a dual graphic representation of the blast furnace mass and heat balances

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 present such a model, incorporating the most important characteristics of the blast-furnace operation and illus- trating the solution to many problems 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 particularly well suited to illustrate the "thermal pinch point" and the conditions 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 developed by the authors in the past few years.'-"This diagram is particularly well suited to illustrate the "chemical pinch point" and the conditions 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 injection and oxygen in the blast, burden prereduction and ore beneficiation) .

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 authors.'-" 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 process 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 simplified 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 furnace: (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 exchanger 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 between 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 solution 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 discussion 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 direct proportion to the separation between 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 fusion, a major part of the total heat losses, and the heats of the endothermic reactions of solution loss and' direct reduction of the nonferrous 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 segments 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 simplified 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 corresponding heat requirements pertaining to the preparation zone include the sensible heat of the charge, a minor part of the total heat losses, and a small term of indirect reduction of the initial oxides to wustite.

Segment RC represents the heating of the charge from TR up to a mean casting temperature Tc (270OoF, 1480°C) which is intermediate 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 temperature. 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 cooling of the gas between TR and the top gas temperature To, assuming that the indirect reduction of wustite 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 decrease 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 specific 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 approximation, leading to a top gas temperature in slight excess' of the exact value. For the highest and the

lowest degrees of oxidation encountered 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 operation were given with sufficient in- formation to define it unambiguously, and if the data were ex- tremely accurate, Reichardt's diagram 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-furnace thermal efficiency, by means of the minimum separation between the two curves. In practice, the data are always too rough for this purpose 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 operation 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 reduction. 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 combustion, endothermic solution loss and direct reductioi~s; and (2) in the utilization of the reducing gas in the indirect reduction of the iron oxides.

The operating diagram which is presented here illustrates both aspects.

Definition of the Operating Line Formation of the reducing gas in

the absence of hydrogen. If, for simplicity, 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 written 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 reducing gas or the ratio of the flowrate of gas to the flowrate of iron. The x and y terms are the CO contributions in each reference system, respectively, with subscripts relat- ing to the various sources of oxygen: 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 reducing 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 separately, 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 reducing gas, CO and Hz, produced in amounts proportional to the .blast rate,

xr, yf are numbers of moles of reducing gas, CO and H, produced in fixed amounts per unit of Fe.

Hydrogen from natural blast humidity will normally participate in xb and yb. Hydrogen from a hydrocarbon 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 segment representing the oxygen removed from the iron oxides by indirect reduction and partially con- verting CO to COa and H, to KO. The number of atoms of oxygen involved 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 indirect-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 oxygen and sources of hydrogen appear on the negative side.

The interpretation of various points and segments is summed up later, after the study of the properties of the operating line.

Properties of the Operating Line The operating line has two im-

portant groups of properties respectively 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 balance for an infinitesimal volume between 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 function of Y. The drawing of this contour is greatly simplified if one re- calls the results of probing cam- paigns,","-'" which revealed the characteristics of the blast furnace as an oxygen exchanger. Most of the indirect 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 favorable 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 isothermal 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 reducing 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 possible to express in Reichardt's diagram the condition of chemical equilibrium just discussed, but it is possible to express in the operating diagram the condition of thermal equilibrium 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 temperature, the balance equation is re- markably simple to write. The reason is that the heat input by the charge and the heat output by the gas are both equal to zero. The following 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 between TI, and TR, the various endothermic reactions associated with the presence of hydrogen (if present in fixed proportion with the blast), etc.

2. The heat requirement of solution loss: the product of y.1 (at. O/ at. Fe) by the endothermic heat effect of the solution loss reaction at TR, qal (kcal/at. C gasified).

3. The whole of the heat requirements Q which are fixed per unit of iron produced at steady state: heating and melting of the charge, direct reduction of nonferrous oxides, indirect reduction of wustite, heat losses, and the various endothermic reactions associated with the presence 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 measure 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 coordinates of point P are practically independent of the amount of solution loss to be performed in the elaboration zone. XP is a function of the blast characteristics only (temperature and composition), Yp is a function 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 operating diagram to take advantage of the equivalence of 1 at. 0 , 1 at. C, 1 mole CO and 1 mole H, in the reducing 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 oxidation 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 reduction) of iron, at. O/at. Fe

Point D. , XU = xr, the fraction of each

mole of reducing gas originating from the blast, and thereby bearing a fixed ratio to the nitrogen. XI, is proportional 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 influence of factors affect- ing the amount of solution loss without chang- ing the other thermal requirements of the elaboration 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, produced 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 production of iron and proportional to the retention time of the charge. Seg- ment UE is under all circumstances proportional to the total heat input into the elaboration 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 elaboration 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 reducing gas

YK = overall degree of oxidation 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 metallic iron in the burden

p, slope of the operating line: number of moles of reducing gas (CO, Hz) required for the production 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 operation 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 thermal and chemical efficiencies. If ideality is assumed for both, any chosen set of operating variables (type of burden, blast characteristics, hot metal composition, nature and rate of injection, etc.) leads to an operating line PW and to a practical 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 transfer. A qualitative but valuable check can be provided by Reichardt's diagram. 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 illustrated 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 requirements of the elaboration zone are then represented by segments of equal length, VB in the operating diagram and cr in Reichardt's diagram (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 (except with injections, as shown below).

The following examples will show how the dual graphic representation is used, first to illustrate the influence of single parameters varying within and to the limits of the ideal range, and second to illustrate coupled variations of pairs of parameters 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 applications, 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 (provided 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 temperature, 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 thermal coefficient q,, the heat input in kcal/mole of reducing gas originating 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.


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 ideality. If chemical ideality had not been assumed in the first place, it would be necessary to associate a decreasing shaft efficiency to any increase of blast temperature. The coke saving would then be less than ideal. The transition from ideal to nonideal behavior occurs at blast temperatures 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. lowering of 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 specifically under either one of two assumptions:

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 increase in the ratio of UE to UE'.

The modifications observed on the operating diagram involve corresponding 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 nitrogen); (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 represented, 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 materials to T,, UU' and VV' are both proportional to the amount of natural 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 operating diagram of Fig. 7a are (1) an increase in slope of the operating line, ~ p ; (2) an increase in the blast consumption EEf-UU'; (3) a decrease BB' in the amount of solution loss.

The increase in slope of the operating 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 remain unchanged and the replacement ratio would be equal to 3 at. C coke/mole CH,. In fact, with an increase in slope A p for the injection of i moles of methane/at Fe, the replacement 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 production when the blowing rate is constant.

The decrease in solution loss observed 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, important improvements in shaft efficiency 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 increase VV' is not included here because it represents heat consumed on the site of combustion with the effect of lowering the true flame temperature) ; (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 horizontal 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 reduction. Thus, if the chemical efficiency is not unity to begin with, it is improved by the injection, an effect which is further accentuated by faster reduction rates in hydrogen-bearing gases. -

When the shaft efficiency is improved 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 representation, one is able to visualize the two phenomena which sooner or later reverse the tendency to improve 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 temperature 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 apparent on 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 replacement 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 decreased, as is shown by the operating diagram of Fig. 8a. Provided iron metal is present in the charge and resists reoxidation, point W is depressed. Its abscissa remains constant 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 following 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 decrease 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 prereduction is an example of a variable which induces a high saving of coke (and a correspondingly high increase 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 efficiency).

The decrease in degree of oxidation 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 pronounced 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 particularly 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 component 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 requirements of the preparation zone due to the decrease in coke rate; (5) a marked decrease in top gas temperature measured by the horizontal component of GG'.

For the preparation zone the major 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 further prereduction of the burden is inevitably less than under ideal conditions because of the separation between 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 assumptions by heat-transfer and temperature 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 excessively low amount of solution loss 37.1.

Due to the fact that some variables affect these characteristics in opposite 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 parameters of interest for their influence on coke rate or production and indicates by +, -, or 0 signs the direction of variation of the criteria TP, Ti and ye,. This table suggests the pairs: hydrocarbon injection with increased blast temperature," hydrocarbon 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 variations 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 temperature 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 opposite 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 correspondingly 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 temperature ren~ains nearly constant and top-gas temperature moves away from its limiting value. Other limits will come into play, such as excessively low solution loss, combustion problems, maximum stove temperature, 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 enrichment 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 unchanged (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 characteristics 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 capacities of the gas and the charge, temperatures 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 reduction 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 temperature. As found mathematically by Michard and B o ~ d i e r , ~ the maximum rate of gas injection compatible 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 opening angle GRS in Reichardt's diagram, 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).


Fig. 11--Coupled effects of burden prereduction (subscript 1) and burden beneficiation (subscript 2).

oxygen transfer. A similar application 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 particular 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 modifications 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 operation.

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 furnace. Quantitative solutions to problems involving such variations on efficiency are not available from calculations. They must be obtained from e~periments '~~" or from practice. 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 representation 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 available 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 selected rather than ( 0 + Hz)/Fe, where ORFE is the oxygen removed by direct and indirect reduction from the burden. With this selection

REFERENCES 1 P. Reichardt, Arcla. Eisenhiittenzu., vol.

1. 1927 p. 77. 3A. kis t and G. Bonnivard, Rev. Met., vol.

60, 1963, p. 23; Ibid., vol. 63. 1966, p. 197; 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.

Met., vol. 62. 1965, p. 1161. English translation, BISI 4786.

7s. Klemantaski, JISI, vol. 174. 1953, P. mfi

8 J. Szczeniowski. Etrcde d u Halit Fournearc I-Cahiers du CESSID. Metz. France, 1956 and 1964.

0 J. Michnrd. Etude dri Haat Forcrnea~c II- Cahiers d u CESSID. Metz. France. 1959.

' 0 J. M. Ridgion, JISI, vol. 200, 1962, p. 389. 11 W. H. Ceckler. Quarterly Colo. School

Mines, vol. 59, 1964, p. 417. *B. von Gerstenberg and T. Kootz, Stahl

Eisen, vol. 84, 1964, p. 1180. UB. I. Kitaev, Ju . G. Jarosenko and B. L.

Lazarev. 3me Jotirnees Internationales de Sidhrrtryie. Lu.retnbourg. Oct. 1962, p. 47.

14 A. Firket and J . Molderez. Reu. Univ. Mines, vol. 15. 1959, p. 93.

16, E. Bonnaure. AIME BLAST FURNACE. COKE OVENS AND RAW MATERIALS PROC., v01. 18. 1959. p. 75.

la J. Michard. P. Dancoisne, and G. Chanty, BLAST FURNACE. COKE OVENS AND RAW

MATERIALS '?ROC.. v01.'20, 1961. p. 329. 17 J . Michard, 31ne Journees Internationales

de Sid0rurqie. Lzix~?mboziry, Oct. 1962. p. 346.

ISC. Bonn ~ivard and A. Rist. Rev. &let.. - . p - ~ ~ ~

vol. 59. 1962, p. 401. '!'A. Rist, C. Offroy. C. Chartier, and M.

Roubs. Centre Doc. Sider. Circular, vol. 21. - - - . ~ ~. .~ X'L. S. Darken and R. W. Gurrs9. J. Am.

Chem. Soc.. vol. 67. 1945. p. 1398. 3 W. Zist:hkale. G. Heynert, and H. Beer.

Stahl Eiset~, vol. 83. 1963. p. 1117; French translation, IRSID 2336.

"P. Ischebeck. G. Heynert, and H. Beer. 3me JournGes Interi~ationales de Sidhrursie. L~ i ren~bourq . Oct. 1962, p. 378. 3 P. Dancoisne and J. M~chard. Charleroi

Internationlil Coilgress. Sept. 19-22. 1966. Preprint D. 1.

-"a J . Cordier. J. Met.. vol. 1961. no. 1, p. 91 - -.

LCJ. Michard and Y. Boudier. Rev. Met.. vol. 60, 1963. p. 513.

% A . Rist. P . Dancoisne, and R. Jon. IRSID. RE 131. presented a t Assoc. Tech. Siderurgie Francaise. Journee de la Fonte. June 1. 1966 lpublished in Rev. Met., vol. 64, no. 2. 1967.

?'C. Staib. A. Rist. and J. Michard. IRSID, RE 144. presented a t the I.S.I. Autumn Meet- ing. London. Nov. 22-23. 1966 !to be pub- 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 hydrogen 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 diagram.

HBO? = Pct O2 in hot blast, including injected O3

HBN? = Pct N3 in hot blast, including injected 01

In order to fix the operating point P on the diagram, because of simplicity, reference is made to heat balance data based on 77°F rather than the thermal pinch point temperature 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, graphically 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 available 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 utilization, 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 chemical 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 convenience. 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.

a dual graphic representation of the blast furnace mass and heat balances

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