A DUAL GRAPHIC REPRESENTATION OF THE BLAST FURNACE MASS AND HEAT BALANCES RIST

Prévia do material em texto

1 88 lronmaking Proceedings, 1966 
A Dual Graphic Representation of the 
Blast=Furnace Mass and Heat' Balances 
by A. Rist and N. Meysson 
- . 
The understanding and application 
of blast-furnace theory can be 
helped greatly by a graphic model. 
The purpose of this paper is to pre- 
sent such a model, incorporating the 
most important characteristics of the 
blast-furnace operation and illus- 
trating the solution to many prob- 
lems which can otherwise be solved 
by appropriate steady-state mass 
and heat-balance equations. 
For a graphic representation of 
heat balances, we adopt the familiar 
Reichardt diagram: which is par- 
ticularly well suited to illustrate the 
"thermal pinch point" and the con- 
ditions of the heat transfer from the 
gas to the charge. 
For a graphic representation of 
mass balances, and specifically 
balances of the elements carbon, 
oxygen and hydrogen, involved in 
the formation and utilization of the 
reducing gas, we propose to use the 
"operating diagram" which was de- 
veloped by the authors in the past 
few years.'-"This diagram is par- 
ticularly well suited to illustrate the 
"chemical pinch point" and the con- 
ditions of oxygen transfer from the 
charge to the gas. 
After reviewing the procedures 
involved in drawing both diagrams, 
it will be shown that there are 
shortcomings in the use of either 
one separately and that considerable 
advantage can be derived from the 
simultaneous manipulation of both. 
Applications of this dual graphic 
method will be given by studying 
in turn: 
1. The effect of variations of a 
single operating parameter (hot- 
blast temperature, injection of 
natural gas, prereduction of the 
burden). 
2. The effect of coupled variations 
of pairs of operating parameters 
(natural-gas injection and increased 
blast, temperature, natural-gas in- 
jection and oxygen in the blast, 
burden prereduction and ore bene- 
ficiation) . 
A. RlST and N. MEYSSON are with IRSlD 
(The French Iron and Steel Research Insti- 
tute), Maizieres-les-Metz, France. 
It is stressed that the proposed the charge is an average of practical 
graphic method does not involve significance, i.e., the gradients within 
painstaking work on the drawing or between the solid particles are 
board, nor does it bypass numerical not excessive; and (2) that a coun- 
calculations if quantitative answers ter-current plug flow for the gas 
are required. and the charge is reasonably well 
established. 
HEAT BALANCES 
REICHARDT'S DIAGRAM 
Definition and Properties of 
Reichardt's Diagram 
Reichardt's diagram1 is an elegant 
and attractive graphic method which 
has been practiced by many au- 
thors.'-" It is able to represent in a 
single graph, and with due regard 
to the second law of thermodynam- 
ics, all the possible heat balances 
one may wish to establish for the 
blast furnace, whether for the proc- 
ess as a whole or for separate stages. 
The diagram consists of two curves 
showing the temperature of the gas 
and the temperature of the charge as 
a function of the heat transferred 
from the gas. Fig. l a shows a sim- 
plified version of the kind we shall 
discuss and use later in this text. 
Reichardt's representation is ap- 
plicable under the two main condl- 
tions: (1) that the temperature of 
Temperature 'F 
I I I t 
Fig. 1-Ideal heat exchange in the blast fur- 
nace: (a) Reichardt's diagram, (b) Tempera- 
ture profiles of the gas and the charge. 
The drawing of both curves should 
take into account the variations in 
mass and composition of the gas and 
the charge, as well as the variations 
of the specific heats of their compo- 
nents. The heating curve of the 
charge is greatly affected by the 
splitting up of the heat transferred 
from the gas into contributions to the 
sensible heat of the charge, to heats 
of reactions, to heats of fusion, and 
to heat losses. In spite of these com- 
plexities it is convenient to speak of 
the slopes of both curves as "heat 
capacities" of the gas and the 
charge, with the required extension 
of the concept to chemical heat in 
particular. 
The outstanding features of the 
diagram, reflecting the chracteristics 
of the blast furnace as a heat ex- 
changer are: (1) the bend in the 
solids curve at the onset of major 
endothermic reactions adding to the 
charge heat capacity; and (2) the 
minimum in the difference AT be- 
tween gas and charge temperatures 
at the level of the bend. 
The latter feature is commonly 
referred to as the "thermal pinch 
point" and the value of the mini- 
munl temperature difference is taken 
as a criterion of the efficiency of the 
blast furnace as a heat exchanger. 
The original work of Reichardt 
emphasized the role of limestone 
decomposition in determining the 
pinch point in the range of 1450- 
1650°F (800-900°C). Probe work 
in furnaces with self-fluxing bur- 
d e n ~ ~ - ' ~ later showed that a pinch 
point remains in the absence of 
limestone. This was the basis for 
Michards to conclude that the solu- 
tion loss reaction alone can be re- 
sponsible for a pinch. point, a t a 
temperature determined by the coke 
reactivity in the range of 1650- 
1850°F (900-1000°C). Both cases can 
be found, and also intermediate 
cases with two pinch point^,^ but 
for simplicity we shall base our dis- 
cussion on self-fluxing operations 
only. 
There is ample evidence in this 
Blast Furnace Theory 89 
case that the ideal heat exchange, 
with zero difference in gas and 
charge temperatures (Fig. l a ) , is a 
good approximation to reality. The 
temperature profiles (Fig. lb ) then 
show an isothermal reserve zone at 
TR between two curved portions, 
concave in opposite directions. The 
slopes of these profiles, measuring 
the rate of heat transfer, vary in di- 
rect proportion to the separation be- 
tween Reichardt's curves. 
The zones of heat exchange in the 
blast furnace are represented in Fig. 
2 (left-hand side). The isothermal 
zone is suitable to divide the blast 
elaboration zone include the sensible 
heat of the charge, the heats of fu- 
sion, a major part of the total heat 
losses, and the heats of the endo- 
thermic reactions of solution loss 
and' direct reduction of the nonfer- 
rous elements. All items but the 
first in this list usually make the 
slope of RC so markedly greater 
than the slope of SR that point R 
is exposed to become the thermal 
pinch point. 
The cooling curve of the gas. The 
simplified cooling curve for the gas 
in Fig. l a i s made of the two seg- 
ments FR and RG. Segment FR 
PREPARATION EXCHAN I -45 
1 
CHEMICAL RESERVE 
ZONE( F a ) 
INDIRECT 
REDUCllON 11 
I T I 1 ............,, EXCHANGER I 
REDUCTION -rl 
Fig. 2-Distribution of thermal and chemical zones in the blast furnace. 
furnace by a plane a t TR into a prep- represents the cooling of the gas 
aration zone (T < TR) and an elab- down to TR from a "virtual flame 
oration zone (T > TR), according to temperature," TF. This latter tem- 
the suggestion by Mi~hard.~," The perature is calculated, assuming that 
advantage of this procedure will the CO generated by solution loss 
later be fully explained. and direct reductions is incorporated 
A Simplified Version of 
Reichardt's Diagram 
In drawing Reichardt's diagram 
for our purpose, we adopt a simpli- 
fied procedure, already used by 
others,"," which saves time without 
giving up any of the essential in- 
formation. The cooling of the gas 
and the heating of the charge are 
both represented by a pair of 
straight segments joining a t the 
thermal pinch point, R, with a more 
or less pronounced angle. 
The. heating curve of the charge. 
In Fig. la, segment SR represents 
the heating of the charge, assumed 
to be self-fluxing and dry, from 
room temperature (77"F, 25°C) up 
to the temperature of the reserve 
zone Tn (1800°F, 980°C). The cor- 
responding heat requirements per- 
taining to the preparation zone in- 
clude the sensible heat of the charge, 
a minor part of the total heat losses, 
and a small term of indirectreduc- 
tion of the initial oxides to wustite. 
Segment RC represents the heat- 
ing of the charge from TR up to a 
mean casting temperature Tc 
(270OoF, 1480°C) which is interme- 
diate between metal and slag casting 
' temperatures. The corresponding 
heat requirements pertaining to the 
in the combustion gases formed at 
the tuyeres. I t is therefore lower 
than the adiabatic flame tempera- 
ture. The difference, which is rn-ainly 
a function of the amount of solution 
loss, is usually less than 300°F 
(166°C). 
Segment RG represents the cool- 
ing of the gas between TR and the 
top gas temperature To, assuming 
that the indirect reduction of wus- 
tite takes place mainly a t Tn and 
that the gas, as it cools, has the very 
composition of the top gas. 
In most cases segments FR and 
RG have about equal slopes, in 
agreement with the findings of Kle- 
mantaski7 and K i t a i e ~ . ~ The de- 
crease in molar specific heat of the 
component gases between the high 
and the low temperature ranges is 
closely balanced by the oxygen 
pickup of the gas, forming C03 and 
H20 which have higher molar spe- 
cific heats than CO and H,. 
In all the following applications of 
Reichardt's diagram, segments FR 
and RG of the gas-cooling curve will 
be assumed to be borne by one and 
the same straight line, defined by 
FR. Segment RG will thus be an ap- 
proximation, leading to a top gas 
temperature in slight excess' of the 
exact value. For the highest and the 
lowest degrees of oxidation encoun- 
tered for top gases in self-fluxing 
practice, the errors are respectively 
9 and 90°F (5 and 50°C). 
Applications and Shortcomings of 
Reichardt's Diagram Alone 
If an actual blast-furnace opera- 
tion were given with sufficient in- 
formation to define it unambigu- 
ously, and if the data were ex- 
tremely accurate, Reichardt's dia- 
gram could be drawn often with 
more details than we have chosen to 
put in, and it could be used for 
what it was originally meant for, 
i.e., the assessment of the blast-fur- 
nace thermal efficiency, by means of 
the minimum separation between 
the two curves. In practice, the data 
are always too rough for this pur- 
pose and the diagram is rather to be 
used as n check on the consistency 
of the data and of the incorporated 
assumptions (particularly on the 
distribution of heat losses and on 
the temperature range of chemical 
reactions:). As illustrated by the 
work of Gerstenberg and Kootz,= 
one can be lead to intersecting 
curves, which is beyond question a 
sign of inconsistency. 
In planning a blast-furnace oper- 
ation wj.th a given burden, one 
would of course make a reasonable 
assumption regarding the pinch 
point, such as ideality, with AT = 0 
in the reserve zone. But even in the 
simple case of a self-fluxing burden, 
one will remain short of a method 
to determine, a priori, the amounts 
of solution loss and indirect reduc- 
tion. These do not follow from heat 
balances and if an assumption is 
made, no heat balance can be used 
as a justification for it. The gap can 
be filled only through consideration 
of the counter-current reduction in 
the shaft. This is the primary object 
of the operating diagram. 
BALANCES FOR CARBON, OXYGEN, 
AND HYDROGEN-THE OPERATING 
DIAGRAM 
Mass balances can be established 
for any element and they must be 
established for iron in the first place 
when assessing blast-furnace data. 
In blast-furnace theory, however, 
the ba1a:nces of carbon, oxygen, and 
hydrogen come first and foremost in 
view of the participation of these 
elements (1)in the formation of the 
reducing gas, via reactions of high 
heat effects : exothermic combus- 
tion, endothermic solution loss and 
direct reductioi~s; and (2) in the 
utilization of the reducing gas in the 
indirect reduction of the iron ox- 
ides. 
The operating diagram which is 
presented here illustrates both as- 
pects. 
Definition of the Operating Line 
Formation of the reducing gas in 
the absence of hydrogen. If, for sim- 
plicity, we first consider a blast- 
furnace operation without hydrogen, 
the contributions to the reducing gas 
90 lronmaking Proceedings, 1966 
can be organized according to the 
sources of oxygen-producing CO. 
The associated CO balance is writ- 
ten below in two ways: 
1. with reference to the formation 
of 1 mole of reducing gas (Eq. [ I ] ) 
2. with reference to the formation 
of the number of moles of reducing 
gas necessary to produce 1 atom of 
Fe (Eq. 121). 
Xb + X r + X S I = 
1 mole reducing. gas [I] 
yb + yf + Y.1 = 
p moles reducing gas/at. Fe [2] 
p is the specific consumption of re- 
ducing gas or the ratio of the flow- 
rate of gas to the flowrate of iron. 
The x and y terms are the CO con- 
tributions in each reference system, 
respectively, with subscripts relat- 
ing to the various sources of oxy- 
gen: b, blast; sl, solution loss; and 
f, other sources giving a fked 
amount of gas per unit Fe for a 
given hot metal composition (e.g., 
reduction of SiO,, MnO, etc.). 
The corresponding terms of both 
equations form sets of proportional 
numbers and, as such, they can be 
read on two rectangular axes as the 
projections of segments of one and 
the, same straight line, with the 
slope p. 
Fig. 3, with coordinates labeled X 
= O/C and Y = O/Fe, shows the 
straight line thus obtained, called 
Fig. 3-The operating line. 
the operating line. The segments 
showing the formation of the reduc- 
ing gas, BC, CD, and DE are con- 
fined in the interval 0 < X < 1. 
The various contributions appear in 
their relative proportions, whether 
as the segments themselves or as 
their projections on the axes. 
Formation of the reducing gas 
with hydrogen contributions. If 
water vapor or hydrocarbons enter 
the blast furnace through the 
tuyeres and if account is taken of 
the coke hydrogen, there may be 
several hydrogen contributions to 
the reducing gas. Instead of noting 
them and representing them sep- 
arately, we lump them with one or 
the other CO contribution. Thus Eqs. 
[I] and [21 are unchanged, but the 
interpretation of the symbols is ex- 
tended in the following way: 
XC, yb are numbers of moles of re- 
ducing gas, CO and Hz, pro- 
duced in amounts proportional 
to the .blast rate, 
xr, yf are numbers of moles of re- 
ducing gas, CO and H, pro- 
duced in fixed amounts per 
unit of Fe. 
Hydrogen from natural blast hu- 
midity will normally participate in 
xb and yb. Hydrogen from a hydro- 
carbon injection can participate in 
either (xb, yb) or (xr, y f ) , depend- 
ing on whether the rate of injection 
is given as a weight or volume per 
unit volume of blast or as a weight 
or volume per unit iron produced. 
The coke hydrogen does not strictly 
belong to one class or the other, but 
since it is a small contribution it is 
a convenient approximation to lump 
it with (xf , y ~ ) . 
Utilization of the reducing -gas. 
Following. the same principle, it is 
simple to represent the utilization of 
the reducing gas by means of a seg- 
ment representing the oxygen re- 
moved from the iron oxides by in- 
direct reduction and partially con- 
verting CO to COa and H, to KO. 
The number of atoms of oxygen in- 
volved is X I when referred to 1 mole 
of gas and y l when referred to 1 
atom of Fe. The two values are in 
the same ratio as the other x and y 
pairs, since the oxidation of the gas 
takes place without change in the 
total number of moles of gas, and 
therefore they can also be read as 
projections of a segment of the same 
straight line of slope p. Segment AB 
in Fig. 3 thus represents the in- 
direct-reduction oxygen. It is con- 
fined in the interval 1 < X < 2. * 
The origin on the Y axis of the 
operating diagram is arbitrary. For 
convenience, it is chosen so that the 
oxygen originally combined to iron 
(y.1 + yi) appears on the positive 
side, whereas other sources of oxy- 
gen and sources of hydrogen appear 
on the negative side. 
The interpretation of various 
points and segments is summed up 
later, afterthe study of the proper- 
ties of the operating line. 
Properties of the Operating Line 
The operating line has two im- 
portant groups of properties respec- 
tively associated with the indirect 
reduction in the shaft and with the 
heat balance of the elaboration zone. 
Properties of the operating line 
associated with indirect reduction. 
The chemical pinch point. If one as- 
sumes true counter-current plug 
flow for the gas and the solids in the 
shaft, in addition to a carbonate-free 
burden, the X and Y coordinates of 
any point on segment AB (Fig. 3) 
can be interpreted as measuring the 
degrees of oxidation of the gas and 
solids respectively, at a particular 
level. The steady-state oxygen bal- 
ance for an infinitesimal volume be- 
tween two horizontal planes at that 
level can be written: 
where n, and nr. are the flow rates 
of reducing gas and iron respectively 
(in moles and atoms per unit time). 
Eq. [3] is precisely the differential 
equation of the operating line. 
Since the gas can never become 
oxidizing with respect to the solids, 
the points of segment AB must nec- 
essarily remain on the left of an 
equilibrium ' contour showing the 
equilibrium values of X as a func- 
tion of Y. The drawing of this con- 
tour is greatly simplified if one re- 
calls the results of probing cam- 
paigns,","-'" which revealed the char- 
acteristics of the blast furnace as an 
oxygen exchanger. Most of the in- 
direct reduction takes place in or 
near the thermal reserve zone and 
equilibrium at the wustite-iron 
stage is closely approached a t TR, SO 
that a chemical reserve zone of pure 
wustite can be formed under favor- 
able circumstances. The resulting 
distribution of chemical and thermal 
zones is shown in Fig. 2. It follows 
that the limit to the oxidation of the 
gas is usually given by the isother- 
mal equilibrium contour at TR. Fig. 
4 illustrates the situation for pure 
CO, TR being 1800°F. 
Fig. kConstruction of the operating line 
under conditions of ideal heat exchange 
(point P) and ideal oxygen exchange (point 
W). 
It can be shown simplp that for 
parallel operating lines with a slope 
in the blast-furnace range (2 to 3 
moles of reducing gas/at. Fe) the 
oxygen exchange reaches a maxi- 
Blost Furnace Theory 91 
mum when the operating line 
touches the pure wustite corner W. 
The operating diagram thus pro- 
vides a "chemical pinch point" as the 
explanation for the chemical reserve 
zone observed in practice or in the 
laborat~ry.'~,'~ 
The coordinates of point W can be 
obtained from the work of Darken 
and GurryS: 
YW is the atomic O/Fe ratio of 
wustite in equilibrium with iron, 
which is practically independent of 
temperature and equal 1.05 at. 
O/at. Fe. 
Xw is a function of TR and of the 
mole fraction of hydrogen in the re- 
ducing gas? It is available in the 
form tables, formulae, or Chaudron 
diagrams. 
Illustration of the part played by 
point W in the determination of the 
minimum coke rate must await the 
derivation of other properties of the 
operating line. 
Properties of the operating line 
associated with the heat balance of 
the elaboration zone. It is not possi- 
ble to express in Reichardt's dia- 
gram the condition of chemical equi- 
librium just discussed, but it is pos- 
sible to express in the operating dia- 
gram the condition of thermal equi- 
librium and the heat balance of the 
elaboration zone, already illustrated 
in Reichardt's diagram. If the blast 
furnace is divided, as proposed by 
Michard,Bnn by a plane cutting across 
the thermal reserve zone at TR and 
across the chemical reserve zone 
when it is present (Fig. 21, and if 
TR is used as the reference temper- 
ature, the balance equation is re- 
markably simple to write. The rea- 
son is that the heat input by the 
charge and the heat output by the 
gas are both equal to zero. The fol- 
lowing equation is obtained after 
lumping terms together for the 
needs of the graphic representation: 
ybqb = yslqsl + Q 141 
which brings out: 
1. A single heat input term on the 
left hand side, which is proportional 
to the blast volume through yb, and in 
which the coefficient qb (kcal/mole 
reducing gas) takes into account the 
heat of combustion of coke at TR, 
the sensible heat of the blast be- 
tween TI, and TR, the various endo- 
thermic reactions associated with the 
presence of hydrogen (if present in 
fixed proportion with the blast), etc. 
2. The heat requirement of solu- 
tion loss: the product of y.1 (at. O/ 
at. Fe) by the endothermic heat ef- 
fect of the solution loss reaction at 
TR, qal (kcal/at. C gasified). 
3. The whole of the heat require- 
ments Q which are fixed per unit of 
iron produced at steady state: heat- 
ing and melting of the charge, direct 
reduction of nonferrous oxides, in- 
direct reduction of wustite, heat 
losses, and the various endothermic 
reactions associated with the pres- 
ence of hydrogen (if present in fixed 
proportion to the iron produced). 
Eq. [4], a linear relationship be-, 
tween the two variables yb and y.~, 
expresses that the operating line 
goes through a fixed P in 
Fig. 4. The easiest way to place P 
consists in writing Eq. [4] in the 
form of a proportion: 
which translates graphically as: 
In Fig. 4, UE can be interpreted as 
a measure of the heat input in units 
of combustion, qb, and VB as a mea- 
sure of the total heat requirements 
in units of solution loss, q.~. Ac- 
cording to simple geometry, Eq. [ 6 ] 
implies that the operating line inter- 
sects segment UV at a point P which 
divides distance UV in the ratio 
qal/qb, and has the abscissa: 
It is worthy of note that the coordi- 
nates of point P are practically in- 
dependent of the amount of solution 
loss to be performed in the elabora- 
tion zone. XP is a function of the 
blast characteristics only (tempera- 
ture and composition), Yp is a func- 
tion of the hot metal composition 
and of all the heat requirements of 
the elaboration zone given per unit 
of iron. 
Point P can be placed with good 
accuracy for a planned operation. 
The operating line will be PW for 
the ideal shaft performance leading 
to the minimum coke rate. But if 
the operation is not chemically ideal, 
the operating line still goes through 
P, although it does not go through 
W. It hinges on point P at variable 
shaft performance. 
Index of the Points and Segments 
of Significance in the Operating 
Diagram 
To help the reader in becoming 
familiar with the operating diagram, 
a list is given below of the most 
important points and segments with 
their interpretation. The letters re- 
fer to Figs. 3 or 4, and are given in 
alphabetical order. Atomic and mo- 
lecular units are used in the operat- 
ing diagram to take advantage of 
the equivalence of 1 at. 0 , 1 at. C, 
1 mole CO and 1 mole H, in the re- 
ducing gas balances. Table I gives 
the conversion factors required to 
revert to industrial units. 
Point A. 
XA - 1 = degree of oxidation of 
the top gas, at. O/mole 
gas 
Y r = initial degree of oxida- 
tion of the iron in the 
burden, at. O/at. Fe, Ya 
= y.1 + yl 
Point B. 
XB := 1, by construction 
Ye := ~ O I , amount of solution 
loss (and direct reduc- 
tion) of iron, at. O/at. 
Fe 
Point D. 
, XU = xr, the fraction of each 
mole of reducing gas 
originating from the 
blast, and thereby bear- 
ing a fixed ratio to the 
nitrogen. XI, is propor- 
tional to the ratio (% 
N2/% reducing gas) in 
the total gas mixture 
Yu = Yu, see U 
Point 
YP 
P. 
= qal/(qb + q,,). 
P is the point dividing 
segment UV in the ratio 
PU/PV = qsl/qb 
The operating line hinges 
around P under the in- 
fluence of factors affect- 
ing the amount of solu- 
tion loss without chang- 
ing the other thermal 
requirements of the elab- 
oration zone 
A chart of XP as a function of blast 
temperature and humidity is given 
in ref. 5. 
Point U. 
XU = 0, by construction 
IYnJ = y,, number of moles or 
reducing gas/at. Fe, pro- 
duced jointly by: (1) the 
direct reduction of SiO-, 
MnO,PnO;, and desul- 
Table I. Conversion Factors from Atomic to Industrial Units 
To convert to Y ~ ~ l t l p l y by 
at. O/at. Fe 
at. C/at. Fe 
Ib O/short ton Fe 573 
kg O/metric ton Fe 286 
cu ft dry blast air/short ton l'e 306.000 
m3 dry blast air/metric ton Fe 955 
Ib C/short ton Fe 430 
kg C/metric ton Fe 215 
cu f t CO/short ton Fe 128.500 
ma CO/metric ton Fe 401 
solution loss thermal units (at. 0, Btu/g at. Fe 
at. C, or mole CO) per at. Fe Btu/short ton Fe 
kcal/g at. Fe 
th/metric ton Fe 
92 Ironmaking Proceedings, 1966 
furization, (2) the coke 
hydrogen, and (3 ) the 
injection hydrogen (and 
oxygen), when the rate 
of injection is defined 
per unit Fe 
Segment UE. 
UE = yb, number of moles of 
reducing gas/at. Fe, 
originating from the 
blast and including the 
injection hydrogen (and 
oxygen). when the rate 
of injection is defined 
per unit volume of blast 
air. At constant blowing 
rate, UE is inversely 
proportional to the pro- 
duction of iron and pro- 
portional to the retention 
time of the charge. Seg- 
ment UE is under all 
circumstances propor- 
tional to the total heat 
input into the elabora- 
tion zone per at. Fe . 
Point V. 
X, = 1, by construction 
lYvl = Q/qBl, heat requirements 
of the elaboration zone 
1 exclusive of solution loss, 
measured in solution loss 
units, at. O/at. Fe 
I 
Segment VB. 
VB = Q/q., + ye,, total heat 
requirements of the elab- 
oration zone, measured 
in solution loss units, at. 
O/at. Fe 
Point W. 
X1v - 1 = degree of oxidation of 
the gas in equilibrium 
with wustite and iron at 
Ta, at. O/mole reducing 
gas. 
XlV is a function of Tn 
and of the hydrogen 
mole fraction in the re- 
ducing gas 
YK = overall degree of oxida- 
tion of iron in the 
charge after reduction 
of . the initial oxides to 
wustite in equilibrium 
with Fe, at. O/at. Fe. 
Y, = 1.05 at. O/at. Fe 
in the absence of metal- 
lic iron in the burden 
p, slope of the operating line: num- 
ber of moles of reduc- 
ing gas (CO, Hz) re- 
quired for the produc- 
tion of 1 at. Fe, moles/ 
at. Fe. The total carbon 
consumption is equal to 
the CO fraction of plus 
the hot metal carbon 
Applications and Shortcomings of the 
Operating Diagram 
If an actual blast-furnace opera- 
tion is given with sufficient informa- 
tion to define it unambiguously, the 
operating line can be drawn by two 
points or by one point and the 
slope. In blast-furnace control, for 
instance, the complete gas analysis 
can be used to place points A and D. 
In the assessment of blast-furnace 
data, the operating diagram offers a 
check of consistency and, when 
there is consistency, a means of 
evaluating the chemical efficiency of 
the shaft, by the separation between 
the operating line and point W. 
In planning new operations, .an 
assumption must be made on ther- 
mal and chemical efficiencies. If 
ideality is assumed for both, any 
chosen set of operating variables 
(type of burden, blast characteris- 
tics, hot metal composition, nature 
and rate of injection, etc.) leads to 
an operating line PW and to a prac- 
tical minimum coke rate. 
Although a solution is obtained 
by the operating diagram alone, a 
doubt remains as to whether it is 
compatible with the assumption of 
ideality, from the point of view of 
the rates of oxygen and heat trans- 
fer. A qualitative but valuable check 
can be provided by Reichardt's dia- 
gram. A combined reference to both 
diagrams is thus necessary in most 
cases. It can be vital in particular to 
predict the inhence of an operating 
parameter beyond its common range 
of variation. The advantage of the 
dual graphic representation is illus- 
trated below. 
is a linear combination of the vol- 
umes of the three gases CO, Hz, and 
N,, associated to the production of 
the same unit of iron. 
Another link is obtained if the 
same scale is used in both diagrams 
for quantities of heat: The heat re- 
quirements of the elaboration zone 
are then represented by segments of 
equal length, VB in the operating 
diagram and cr in Reichardt's dia- 
gram (Fig. 5). For a base operation, 
the two segments can be drawn to 
face each other, but when variations 
will be studied this match will not 
be preserved since B and V may 
move up and down, whereas r will 
be fixed and c only will move to 
satisfy the equation VB = cr (ex- 
cept with injections, as shown be- 
low). 
The following examples will show 
how the dual graphic representation 
is used, first to illustrate the influ- 
ence of single parameters varying 
within and to the limits of the ideal 
range, and second to illustrate cou- 
pled variations of pairs of parame- 
ters so chosen as to preserve ideality 
over far more extensive ranges of 
either parameter than would be per- 
missible in single variations. 
EFFECT OF INDIVIDUAL 
PARAMETERS ON THE BLAST 
FURNACE OPERATION 
SIMULTANEOUS REPRESENTATION 
OF THE OPERATING AND 
The dual graphic representation 
will be applied here to three indi- 
REICHARDT'S DIAGRAMS vidual parameters of interest in 
Before commenting on specific ap- 
plications, it is necessary to present 
the two diagrams side by side (Fig. 
5) and to point out some of the 
graphic links between them. 
First, it should be noted that the 
slopes of the operating line and of 
Reichardt's gas line vary in the 
same direction in most cases (pro- 
vided of course the temperature axis 
is oriented towards the left, as we 
have chosen to do). The slope of the 
operating line is proportional to the 
volume of reducing gas (CO, H?) 
generated to produce one atom of 
iron, while the slope of the gas line 
modern -blast-furnace technique to 
save coke and/or to increase iron 
production, namely hot-blast tem- 
perature, natural gas injection, and 
burden prereduction. 
Graphic Study of the Effect of High 
Blast Temperatures 
An increase in blast temperature 
amounts to an increase of the ther- 
mal coefficient q,, the heat input in 
kcal/mole of reducing gas originat- 
ing from the blast. The abscissa of 
point P (Fig. 6a), given by Eq. [7], 
is thereby decreased.3,Tnder the 
assumption that the coke rate is cor- 
Fig. 54imultaneous representation of the operating diagram and Reichardt's diagram. 
Blast Furnace Theory 93 
serve tends to shrink and vanish. If 
the increase in blast temperature 
were too large, the assumption of 
chemical ideality could not hold any 
longer and the operating line would 
have to be drawn away from point 
W. 
Reichardt's diagram thus brings 
out the interaction between heat 
transfer and reduction in the shaft 
and thereby sets a limit of validity 
to the assumption of chemical ideal- 
ity. If chemical ideality had not been 
assumed in the first place, it would 
be necessary to associate a decreas- 
ing shaft efficiency to any increase 
of blast temperature. The coke sav- 
ing would then be less than ideal. 
The transition from ideal to non- 
ideal behavior occurs at blast tem- 
peratures which are the higher the 
lower the weight of slag-making 
materials is in the burden. 
Fig. &Effect of an increase in blost temperature. Beyond the range of nonideality 
for the reduction, one would find 
rected so as to maintain the same zone: BB' = CC' = vertical compo- also a range of nonideality for the 
hot metal composition, points U and nent of FF'; (3) an increase of the heat transfer involving separation of 
V remain fixed. Segment UV is the virtual flame temperature equal to the gas and solicL lines at R. The 
locus of point P, which is displaced the horizontal component of Fp; evolution of Relchardt's diagram 
towards the left, to P . If the shaft (4 ) a small decrease in the heat re- from a pinch point at R to a pinch 
reduction is assumed ideal initially quirements of the preparation zone point at the top has been clearly 
and assumed to remain ideal, the equal to SS' or to the vertical com- illustrated by Zischkale, Heynert, 
operating line hinges on point W ponent of GG', and related to the and Beer.- 
and changes from PW to P'W. loweringof the coke rate; (5) a de- 
The resulting modifications ap- crease in the top gas temperature Graphic Study of the Effect of a 
pearing on the diagram are the fol- equal to the horizontal component Natural-Gas Injection 
lowing: (1) a decrease in the slope of GG'. The injection of natural gas will 
of the operating line, corresponding In Reichardt's diagram, the de- be studied here in the absence of 
to the decrease in coke rate; (2) an crease in the slope of the gas line any other variation of operating 
increase, BB', in the amount of solu- is the major effect, the vertical dis- parameters and in particular at con- 
tion loss, both as gas generated and placements of the end points C, F, stant blast temperature. The injec- 
as heat required; (3 ) a decrease of S, and G being small compared to tion affect!; both mass and heat bal- 
the blast consumption, proportional the horizontal displacements of ances of the blast furnace. For sim- 
to EE'; (4) an increase AA' of the points F and G. As a consequence, plicity, it is assumed that the rate 
degree of oxidation of the top gas; the new angle GRS' is smaller than of injection is given as a volume of 
(5) a decrease of the NJreducing the initial one, GRS. This indicates CH, per unit of metal produced. The 
gas ratio, proportional to DD'. that the difference in temperature injection hydrogen can thus be 
The increase in solution loss BB' between gas and solids at all levels treated in the operating diagram as 
cannot be mistaken for nonideal in the shaft is decreased and that a part of the reducing gas bearing a 
shaft reduction. As is evidenced by the transfer of heat is slower. The fixed ratio to the iron (yr). Point U 
the corresponding increase in top- new temperature profile is thus less in Fig. 7a is displaced vertically to 
gas oxidation, it is merely the effect favorable to fast reduction than the Up, segment UU' representing the 
of the operating line hinging on original one and the chemical re- number of moles of H, injected per 
point W. 
The decrease in blast consumption 
EE' can be interpreted more spe- 
cifically under either one of two as- 
sumptions: 
1. If production is to be main- 
tained constant, the blowing rate 
must be decreased in the ratio of 
WE' to UE. 
2. If the blowing rate is main- 
tained constant, production will in- 
crease in the ratio of UE to UE'. 
The modifications observed on the 
operating diagram involve corre- 
sponding modifications in Reichardt's 
diagram. Under the assumptions of 
ideality for the heat exchange, the 
gas straight line and the segments 
of the solids curve all hinge on point 
R, which is kept fixed. One notes 
the following changes (Fig. 6b) : (1) 
a decrease in slope for the gas line, 
due to the decrease in total volume 
of gas (both reducing gas and nitro- 
gen); (2) an increase in the heat 
requirements of the elaboration Fig. 7-Effect of o natural gas injection. 
94 lronmoking Proceedings, 1966 
at. Fe. The carbon need not be rep- 
resented, since it is taken care of 
by blast oxygen which is already 
represented in yb. 
From the heat-balance point of 
view, the thermal requirements of 
the elaboration zone independent of 
solution loss are increased by an 
amount VV', representing the crack- 
ing and heating of the injected ma- 
terials to T,, UU' and VV' are both 
proportional to the amount of na- 
tural gas injected and, as a result, 
the line U'V' hinges around a fixed 
point J. The abscissa X, is a charac- 
teristic of the injected material and 
is equal to 2.27 for methane.6 The 
blast temperature being constant, 
point P is displaced vertically (X, = 
cst) to P' on U'V'. 
If the operation is assumed to be 
ideal initially, the base operating 
line goes through point W. Follow- 
ing the introduction of hydrogen in 
the reducing gas, this point is 
slightly displaced towards the right, 
and if the operation is assumed to 
remain ideal, the new operating line 
is P'W'. It may be shown6 that the 
two operating lines intersect at a 
point I, at a fixed abscissa X, which 
depends mainly upon the nature of 
the injection and slightly upon the 
blast temperature. For methane and 
T, = 1800°F, XI = 1, 41. 
Other modifications of the operat- 
ing diagram of Fig. 7a are (1) an in- 
crease in slope of the operating line, 
~ p ; (2) an increase in the blast con- 
sumption EEf-UU'; (3) a decrease 
BB' in the amount of solution loss. 
The increase in slope of the oper- 
ating line A p is an important factor 
in the evaluation of the replacement 
ratio. If the reducing gas made from 
1 mole of methane were strictly 
equivalent to the CO made from the 
coke, the operating line would re- 
main unchanged and the replace- 
ment ratio would be equal to 3 at. C 
coke/mole CH,. In fact, with an in- 
crease in slope A p for the injection of 
i moles of methane/at Fe, the re- 
placement ratio, p, is only: 
p = 3 - Ap/i at. C coke/mole CHI 
i.e., about 1.2 at. C/mole CHI or 0.04 
lb C/cu ft CHI. 
The increase in blast consumption 
is the reason for a decrease in pro- 
duction when the blowing rate is 
constant. 
The decrease in solution loss ob- 
served on Fig. 7a cannot be a sign of 
improved shaft efficiency, since 
ideality is assumed. Yet in practice, 
when the base line is not ideal, im- 
portant improvements in shaft effi- 
ciency are obtained by injection. 
The explanation for this effect is 
best brought out by Reichardt's 
diagram. 
Fig. 7b shows the modification of 
Reichardt's diagram by an injection 
of methane. The line of the gas and 
the segments of the solids hinge on 
point R, with the following charac- 
teristics: (1) an increase in slope 
of the gas line, due to the increase 
in total volume of gas (reducing gas 
and nitrogen) ; (2) a decrease of the 
virtual flame temperature equal to 
the horizontal component of FF'; 
(3) a decrease in the amount of heat 
to be transferred from the gas in 
the elaboration zone: BB' = CC' = 
vertical component of FF' (the in- 
crease VV' is not included here be- 
cause it represents heat consumed on 
the site of combustion with the effect 
of lowering the true flame tempera- 
ture) ; (4) a small decrease in the 
heat requirements of the preparation 
zone related to the decrease in coke 
rate; and (5) an increase in the top 
gas temperature equal to the hori- 
zontal component of GG'. 
The increase in slope of the gas 
line is the major effect. At the top 
the horizontal displacement of G is 
far greater than the vertical one and 
the new angle G'RS' is greater thali 
the initial one, GRS. This is a sign of 
faster heat exchange and corre- 
sponds to a temperature profile 
%which is more favorable to fast re- 
duction. Thus, if the chemical effi- 
ciency is not unity to begin with, it 
is improved by the injection, an 
effect which is further accentuated 
by faster reduction rates in hydro- 
gen-bearing gases. - 
When the shaft efficiency is im- 
proved by the injection, the increase 
in slope of the operating line ap is 
less than in the ideal case and the 
replacement ratio is higher. There is 
a limit of course to the improvement 
and as the injection rate is further 
increased the replacement ratio re- 
sumes a smaller value, closer to 
ideality.' This effect is substantiated 
by practiceg and often sets an eco- 
nomic limit to the injection rate. 
In studying very high injection 
rates on the dual graphical repre- 
sentation, one is able to visualize the 
two phenomena which sooner or 
later reverse the tendency to im- 
prove shaft efficiency and invalidate 
the assumptions of ideality: 
1. One is the lowering of the flame 
temperature apparent on Reichardt's 
diagram. With the decreasing tem- 
perature difference between gas and 
solids in the elaboration zone, heat 
transfer is slowed down and a longer 
exchanger is required. The reserve 
zones tend to shrink and vanish, 
causing the shaft efficiency and the 
replacement ratio to decrease. 
2. The other is the increase of the 
amount of indirect reduction ap- 
parenton the operating diagram. 
The more thorough the reduction, 
the more time it requires, and it is 
expected that operations with high 
injection rates will not reach the 
ideal degree of indirect reduction 
aimed for in the ideal operation. The 
shaft efficiency and replacement 
ratio will therefore be simultane- 
ously impaired. 
It is not possible to tell which 
limit would be met first, because of 
interaction between the phenomena 
involved. In addition, one must keep 
in mind the possibility that incom- 
plete combustion may cause low re- 
placement ratios at high injection 
rates." 
Graphic Study of the Effect of 
Burden Prereduction 
With burden prereduction, the 
amounts of reduction, both direct 
and indirect, to be performed in the 
blast furnace are markedly de- 
creased, as is shown by the operat- 
ing diagram of Fig. 8a. Provided 
iron metal is present in the charge 
and resists reoxidation, point W is 
depressed. Its abscissa remains con- 
stant and its ordinate decreases by 
an amount proportional to the ratio 
a of metallic to total iron: 
WW' = a Y w 
Point P is practically unchanged 
and the operating line essentially 
hinges around point P when W is 
displaced. One observes the follow- 
ing modifications on Fig. 8a: (1) a 
decrease in the slope proportional to 
the coke saving; (2) a decrease EE' 
Fig. &Effect of bu rden prereduction. 
Blast Furnace Theorv 95 
in the blast consumption, allowing 
a large increase in production at 
constant blowing rate; (3) a de- 
crease BB' in the amount of direct 
reduction; and (4) a decrease in the 
degree of oxidation of the top gas 
equal to the horizontal component of 
AA'. 
It is worthy of note that prere- 
duction is an example of a variable 
which induces a high saving of coke 
(and a correspondingly high in- 
crease in production) due to the 
coupled effects of lower carbon 
gasification by solution loss and of 
lower heat requirements in the 
elaboration zone. A similar situation 
is encountered with any variable 
causing the operating line to hinge 
around P instead of around W (not- 
ably, improvements in shaft effi- 
ciency). 
The decrease in degree of oxida- 
tion of the gas is very small in the 
example of Fig. 8a, where the O/Fe 
ratio of the oxidized fraction of the 
iron charged is assumed to be 
normal. But it would be more pro- 
nounced if that ratio were low, for 
instance, as low as 1.05 in wustite. 
The study of prereduction by the 
operating diagram alone would give 
a wrong idea of the effect of high 
degrees of metallization. It is par- 
ticularly important in this case to 
combine the two diagrams. 
The displacements in Reichardt's 
diagram are shown in Fig. 8b. The 
gas line and the solids segments 
hinge around point R as long as 
thermal ideality can be assumed. The 
following changes are observed:. (1) 
a decrease in the slope of the gas 
line, due to the decrease in total 
volume of gas (reducing gas and 
nitrogen) ; (2) a decrease in the heat 
requirements of the elaboration 
zone: BB' = CC' = vertical com- 
ponent of FF'; (3) a slight increase 
in the virtual flame temperature due 
to the decrease in solution loss CO; 
(4) a slight decrease in the heat re- 
quirements of the preparation zone 
due to the decrease in coke rate; (5) 
a marked decrease in top gas tem- 
perature measured by the horizontal 
component of GG'. 
For the preparation zone the ma- 
jor effect is to close the angle G'RS' 
to the point where neither chemical 
nor thermal ideality can be claimed 
for high degrees of metallization. 
Beyond that point, the. effect of fur- 
ther prereduction of the burden is 
inevitably less than under ideal con- 
ditions because of the separation be- 
tween point W and the operating 
line and also because of the depres- 
sion of point P associated with an 
imperfect thermal pinch in Reic- 
hardt's diagram. A more complete 
study of this subject has been given 
elsewhere? Our purpose here is 
merely to illustrate the ability of 
Reichardt's diagram to point out the 
limits assigned to the ideal assump- 
tions by heat-transfer and tempera- 
ture profiles, and to act as a safe- 
guard against erroneous use of the 
operating diagram. 
EFFECT OF COUPLED VARIATIONS the key points, light arrows for the 
OF TWO OPERATING PARAMETERS component variations. and heavv 
Selection of Suitable Pairs of 
Parameters for Coupled Variations 
From the previous section, it is 
clear that the range of validity of 
the ideal blast-furnace model is in 
most cases the range in which the 
maximum benefit is drawn from a 
unit variation on a given parameter. 
Beyond that range, the lowering of 
the chemical, and eventually the 
thermal efficiency, considerably re- 
duces the savings of coke and the 
increases in production, although 
they do not usually reverse the 
trends. The examples chosen above 
focused attention on the three major 
limits to ideal behavior: ( I ) an 
excessively low flame temperature 
TP; (2) an excessively low top gas 
temperature T,:; and (3) an exces- 
sively low amount of solution loss 
37.1. 
Due to the fact that some variables 
affect these characteristics in op- 
posite directions when varied so as 
to improve the coke rate, it seems 
attractive to combine at least two 
such cooperative variables and 
thereby to preserve ideality and 
benefit by the additive ideal effects 
of both. "'." Table I1 lists the param- 
eters of interest for their influence 
on coke rate or production and indi- 
cates by +, -, or 0 signs the direc- 
tion of variation of the criteria TP, 
Ti and ye,. This table suggests the 
pairs: hydrocarbon injection with 
increased blast temperature," hydro- 
carbon injection with increased blast 
oxygen," and burden prereduction 
with burden beneficiati0n.O 
These examples are studied below. 
Graphical Study of the Effect of 
Coupled Variations 
In Figs. 9-11, the base operation is 
referred to by letters without prime 
or subscripts and is represented by 
heavy full lines. The new operation 
obtained after the coupled varia- 
tions is referred to by primed letters 
and represented by heavy broken 
lines (except when the new line is 
superimposed over the base line). 
The two single-parameter variations 
which must be added to obtain the 
new operation are indicated in light 
full line and are referred to by 
letters with subscripts 1 and 2. 
Arrows show the displacements of 
ones for the resulting variatioi. 
Vectorial composition is suggested 
on the graphs, although this is only 
an approximate solution. 
Natural gas injection and increased 
blast 'temperature. The two separate 
parameters involved in this case 
have been studied in the previous 
section and in Figs. 6 and 7. In Figs. 
9a and 9b, the combined variations 
of injection rate and blast tempera- 
ture are so adjusted as to maintain 
the gas Pine fixed in Reichardt's 
diagram, a case which is particularly 
simple to interpret. Point F moves 
slightly upwards to F' and point G 
moves downwards to G' on the 
initial and final gas line. Under those 
circumstances, the blast temperature 
increase and the rate of injection are 
so adjusted as to balance the oppo- 
site variations in total gas volume. 
In view O F the resulting decrease in 
nitrogen volume, the reducing gas 
volume must be increased and the 
slope of the operating line is cor- 
respondingly increased. 
In Fig. 9b the opening of angle 
GRS to G'RS' and the relative sta- 
bility of angle FRC are signs that 
ideality in no less compatible with 
the new operation than it was with 
the base operation. Flame temper- 
ature ren~ains nearly constant and 
top-gas temperature moves away 
from its limiting value. Other limits 
will come into play, such as exces- 
sively low solution loss, combustion 
problems, maximum stove temper- 
ature, or ultimately excessive coke 
replacement with respect to bosh 
permeability. 
Natural gas and oxygen enricla- 
ment of the blast. Of these two 
parametelSs, only gas injection has 
been studied above. But oxygen en-richment alone (subscripts 2 in Fig. 
10) is very simple to represent: if, 
as is assumed in Fig. 10a, the blast 
temperature is equal to TR ( W 
1800°F), the reference temperature 
of the heat-balance yielding point 
P, the operating line is strictly un- 
changed (and it would otherwise 
undergo only very minor changes). 
Thus Ps and P are identical. In 
Reichardt's diagram (Fig. lob), the 
slope of the gas line decreases (from 
FR to F,R) under the effect of the 
equivalent nitrogen removal, the 
Table II . Variations of Some Operating Characteristics Following Changes on 
Selected Single Parameters 
Variations 
of 
following an 
increaae In 
Flame Top gas 
tempera- tempera- Amount of 
Coke tnre, ture, solution loss, 
rate Production TF To Y S I 
Blast temperature 
Hydrocarbon injection 
Blast oxygen 
Burden prereduction 
Burden beneficiation 
96 Ironmaking Proceedings, 1966 
CONCLUSION 
The dual graphic representation 
proposed in this text combines the 
operating diagram and a simplified 
version of Reichardt's diagram. It 
offers a means of materializing the 
balance equations for heat and for 
the elements carbon, oxygen, and 
hydrogen which are involved in the 
formation and the utilization of the 
reducing gas. 
The operating line and diagram 
illustrate most of the chemical char- 
acteristics of the operation: coke 
rate, reducing-gas consumption, gas 
and charge composition at various 
stages, and approach to chemical 
equilibrium. But they are also cap- 
able of incorporating heat balances 
as constraints on the operating line, 
such as fixed points. Reichardt's 
diagram illustrates most of the 
thermal characteristics: heat capaci- 
ties of the gas and the charge, tem- 
peratures of the gas and the charge 
Fig. 9-Coupled effects of natural gas injection (subscript 1) and increased blast temperature various stages, to ther- 
(subscript 2). mal equilibrium. 
In the interpretation of plant data, 
heat requirements in both zones re- duction and beneficiation are cou- the dual graphic representation may 
maining constant. Obviously, if pled, illustrate the fact that if a be used to guide and to illustrate 
ideality is to be preserved, there is given degree of metallization is in- the balance calculations required 
a limit to oxygen enrichment of the compatible with ideality at a given for a check of internal consistency 
blast alone set by an excessive low- slag volume, ideality may be re- of the data and for the assessment 
ering of the top-gas temperature. stored by beneficiation. This amounts of thermal and chemical efficiencies. 
When natural-gas injection and to saying that the range in which In the planning of an entirely new 
oxygen enrichment of the blast are maximum benefit can be drawn operation or of modifications to an 
I combined, in a ratio so adjusted as from prereduction is the wider the existing operation, one starts from 
to maintain the gas line fixed in lower the slag volume. A limit al- assumed or given initial diagrams 
~ ~ i ~ h ~ ~ d t ! ~ diagram ( ~ i ~ . lob), ways remains, however, and devia- to be altered under the effect of one 
angle GRS tends to open to GRS* tion from ideality can in no case be or several parameters. The calcula- 
and angle FRC tends to close to avoided with high degrees of met- tions involved are based on the 
FPRC?. ~ ~ ~ t h ~ ~ increases of the gas allization, even at zero slag weight. same principles as Michard's mathe- 
and oxygen rates, in the same pro- The cupola with its thermal pinch matical model? but they can be 
portion, would in this case even- point at the topa is ample evidence conducted as suggested or as needed 
tually invalidate the ideal assump- this statement. by the diagram's geometry. In this 
tions for the reason of an excessively The very mechanism, by which text, blast temperature, oxygen en- 
low flame temperature. beneficiation is found favorable to richment of the blast, natural-gas 
prereduction, could also be put for- injection, burden beneficiation, and 
By combining the gas and Oxygen ward to show that it is likewise prereduction have been studied .rates with a greater proportion of favorable to the use of high blast alone or by pairs, at constant hot- 
Oxygen per of injected temperatures and oxygen enrich- metal quality and under the as- natural gas, one can be lead to a merit of th'e blast (Table II). marked decrease of the slope of the sumption of ideality for heat and 
gas line, thereby closing angle GRS 
and opening angle FRC. Ideality 
would then be impaired a t high gas 
and oxygen rates for the reason of 
an excessively low top-gas tempera- 
ture. As found mathematically by 
Michard and B o ~ d i e r , ~ the maxi- 
mum rate of gas injection compati- 
ble with ideality is obtained with 
the particular proportion of gas and 
oxygen leading to simultaneous 
reaching of the two limits under 
consideration. 
Burden prereduction and burden 
beneficiation. Burden beneficiation, 
referred to on Fig. 11 by letters with 
subscript 2, offers a means of open- 
ing angle GRS in Reichardt's dia- 
gram, mostly because the lowering 
of the heat requirements is more 
pronounced in the preparation zone 
than in the elaboration zone under 
the effect of a decrease in slag 
volume. 
Prereduction on the other hand 
has been shown to close angle GRS. Fig. 10--Coupled effects of natural gas injection (subscript 1) and oxygen in the blast 
Figs. l l a and l lb , in which prere- (subscript 2). 
Blast Furnace Theory 97 
Fig. 11--Coupled effects of burden prereduction (subscript 1) and burden beneficiation (sub- 
script 2). 
oxygen transfer. A similar applica- 
tion was recently suggested for the 
study of the effects of perturbations 
and control actions on the thermal 
state of the furnace and on the hot 
metal quality." 
Under the assumption of ideality, 
the operating diagram always com- 
pletely defines some solution to a 
given problem. Reichardt's diagram 
is used to decide whether this par- 
ticular solution is valid or not, and 
to calculate the limiting values of 
the variables at conventional borders 
of the ideality range set by flame 
temperature, top gas temperature, 
and solution loss. 
Beyond those limits, variations in 
chemical efficiency can no longer be 
neglected. Their sign usually follows 
from consideration of Reichardt's 
diagram which indicates the modifi- 
cations of temperature gradients and 
The theory and logic the authors 
have applied to the formulation of 
the Rist and Reichardt diagram are 
a significant contribution to the 
technology of the blast furnace op- 
eration. 
The Rist diagram has proven itself 
to be a valuable tool when used 
to compare operating periods on a 
R. E. KUSNER is with Republic Steel Corp. 
Research Center, Cleveland, Ohio. 
of the topography of the heat and 
oxygen exchangers in the blast fur- 
nace. Quantitative solutions to prob- 
lems involving such variations on 
efficiency are not available from 
calculations. They must be obtained 
from e~periments '~~" or from prac- 
tice. A particular group of operating 
variables which was not studied here 
is inseparable from efficiency consid- 
erations since their effects on the 
diagrams appears only as efficiency 
variations: they are blowing rate, 
burden reducibility, and high top 
pressure. 
Even when limited to qualitative 
answers, the dual graphic represen- 
tation is, in the authors' belief, a 
help to the student in becoming 
familiar with the blast-furnace 
process and a useful tool for the 
full-fledged engineer in exerting 
judgment in blast-furnace problems. 
Discussion 
by R. E. Kusner 
blast furnace. However, since the 
majority of the pertinent data avail- 
able is a result of a computer- 
calculated mass and heat balance 
using a datum temperature of 77"F, 
I find it easier to take a few liberties 
with the established coordinates of 
the Rist diagram. The abscissa is 
kept the same, namely, ( 0 + Hz)/ 
(C + H,). For the ordinate, the 
parameter ( 0 +H-)/ORFE is se- 
lected rather than ( 0 + Hz)/Fe, 
where ORFE is the oxygen removed 
by direct and indirect reduction 
from the burden. With this selection 
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3A. kis t and G. Bonnivard, Rev. Met., vol. 
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Ibid., vol. 63, 1966, p. 296. 
8A. Rist and N. Meysson. Rev. Met., vol. 
61. 1964. D. 121: English translation, BISI . - 
J . Weber. and A. Rist, Rev. 
...-. 
4 N. Meysson. 
Met., vol. 61, 1964. p. 623. 
6A. Rist and N. Meysson, Rev. Met.. vol. 
62, 1965. p. 995; English translation, BISI 
4497. 
EN. Meysson. A. Maaref, and A. Rist, Rev. 
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7s. Klemantaski, JISI, vol. 174. 1953, P. 
mfi 
8 J. Szczeniowski. Etrcde d u Halit Fournearc 
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' 0 J. M. Ridgion, JISI, vol. 200, 1962, p. 389. 
11 W. H. Ceckler. Quarterly Colo. School 
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*B. von Gerstenberg and T. Kootz, Stahl 
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UB. I. Kitaev, Ju . G. Jarosenko and B. L. 
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la J. Michard. P. Dancoisne, and G. Chanty, 
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MATERIALS '?ROC.. v01.'20, 1961. p. 329. 
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de Sid0rurqie. Lzix~?mboziry, Oct. 1962. p. 
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vol. 59. 1962, p. 401. 
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lished as I.S.I. Special Report). 
and with the computed values of 
Reducing Gas Utilization (Rg) and 
Fraction Carbon Reduction or Solu- 
tion Loss (CR) , .the operating line is 
easily fixed by points A and B in 
Fig. 3. The coordinates are: 
XA = 1 + Rg, YA = ORFE/ORFE 
= 1 and XB = 1, YB = CR 
If a computer calculation is not 
available, the coordinates of points 
A and B are calculated as follows, 
assuming that the degree of hydro- 
gen utilization equals the degree of 
carbon monoxide utilization: 
I 98 lronmaking Proceedings, 1966 
I 1 ( 0 + H d T 
ORFE 
ORFE ORFE 
and 
(0 + H?)T 
CR = (1 + Rg) -Rg 
ORFE 
02STN 
-- - Oa in stone/O in burden 
ORFE 
(0 + Hz)T 
= (0 + Hz) 
ORFE 
total/O in burden 
If the wind is known to be accurate, 
the factor 
(0 + Hz)T 
can be readily deter- 
ORFE 
mined as 
If the wind must be calculated from 
top gas analyses, etc., 
(0 + Hz)T - (K + - 
ORFE 
ORDM + OCOK + OFAD 
ORFE 
OSTN 
+ K X - 
ORFE 
HZCOK + HzFAD 
- ( K - 1) ( ORFE 
- RTK 
where: K = 
N,CG + N,FAD 
( ORFE 
. , -, 
ORFE OSTN = 0 from stone 
(0 + H,)C + (0 + H2)W NXOK = Nz from coke 
- 1 1 N I A D = N3 from fuel additions - - T 
ORFE HBM = Hot blast moisture, gr/cf 
(0 + Hz) W 
= 0 in dry wind (in- 
ORFE cluding injected 0.) 
plus (0 + H?) in hot 
blast moisture per 
unit of 0 in burden. 
\ ' 
= \i)RDM + OCOK 
ORFE 
+ OFAD -t HXOK 
ORDM = 0 from reduction of met- 
alloids and lime for S 
removal 
OCOK = 0 from coke 
OFAD = 0 from fuel additions 
H,FAD = Hz from fuel additions 
' H,COK = H3 from coke 
Dr. Kusner's suggestion to use a 
different unit on the ordinate axis 
does not change the properties of 
the diagram in any respect. His com- 
ments on how to place the operating 
line, using mass balance data only, 
appropriately stress the fact that the 
operating line is in no way associated 
to a theoretical model of the blast 
furnace. Our reference-eals with 
some of the aspects of limestone 
decomposition in the operating dia- 
gram. 
HBO? = Pct O2 in hot blast, in- 
cluding injected O3 
HBN? = Pct N3 in hot blast, in- 
cluding injected 01 
In order to fix the operating point 
P on the diagram, because of sim- 
plicity, reference is made to heat 
balance data based on 77°F rather 
than the thermal pinch point tem- 
perature of 1800°F selected by the 
authors. The coordinates of point P 
are: 
co'+ H ~ C 
Yi = (c; 
ORFE 
+ c.) / 
(CI + C3) 
If one wishes to establish Yr, graphi- 
cally using the line UV, the coordi- 
Aufhor's Reply 
Once the line is drawn, it can 
always be compared to the ideal 
reference line, using a measured or 
estimated value of the pinch point 
temperature. Point W is easily 
placed in the diagram, regardless 
of the units used on the Y axis, and 
can be used to assess the chemical 
efficiency, if needed. 
Point P, to be used in predicting 
operating variations, is based on the 
heat balance of a particular stage. 
nates of U and V (Fig. 4) are: 
Xu = 0 Yo = - (0 + H?) C/ORFE 
xv = 1 Yv = -C?/C3 
where: C1 = HEF X qw 
HEF = Heat efficiency of stack 
HLH 
= 1- 
TOTH - TGSH 
HLH = Heat losses 
TOTH = Total heat developed 
above 77°F from wind, 
including hot blast heat, 
hot blast moisture heat, 
heats of combustion of 
coke and fuel 
TGSH = Sensible heat of top gas 
above 77°F 
q!tr ' = (TOTH - TGSH) / (0 
+ H2) W = Heat avail- 
able per unit of ( 0 + 
Ha) in wind 
C 3 = (PRODH + RCOH + 
HZH) /ORFE 
PRODH = Hot metal heat + slag 
heats + calcination heat 
above 77°F 
RCOH = Heat of reduction of all 
0 in burden with CO at 
77°F 
H,H = Heat of hydrogen util- 
ization, H2 + C02 a t 
77" F 
C3 = Solution loss heat, C + 
COa at 77°F per unit of 
C or 0 
The above means of determining the 
operating line and operating point 
neglects the concept stressed by the 
authors, namely, the approach to 
chemical and thermal equilibrium. 
This is unfortunate, since it would 
be an advantage to know the chemi- 
cal efficiency of the stack. However, 
if this approach, because of the 
availability of the data, permits one 
to use more readily the Rist diagram 
to indicate changes in blast furnace 
performance, the advantage of the 
Rist diagram will not have been 
lost entirely. 
Dr. Kusner suggests using an overall 
heat balance instead, with a 77°F 
temperature reference for conven- 
ience. The point associated to such 
an overall balance will unfortunately 
depend on the unkown and variable 
top gas temperature. By using the 
heat balance of the elaboration zone, 
one does away with this difficulty. 
The associated point P then varies 
in a manner which can be calculated 
a priori from the proposed changes 
on the operating variables.