Conclusion
T h e considerations of this report, although based on certain limiting assumptions, point the way to explanations of the wide range of coke displacement ratios obtained in blast furnaces by the use of blast additives. T h e potential improvements in blast furnace economics can be affected appreciably by the influence of the chosen furnace operating conditions on the effect of the additives. I t is hoped that the economic value of obtaining much more commercial data on the effect of additives, particularly a t limiting furnace conditions, is emphasized by this discussion. literature Cited (1) AIME Blast Furnace, Coke Oven, and Ra\\ hlaterials Conf., panel discussion, Philadelphia, Pa., April 1961, AZ,ME Proc. 20, 540-604 (1961). (2) Baily, T. F., Iron Age 184, 104-5 (July 16, 1959). ( 3 ) Burnside, H. E. W., Esso Research and Engineering Co., Linden, N. J., unpublished commercial blast furnace data. (4) “Chemical Engineers’ Handbook,” J. H. Perry. Ed., 3rd ed., p. 220, McGraw-Hill, h’ew York, 1950.
(5) Knepper, W. A., Woolf, P. L., Sanders, Am. Iron & Steel Inst. Meeting, Chicago, Ill., September 1961. (6) Kobrin, C. L., Iron Age 187, 107-9 (Feb. 9, 1961). (7) Negomir, J. M., Pearson, E. F., Assoc. Iron & Steel Engrs. Meeting, Cleveland, Ohio, September 1960. (8) Ostrowski, E. J., Melcher, N. B., Kesler, G. J., J . Metals 13, 25-30 (January 1961). (9) Rombough, LV. R., AIME Blast Furnace, Coke Oven, and Raw Materials Conference, Philadelphia, Pa., 1961. (10) Rossini, F. D., Pitzer, K. S., .4rnett. R. L., Braun, R. M., Pimentel, G. C., “Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds,” Comprising the Tables of the American Petroleum Institute Research Project No. 44 (extant as of Dec. 31, 1952), pp. 464, 557-610, Carnegie Press, Pittsburgh, Pa., 1953. (11) Taylor. H. C., Rombough, W. R., .4nn. Joint Meeting, Eastern and [Vestern States Blast Furnace and Coke Oven Assoc., Pittsburgh, Pa., No\ ember 1961. RECEIVED for review April 5, 1962 A C C E P T E D November 9, 1962 Symposium on Process Metallurgy, Division of Industrial and Engineering Chemistry, 141st Meeting, ACS, Washington, D. C., March 1962.
APPLICATION OF HEAT-TRANSFER PRINCIPLES T O A METALLURGICAL PROCESS PROBLEM Relationsh$ of Ladle Preheating t o Temperature Losses W.
M . D A N V E R , J.
K. M c C A U L E Y , A N D F . C. L A N G E N B E R G
Crucible Steel Co. of America, Pittsburgh 73, Pa. The chemical engineer plays an important role in process research and development activities in the steel industry. The use of material and energy balances, the concepts of unit operations, and the principles of heat and mass transfer are being applied to an increasing number of metallurgical process problems. This paper presents a simple example of the application of heat-transfer principles to a metallurgical process problem. The conclusions are applicable to many other high-temperature heat-transfer studies.
all the steel made in the United States is in open-hearth furnaces, electric furnaces, or oxygen converters. The metal is removed or tapped from the furnace into a refractory-lined ladle. When the ladle is filled, it is transported to the pouring-pit platform and the metal is poured or teemed into molds. The quality of steel is strongly influenced by the temperature of the liquid metal entering the ingot molds. Investigators have shown that the as-cast qrain size is related to the pouring or teeming temperature; transverse ingot cracks have been traced to heats poured too rapidly a t high temperature; and ingots poured cold often exhibit shell or double skin. Production yields also suffer when the metal cools excessively in the ladle. I n such cases. part of the molten metal freezes in the ladle, and the resulting skulls represent lost production and increased operating cost. Therefore, the temperature losses during tapping. holding the ladle, and teeming must be carefully controlled. This requires accurate temperature measurements in the metal in the range of 2600’ to 3200” F. and a knowledge of the heat losses betlreen the furnace and molds. RACTICALLY
p melted
Heat loss Calculation The calculation described here \vas undertaken to obtain a relationship between ladle preheating and steel temperature drop. Heat is lost from steel during tapping, holding, and teeming by the three mechanism-radiation, convection, and conduction. Radiation and convection occur a t the exposed liquid surface? and conduction takes place at the ladle brickmetal interface. The exact values of these heat losses are difficult to calculate; holiever, it is possible to show the relative importance of the individual mechanisms and the effect of ladle preheating on them. Radiation and convection losses subtract heat from steel during tapping, but neither is a function of ladle preheating. The resulting steel temperature drop from these sources is comparative1)- small for large quantities of steel. -4fter tapping, the slzg or oxide layer, which is present on liquid steel, tends to minimize the temperature drop created by radiation and convection losses. I n fact, most of the heat loss from the dark slag cover is supplied by the fusion and sensible heat of this material and not the steel. VOL. 2
NO.
1
JANUARY
1963
11
Table 1. Physical Properties of Fire Clay Brick Thermal Heat Conductivity, Capacity, Thermal Temp., B.t.u./Hr./ Density, B.tbu./Lb./ Dz$kivzty, ' F. Ft./' F. Lb./Cu. Ft. F. Sq. Ft./Hr. 0 0 546 130 0.190 0 0214 400 0 582 126 0 206 fl 0224 800 0 634 124 0 222 0 0231 1200 0 685 121 0 238 0 0237 1600 0 734 119 0 254 0 0242 2000 0 781 117 0 269 0 0248 2400 0.825 115 0.285 0.0252 2800 0.870 113 0,301 0.0256
Ladles are lined with refractory brick, and conduction occurs a t the metal-brick interface for the duration of contact. The rate of heat extraction is influenced by ladle preheating. Extensive theoretical studies have been made in this area. Samways et al. ( 5 ) , and Henzel and Keverian Paschkis (3) have published papers on this subject. Their results came from general conduction equations such as those shown below.
(4,
0,
=
kA(T, - T , )
[('G) +
2
3
Figure 1.
Graphical method of Dusinberre
where k = average thermal conductivity between T I and T2 A = area normal to heat flow Ax = distance as shown 4s = time increment T = temperature T' = temperature after 40 ~ 2 - 2 ' = average density between Tz and Tz' C+Z' = average heat capacity between T z and Tz' After the terms are rearranged and combined, the heat balance reduces to the equation =
7-2'
2(&)"']
where heat flow into a cylindrical surface Q, = heat flow into a flat surface k = thermal conductivity of brick A = brick surface area, normal to heat flow Ti = brick temperature prior to contact T , = brick surface temperature after metal contact e = time of metal-brick contact CY = thermal diffusivity of brick R = radius of vessel
Qc =
These equations were developed on the assumption that the thermal properties of the conducting material (in this case, ladle brick) are constant or independent of temperature. This assumption is not true, and in all the references mentioned a n average value of k was used. Since Q and k are directly related, this is a source of appreciable error in high temperature problems. Table I shows the variation in the thermal and physical properties of fire clay. Adams and Taylor ( 7 ) recognized the problem of the variable properties. They pointed out that for sand, the density and specific heat vary only slightly with temperature, but the effective value for thermal conductivity to be used in the general equations for heat conduction must be obtained experimentally. The same experimental approach could be adapted to the ladle-brick problem to obtain a n effective k value; however, the following simpler approach was used to obtain the same end. The Dusinberre method ( 2 ) , which is valid for temperature-dependent properties, was used to calculate the temperature profile in ladle brick. Briefly, the Dusinberre method of obtaining a temperature profile in a nonhomogeneous conducting body such as ladle brick involves first dividing the solid into equal slices (Figure 1). If heat flows, as shown, in the x direction only, a heat balance on the solid faced by points ABCD provides the following basic equation :
12
I
l & E C PROCESS DESIGN AND DEVELOPMENT
7-2
+
x1- ?
+ x3-
2
These X's can be looked upon as correction factors that are added to T2 to find the new temperature, Tz', reached in plane EF after finite time e. Actually,
and
For a particular conducting medium, it is convenient to develop a plot of X a s a function of temperature. The development requires great patience. The method is outlined by Dusinberre ( 2 ) . The plot derived for ladle brick is shown in Figure 2. The time increment, Ae, and distance, 4x, for this plot are 6 minutes and 1 inch, respectively. From this plot, correction factors were obtained and a temperature profile curve was calculated for ladle brick in contact with steel for one hour. Table I1 is the work sheet used. A sample calculation of the temperature after contact time 448 or 0.4 hour and at point 2 inches from interface illustrates use of the correction chart. The work sheet (Table 11) shows that a t time 3AO or 0.3 hour temperatures T I , T z , and T3 equal 2700', 1580°, and 681' F., respectively. At these points on the correction chart, or more specifically a t T , = 1580 and T, = 2700. ,x was found to equal 428; likewise, = -293. Hence, a t T , = 1580 and T , = 681, x,, Tz' T?'
=
7-2
+ XI-2 +
1580
'Y-2
+ 428 + (-293)
1715OF.
where T 2 is the temperature a t point 2 after time 3AO or 0.3 hour, and T2' is the temperature at point 2 after 448 or 0.4 hour. The temperature profile obtained from the results of the work sheet is shown in Figure 3. From such a profile and a knowledge of the physical dimensions of a 165-ton Crucible ladle, the heat absorbed by the bricks during 1 hour of steel contact was calculated. This heat pickup was then used in the general conduction equations and an effective value of thermal conductivity \vas calculated to be 0.832 B.t.u/hr./ft./' F
Table II.
e H2.
7 :, F., at x = 0
0.1
2700 2700
02
2700
0.3
2700
0.4
2700
0.5
2700
0.6
2700
0.7
2700
0.8
2700
0.9
2700
0
T2, O F., at
T3, F., at
7-4
Profile Developed from Correction Chart TK, F., at
9
x = 5
x = 6
x = 7
x = 8
x = Y
x =
Inches 150 150
Inches 150 150
Inches 150 150
Inches 150 150
Inchcs 150 150
Inches 150 150
Inches 150 150
150
150
150
150
150
150
150
150
150
150 3 0 153 9
150
150
150
150
150
150
150
150
150 3 0 153 3 0 156 12
150
150
150
150
150
150
150
150 3 0 153 3 0 156 5 -3 158 6 -3 161 12 -3 170
150
150
150
150
150
150
150 3 0 153 3 0 156
150
150
150
150
150
150
150
150
150
150
153
150
150
150
150
156
153
150
150
150
150
156
153
150
150
150
150
x = 3
-
0
162 21 -1 182 37 -6 213 56 - 12 257 62 - 25 294 62 - 25 331
This value is 15y0 above the average value for k , and it approaches the value of k a t the brick-steel interface temperature. I n this case the effective k is '97% of the k a t the interface temperature. I t would be interesting to see if a general relationship could be developed for this type of hightemperature problem-Le. kerf = constant (kIrnterrace
but, unfortunately, no other data are available. T h e experimental data obtained by Adams are not applicable because his
Xmn= -624
Xmn= -312
,-,Xmn= 0
2500 LL 0 -
TB, F., at
x = 4
x = 2
-
a
Ts, F., at
Inch Inches Inches Inches 150 150 150 150 775n 200a 150a 150 761 197 16 - 143 - 16 0 1393 381 106 150 505 69 6 365 -318 - 65 -6 0 1580 681 229 156 324 150 25 428 - 293 -140 - 25 0 1715 865 354 181 312 56 381 181 -281 -162 -6 - 53 1815 1015 482 231 337 293 181 84 -268 -168 -25 -19 1884 1140 638 296 310 265 175 122 -250 -162 -131 - 37 1944 1243 682 381 287 259 200 103 -234 -197 -97 50 1997 130.5 785 434 265 250 181 119 234 -172 -109 -59 2028 1383 857 454 256 234 187 125 220 -172 -125 62 2064 1445 557 919 b Corrections obtained from correction chart.
x = 7
O
-
2700 Ajproximated.
T7 , F., at
O
F., at
-
1.o
TB,
' F., at
O
2000
C
-1 167 19 -6 179 25 -3 201 62 -12 251
O
'
O
Table 111.
Initial Ladle TzmP., F. 50 100 150 1000
10 x =
12 x = 13 Inches Inches 150 150 150 150
17 x =
Heat Absorbed by Fire Clay Brick
Heat (108 B.t.u.) Absorbed by Brick after 75 min. 30 min. 60 min. 4.55 4.47 4.40 2.92
3.25 3.18 3.14 2.09
6.33 6.20 6.07 4.05
sand casting contained water, an additional problem not encountered with ladle brick. By using the effective value of 0.832 B.t.u./hr./ft./' F. in the general conduction equation, the heat pickup by the brick shown in Table I11 was calculated. Table I V lists the temperature drop in 165 tons of steel corresponding to the heat values in Table 111.
I-
1500 3 L
e $
1000
b-
500
loolOO 500 Figure 2.
1000 1500 2000 T e m p e r a t u r e , T m , OF:
2500
Figure 3. Temperature profile in ladle brick
Temperature correction chart for ladle brick
= 0 . 5 4 6 B.t.u./hr./ft./O F. = 130 Ib./cu. foot C p = 0.1 95 B.t.u./lb./O F. a t datum temperature of 100' F. k
b
0 ' 0
2 4 6 1'0 1l2' Distance from hlolten Stee! Brick Interface, X , Inches
p
VOL. 2
NO.
1
JANUARY
1 9 6 3
13
The values in ‘Table IV represent the temperature drop of
330,000 pounds of steel if that quantity were instantaneously placed in a ladle and then permitted to remain there for 15, 30, or 60 minutes. Such is not the case in actual practice. Actually, it requires approximately 60 minutes’ total time to tap, hold, and completely teem 330,000 pounds of steel; and during this time, two variables, the weight of steel in the ladle and the exposed brick area, are constantly changing. These variables were treated as constant for this computation. Consequently, Table I V is presented not as the expected temperature drop of the steel during tapping and teeming, but as a qualitative illustration of the relationship between steel-temperature drop and ladle preheating. For example, preheating a ladle to 150’ F. does not retard steel heat loss; preheating to over 1000” F. retards it significantly. Table IV also shows that the rate of temperature drop is greatest during the first minutes of holding time. Conclusions
Preheating large ladles does not affect steel temperature drop during teeming unless the preheating is of considerable magnitude (over 1000 O F.). The rate of conductive heat loss from steel is greatest during the first minutes of steel-brick contact. General conduction equations and relationships can be applied to the ladle problem, even though the physical and thermal properties of the brick change with temperature, if the proper k value is used. The thermal conductivity value, k , which gave the best heat-loss estimation, was not estimated a t a n average temperatcold faee)//2. Instead it w-as evaluated ture-i.e., (that near the hot-face temperature.
+
Table IV.
Relationship between Steel Tempercrture Drop and ladle Preheating
Initial Ladle Tcmp., ’F . 50 100 150 1000
Temp. Drop, F., in Steel after 75 min. 30 min. 60 min.
55 54
53 35
77 75 74 49
107 104 102 68
Acknowledgment
The authors express appreciation to the Crucible Steel Co. of America for permission to publish this paper. literature Cited (1) Adams, C. M., Jr., Taylor, H. F., Trans. Am. Foundrymen’s Sod. 65, 170-6 (1957). ( 2 ) Dusinberre, G. M., “Numerical Analysis of Heat Flow,” pp. 186-97, McGraw-Hill, New York, 1949. ( 3 ) Henzel, J. G.. Jr.. Keverian. J., “Ladle Temperature Loss.” Electric Furnace Conference, Pittsburgh, Pa.?Dec. 6-8, 1961. ’ (4) Paschkis, V., Tranr. Am. Foundrymen’s SOP,64, 565-76 (1956). (5) Samways, N. L., Dancy, T. E., Li, K., Halapatz. J., “.4nalysis of Factors Affecting Temperature Drop between Tapping and Teeming in Steelmaking,” International Symposium on the Physical Chemistry of Process Metallurgy, Pittsburgh, Pa.. April 27 to May 1, 1959. \
,
RECEIVED for review May 22, 1961 ACCEPTED May 14, 1962 Division of Industrial and Engineering Chemistry, 141st Meeting, ACS, Washington, D. C., March 1962.
THE SIGNIFICANCE OF FLUID DYNAMICS IN THE BLAST FURNACE STACK J. C. A G A R W A L A N D W . L. D A V I S , J R . Applied Research Laboratory, United States Steel Gorp., Monroeuille, Pa.
To improve the productivity and thermal and chemical efficiency of the blast furnace process, it is important to establish favorable fluid-flow characteristics in the blast furnace stack. These characteristics are related to the permeability of the burden m a t e r i a l s q r e , coke, and limestone-within the stack, the particle size and distribution of solids, and gas velocity, density, viscosity, pressure, and temperature. The application of chemical engineering techniques and process engineering analysis indicated that considerable improvement in blast furnace operation would result from various procedures for beneficiating the burden materials. The chemical engineering aspects of beneficiation processes such as sintering, pelletizing, and briquetting are discussed, together with the resulting improvements in fluid-flow characteristics and blast furnace performance.
HE BLAST FURNACE
is a countercurrent, packed-bed reactor
Tin which the burden materials are heated, dried, calcined, reduced, smelted, and partly refined by the hot ascending gases generated by the combustion of coke with preheated air. There has recently been a great leap forward in blast-furnace technology, which is evidenced by a n approximately twofold increase in production rate for some furnaces and a one-third decrease in coke consumption per ton of molten pig iron or hot metal. These spectacular improvements could not have 14
I & E C PROCESS D E S I G N AND D E V E L O P M E N T
been achieved without more uniform gas flow and gas-solids contact in the stack. The efficient utilization of the reducing gases and heat generated in the furnace depends upon the intimacy and uniformity of gas-solid contact. The amount of reducing gases and heat depends upon the moles of oxygen (contained in the air blast) blown into the furnace in a unit of time, usually referred to as the wind rate. The two factors, gas-solid contact and wind rate, determine the productivity and efficiency of the furnace. .4ccordingly. attempts to apply
