MATHEMATICAL MODELLING OF BLAST FURNACE PROCESS AT SMELTING SMELTING OF NON-TRADITIONAL NON-TRAD ITIONAL RAW MATERIALS Yu.A. Chesnokov, A.N. Dmitriev Institute of Metallurgy of Ural Branch of Russian Academy of Sciences Ekaterinburg, Russia ABSTRACT. The offered balance logic-statistical model of blast furnace rocess is based on use of the material and thermal balances added !ith calculations of heat- and mass e"change taking into account non-uniformity of gas and burden distribution on radius of the furnace and characteristics of the basic metallurgical characteristics of iron ore ra! materials and coke on indices of blast furnace oeration# $or check of alicability of model the calculations on the most critical arameters of blast furnace rocess % smelting of ferromanganese and iron nickel !ith grahic reresentation of heat- and mass e"change rocesses, dynamics of o"ides reduction on height and radius of blast furnace ha&e been carried out# 1. INTRODUCTION
The The blas blastt furn furnac acee roc roces esss is char charact acteri eri'e 'ed d by a subst substan anti tial al scale scale,, o!e o!er r consumtion and orientation to the e"ensi&e energy carriers# Thereuon !orks on its mathematical modeling for the urose of maintenance of ossibilities of forecasting of the furnace !ork indicators and otimi'ation of the technological arameters of the blast furnace rocess are e"ecuted# Because of the comle"ity of hysical and chemical rocesses the research in the gi&en direction de&eloed on a !ay of creation of ri&ate models( balance, kinetic-mathematical, dynamic, e)uilibrium and others# In articular, at Institute of metallurgy of Ural Brunch of Russian Academy of Sciences last years is !idely used balance logic-statistical model of blast furnace rocess *+ !hich is based on use of the material and thermal balances added !ith stati statisti stical cal data data and and most most signi signifi fica cant nt regul regular arit itie iess of heat heat e"ch e"chan ange ge and and bala balanc ncee conditions of iron o"ides !ith a gas hase# Recently the model ha&e added !ith the integral e)uations for calculation of the distribution of the burden temeratures both gas on height and radius of the furnace and differential e)uations % for calculation of kinetic cur&es of iron o"ides reduction in blast furnace shaft# 2. REDUCTION OF IRON OXIDES IN THE BLAST FURNACE
$or calculation of the iron o"ides reduction rocesses in the dry art of a blast furnace is offered to use the follo!ing modified e)uation *+
∆
g , m , w ω CO , H /
=
g , m , w ( СО012 3 ! X
2,+ P +
− A g , m, w ) B g /,.m-, wС g +., m- , w ∆τ g , m , w ! X P / ( B g + ., m- , w − В g /,.m-, w ) ,
( D
)
g , m , w E СО/ , H / O
+. g , m , w
С
+-+++
4+5
g ,m ,w ∆ω CO , H % increment
!here
/
of degree of reduction of hematite 4g5, magnetite 4m5
and !ustite 4!5 at the e"ense of CO 676 H / agreeably# 8ther designations are resulted in Section 3# Balance constants 49:/.9:5 of reactions - "e/O-
+ CO = / "e-O; + CO/ ,
+ CO = - "eO + CO / "eO + CO = "e + CO/ "e-O;
4/5 45
, 4;5
are described by the e)uations */
= /
lg ! g CO
415 435 4<5
Balance constants of iron o"ides reduction reactions by hydrogen 4 H /O . H / 5 >?@@6CD?@F GH >?DJKJ6FL are calculated on the e)uations H / ! g , m, w
= ! g M8, m , w ! wg ,
4=5
!here ! wg % balance @onstant of reaction of !ater gas CO/ + H /
= CO + H /O #
405
Total degrees of reduction of iron o"ides are calculated in model according to the e)uations
∑∆ ∑ ∆ω
∑∆ = ( ∑ ∆ω
g , m, w ω
CO
∑∆
ω H
/
=
g , m , w ω
=
∑∆
CO
ω
H /
g , m , w g , m, w + ∆ω CO + ∆ω H , 4+25 g m w + + + 2#++∆ω CO 2#+33∆ω CO 2#
/
g m w 2#++∆ ω H 2#+33 ∆ ω H 2 #
/
/
#
4+/5
$or check of ade)uacy of the acceted scheme of reduction of iron o"ides e"eriments on reduction of agglomerate and ellets by hydrogen in an inter&al 022++22 H9 ha&e been made# In $ig#+ the e"erimental and settlement kinetic cur&es constructed !ith use of the e)uations 4+5, 4+2-+/5 are resulted# 3. DISTRIBUTION OF TEMPERATURES ON BLAST FURNACE HEIGHT
The basic e)uations for heat e"change calculation in the differential form look like w g t g
= wm t m + % i & + i g $ τ ,
wg′ t g
= w′m t m ,
wm t m
+ ih τ = α Σ' vm 4t g − t m 5 τ ,
t m
α Σ' v m 4t g
τ
=
− t m 5 − ih
wm
4+5 4+;5
=
4+15
α Σ' v m 4t g
w′m
+-++/
− t m 5
,
4+35
Fig. 1. The e"erimental 4continuous5 and calculating 4stroke-dotted5 kinetic cur&es of ellets reduction 4?5 and agglomerate 4b5 of Nachkanarsky O8N
t g τ
=
α Σ' v m 4t g
− t m 5
wg′
,
4+<5
!here w′m % !ater e)ui&alent of burden, e)uals
ih w′m = wm + + w t m m τ
,
4+=5
′ % !ater e)ui&alent of gas, w g
i & # ′ = w g + − w g t w g g τ
4+05
+-++
Sol&ing in common the e)uations 4+;5 and 4+35, at an assumtion m′ =
′ w ( w g ′
P const !e recei&e the e)uations
e"[ − ϕ 4α 5] m′t H t ) − t H − − m g g m , t = m + − m′ ) H t g ) − m′t H m − m′ t m − t m e"[ − ϕ 4α 5 ] t )
t g =
ϕ 4α 5
+ − m′
=
α Σ' v m
w′m
4/25
,
4/+5
4+ − m′5τ ,
4//5
! H !here % t g and t m % temeratures of gas and material on to 4the final temerature *
+
of gas, the reference temerature of material5Q t g and t m % the same in the end of a 'one of heat e"change 4reference temerature of gas, final temerature of material5# $or the calculation of deendence of the !ater e)ui&alent and !ater number of the burden from temerature !e shall be limited to linear functions wm
= - m + , m t m #
4/5
Integrating 4+5 and 4+;5 in &ie! of 4/5 !e shall recei&e ! + t g = t g
/m w g
( t − t ) + m
H m
,m /w g
[ t
/ m
− ( t H m ) ]+ /
. & + . ! w g
,
4/;5
!here . & + . ! % losses of heat and thermal effects of reactions at height of the +
furnace limited in temeratures t g and t g , k.t of ig-iron# These e)uations recisely enough describe rocesses of heat e"change in the blast furnace at small &alues of a ste on temerature or time# 4. CALCULATION OF NON-UNIFORMITY OF DISTRIBUTION OF GAS ON TOP RADIUS
As the rimary information allo!ing to analy'e the !ork of gas in the furnace use usually ractical data about distributions CO/ and temeratures of gas on radius of to# istinguish t!o basic tyes of the distribution influencing on arameters of !ork of the furnace % a eriheral and a"ial course# In the mathematical model the oortunity of the task of any tyes of distributions as on ractical data, and by e"ert is stiulated# The cur&e СО/ = 0 % r $ !ill be transformed to non-uniformity of distribution of streams of burden and gas, thus the blast furnace is broken into ten e)ual rings# Also follo!ing assumtions are acceted( ore % O $ and flu" % " $ are distributed on section of the furnace in regular inter&als unlike coke + r = 0 ( r ) and gas# Thus these &alues should be distributed on to radius so that to comensate the acceted assumtions and to reflect such henomena, as inching-out of layers of comonents of burden, an ad&ancing, segregation, etc# As a result by means of calculation heat- and mass e"change on model the set cur&e is reroduced СО1 = 0 ( r ) # $or this urose used the e)uations !ith hel !hich the ore loading % OB $ and the coke consumtion %!$ are ut accordingly in direct
+-++;
and in&ersely roortional deendence on % CO/ $ and )uantity of gas in deendence on the coke consumtion
( 8B) r = ! r =
8B ⋅ ( M8 / ) r M8 /
,
4/15
( O + " ) r , ( OB) r
4/35 n
(' g ) r = ρ i Ai + (' g − Ai ) + + + Bi ln N r + (+ − ρ i ) ' g N , N N r
4/<5
!here OB and ! % the a&erage ore loading and the a&erage coke consumtionQ i , Ai , Bi , ni % factors !hich steal u on a condition of maintenance of the greatest ossible coincidence set cur&e and 9:/ = 0 ( r ) recei&ed as a result of calculations of heat- and mass e"change in +2 rings# 5. EXAMPLES OF PROBLEMS PRACTICAL SOLUTION OF BLAST FURNACE SMELTING
Model ossibilities are illustrated by the analysis of blast furnace rocess at fusion of silikate-nickel and manganous ores# 5.1. S!"# $%"$&"%#i'( ') i*'( (i$+!"
The analysis of de&eloment of rocesses of heat e"change carried out on change of temeratures of gas and burden in hori'ontal sections and on furnace height 4on erihery, on an ore crest and at a furnace !all5# As initial data are set - furnace characteristics, comosition and roerties iron ore ra! materials, limestone, coke, blasting arameters, factors of non-uniformity of the gas stream, coordinated !ith the loading systems rofile 4a site of an ore crest, its height5# As a result of calculation recei&ed ig-iron and slag comosition, the arametres characterising thermal and reducing !ork of gas, and also technical and economic indicators of blast furnace smelting# The basic indicators of smelting and the analysis of blast furnace rocess for conditions of melt of ig-iron about 3 Vi in a blast furnace in &olume /21 L are resulted in tab# + and in fig# /# $rom character of the temerature cur&es it is &isible, that in an ore crest heat e"change is carried out at other relation of !ater e)ui&alents of and gas, unlike the centre and erihery# Therefore this area romotes formation of lo! a&erage temerature of to gas % 1 H9#
T%,"! 1. The basic arameters of smelting of ferronickel in a blast furnace
Indices
Walue
Xroducti&ity, t.day The sinter consumtion, kg.t ig-iron
1 3;2
+-++1
Oeneral contents $e in burden, oke consumtion, kg.t ig-iron $lu", kg.t ig-iron Blast( natural gas consumtion, m .minute temerature, H9 o"ygen contents, Xig-iron, comosition, ( *Si *Vi *r Slag( )uantity, kg.t ig-iron comosition, ( 4a85 4Mg85 4Al/85 basic caacity 4a8.Si8/5
+,03 +1/ =/ +11= ++22 /+,2 +#12 3#0 +#= 1+= /=#= +;#0 /=#= 2#32
Reduction rocesses of iron o"ides in all cuts are de&eloed acti&ely enough because of tall reductibility of sinter# The greatest acti&ity of reduction rocesses of iron o"ides is obser&ed at furnace centre# At the centre of furnace and on the rim the reduction of iron o"ides is terminated comletely in the YdryZ 'one of the board, i#e# to temeratures 012 o9# In the ridge ore the rereduction rocesses are de&eloed less acti&ely and to the emolliating 'one the material is enters in !hich !ustite it is reduced only on 12 # Therefore early slags in this cut !ill differ from slags of central and eriheral cuts both on consumtion and on roerties# 5.2. S!"# $%"$&"%#i'( ') )!**'%(g%(!!
The smelting of manganous ferroalloys in the blast furnace is characterised by the raised coke consumtion bundled first of all !ith high heat consumtion of the reduction rocesses of the manganese o"ides in the bottom of a blast furnace# In these conditions for smelting of )ualitati&e ferromanganese are necessary high blast arameters( ma"imum heat, its dee o"ygen enrichment# $or the analysis it is offered to use the combined diagramme Y2 3 t 3 4 Z allo!ing oerati&ely to estimate the thermal state of furnace together !ith reduction rocesses of iron o"ides deending on the stay time of materials in the furnace# In fig# the cur&es of heat interchange and reduction of iron o"ides at smelting of
entre of furnace
+-++3
8re crest
Xerihery of furnace
Temerature, H9
Reduction degree, share of units
Fig. 2. istribution of temeratures of the burden and gas 4at the left5 and reduction rocesses 4on the right5 in &ertical sections 4rings +, =, +25 of the blast furnace at ferronickel smelting
+-++<
Fig. 3. The analysis of reduction rocesses and heat interchange for ferromanganese smelting conditions
As a result of the fulfilled e"lorations the e"isting mathematical model of the blast furnace smelting is added by a method of the taking into account kinetic singularities of reduction rocess of iron o"ides until temeratures of 022-012 H9# The measure of the registration of irregularity of allocation of gas on shaft to radius is de&eloed# The calculated analysis of the critical conditions and arameters of the combined blast has sho!n essential sreading of functionality and a raise of ade)uacy of the model# . SYMBOLS g , m , w ∆ω CO , H 3 gain of the reduction degree of the hematite, magnetite and !ustite at the /
e"ense of CO or H / accordinglyQ g ,m , w ! 5 3 constants of the reduction &elocities for the hematite, magnetite and !ustiteQ CO012 3 8 content at 012 H9, Q 6 3 diameter of the ore iece, mmQ g , m , w 4 D E 5 CO/ , H /O 3 the effecti&e diffusi&ity defining the diffusi&e resistance of the
reduced layer for hematite, magnetite and !ustite accordinglyQ A g m w , B g m w , C g m w , D g m w 3 au"iliary coefficientsQ t m g % temerature of materials or gas, accordingly, H9Q ,
,
,
,
,
,
,
,
,
+-++=
% &olume heat-transfer factorQ ih % heat effect of the reaction, k.4h [ t5Q i % !armth losses, k.4h [ t5Q m % the ration of !ater e)ui&alents of the burden and gasQ %О$, %+$, %"$ % consumtion of ore, coke and limestone, accordingly, kg.t ig-ironQ OB % ore burdenQ ' g % to gas amount, kg.t ig-ironQ α Σ'
%CO1 $ % contents of the carbon dio"ide in the to gas, # /. CONCLUSION
Thus, the short descrition of a balance logic-statistical model of the blastfurnace smelting and results of the solution of ractical roblems of the blast-furnace smelting are resented# A0NOWLEDGEMENTS
This !ork !as e"ecuted !ith suort from ouncil under Orants for \eading Scientific Schools of Russia 4School ] ;1=#/22=#5# REFERENCES
+# hentso& A#W#, hesnoko& ^u#A# and Sha&rin S#W#( The \ogic-Statistic Balance Model of Blast $urnace Smelting# Ural Branch of Russian Academy of Sciences, Ekaterinburg, /22# /# Xoel S#I#, Sotniko& A#I# and Boronenko& W#V#( The theory of metallurgical rocesses# Mosco!, Metallurgy, +0=3# # hentso& A#W#, hesnoko& ^u#A# and Sha&rin S#W#( _ontrollable arameters of system of loading and elements of modelling of domain rocess_# I'&estia Wu'o&, hernaya Mettalurgia /223 < //-/;# ;# Belyae& I#\, hentso& A#W#, hesnoko& ^u#A# and Sha&rin S#W#( _Use of t!odimensional model of blast furnace rocess at ig-iron melt about 3 Vi_# I'&estia Wu'o&, hernaya Mettalurgia /223 0 +=-/2# 1# Nudino& #`#, hesnoko& ^u#A# and Sha&rin S#W#( $eatures of blast furace rocess at melt of manganous alloys in the form of diagrams 2 3 t 3 4. I'&estia Wu'o&, hernaya Mettalurgia /22/ <3-<<#
+-++0
