

Fig. 1. Algorithm for solving reduced order lumped model for blast furnace.

he substantial rate of outflow of gas through the combustionone is estimated by Fy multiplied by a coefficient. This coef-cient represents the fractional area of the effective outflowurface.

.2. Kinetic model of tuyere combustion zone

The principle reactions occurring in the tuyure zone are:

+ O2 → CO2

+ CO2 → 2CO

+ H2O → H2 + CO

2 + 12 O2 → H2O

mical

r

r

r

r

r

wa

R

weTp

k

war

k

wtnR

S

Tcf

k

Tg

k

Tg

k

pwr

rm

R

3

co

m

Fe

ige

a

T

Spt

3

(si

4

cotaTt

A. Jindal et al. / Computers and Che

Component dissipation rate, ri

i = −ε dCidθ

= −ε d(Pyi/RTg)

dθ(i = 1, 2, . . . , 5) (36)

1 = R∗1 + 1

2R∗4 (37)

2 = −R∗1 + R∗

2 (38)

3 = −r5 = R∗3 − R∗

4 (39)

4 = −2R∗2 − R∗

3 (40)

here ε is the voidage of the combustion zone, R the gas constant,nd θ is time.

Overall reaction rate can be expressed as follows:

∗ = kiCi (i = 1, 2, 3) (41)

here ki (s−1), denotes the overall rate constant covering theffects of gas film resistance and first-order chemical reaction.he expression for ki based on the unit volume of the looselyacked combustion zone can thus be written as

i = 1

(1/kfia) + (1/ηikmiρbc)(i = 1, 2, 3) (42)

here kfi is the mass transfer coefficient; a the specific surfacerea; ηi the effectiveness factor of catalytic factor of catalyticeaction; kmi the chemical rate constant; ρbc is the bulk density.

The mass transfer coefficient can be expressed as

fi =(Di

φdp

)Sh (i = 1, 2, 3) (43)

here Di is the diffusivity of reactant gas, φ is the shape fac-or, dp is the particle diameter of coke, and Sh is Sherwoodumber.The following relationship may be applied to the higheynolds number (Rep) region:

h = 1.5Re0.55p (44)

he chemical rate constant for the C–O reaction of a singlearbon particle may be revised to yield the following expressionor the bed:

m1 = 6.53 × 105(a

ρbc

) √Tm exp

(−22140

Tm

)(45)

he chemical rate constant for the C–CO2 reaction has beeniven as follows:

m2 = 8.31 × 109 exp

(−30190

Tm

)(46)

he chemical rate constant for the C–H2O reaction has beeniven as follows:

m3 = 13.4Tm exp

(−17310

Tm

)(47)

The H2–O2 reaction is one of the chain reactions and usuallyroceeds exceedingly fast. However, the reaction would stophen the oxygen decreases to the state of approximate equilib-

ium. The critical oxygen content, y∗1, may be nearly 5% with

rdoi

Engineering 31 (2007) 1484–1495 1489

espect to the combustion in the tuyere zone. Thus reaction rateay be expressed as

∗4 = R∗

3 at y1 ≥ y∗1 R∗

4 = 0 at y1 < y∗1 (48)

.3. Model formulation

The steady state heat and mass transfer processes in theombustion zone are formulated on the basis of the idealizedne-dimensional model.

The mass balance for the total gas over the differential ele-ent becomes

−dFxdx

= 4Fyζ

DT+

5∑i=1

ri (49)

or each component of the gas, the mass balance results in thequation

dyidx

= (yi∑5i=1ri − ri)

Fx(50–54)

The differential heat balance, taking into account of the heat-n-mass flows of the gas and coke, the heat exchange betweenas and solid and heat generated by chemical reactions, can bexpressed as

dTg

dx= CgTg

∑5i=1ri + CCTC

∑3i=1R

∗i +

∑4i=1R

∗i (−�Hi) − hgca(Tg − TC)

Fx(Cg + Tg dCg/dTg)(55)

The temperature of coke particles in the combustion zone isssumed to be related to the surrounding gas temperature:

C = 0.80Tg (56)

imultaneous numerical solution of these differential equationrovides the gas temperature and gas compositions at any dis-ance.

.4. Method of solution

The solution to the raceway zone is obtained by solving Eqs.49)–(56) using the boundary conditions mentioned above. Thisolution scheme has been represented in the form of an algorithmn Fig. 2.

. Integration of Shaft and Raceway model

In the shaft model explained earlier, constant temperature andomposition of tuyere gas at tuyere level were assumed. Becausef the reactions in the raceway zone, the boundary conditions atuyere level for the shaft model change with radii. Temperaturet the centre of furnace is high and decreases towards the wall.his is due to heat loss and external cooling at the walls. This

emperature gradient in the radial direction causes heat to flow

adially as well. In one-dimensional modeling of shaft, radialistribution of heat is neglected. However, during integrationf the raceway and the shaft models, radial distribution of heats taken into account. In the integrated model, both the phases,

1490 A. Jindal et al. / Computers and Chemical

iicob

pib

c

c

wsi

tptm

5

Fig. 2. Algorithm for solving the Raceway model.

.e. condensed phase and gas phase are assumed to be flowingn five concentric cylinders as shown in Fig. 3. The boundaryonditions at tuyere level, for the shaft model are taken as theutput from the raceway model. Thus there are five differentoundary conditions at tuyere level.

There is transfer of heat between these five cylinders for bothhases. To take care of this, an integration factor ξ is introducedn the gas phase energy balance to account for the heat interactionetween two adjacent cylinders.

5

t

Fig. 3. Integration scheme used for material and heat

Engineering 31 (2007) 1484–1495

The reformed equations are explained belowEnergy balance for solid phase:

omp∑j

hi−1,jli−1,j −comp∑j

hi,jli,j +nreactn∑k

(−�Hrk)Rk(�V )

+ hgs(Tgm,i − Tsm,i ) = D3 (57)

Energy balance for gaseous phases:

omp∑j

Hi+1,jVi+1,j −comp∑j

Hi,jVi,j +nreactn∑k

(−�Hrk)Rk(�V )

+ ξ(Tgm+1,i− Tgm,i ) − ξ(Tgm,i − Tgm−1,i

)

− hgs(Tgm,i − Tsm,i ) − UA(Tgi − Twe) = D4

(58)

here m is the cylinder number, k the reaction number, i thetage number, j the component number and ξ represents the heatnteraction parameter for gas phase.

The effect of external cooling is felt only in the cylinder closeo the wall. Its effect passes on to other cylinders through thearameter ξ. The cylinder at the centre of furnace undergoes heatransfer with only one cylinder. The algorithm for solving these

odel equations is schematically presented in Fig. 4.

. Results and discussion

.1. Study of Raceway zone and combustion

The raceway zone is the principle reaction zone where theuyere gas enters the furnace. This is also the region with max-

flow in the integrated shaft and raceway model.

A. Jindal et al. / Computers and Chemical Engineering 31 (2007) 1484–1495 1491

F

ictavtTa‘tp

5

iicp

Fig. 5. Temperature profile in the axial direction of the tuyere region.

F

ip

5

Ftcthatd

5

ig. 4. Algorithm for solving integrated model of Raceway and Shaft model.

mum temperature. Hence the prediction of temperature andomposition profiles in this region are very important for con-rol and optimization. As seen in Figs. 5 and 6, there exists

preferential reacting space where the combustion proceedsery fast. In this space, the temperature is nearly equal to theheoretical flame temperature, Tf. The maximum temperature,max, is established in this space owing to successive exothermicnd endothermic reactions. This vital space is now named thecombustion focus’. It is also found from the computed resultshat only in the combustion focus, the film diffusion steps areredominant.

.2. Lumping of kinetic constants

The kinetic constants are lumped together as was mentioned

n Section 2.3. The lumped kinetic constants affect only the zonen which they have been lumped together. Changing a kineticonstant is seen to affect the reactions and the profiles at thatosition in the furnace. For example the indirect reduction of

dc

ig. 6. Gas composition profile in the axial direction of the tuyere region.

ron by CO occurs near the top of the furnace. Thus the gasrofile at this is region is seen to be most sensitive (Fig. 7).

.3. Effect of overall heat transfer coefficient

The effect of the overall heat transfer coefficient is shown inig. 8. As expected, this parameter has maximum sensitivity near

he wall of the furnace. Its effect reduces as we move towards theenter of the furnace. As the value of the parameter is increased,he temperature inside the furnace decreases suggesting greatereat loss from the wall. If the parameter value is too low, there isn increase in temperature nearer to the tuyere region suggestinghat the rate of heat generation in this region exceeds the net heatissipation.

.4. Effect of integration factor ξ

The effect of the integration factor is felt along the entireiameter of the furnace. But the sensitivity is higher at theenter. This is because the center of the furnace experiences

1492 A. Jindal et al. / Computers and Chemical Engineering 31 (2007) 1484–1495

Ft

ahstgoF

5

5

ttawa

Ff

Ft

tf

m

wfhtcF

ig. 7. Effect of first reaction parameter on the CO2 profile near the center ofhe furnace.

continuous flow of condensed and gas phase flow along witheat transfer from the neighboring cylinders. This factor is alsoeen to affect the condensed phase temperature profile morehan the gas phase. The reason for this is that the gas phaseets more homogeneously spread inside the furnace. The effectf this parameter near the wall and at the center is shown inigs. 9 and 10, respectively.

.5. Validation of the model using parameter estimation

.5.1. Parameter estimation algorithmThe Gauss Newton algorithm was found to be extremely

ime consuming and unsatisfactory for parameter estimation of

he integrated model. After studying the behavior of differentlgorithms, the function DUNLSF of IMSL library functions,hich is used for solving nonlinear least-square problems usingmodified Levenberg–Marquardt algorithm, was selected for

ig. 8. Effect of overall heat transfer coefficient on temperature of gas insideurnace.

t3os

Ft

ig. 9. Effect of integration factor on condensed phase temperature profile nearhe wall of furnace.

he problem. This algorithm was found to be most stable andast converging among the rest of the algorithms.

The objective function used is as follows:

inΦ =∑i

[(Sexperimental − Smodel)2iwiFi] (59)

here Sexperimental = (a) temperature at available locations in theurnace; (b) pressure at measured points; (c) slag flow rate; (d)ot metal flow rate; (e) slag and hot metal analysis results; (f)uyere level temperatures; Smodel = corresponding values cal-ulated by the model; wi = weight assigned to the variable;i = flag.

One set of the steady state data around which the optimiza-

ion problem was executed are as follows: blast flow rate of000 N m3/min; feed rate of 250 × 103 kg ore/h; blast pressuref 2.45 kg/cm2; top pressure of 1.0 kg/cm2; hot metal analysishowed 1.2% Si; 0.1% Mn; 0.025% S and 0.13% Ti.

ig. 10. Effect of integration factor on condensed phase temperature profile athe center of the furnace.

A. Jindal et al. / Computers and Chemical Engineering 31 (2007) 1484–1495 1493

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5efficient and lateral heat transfer co-efficient). Apart fromoverall heat transfer coefficient, the lateral heat transfer coef-ficient is also seen to have significant effect on the temperature

ig. 11. Schematic diagram of the furnace showing the measurement points.

.5.2. Effect of length of parameter vector

.5.2.1. Single parameter estimation (overall heat transfer co-fficient). The various parameters discussed in the previousections do not affect the temperature of the furnace equally.ome parameters like the overall heat transfer coefficient havemarked effect on the profile whereas the heat transfer between

he phases does not show significant effect. Also, the tempera-ures of different locations in the furnace are affected differentlyy the parameters. The overall heat transfer coefficient showsreater effect near the wall whereas the lateral heat transferoefficient show greater effect at the center of the furnace. Thus

uring parameter estimation, the overall heat transfer coefficientas greater weight than the lateral heat transfer coefficient. Dur-ng the formation of the objective function, these factors areaken into account and various weights and flags are allotted to

Fig. 12. Change of temperature profile of gas with iteration.

he temperature at various locations. The next section presentshe parameter estimation results.

Parameter estimation studies have been first attempted on aingle parameter. Overall heat transfer coefficient is taken ashe parameter to be estimated since it has maximum effect onhe temperature profile for both gas and condensed phase. Theesults of the simulation have been illustrated in Figs. 12 and 13.

The plots show that as the initial guess moves away from thexperimental data, the number of iterations required in attainingonvergence increases. The plots show a fairly good degree ofolerance. If the tolerance is decreased further, the computationime increases. The algorithm has an average convergence timef 12–15 min. The results were found to be fairly satisfactory.

.5.2.2. Two parameter estimation (overall heat transfer co-

Fig. 13. Single parameter estimation results.

1494 A. Jindal et al. / Computers and Chemical Engineering 31 (2007) 1484–1495

Fn

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ig. 14. Result of parameter estimation experiment on gas temperature profileear the wall.

rofile inside the furnace. Thus lateral heat transfer coefficient islso included for parameter estimation. Figs. 14 and 15 show theesults of optimization for two parameter estimation problem.

At the center of the furnace, the effect of overall heat transferoefficient is not significant. Thus, it is seen that greater con-ergence is achieved for the center profile when the lateral heatransfer coefficient is added to the estimation objective func-ion. The weight of the parameter is selected depending uponhis sensitivity. By manipulating the values of the weights, themoothness of convergence was manipulated. The optimized runonsumed about 28–35 min for convergence in around 15–20terations.

.5.3. Effect of distant initial guess on convergenceIn this section, the effect of distant initial guesses on conver-

ence was studied. The results of these studies have been shown

ig. 15. Result of parameter estimation experiment on condensed phase tem-erature profile near the wall.

tcah1

Fig. 16. Parameter estimation using plant data (initial guess = 25,000).

n Figs. 16 and 17. The measurement points for temperaturend pressure are shown in Fig. 11. The Figs. 16 and 17 showhe movement of the temperature profile from the initial guessalue to the final converged result.

ase 1 (One distant guess). Initial guess for overall heat transferoefficient was 25,000 and for the lateral heat transfer coefficientas 600. The converged result obtained for overall heat transfer

oefficient was 28023.68 and for the lateral heat transfer coef-cient was 1178.45. The convergence time was 6 min with 5

terations.

ase 2 (Two distant guesses). Initial guess for overall heatransfer coefficient was 50,000 and for the lateral heat transferoefficient was 600. The converged result obtained for over-ll heat transfer coefficient was 27995.29 and for the lateraleat transfer coefficient was 1201.76. The convergence time was

0 min with 7 iterations.

Fig. 17. Parameter estimation using plant data (initial guess = 50,000).

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Viswanathan, N. N., Srinivasan, M. N., & Lahiri, A. K. (1998). Pseudo 2-D math-ematical model for shaft type counter current reactor—A study of cupola.ISIJ International, 38(10), 1062.

A. Jindal et al. / Computers and Che

. Conclusion

A reduced order lumped parameter model was developed toimulate the working of a blast furnace. Available literature andork suggest that 2D and 3D models currently available takelong time to converge (in hours and days) and often do not

onverge to required accuracy using plant inputs. The proposedodel was found to be fairly accurate, flexible with a small con-

ergence time (in minutes). Computational effort was reducedsing a novel concentric cylinder approach with lumped param-ters which ruled out a lot of redundant calculations. Profiles ofarious process variables including temperature, pressure andomposition profiles have been studied using this model. Sen-itivity study of various parameters has also been conducted.ange of validity of each parameter has been determined alongith its effect on the computational time and accuracy. Simula-

ion experiments have been conducted by using data collectedrom blast furnaces that are in operation.

eferences

iswas, A. K. (1981). Theory and practice of blast furnace (pp.1–13).avenport, W. G., & Peacey, J. G. (1979). Iron blast furnace: Theory and practice

(Materials Science and Technology Monographs). Elsevier.

Y

Engineering 31 (2007) 1484–1495 1495

ruehan, R. J., Goldstein, D., Sarma, B., Story, S. R., Glaws, P. C., &Pasewicz, H. U. (2000). Recent advances in the fundamentals of kineticsof steel making reactions. Metallurgical and Material Transactions, 31B(5),891–898.

indal, A. (2004). Master of Technology Thesis Dissertation. Indian Institute ofTechnology, Kharagpur, India.

uchi, I. (1967). Mathematical model of blast furnace. Transactions of ISIJ,223–236.

mori, Y. (1987). Blast furnace phenomena and modeling. Transactions of ISIJ,121–151.

eters, A. T. (1982). Ferrous Production Metallurgy. New York: Wiley., pp.46–62.

asaki, M., Ono, K., Suzuki, A., Okuno, Y., & Yoshizawa, K. (1977). Formationand melt-down of softening-melting zone in blast furnace. Transactions ofISIJ, 17, 391–399.

orssell, K., & Wijk, O. (1992). Simulation of blast furnace process by a math-ematical model. Transactions of ISIJ, 470–480.

iswanathan, N. N., Srinivasan, M. N., & Lahiri, A. K. (1997). A steadystate 3-D mathematical model for cupola. Iron and Steel Making, 24(6),476.

agi, J., & Muchi, I. (1970). Improved mathematical model for estimatingprocess variables in blast furnace. Transactions of ISIJ, 181–187.