ISIJ International, Vol. 39 (1999), No. 1, pp. 15-22

Three dimensional DynamicSimulator for Blast Furnace

Kouji TAKATANl.TakanobuINADAand Yutaka UJISAWACorporate Research &DevelopmentLaboratories, SumitomoMetai Industries, Ltd.

lbaraki-ken, 31 4-0255 Japan,

(Received on May14. 1998.• accepted in final form on September14.

,Sunayama,Hasaki-machi, Kashima-gun,

1998)

Three-dimensiona[ dynamic mathematical model which is constructed as a simulator of an actual blastfurnace is developed based on the mass, momentumand energy conservation in the furnace. In this paper,following things are investigated.

(1) The wholesomeof this mathematical model is clarified checking the total mass and energyconservation.

(2) Then, comparison with simulated and measuredresults for steady state is done for actual operatingconditions in order to clarify the validity of this simulator.

(3) Dynamicbehavior of the blast furnace such as the blown-in/off operations which are most hardlyestimated is simulated by this model.

(4) The effects of the shape of a blast furnace on the operating results such as total pressure loss, fuei

rate and so on are investigated by this model,

KEYWORDS:blast furnace; mathematical model; dynamic model; heat and mass transfer; fluid flow;chemical reactions.

l. Introduction

Various phenomenain a blast furnace that are effected

by gas flow, chemical reactions, descent of burden ma-terials, gas flow resistance and shape of cohesive layer,

combustion in the raceway and so on are very com-plicated. Overhaul investigations of quenchedblast fur-

nace, basic experiments, information of manysensorsand mathematical modelshave been used to understandthe phenomenain the blast furnace. The image of theinner states of the blast furnace has been formed based

on these works.Especially, a mathematical model is very useful for

understanding the complicated phenomenalike that in

the blast furnace. Various mathematical models for blast

furnace have beendeveloped in previous works. I ~ 9) Themathematical model began from l-dimensional steady

state modell'2) based on the kinetics and 1-dimensionaldynamic3 5) and 2-dimensional steady state models6~9)

havebeendeveloped. Manyphenomenacan be estimatedquantitativeiy by these mathematical models. Though3-dimensional dynamic model is necessary to under-stand the inner behavior of the blast furnace precisely,it does not exist in the previous works.

On the other hand, the improvement of the perfor-

mance of the recent digital computer is remarkableand it is possible to construct the 3-dimensional dynamicmathematical model for the blast furnace by using ofhigh performance computer. In this paper, 3-dimensionalmathematical model Is constructed that does considergas-1iquid-solid phase chemical reactlons and phase

change based on the mass, momentumand energy con-servation. One of the purpose of this research is tomakea simulator that can be operated in the samewayasoperating an actual blast furnace.

2. Modeling

The following assumptions and simplifications aremadein this model.

(1) Ergun's equationlo) js applied to gas flow re-sistance through the moving bed.

(2) Kinematic modelll) is applied to solid flow ofburden materials.

(3) Liquid flow is assumedto movedownwith aconstant dripping velocity since momentumbalanceequation for dispersed liquid phase has not been fully

established yet.

(4) Gasphase is according to an ideal gas low.(5) Temperature of coke and ore in solid phase is

sameand temperature of metal and slag in liquid phaseis same.

(6) Species of gas, Iiquid and solid are consideredlisted in Table l.

(7) The chemical reactions and phase transforma-tions llsted in Table 2are considered.

(8) The indirect reductions ofore are according to athree interface shrinking core model.12)

(9) Solution-loss reaction of coke are according to areaction model in which the resistances to pore diffusion,

gas film and chemical reaction are considered.13)

(10) Thecombustion in the raceway is not treated in

15 O1999 ISIJ

Table

ISIJ International, Vol. 39

l. Specles ofgls solld Ind liquid phrse

(1 999), No. 1

Phase Gas Ore Coke Liquid

Burdenmaterialsboundary conditions

~~Species (n) CO

CO_,

H2H20N2SiO

Fe203Fe304FeOFeSIO,etc.

CSi02SiCe!c'.

Fe203Fe304FeOFeSi02

Ce!c.

Table 2. Chemical reactions and phase transformationsconsidered in the mathematical model.

N Formula(RateN) Ref.

1,4 3Fe203(s) + co(g)/H2(g)

- 2Fe304(s) + C02(g)/H20(g)

23,24

2,5 Fe304(s) + CO(g)/H2(g)

- 3FeO(s) + C02(g)/H20(g)

23,24

3,6 FeO(s) + co(g)/H2(g)

- Fe(s) + •C02(g)/H20(g)

23,24

7,8 C(s) + c02(g)/H20(g)

- CO(g)/H2(g) + CO(g)

25

9 FeO(1) + C(s) - Fe(1) + CO(g) 26

10 C(s) - [Cl(1) equilibrium

11 H20(g) + co(g) = H2(g) + C02(g) 27

12 Si02(ash) + c(s) - SiO(g) + CO(g) 28

13 SI02(ash) +3 C(s) - SiC(s) + 2CO(g) 28

14 S*02(1) + C(s) - SiO(g) + CO(g) equilibrium

15 S*O(g) + C(1) - Si(1) + CO(g) 29

16 Fe(s) - Fe(1),

FeO(s) - FeO(1),

Si02(s) - Si02(1),

etc(s) - etc(1)

(Melting rate)

1718

Degradation of coke diameterDegradation of ore diameter

1415

19C(s) +1/2 02(g) - CO(g)

C(s) + H20(g) - H2(g) + co(g)

SiC(s) + 31202- Si02(1) + CO(g)

(Coke combustion in the raceway)

wustite is described tormany with FeO.

this model directly. Overall combustion rate is calculat-

ed from the gas componen~sand temperature of blowinggas into the tuyere and temperature of coke incominginto the raceway based on the total mass and heatconservation. It is assumedthat the gas that has com-ponents and temperature after burning is blown intothe tuyere.

(1 I) Changesof the sinter particle diameter causedby indirect reduction and of the coke particle diametermainly caused by solution-10ss reaction are consid-ered, 14, 15)

(12) Heat transfer in the refractories is described as

one dimensional heat conduction in the thicknessdirection. Where, heat transfer resistance between thepacked bed and the wail surface is taken into con-sideration. 16)

(13) Molten metal pool atthe hearth can be describedwith the perfect mixing model.17)

Schematic diagram of this mathematical mode] is

shownin Fig. 1.

C 1999 ISIJ 16

Fig. l.

1-dimensional heatconduction model//:::~1=sq:~~

Heat transfer~D ':ol~ boundary conditionsc:)

3-dimensiOnaldynamicmodel

) 4~~ f boundaryconditions~ Blast

~~ ~-

perfect mixing Heat transfermodel

(hot metal pool) boundary cond{tions

Schematic diagrams of 3-dimensional dyn'amic mathe-matical model for blast furnace.

2.1. Governing EquationsIn this mathematical model, governing equations

which have been used for one dimensional dynamic andtwo dimension'al steady state mathematical model areadopted because there wasno substantial difference butgoverning equations are selected so that their consistencymight be kept on their transformability of the coordinatesystem. 18) Theconstants andparameters in the governingequations that have been reported prevlously are usedwithout modification.

The governing equations are written for mass, mo-mentumand energy balance in the following form.

2. I . I .MassBalance

a(8k Pk(()kn)

at +div(8kpka)knUk)

=ek div( pkDkgrad cokn) +RWkn" " - "" -" " (I)

a(ek pk)

. . . . . . . .

(2)+div(8kPkUk)=~RWkn"""at n

RWkn=Mn~RateN' aknNn

where k= g, s, 1,

n=CO,C02' ' ' (gas),

Fe203, Fe304' ' ' (solid),

Fe203, Fe304' ' '(liquid),

N=1, 2, 3• • •.

2.1 .2. MomentumBalance(1) GasPhase

a(egPgUg)

= _eggrad Pat

- eg(fl +'/~ 18gPgUgl)(8gPgUg)..............

(3)

f=1501-e)2 ~g f _1

75(

8 d1

,

, .2_ '

1-8g8g2

Pg8gdp 8gPg g p

(2) Solid Phase

U,=BaV,

W=BaV~

ax a_7

(3) Liquid Phase

Vl =const., Ul = Wl=02, I.3. Energy Balance

a(8kPkCpkTk)+div(gk PkCpkTkUk)

at

ISIJ International, Vol, 39

.

(4)

,(5)

~=8kdiv(kkgrad Tk)- {a U (T - T)} +RH...(6)k-,,* k-~ ~ k

~ AHN)nkNRH= RateN(-N

2. I.4. Particle Diameter Change

DVDtP =RWVple,pPp ..........(7)

where D( )/Dt=U~a( )/ax+V,a( )lay+ W,a( )la--

p=0re, coke,

RWpis reaction with the volumetric change.

2.2. BoundaryCondition

Becausethis model is constructed as a simulator of anactual blast furnace, the boundary conditions have onlyto be set in the samewayas the actual blast furnace.

(1) The compositions and particle dlameters of oreand coke are given at the top of the furnace.

(2) Heat transfer coefficient is given at the outersurface of the furnace wall and the hearth.

(3) Gas fiow rate, blast temperature and composi-tions are given at the tuyere.

State variables in the blast furnace are calculated withthese boundary conditions and as the calculated results,fuel rate, hot metal production rate and temperature ofhot metal lron, gas componentand temperature distri-

butions in the furnace and so on are simulated. Really,it is sameas an actual blast furnace operation.

2.3. Rate Constant and Process ParameterThe reaction rate constant and process parameter

which have been used in the previously reported litera-

tures are adopted in this model except for the reduc-tion rate of wustite that wasmentioned later in detai].

Rate constants and process parameters used in this

model are shownin Tables 2, 3.

2.4. Solving Procedure and MethodThedifferential equations (l)(7) abovementioned are

solved numerically under the appropriate boundaryconditions and the initial conditions.

The boundary fitted coordinate system was adoptedto treat the shape of blast furnace precisely,i9) Com-putational grids are transformed from physical to com-putational domainas shownin Fig. 2. Thehole radius is

actually zero, though it is expressed as cylinder-shapedgrids with a hole at the center in Fig. 2. The algorithmadopted in the solving of gas flow is the SOLAmeth-od20) and the governing equations are discritized on thestaggered grid. The equations of energy and masscon-

17

(1 999), No. 1

Table 3. Process parameters.

Process parameter Symbol Ref.

Effective thermal conductivity for moving ks 16bed

Effective thermal diffusion coefficient of kg 30gas phase in the movingbed

Effective diffusion coefficient of gas phase Dg 31in the movingbed

Solid•gas heat transfer coeffieient Us-g 32

Gas-liquid heat transfer coefficient Ug_l 'l)

Liquid-solid heat transfer coefficient Ul's 33

Solid-gas effective contact area asl~ .2)

Gas-liquid effective contact area ag•I 34

Liquid-solid effective contact area al-s 35' I ):Ug.1=0

'2):as'g=aall~ al s

aall=6 E s/dp,

y

physical grid

Fig. 2.

dp:Meandiameter of solid phase

c

nD

transformed grid

Grid system.

time incliment

Calc. gas flowEqs.(3),(2)

Calc, solid flowEqs (4),(2)

Calc. Tg,Tl

,Ts

simultaneouslyEQ.(6)

Calc gas componentEq(1)

Calc solid componentEq.(1)

Calc. liquid componentEq (1)

Calc particle diameterEq (7)

Fig. 3. Solution procedure diagram.

C 1999 ISIJ

ISIJ International, Vol. 39 (1 999). No. 1

Fig.

Tuyeres

#1#2 #10

/

I\

!

l!jJ

/lllj

!jl

11lj

I,II\tl

Illl

IllliIIII

tlllli

I

Tg(~C)

400

600

It

800

l}

II

I

/

lOOO

12OO

2000

11lrf

,Il

!"'Ill

'l' IFfl

l' If

,Ill

f jt tll r'll,'f rfll

rf'r I,lt

f" t, I :

ff'irtf

f'

-* !11

--- , /" lll"

' ~/// '

/ll 'ri ,f tl

,, 1

wlthout blast

4. Computational results under lhe un-evenness blast conditions. (Blast volume rate: 7800Nm3/min,Blast

temperature: I 098'C, Blast moisture: 49.8 g/Nm3, PCI: 198 kg/min, Ore/coke weight ratio: 3.45)

20011

1600

1IIII

ll'l

li

Tg( O I Il II:{lf It l

"II Il

l rttlll

,,Irl ll

' l'llll'f

l~I Ifl

20

TI(~O15

f'ffl"'

1000 :: 1400 10 (wt%) 0,065 0.0 0,05

LII*'1'11l ' I l'{,14001 , !1!' '

1800V///i "

(vol%)o.04~

0.4

/'1500 i O

0.60,03

Gasflow and Llquldflow and COgas Slcontent Coke

Table 4. Computatlon 11 condrtrons

Blast volume rate (Nm3/min)

Blast temperature (1O

Blast moisture(glNm3)

PCI and 02 (kg/min)

Ore/Cokeweight ratio (')

7239

1099

40.6

541,138

3.975

temperature temperature concentration

Fig. 5. Computational results of blast

sional dynamic model.

in liquid

furnace by

diameter

3-dimen-

06

servation for gas, solid and liquid phase were solved

by the point SOR(Successive Over Relaxation) methodand the time Integration wasconducted under the fully

implicit method. Schematic numerical procedure can be

shownin Fig. 3.

3. Computational Results and Discussion

3.1. Three-dimensional Behavior

In this section, 3-dimensional behavior in the blast

furnace derived from the un-evenness blast conditions

at tuyeres are examined. Thecalculations under the con-ditions as shown in Fig. 4 were carried out. Inner

states of blast furnace such as gas temperature or veloclty

becomeun-uniform near the tuyere as shownin Fig. 4.

It is clarified that 3-dimensional behavior in the blast

furnace can be represented by this mathematical modelbut there are not enoughdata to verify this 3-dimensionalbehavior by the actual measurementsin the blast furnace.

Therefore, discussion about 3-dimensional behavior is

finished here.

In the subsequent calculations, uniformity in the cir-

cumference direction is supposed, and grid division in

the circumference direction is madeone.

Table 5. MsISS~llld heat balance.

Element Input(kmol/s) Output(kmol/s) Error(%)

o o.07709 O.07701 -0.109

C 0.05592 0.05604 +0.222

H 0.01313 0.01315 +0.132

N 0.11810 O, I 1830 +0,l03

Fe 0.02638 0,02629 -0.344

Totai 0.2907 0.2907 +0.031

Input(k Jls) Output(k Jls)

Blast gasBurden materlals

6860-13

Hot metal iron

WastegasHeat loss

Heat of reactions

Cokeconsumption at

the raceway

264596746

22181051

Total l 6847 Total 6927Total error(96) +1 15Total error(96)

3.2. BaseResults and Verification

Examplesof inner state variables computedby this

mathematical model are shown in Fig. 5. All of inner

state variables in the blast furnace can be simulated bythis model. At first, the wholesomeof this mathematicalmodel is examined under the operating conditions asshown in Table 4 since the model is very complicated

and mayhave somenumerical errors. Then, it could

be confirmed that computationa] error in the material

balance is within +0.50/* and is within + 1.50/* in the

heat balance as shownin Table 5.

Then, comparison with the calculated results and the

actual measuredvalue is done to clarify the validity ofthe mathematical simulation model. After manysimula-

C 1999 ISIJ 18

ISIJ International, Vol. 39 (1999), No. 1

Fig. 6.

2000

~Q)

~ 60~~ 1000 a5'

Q):~ 800Ee)

h ~ ~~

a) c:COgas utilization~ o~cU*

60040 '-~~;

o)~~!

~E ~~o_~

~~ zo\Gastemperature

u a eo CQ

o~ o)u)CQ

CL O 400Oo

20(21 .9m abave tuyere)

25 O, 0.5 1.

Height from tuyere (m) Center WallDimensionless radius position (-)

(a) Solid temperature in the furnace (b) COgas utilization andgasat the middle and center position temperature at the top of the furnace.in the radius direction and pressureat near the wall.

Examplesof the comparison with the measuredand simulated results of WakayamaN0.5 blast furnace.

Postfon Calculated MeasuredOoo center A

Middle o

ooo a) (~)_•~:--100----- Q

o A*,

o(~)'

xlC5

08 o MeasuredCaculated

~ oPt :

0.4 ~~--Pressure at the topof the furnace

o

0,0 5 Io 15 2C F

1OOOO1;;cls

_~:;c~~~ISoE~-a)o~~;

l::=~o(T~IS

~::o =' 5000~~8OCL

o WakayamaN0.5BF:1 WakayamaN0,4BF

KashimaN0.3BFAKekura N0.2BF

.' ~~~.'l

;~'

+5%.

-5 %o

5000 1OOOOMeasuredhot metaiproduction rate (ton/day)

(a) Hot metal production rate

60

~~

~o':T~

o) 50ooCQ

~~o

4040

i600

Measuredco gas utilization (%)

(b) COgas utilization

60

o

o(1'

o,1:

o

oCTS

CQ

O

o(1'

CQa'cL

~~~G)

ES1:'(Dce

~iO

400 500 600 1400 1500Measuredtotal fuel rate (kg/ton) Measuredhot metal temperature(~))

(d) Hot metal temperature(c) Total fuel rate

Fig. 7. Comparisonwith the measuredand calculated results for macroscopic data.

tions changing the rate and process parameters, it is

found that the reduction rate of wustite must be madeabout 0.03 times of the literature value to makethecomputed and actual measured value coincide. If thereduction rate of wustite is not madesmall total fuel

rate becomessmall by no less than 50 kg/pig-ton.21) It

is assumedthat the reaction rate of wustite must bechangedbecause the reduction rate of calcium-ferrite in

the sinter is slower than wustite.22) Furthermore, the

1600

stagnation of the reduction due to softening of the iron

ore under the high temperature is a cause, too. This scale

parameter is used as the fitting parameter that representsthe characteristics of individual blast furnaces that aredifferent in the scale.

Examples of the comparison with the actual mea-sured and simulated results like that the temperaturedistribution in the furnace, the radius direction dis-

tribution of the gas composition at the top of the fur-

19 C 1999 ISIJ

ISIJ International, Vol. 39 (1999), No. 1

,,,

'T'Teo- ^*cl o ~.~oVh s? 0.4

~) 0.2-~~~~a'~E * 1600

~~i500

IS ~1000Q.*~~ 800

~~ 600c~ u 400E~~+~q,* 200

~1500

e'

2 ~1000~5cT~(!'~

CLE 500~3

4)~

'~ 3000

~S " 2000>Et; z 1000,eo'~S~

0~0C~] 77 ca : COgas utilization

OADV: Measured

: Calcu ated

6)(P o cPo oo oo o o

2.0mabove tuyere and 0.28mfrom inner surface

u'!F'~5,4mand0.25m

7.2mand O45m

8m~2m 9m 6m

v~~ vw 15mabove tuyere

(at the middle position in the radius direction)

c O E F eB

A20 40

Time (hr.)

60 80

A B, c D E l F G i

I,1, I llj , i

i, , l f ,l l,i jl

llf,, ,l

i $J l " ,, l l l, Ir ,"f l,1 ,, ,il, l

=> I I'

,llT fl flf,1 ~l

:::> ' ~> ': ~ !!: ,1 Jl,~> '!f ,j, '$1=> Ill

'~t" tlll

,',:/r

400 ,

80020 '

+

"~ ;" Lt' L'

160 ; 1800f

lg

Ts(1O

Fig. 8. Computational results of WakayamaNo. 5blast fur-

nace blow-in operation.

nace and the height direction distribution of the pres-

sure at the wall are shown in Fig. 6. Furthermore, the

comparison with the measured and simulated results

for the macroscopic data such as total fuel rate, COgasutilization and so on for blast furnaces that are different

in the scale are shownin Fig. 7. At this time, simulations

are carried out as O.032 times of the literature value ofwustite reduction rate. Even if it is used fixed value ofthe scale parameter, computational results coincide withthe actual measurementswithin the range of :!1 5o/o errorfor blast furnaces that are different in the scale. Themodification of the reduction rate of wustite is notconcerned with the size of the blast furnace and it is anessential problem. Future research is expected.

The validity of this mathematical model could beconfirmed from these results for the steady state sim-ulation.

3.3. DynamicBehaviorIt is very important to clarify the dynamic response

of the unsteady state operation such as blow-in andblow-off in order to operate the blast furnace properly.It is examinedhere whether the dynamicbehavior of the

blast furnace can be simulated by this model. Simulationsof blow-in and blow-off operations are carried out asfollows.

20

0.54,~s?oeao

'+'ov

0.50

Hf~0.46

~1550

~5e,*

* s 150Q,* OE~~o CL 1450:!:E

J3400

o ~ 300(D~~~(L)c~$*~(1)~Q o,ti 200Ea)~5

H*1oo

?Eq':' ~8000

~5 ~6000

~Z_ 4000

~*~s 2000

I, ,

,l t Calculatedl L

Measured

o o o a ooo o __.pS,1,~ ~ ~

Measuredo oa9'Caiculated

Calculated

o oa aoa o

Qoo oOQO oo oo o Measured

OQO ooo

Calculatedo o

Measured Qooooooo e

o : 3.5mabove tuyere

D 7,4mabove tuyere

A E15hours

B blow-offD

c

6 12 o 12 oTime(hr.)

12 o

Q1999 ISIJ

BTs

(cj!i

,j;;!!1!i:llj!1 ;,

Ifllllll

Boo ll' fl~ fl

Ill f"" l'l

i 1111 flJ!/ ']lllllll => ,"rTit, Il~>

ii !tlIlooo l'll

l/'! I lJlll,1 ,:

loo ll$ :1400 11

, '

16 otil:

IB o !l

Reguiar Bl ast volumeoperation decreasing jncreasing operation

Fig' 9' Computational results of KashimaNo. 3blast furnaceblow-off operation.

c D E!l

/

Vyl

l 111

'If

'!'1!~~l

Ifff 'llil ,,

l,

'f"'TI:,1,,

l,t,,

ll

~:>~ll

If'I'l,::1!:

lll "l ll"

,.

tf",'

Blow-off BI ast volume Regularin reasin eration

3.3. I .Blow-in Operation

The blow-in operation can be simulated according tothe real operating conditions. The blow-in operationprocedure of SumitomoWakayamaNo. 5blast furnace

are carried out and the computational results are shownin Fig. 8. Calculated results like that gas componentsat

the top of the furnace, temperature of hot metal iron,

temperature of the refractories and solid temperature in

the furnace coincide to the actual measuredvalues. It

is possible to estimate the procedure of the blow-in op-eration quantitatively by this model.

3. 3.2. Blow-off OperationThe blow-off operation of SumitomoKashimaNo. 3

blast furnace is simulated as shown in Fig. 9. Compu-tational results of the hot metal iron temperature and

COgas utilization coincide well with the actual mea-sured values. The temperature of refractories decreasesright after blow-off and rises rapidly after restart blow-in. It is possible that thermal stress which acts on the

refractories is estimated from the change in the tem-perature distribution of the refractories. Furthermore,

even a time change in cohesive layer can be knownand

ISIJ International, Vol. 39 (1999), No. 1

1.2

Db/Dh=1.4 il

1.o

l•',Lf =.•=,:::;~~

*=',.,~

Db/2

, Dh/2Lt

Lb

Lo

Fig, lO, Profiles of the blast furnace.

CL

o*

o-

XI05

1O 20Tuyere Top

Height from tuyere(m)

Fig. 12. Computational results ofthe pressure distributionfor

case I.

Table 6. Computational conditions.

Productivity 22 Toppressure 3.5(ton/m3/day) (Pa) X105

Blast temperature 1250 PCI 200(1o (kg/ton)

Blast moisture 25 02 enrichment 3,0(glNm3) (%)

Hot metal 1500 Volumeof blast 3000temperature(1O furnace (m3)

l~

o~5

EcO

:t5

(D~,oO

~ lovQ)o~(S:~otlSo

~)Jc:c:~ece

.~5 (t,

~:~

CokeCaselCase2

Ore

80

60

40

20

o10

o

40

3G

2C

IC

O

O

Case2..

Casel

center0,5

Dimensioniess radius position(-)

1.

Wail

40

30

20

10

e)

oEcQ~5a)

~

Dimensioniess radius position(-)

Fig. Il. Distributions of the burden materials at the top ofthe furnace.

these results provide very useful information whentheconditions of blow-off operation are designed.

It is clarified that unsteady state phenomenaof theblast furnace can be estimated quantitatively by this

model with these examples. It is possible to design theoperating conditions because the changes of the innerstates of the blast furnace and temperature of the re-fractories are estimated before the real operation.

4. Optimization of Blast Furnace Shape

The effects of the shape of a blast furnace on the op-erating resuits such as total pressure loss, fuel rate andso on have not been investigated in the previous work.Then, in this section, optimization of the shapeof a blast

furnace is investigated under simple restrictions by usingthe present model. The following restrictions are made.As shownin Fig. lO, the profile of the blast furnace is

o,~:Q)(Q

Q)::

cQ

oH

1,O I ,2 i ,31.1

D~Dh(-)

Fig. 13. Computational results of fuel rate,

changedunder the constant inner volumeof the furnace.Computational conditions are shownin Table 6and thedistributions of the burden materials at the top of thefurnace that are two typical ones are shownin Fig. 11.

Simulations are conducted changing the averageweight ratio of ore and coke and blast volume rate sothat the conditions shownin Table 6are fixed. Becausethere are no great differences in the computedpressuredistributions for cases I and 2, the distribution of the

pressure loss only for case I is shownin Fig. 12. Pressureloss becomesminimumvalue whenDb/Dh(Db,Dh: Di-ameters of belly and hearth) is about I.2 and pressureloss decreases as Db/Dhbecomeslarge.

Onthe other hand, fuel rate becornes small as Db/Dhbecomeslarge and fuel rate for case 2is lower than casel as shownin Fig. 13. Heat exchangeand reaction ef-

ficiency are improved because residence time of the bur-den materials at the lower part of the furnace increases

as Db/Dhbecomeslarge and the gas fiow is moreuniformin case 2 than case I .

Db/Dh should be taken large asmuchas possible until the upper limit of the pressureloss because these demandsare inconsistent.

5. Conclusion

(1) Three-dimensional dynamicmathematical modelthat can act as an actual blast furnace has beendevelopedbased on mass, momentumand energy conservation.

21 C_.c) 1999 ISIJ

ISIJ International, Vol. 39 (1999), No. 1

(2) This model can estimate quantitatively the innerbehavior of the various blast furnaces that are different

in the scale with only the adjustment of the reduction

rate constant of wustite.

(3) It is clarified that the dynamic behavior of the

blast furnace such as blow-in/off operations can be es-

timated quantitatively by this model.(4) Theeffects of the shape of a blast furnace on the

operating results are investigated. Pressure loss takes

minimumvalue whenDb/Dh is about I .2 and fuel ratebecomessmall as Db/Dhbecomeslarge.

Nomenclature

ak,,N : stoichiometric constant of species n of phasekin reaction N

a,,*_k: contact area betweenphases mand kB: kinematic model's parameter

Cpk: meanheat capacity of species nDk: diffusivity of phase kkk : thermal conductivity of phase k

M,, : molecular weight of species nP: pressure in gas phase

RateN: rate of reaction NTk : temperature of phase k

U,,,_ k : heat transfer coefficient betweenphasesmandkUk: velocity vector of phase kVp: Particle volume ofcoke or ore

Greek symbolsAHN: heat of reaction N

ek : volume fraction of phase kn: distribution ratio to phase k of the heat of

reaction Nptk : viscosity of phase kPk : density of phase k

a)k,* : massfraction of species n in phase kSubscri pts

g: gasl : Iiquid

s: solid

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4)

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lO)

l 1)

l2)

l3)

l4)

l5)

16)

l7)

18)

19)

20)

21)

22)

23)

,~4)

25)

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,~9)

30)

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