0
Pressure Drop in Blast Furnace and in Cupola
0 0
.
0 0
SABRI ERGUN C o d Research Laboratory, Carnegie Instifute o f Technology, Pittsburgh, Pa.
T
HE pressure loss accompanying the flow of fluids through
blast furnaces is of prime interest to the iron industry. I n the design and operation of blast furnaces several factors must be considered: rate of production of the furnace, cost or economy of operation, performance and ease of control, size of the furnace, quality of iron produced, and miscellaneous factors. It is difficult to ascribe a sequence of importance to these factors: All are interrelated and important. For example, the rate of air blast determines the rate of combustion of coke, which in turn determines the rate of iron production. A blast furn?ce usually requires pumping of enormous quantities of preheated air, the tonnage of air exceeding that of all other materials passing through the furnace. The need of maintaining high temperatures in the furnace restricts the materials of construction and thus places a limit on its mechanical strength. The necessity of pumping the required quantities of air a t pressures provided in the construction of the unit likewise places limits on the size of the furnace and its operating conditions. The relation of these problems to economy and performance needs no elaboration. It has been generally agreed that the quality of pig iron produced depends upon the chemical composition of the charge-vie., ore, coke, stone, etc.-and the operating conditions, which are largely determined by the physical properties of the charge. Physical and chemical tests are needed on all the materials charged and the significance of these tests to blast furnace performance should be evaluated. To date, however, emphasis has been directed princip'ally toward measurement of the properties of coke. The effects of the size and strength of coke have been the subject of numerous investigations and have led to development of tests (11, $1, 24) such as the tumbler test and the shatter test. The aim was a practical one-i.e., to find the best size and to formulate a specification for size stability. Investigations of the effects of physical properties of ore have been carried out to a relatively limited extent. The effect of sized and sintered ores on blast furnace performance has been studied and discussed by various workers (3, 13-16, 18, 19),most of whom have reported that size preparation of iron ore led to considerable improvement in blast furnace performance, and recommended that all the miscellaneous materials should be kept in mind and their sizing should be controlled. These and various other efforts t o improve the pePformance of blast furnaces are extremely important if one considers the size of the iron industry and its importance in the national life. The procedure followed in most investigations can be classed as improvement by trial and error. Nevertheless, theoretical analysis of the problems in operation of the blast furnace should not be overlooked. It seems reasonable to suppose that the basic answers can be formulated on sound theoretical grounds only. The present theoretical studies are concerned with the field of fluid dynamics-i.e., the pressure loss in blast furnaces. Additional studies are needed on heat and mass transfer rates ( 7 ) and on reaction kinetics for a better understanding of what occurs in a blast furnace and how better control of practice can be assured.
The physical properties of the charge are of major importance in blast furnace operation. For a given blast pressure and fixed furnace dimensions they determine the rate of air flow, which in turn limits the rate of driving of the furnace. Formulation of an equation for pressure loss will not only lead to numerical answers t o problems arising from the physical properties of the charge, but will also guide experiments for the improvement of operation. Pressure drop expressions adopted for use in blast furnaces (9)are empirical and are not suitable for such purposes. The importance of evaluation of pressure drop in a blast furnace on fundamental principles will become clearer as the factors influencing pressure drop are discussed.
Theory The blast furnace is essentially a packed column. I n the formulation of pressure loss through blast furnaces it is necessary to resort to the laws of fluid flow through beds of broken solids. Recent studies in this field have led to the development of the following general expression for pressure drop in packed columns (6):
dP/dL = u ' p U / D i $- b'pU2/Dp U' =
4.67 (1
b' = 4.67 X
-
(1)
€)'/e3
(1 - € ) / e 3
where dP/dL is the pressure gradient, fi is the absolute viscosity of the gas, U is its superficial velocity, p is its density, D , is the mean size of the solids, and c is the fractional void volume (for units employed see nomenclature). A rigorous application of Equation 1 to the b l a ~ tfurnace requires that the variables and the changes in the variables from air tuybres to stock level be known. Simplifying assumptions, however, must be made so that practicable expressions can be derived. The assumptions should be consistent with current knowledge of blast furnace practice and with test data obtained in actual and model furnaces. The first term of Equation 1 represents the viscous energy loss and the second, the kinetic energy loss. Under the flow conditions encountered in blast furnace operation viscous energy loss accounts for less than 27, of the pressure drop, and hence the first term can be omitted. Equation 1 then becomes:
dP/dL = 4.67 X 10-3
(+)
pUZ/D,
I n order to carry out integration of Equation .2, the factors to be considered in the evaluation of gas density and superficial velocity at any level are: composition of the gas, its temperature, static pressure, and cross-sectional area of the furnace. Because chemical reactions in the furnace will result in changes in composition and the total amount of the gas passing, these changes with level and their effects upon pressure drop must be studied. The most extensive data in a n actual blast furnace stock column were collected by Kinney and coworkers ( 2 7 ) . Gas samples,
INDUSTRIAL AND ENGINEERING CHEMISTRY
478
Vol. 45, No. 2
furnace varies with height, variations relative, to height are not great (see Figure 1); therefore, the average cross-sectional area-i.e., internal volunic of the furnace between center line of tuybres and Moles Av. STP Total zero stock line divided by the distance between Av. Gas Ar. Density, Gas/ the two lines-might be advantageously used as Plane Positiona, Temp., Gas Composition, % Mol. Lb./Cu. Mole NO. Feet 0 F. C 0 2 CO H2 Ks Weight Ft. Air an effective value and l / A i can be brought out0 68 14.6 24.6 4 . 1 5 6 . 7 29.3 0.0815 1.36 side the integral term. Using the information re1 65 ii5 14.9 25.2 3 . 4 56.5 29.6 0.0824 1.40 0.0827 1.40 15.2 2 6 . 3 3 . 2 5 6 . 3 garding furnace dimensions and temperature varia29.7 2 57 1300 0.0809 1.36 3 46 lL.2 2 7 . 7 2 . 3 5 8 . 1 2 9 . 0 1575 tions with level included in Kinney's report, the 0.0800 1.34 28.7 a . o 3 4 . 7 0 . 9 58.9 4 24 1727 of such a simplification on pressure drop effect a Distance above tuyeres level. calculations has been checked and found t o be negligible. The temperatures, as found by integration for each plane, have been plotted against elevation in Figure 4. From this information and the furnace temperature observations, and static and velocity pressure readings were taken a t different points both vertically and radially. dimensions, T L dL has been integrated graphically (see Four horizontal planes were selected for the measurements. A sectional diagram of the furnace used in the investigation and the positions of the four planes are shown in Figure 1. The readings were taken a t intervals of 3 to 6 inches along the radius starting from a point on the inwall, on the back of the furnace, t o the center. The radial variations in average composition of TO' =J samples obtained on several days on plane 2 are plotted in Figure 2. Average gas compositions of samples taken on each of the four planes and of the flue gas are tabulated in Table I, and the results are plotted in Figure 3. Table I also contains the average molecular weight of gas, its density (STP), and the total number of moles of gas per mole of air input. From inspection of Table I the following conclusions can be drawn: ( 1 ) The total number of moles of gas flowing through any plane of the furnace is substantially constant and equal to that of the blast furnace top gas-viz., approximately 40y0higher than the blast. ( 2 ) The density (STP) of the gas along the height of the furnace is also essentially constant-viz., equal to that of blast furnace top gas. In Equation 2 , the velocity, U , can be eliminated by the total flow rate, Q ( = 60 UAL) where A L is the cross-sectional area of the furnace. Because the actual molar flow rate of gases in a furnace at all levels is higher than air by 40%, Q can simply be 1 0 ' 4 expressed in terms of the rate of blast of air. If Q0 is the blast rate a t standard temperature and pressure, then Table 1.
Gas Compositions at Various Elevations in a Blast Furnace (77)
Q = 1.4
Q o
( T L / T ~()P ~ / P L )
(2a)
where T is the absolute temperature of gas, P is its absolute pressure, and the subscripts L and 0, respectively, denote conditions a t level L and under standard conditions. Inasmuch as the average molecular weight of the gases is constant and equal to that of blast furnace top gas, the density, p , a t any level can be expressed as p =
P,(T,/TL)( P L / P ~ )
(2b)
Substitution of Equations 2a and 2b into 2 and replacement of 0'by Q lead to
JPLdP
=
f
2.54
x
lo-~(')(Pog)(&E
3 d L
(3)
IO'
Figure 1.
Accepting, for the moment, that numerical values can be assigned t o fractional void volume and to particle size, E and D, can be taken outside the integral sign. Substituting P o = 14.7 pounds per square inch and p o = 0.078 pound per cubic foot (at 60" F. and 29.9 inches of mercury) in Equation 3 and taking the constant terms outside the integral,
0
I 0'
Section Diagram of Furnace
Furnace 4, South Works, Illinois Steel Co., South Chicago, 111. (17)
Figure 5 ) and found to be 1.33" F. per cubic foot, whereas 1/24:
LH
TLdL has yielded a value of 1.30" R. per cubic foot.
It is
thus demonstrated that the simplification is justified. The proper average gas temperature, therefore, can be defined by where subscripts i and e, respectively, correspond to inlet and exit conditions. Although the cross-sectional area of a blast
T = & L H TLdL
INDUSTRIAL AND ENGINEERING CHEMISTRY
February 1953
Substituting AP = Pi rearranging properly7
479
- P, and Equation 4a in Equation 4 and
L 0
%
2400
w
-
where t = T 460-i.e., average gas temperature in " F.-H is the average height of the stock above tuybres, and P , is the absolute pressure a t the top of the furnace. Equation 5 is the general expression for the pressure drop in a blast furnace. For a successful application of the equation, the values of effective average gas temperature, size of the stock, and fractional void volume should be estimated. ESTIMATION OF EFFECTIVE AVERAGEGAS TEMPERATURE. Average gas temperature can be determined graphically or algebraically as called for by Equation 4a from a plot of temperature vs. elevation. The resulting curves on plots of temperature us. elevation are functions of rate of blowing, temperature of inlet gas, height of the stock, size of the stock, etc. The shapes of the curves, however, for blast furnaces will be similar, and the curves are not expected to yield widely different results for average gas temperature. A plot of temperature us. elevation for
0
IO
i?O
30
40
SO
60
DISTANCE ABOVE TUYERE LEVEL. Ft.
Figure 4.
Average Temperature of
Gas at Various Elevations
(77) h nr
I
IO
I
I
20
30
DISTANCE ABOVE
I
I
I
I
40
50
60
TO
TUYERE LEVEL, FTo
Figure 5. Graphical Integrationj%
DISTANCE CROU INWALL. C Z
Figure 9.
Composition of Gas on Plane
DISTANCE ABOVE
Figure 3.
P (77)
N Y E R L LEVEL, FT.
Average Composition of Gas at Various Elevations (77)
the furnace investigated by Kinney ( 1 7 ) is shown in Figure 4, the graphical integration of which yielded an average gas temperature of 1650" F. I n the absence of any other data on gas temperatures in blast furnaces, this figure can be used as a first approximation in the calculation of pressure drop in blast furnaces. (Inasmuch as the gas is hotter than the solids in the major portion of the blast furnace, it is likely that the actual gas temperatures are higher than the observed values, if extreme care is not taken in the measurements. Therefore, a slightly higher temperature-e.g., 1700" F.-is recommended for use in Equation 5.) It would indeed be desirable to have similar data for temperatures in other furnaces. Such data are essential not only in the establishment of average gas temperatures, but also in the analysis of heat transfer, reaction rates, and mass transfer problems which must be solved to establish optimum operating conditions. ESTIMATION OF EFFECTIVE AVERAGE PARTICLE SIZEOF BURDEN. Determination of the effective average particle size of the materials contained in the stock column presents a difficult problem. The stock is made of different materials, such as coke, ore, stone, scrap, and sinter, which have wide ranges of size. The mode and sequence of charging these materials depend upon the practice adopted. Chemical reactions between gas and solids, decomposition of stone, melting of some of the solids, and size degradation due to breakage as the stock is charged and as it descends in the furnace will affect the size. These factors must be considered in estimating the effective average size of the stock.
INDUSTRIAL AND ENGINEERING CHEMISTRY
480
Table II.
Screen Analysis of Some Ores (Percentage by weight)
Screen o n , Inches 6 4 3 2 f.5 1
0.75 0.5 s/a
Cliffs Richards Group Lump (1)
... ... ,..
8.8 9.E 22 4
...
44.1 10.0 4.1
Quensa
(1)
(1)
...
50.1
8.2 , . .
9.1
.,
,
8.1
... ...
6.8
43.6
10.1
14.8
3.0
...
5'2 0.25 ... 2.5 No. 4 No. 6 ... 2.7 2.3 No. 8 K O . 10 ... 1.9 ... 2.3 No. 14 No. 20 ... 1.5 1.6 hTo. 28 ,.. 0.8 No. 35 1.1 3.4 Through bottom screen Av. sizea, 0.79 0.76 inches a For plus 8-mesh fractions.
...
3:3 1.9 1.4 1.8 1.5 1.7 1.3 1.6 0.9 6.5
Avon (1)
Benson (1)
...
...
...
...
...
... ...
Canby (1)
...... . . . . . . ... ... ... ...
6.5 7.9 13.1 12.0
3i:5
37 1
32.1
22'6
25.4
5.5
7.6
11 1
5.5
... ... ..
3.0 10.0
Blain (1)
... ... ...
2.9 4.6 6.2 8.8
... ...
12.1 10.2 8.1 10.5
., .. .. ...
Elisa Sinter (1)
...
Williamson (1)
...
3:i 6.5
...
27.6
...
38:o
... ...
... ... ... ...
8.8 17.4 11.5 11.4
... ... 24.9 ... 6.5 ...
Utah
(4)
i:s
9.0 17.3 8.1 10.8
Eagle Mountain
(4)
...
... ...
10.4
0.7 18 3 43 3 28.3 1.8
10.1
2.4
,..
... ...
Vol. 45, No. 2 charged during a completc cycle. Following the development ( 6 ) of Equation 1, which is in accordance with the principle of hydraulic radius, the average size of a bed composed of solids of various sizes can be expressed as :
... ...
where X i is the fraction by volume occupied by solids hav1.3 5 8 1.1 2 8 3.0 ing the size Di. It may not ... ... ... 4.5 ... 1.6 5'7 3.6 4.6 3:2 be practical to obtain a rep0.7 2.9 4 4 1.8 2.8 1.9 ... resentative sample of the total 5.2 14.0 20.2 6.3 14:7 27.9 11.3 3 8 charge so that a size analysis can be made. However, size 1.35 0.43 0.43 0.33 0.48 0.39 0.48 0.50 1,02 analyses for individual comDonents-viz.. coke., ore., stone. sinter, etc.-are sometimes available. The average size It would be, of course, desirable to have a knowledge of the of each component can be determined by the use of Equasize of the stock a t different elevations, but this presents an tion 6. The over-all size of the charge should be determined, impracticable, if not impossible, task on account of the difficulty using Equation 6 again, knowing the size and volumetric fracin obt,aining a representative sample of solids. From the viewtion of each component. If sizing is done by sieve analysis, coke-in point of fluid dynamics the breakage of solids-e.g., which is the most common and simple method, Di corresponds the furnace is undesirable. Generally a decrease in size increases to the average of the openings of the two successive sieves which pressure loss. For example, a charge of coke, the average size specify the fraction. of which is reduced to one half of its original size, a t a level 15 Experiment'al verification of the validity of Equation 6 in the feet above tuyhres, would roughly cause 20% more pressure drop determination of average size has been tried ( 6 ) with pressure than if no appreciable reduction had occurred. This in itself drop data for beds having a size ratio up to 6 to 1. Better is not. serious, as a decrease in size causes an increase in surface agreement with theory is obt,ained with closer ratios of size. which favors increased reaction rat'e, and heat and mass transfer. Blast furnace charges have, in some cases, a wider size range, as But a study of breakage of coke reveals that size degradation seen from some typical sieve analyses for ores, sinters, and cokes results in a certain size distribution depending upon the type of shown in Tables I1 to VI. I n blast furnaces, minus 35-mesh ore breakage causing the increase in size range. Certain fines are and minus 20-mesh coke will be lifted but not necessarily blown either blown off or forced into pockets where they are held by off. I n some northern furnaces which charge Mesabi ores as surface friction, and some fill in spaces between large particles. much as lOYGof the ore is carried out in t,he top gas. Some fines The immediate result may be either excessive channeling or decrease in fractional void volume. Channeling is very undesirable, for when it occurs, a major portion of gas passes through the Table 111. Screen Analyses of Mesabi Ores (3) channels and only the surfaces surrounding them are fully effective for reaction, heat, and mass transfer rate. The major (Pelcentage by weight) 7-Concenportion of solid surfaces is thus rendered ineffective. Decrease Sire 3-Sormal 3-Coarse 3-Sinter 7-Normal trates in the fractional void volume, on the other hand, causes excessive On o.5 inch 29.1 59.6 35.2 28.1 35.2 24.3 11.7 46.5 22.1 27.9 pressure loss. The size stability of raw materials, therefore, is No. 'Isinch 20 12.1 7.0 7.9 13.9 18.6 very important in furnace performance. S o . 40 7.2 5.6 2.9 9.2 4.1 a.4 4.9 2.0 4.8 3.0 For the major portion of its height, however, the blast furnace 3.9 3.0 1.0 3.5 2.5 2.0 2.4 2.2 2.7 1.9 is primarily a heat exchanger and no appreciable change in size Through KO. 100 KO.20 34.5 21.7 11.4 35.9 18.3 of solids, especially of coke, occurs on account of reaction. MoreThrough S O . 100 16.0 5.8 3.3 15.7 6.8 over, it is generally believed that coke forms the skeleton of the stock in blast furnaces, which is possible only if no Table IV. Screen Analyses of Some Sinters (7) excessive breakage occurs. It seems (Percentage by weight) therefore, possible to use the particle size Screen Sample No. on, of the charge as a criterion on the particle Inches 1 2 3 4 5 6 7 8 9 10 size of the stock in furnace. If major 8 5.7 4.6 4.7 4.8 . 7.4 .. 9.4 .. 6 412 5,7 7.8 8.0 8 8 2.4 10.2 5:3 degradation occurs during the process of 218 7.3 6.1 2.3 3:i 7.2 19.1 4.4 4.8 3,3 4 charging, which seems to be likely, and 2 11.1 2.1 4.0 2.4 1.6 2.7 6.5 4.3 4.2 4.0 14.9 13.0 12.8 16.2 16.4 11.8 8.9 6 3 6 9 9.6 1 if this degradation is appreciable, the size 0.5 18.0 23.3 27.7 32.8 34.7 24.6 26.7 21.3 28.4 24.8 18.9 23.3 24.5 30.8 17.8 14.1 13.3 25.4 21.3 29.4 0.25 of the shattered charges should be used 1.4 2.1 2.3 4.5 0.9 3.8 3.3 4.2 1.3 3.7 To.4 2.4 2.0 1.1 6.4 in the calculation of pressure drop. This KO.6 4.2 2.3 1.6 2.3 7.7 4.6 5.5 2.1 2.4 1.8 2.1 1.6 0.9 No.8 4.0 3.7 5.9 offers an excellent opportunity for transThrough No.8 17.5 12.4 10.8 10.7 11.5 11.7 9.5 10.0 8.1 15.1 lation of coke strength data into pracAv. sizea, tical bearing o n furnace operation. inch 0,367 0.472 0 502 0.651 0.612 0.578 0.511 0.781 0.849 0.374 There remains the problem of detera For plus 8-mesh fractions. mining the average size of the solids
...
... 1.5 ...
...
,..
9.5
E:: Et
7.2
...
7.6
1.4
February 1953 Table V.
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y Screen Analyses of Some Prepared Ores
a
__
(The reauired average - channel size would be aouroximatelv
0.5 inch.) Using Kinney's figures, 8.15% of the cross-sectional
area was used by the gas passing, whereas 33.2% could have been utilized-Le., only one fourth of the available area was used by Screen Screen Soreen Agglomthe bulk of the gas. Neglecting minor diffusion effects, the on, Nodiiles on, Briquetted on, erated Inch ($0) Inches Ore (8) Inch Ore (8) channels rendered the main section of the furnace less effective 2 0.75 70.0 0.742 7.7 by 75% for reaction, mass, and heat transfer. Formation of 7 6 . 2 1 99:3 0 . 5 2 5 0.5 12.0 0.375 10.2 channels permits the passage of larger amounts of gas for an -1 0.7 0.25 12.0 -0.25 6.0 ... .. -0.375 5.9 available blower pressure, but a much shorter column would serve the same purpose had no channels been formed. Channels result from a wide size range, as discussed in earlier paragraphs. A certain amount of channeling may not be prevented; the advantage of minimizing channeling, Table VI. Screen Analyses of Some Blast Furnace Cokes (7) however, is apparent. (Percentage by weight) Screen ClairClair- Bethle- Brook- InterThe accuracy of estimating fractional on, Inches ton 1 ton 2 hem lyn lake Ford Inland Geneva Koppers void volume from density determinations 4 2.5 .. 19.1 depends upon the accuracy of particle 3 z i : i 2316 i4:6 4O:z 917 5716 18.4 31.6 density determinations. [For a detailed 2 40.8 45.3 54.4 39.7 37.8 23.6 39.7 42:O 32.8 1.5 .. .. 23.5 9.9 33.9 6.3 35.3 9.9 discussion on particle density of porous 1.25 29:s 1 35:s 29:s 4:7 4:6 1714 5:9 . . 12:s 418 materials see ( 5 ) . ] A study of available 0.5 1.2 2.2 3.3 4.3 1.1 Through 2:3 i:3 1.6 3.4 i:2 3.3 Q:9 5.8 0.7 information on bulk weight and bulk bottom density of raw materials, their relative screen .4verage amounts, and apparent specific grkvities size, inches 2 1 2.2 2.2 2.4 1.9 2.5 e.3 1.8 2.6 of blast furnace charges has led to a revision of the value reported by Kinney from 33.2 to 29.0%. In the absence of any other detailed information the above figure is recommended for use in blast furnaces. adhere to coarse particles, while most are forced by gas into pockets TOPPRESSURE. The effect of static pressure, P,, a t the top between coarse pieces, resulting in the formation of channels. of the furnace upon pressure drop can easily be evaluated from Therefore, there is a lower limit to the size of the fractions to be Equation 5. I n most furnaces the static pressure is slightly included in Equation 6. above atmospheric. Increased top pressure decreases the presCalculated average sizes for ores, sinters, and cokes shown in Tables I1 to VI are included a t the bottom qf the tables. In sure drop for a fixed blast rate a t standard temperature and presthese calculations only plus %mesh size fractions have been sure or allows increase in blast rate for a fixed pressure drop. This observation led some workers ( I d ) t o suggest increase in top included. ESTIMATION OF FRACTIONAL VOID VOLUME. There are two pressure in order to increase production rate, and experiments methods available to determine fractional or per cent void volume. have been carried out in blast furnaces. There are, however, definite limitations to the increase in production rate to be gained The first method requires the knowledge of bulk weight and bulk by such a procedure. The effects of other operating variables volume of stock, relative amounts, and particle densities-Le., apparent specific gravities-of components. Such data enable along with top pressure upon production rate are discussed below determination of the volume occupied by solids and the volume and their limitations demonstrated. of the bed, which leads to the value of the fractional void volume. The second method requires measurements of gas velocity in Application of the Theory the furnace. The ratio of the superficial gas velocity to the A severe test of the preceding theoretical development was average actual velocity is the fractional void volume. The based on the data on pressure drop through twenty furnaces radioactive tracer technique ( 2 3 ) for determining gas transit time for which data were obtained in the coke evaluation project ( 1 ) in blast furnaces might advantageously be used for this purpose. and through one cupola. For the sake of clarity in the underFurnas (IO), who used the first method, quoted values ranging up standing and application of the theory on the above-mentioned to 58% voids. The values reported are for 4.5-cm. ore, 12-cm. data, examples of the calculation involved will first be demoncoke, and 10-cm. stone corresponding to a size ratio less than 2.7. strated. Based on the same method, Kinney ( 1 7 ) reported 33.2% voids Example I. for a different blast furnace charge. Compared to 33.2y0 voids, DATA ON FURNACE. velocity measurements in the furnace yielded 8.15% voids ( 1 7 ) . Height (tuyhres to stock level) = 65 feet The difference between these figures is enormously great if one Volume (tuybres to stock level) = 24,000 cubic feet considers that 8.15% voids would cause, theoretically, 93 times Average cross-sectional area = 24,000/65 = 370 square feet DATA O N OPERATION. as much pressure drop as 33.2y0 voids would. A careful study Ore = 22,000 cubic feet per day of the data, however, reveals that velocity measurements in Sinter = 6,760 cubic feet per day excess of 400 feet per second (270 miles per hour) were recorded. Coke = 71,540 cubic feet per day A gas traveling a t 200 feet per second would cross a 60-foot Stone = 11,700 cubic feet per day Blast rate = 68,000 cubic feet per minute a t 60" F. and distance in the furnace in less than 1 second even if the path was 29.9 inches of mercury so sinuous that the actual path followed by the gas was three Barometric pressure = 29 inches of mercury (14.3 pounds times as long. Voice's experiments (BS), on the other hand, per square inch absolute) employing a radioactive tracer technique, indicated that transit Static pressure a t top of furnace = 2.44 inches of mercury (1.2pounds per square inch gage) times for gas from tuybres to stockline ranged from 2.75 to 6.75 DATA ON SIZEANALYSIS OF CHARGE. Tabulated in Table VII. seconds. The fact that different furnaces under different operatCALCULATIONS. From the sieve analyses given in Table VI1 ing conditions were employed may not account for the discrepanthe average size of each charge has been calculated by the use cies in the transit times. The velocities reported by Kinney of Equation 6 and included in the table. The average size of the indicate that tremendous channeling occurs in the furnace. total charge is calculated, using Equation 6 again, in Table VIII. (Percentage by weight)
FonScreen tana on, Sinter Inches (88) 3 3.3 2 6.5 1.5 6.3 1 16.0 0.5 38.5 0.25 15.8 1,'s 6.0 -1/s 7.6
-
481
Vol. 45, No. 2
INDUSTRIAL AND ENGINEERING CHEMISTRY
482
Table
Calculations of Average Sizes of Burden
VII.
(Example 1) Screen on, Inches
Di inch&
6 4 3 2 1.5 1 0.5 a ia
5:O 3.5 2.5 1.75 1.25
%
Table VIII.
B(Xi/DC)
Sinter
%
X;/DP
... ...
...... . . . . . . ......
...
'3:2 10.0 50.9 27.6 6.8
Ore Xi,
Dz. inchks
Xi/Di 0.64 2.86 20.36 15.77 5.44
. . . . .
D = -
Charge Ore Sinter Coke Stone Total
Coke Xi,
...
2.5 1.75 1.25 0.75 0,438 0.312
8.8 9.5 22.4 44.1 10.0 4.1
3.5 5.4 17.9 58.8 22.8 13.1
0.125
1.1
8.8
1oo.o
130.3
zxi
-
= 2.04 inches
Z(XiiDi)
= 0.77 inch
Calculations of Average Sizes of Total Burden
xi,
Di, inches 6.5 5.0
6.3 20.2
3.0
13.2
1.5 0.75
13.8 30.4
9.2 40.5
0:3+5
i4:3
38.1
0.125
1.8
14.4
...
...
%
... ...
r(Xi/Di)
xi, %
1.0 4 0
inches 6.5 5.0
4.5 16.2
Xi/Di 0.7 3.2
4.4
3.0
50.8
16.9
1.5 0.75
20.5 6.4
13.7 8.5
. . . . . .
... ...
...
...
. . . . . .
1.6
0.25
inch
Size of total charge, D, =
...
. . . . . .
...
= 0.90
...
. . . . . .
88
6.4
ioo.0
1oo.0111.6 D=-
Stone
z
Xi/Dt
D=--
z(Xi/Di)
loo
12
-
49.4
2.02 inches
= 1.97 inches
m+m
(Example 1, of. Table V I I ) Rate Average Cu. F t . / D a y %, Xt Size, D% 22,000 19 6 0 77 6,760 6 0 0 90 71,540 63 9 2 04 11,700 __ 10 5 2 02 112,000 100 0 100 D p = - = -ZXZ = Z(X,/Dz) 68 6 46 Inches
XI/DL 2s 4 6 7 31 3 5 2 G8 6 ~
Qe = 795 X 520/(190 4- 460) = 636 cubic feet per minute a t 60" F. and 29.9 inches of mercury H = 18feet For a conical cylinder the effective area for pressure loss c:tlculation is the geometric mean:
A , = ( r / 4 ) DID*= 5.1 square feet Substituting in Equation 5: AP = 1.80 pounds per square inch as compared with mpasured pressure drop of 1.77 pounds per square inch
SUMMARY O F INFORMATION.
Qo = 68,000 cubic feet per minute (blast rate a t 60' F. and 29.9 inches of mercury) p. = 15.5 pounds per square inch absolute (absolute pressure a t top of furnace) H = 65 feet (distance between tuyilres and stock level) A , = 370 square feet (average cross-sectional area of fuinace) D, = 1.46 inches (average size of charge) ASSUMPTIONS BASED ON BLAST FURNACE PRACTICE. t = 1700" F. (average temperature of gas) c = 0.29 (fractional void volume) Substituting the above information in Equation 5 : (1 A P = 4 ( 1 5 . 5 ) 2f 5.9 X
(+)*(s6)
+
- 0.29) (1700 460) 68 000 (0.29)3 520
- 15.5 = 20.7 pounds per square inch = 20.7 + 1.2 = 21.9 pounds per square inch
Blast pressure gage as compared to reported value of 21.2 pounds per square inch gage Example 11. Cupola. DATAGIVEN. Furnace height (tuykres to top of stock) = 18 feet Diameter a t top = 26 inches Diameter a t tuyhres = 36 inches Inside volume = 100 cubic feet (approximately) Blast rate = 795 cubic feet per minute a t 190" F. and 29.9 inches of mercury ilverage temperature = 1200" F. (top = 550" F., metal tap = 2670OF.) Top pressure essentially barometric (14.3 pounds per square inch absolute) The charge, a prepared mixture, had the following size analysis: Inches
%
Inches
75
I n addition to the above, stone of 3 / 4 X 1 inch was used (12% by volume). Although 29y0 voids are recommended for blast furnaces, a higher figure is to be expected for the cupola on account of the closer size range and the absence of excessive fines. Thirtytwo per cent voids is assumed. CALCULATIOSS. Size of mixture =
BxL = 2.38 inches Z(X,/D,)
Data obtained from the twenty furnaces included in the coke evaluation project ( 1 ) did not include all the information necessary for calculation of pressure drop. If, in the project, formulation of pressure drop on theoretical grounds had been considered, such information might easily have been obtained. Sieve analyses for ore, sinter, and stone, distance between air tuykres and stock level, and the barometric pressure recordings mere not reported for most of the furnaces. Upon examination of general information concerning blast furnace practices the following assumptions were made: ore size = 0.75 inch, stone size = 3 inches, barometric pressure = 29 inches of mercury, distance between tuyhres and stock level = over-all height (iron notch to top ring) minus 18 feet. Also, sufficient data were not available regarding gas temperatures and bulk weight and bulk volume of the total charge to enable determination of the average gas temperature and fractional void volume in the furnaces. For these values it was necessary to rely on the data obtained in test plants. As mentioned earlier, 1700' F. for t and 0.29 for E have been chosen. Assuming of necessity that the missing data mere the same for all furnaces, which is not justified, the actual pressure dropa, ranging from 12.6 to 23.4 pounds per square inch, are reproduced by Equation 5 with an average deviation of only 1.6 pounds per square inch. It is reasonable to suppose that a better reproduction of the pressure losses would have been obtained if actual data were available. Table IX contains the calculated results and the observed values, which are represented graphically in Figure 6. For a better understanding of the implications of the assumptions made regarding the missing information, different values (within reasonable limits) have been assigned to the variables which were not reported. The resulting changes in calculated pressure drops are tabulated in Table X. Upon inspection of Table X, it is seen that the effect of barometric pressure changes upon pressure loss is small. A reduction or increase in stone size by a factor of 2 causes zk0.5 pound per square inch change in pressure loss. A possible difference of r t 5 feet between the actual height and that estimated from the over-all height causes & l . O pound per square inch difference in
INDUSTRIAL AND ENGINEERING CHEMISTRY
February 1953
pressure loss. Excessive changes in pressure loss are due to ore size. If the ore size is reduced from 3/4 to 3/8 inch, pressure drop will increase 7.3 pounds per square inch; similarly, if ore size is increased to 1.5 inches, pressure loss will drop by 4.3 pounds per square inch. The effect of variations in the size of coke, temperature of gas, and per cent voids is also shown in Table X. It is interesting to note that a change in' average gas temperature by f 200" F. causes 1.4 pounds per square inch change in pressure drop. It can, therefore, be concluded that the possible range of values in the missing data can reasonably account for the deviations of calculated results from the observed values which are shown in Figure 6.
483
per square inch and an increase to 100,000 cubic feet per minute will cause an increase to 35 pounds per square inch. This relationship is valid regardless of the size of the burden and its fractional void volume, provided they are kept the same. TEMPERATURE. The temperature history of a furnace is determined to a large extent by the rate of heat transfer and to a lesser extent by the reaction rate. The effect of temperature upon pressure drop is, therefore, of secondary importance. However, most of the factors affecting heat transfer also affect pressure loss.
Discussion
For a complete understanding of what occurs in a blast furnace and how better control of practice can be assured, i t is necessary to analyze the furnace from the standpoint of fluid dynamics, heat and mass transfer, and reaction kinetics. However, rate of production in most blast furnaces is believed to be limited by the rate of blast. The present studies are, therefore, concerned with fluid mechanics-Le., the effects of operating conditions upon rate of blast. MAXIMUMALLOWABLE PRESSURE DROP. The bulk weight of blast furnace charge is estimated to lie between 80 and 110 pounds per cubic foot. If the distance between tuybre level and stock line is 60 feet, the maximum pressure drop for 90 pounds per cubic foot bulk weight is 60 X 90/144 = 37.5 pounds per square inch. This pressure drop corresponds to that necessary to expand or lift the burden. Because of nonuniform pressure gradient the lifting may be in slug form. RATEOF BLAST AND PRESSURE DROP.The increase in rate of blast as a function of pressure drop is shown in Figure 7. The reference point corresponds to a furnace operating a t a pressure drop of 20.7 pounds per square inch when the rate of wind is 68,000 cubic feet per minute, and top pressure is 15.5 pounds per square inch absolute. The reduction of wind to 41,000 cubic feet per minute will reduce the pressure drop to 10 pounds
Table IX. Plant Clairton 1 2 Jones & Laughlin 1
3 6 Bethlehem Interlake Ford A
B C
Table X.
0
IO
6 '
Figure 6.
OBSERVED
IO
eo
OS
PRESSURE DROP, PSI.
Calculated vs. Observed Pressure Drop in Blast Furnaces Cf. Table I X
Pressure Drop in Blast Furnaces (7)
Pressure Drop, Lb./Sq. Inch Calculated Observed 21.6 18.8
21.4 19.6
21.2 19.7 20.2 16.2 13.4
18.0 19.1 17.2 14.5 12.6
14.5 10.0 18.7
15.6 14.3 18.5
Plant Inland 1 3 5
Pressure Drop, Lb./Sq. Inch Calculated Observed
6
Gadsden 1
3
Genera 2 3 Ironton Granite Cit ~ i s c cupo3Ta o
.
18.9 14.9 18.9 18.3
17.2 15.2 17.8 18.3
18.1 19.0
18.0 19.0
16.5 16.9 19.2 8.0 1.8
16.5 20.4 23.4 13.9 1.77
Effect of Changes in Values of Variables upon Pressure Drop
-
Information available. Q O 70,600 cubic feet per minute. Aa = 394 sq. feet. Top pressure = 1.2 pounds per square inch gage. Composition of charge b y volume = 63.9% coke 25.6% ore, sinter, and scrap, 10.5% stone, Distance between iron notch and top ring = 95 feet. Average size of coke as calculated from sieve analysis = 2.4 inches. General assumptions made. t = 1700' F,., e = 0.29. Assumptions made because of lack of data, Ore size = 0.75 inch, stone size = 3.0 inches, H = over-all height - 18 feet, barometric pressure = 29.0 inches of mercury, calculated pressure drop = 21.6 pounds per square inch, observed = 21.4 pounds per square inch. Unless otherwise stated below, figures quoted above have been used in calcuia tio ns APs Lb./ APs Lb./ Sq. Inch Sq. Inch Ore size, inch 8/s 28.9 Coke size, inch 0 . 2 22.8 1 . 5 17.3 2.8 20.7 Stone size, inch 1.5 22.4 Temperature 1500' F. 2 0 . 1 5 21.3 1900' C. 2 2 . 9 Height, feet 72 20.5 Voids, % 26 27.7 82 22.6 32 16.9 Barometer, inches Hg 2 8 , 4 2 1 . 8 29.9 21.4
.
.
Figure 7.
.
Pressure Drop as a Function of Rate of Blast
PARTICLE SIZEOF BURDEN. The size of the burden is of great consequence t o the rate of production of a blast furnace. For a fixed blower pressure, rate of blast increases with the increase in the size of the burden, whereas rates of heat transfer and reaction decrease with the increase in size. The effect of size of burden upon rate of blast and rate of heat transfer is illustrated diagrammatically in Figure 8. For a corresponding size, the lower of the two curves will determine the rate of production. There is an upper limit to the increase in rate of production to be gained by increasing the size of the burden. This optimum size corresponds to the intersection of the two curves, and its
484
Vol. 45, No. 2
INDUSTRIAL AND ENGINEERING CHEMISTRY
position may be affected by the design of the furnace, and physical and chemical qualities of burden. In connection with size, size distribution and relative sizes of ore, stone, coke, etc., demand attention. The size range of any constituent should be as close as possible. This is most likely to be determined by mechanical and economic considerations. I n selecting relative sizes of ore and coke, however, factors pertaining to heat transfer, reaction rate, and fluid mechanics should be weighed. The heat conductivity of ore is lower than that of coke, and ore is reduced chemically to a much larger extent than coke is gasified in the main shaft of the furnace (upper part).
, !
, !
,
'.
-
AVERAGE LUMP SIZE
Figure 8. Diagrammatic Illustration of Effect of Size of Burden upon Rate of H e a t Transfer and Rate of Blast
These factors require that ore size should be smaller. I n keeping with the aim of the present paper, the effect of size on pressure drop and on flow rates is shown in Figures 9 and 10. In Figure 9 (top) pressure drop is plotted against the average size, The reference point corresponds to a furnace operating a t a pressure drop of 20.7 pounds per square inch when the rate of blast is 68,000 cubic feet per minute, top pressuie is 15.5 pounds per square inch absolute, and the average size of the charge is 1.46 inches. T h e n the size is reduced to 0.6 inch, the required pressure drop is 37.5 pounds per square inch, and when increased t o 3.0 inches, the pressure drop is 12 pounds per square inch. If the burden has a bulk density of 90 pounds per cubic foot and a height of 60 feet, the burden will start to expand a t a pressure drop of 37.5 pounds per square inch The effect of size upon the rate of blast for a fixed pressure drop is shown in Figure 10 (top). The reference point is identical with that of Figure 9. When the size is reduced to 0.6 inch, blast rate will come down to 44,000 cubic feet per minute, a 35% reduction, and when the size is increased to 2.5 inches, the blast rate will be 90,000 cubic feet per minute, a 327@increase. I n these calculations it is assumed that every other variable has been kept constant FRACTIONAL VOID VOLUME. Fractional void volume is perhaps the most important factor in the resistance to the flow in the furnace. I t s evaluation is very difficult if not impossible if the burden has a wide size distribution. Moreover, if channels are formed, the formulation of resistance to flow can no longer be made. I n such a case efficiency of the heat transfer and reaction rates falls sharply. Although larger flow rates can be obtained when channels are formed, the performance of the furnace could become unpredictable unless great care is taken in duplicating the charge. Closely sized fractions-e.g., top X 1 inch-of coke pack to
from 55 to 5QyOvoids (Table XI), and ores are reported (IO) to pack from 41 to 57y0 voids. If the stock mixture of the blast furnace was composed of closely sized materials, the fractional voids would be greater than 50y0. However, because of a greater range of size distribution, void volume is considerably less. Kinney reported that an average of five determinations with actual charges indicated 33.2% voids upon mixing the charge as compared to an over-all 42.7y0 voids had the charge not been mixed. The voids in the furnace will be less than the above figure, owing t o size degradation. I n Figure 9 (middle) the change in pressure drop is plotted against change in the fractional void volume. The reference point corresponds to a furnace operating a t a pressure drop of 20.7 pounds per square inch when the rate of blast is 68,000 cubic feet per minute, void volume is 29y0, and the top pressure is 15.5 pounds per square inch absolute. For 22.4yc voids the necessary pressure drop to niaintain the same flow rate is 37.5 pounds per square inch and for 5Oyc voids, 4 pounds per square inch. The effect of per cent voids upon flow rates for a fixed pressure drop is shown in Figure 10 (middle). The reference point is identical with that of Figure 9. For 22.406 voids the rate of blast is 44,000 cubic feet per minute and for 50% voids, 185,000 cubic feet per minute. 4 537, voids triples the rate of wind. The importance of per cent void volume upon rate of blast is apparent. STATICPRESSURE. The effect of increased top pressure upon pressure drop for a fixed rate of blast is demonstrated in Figure 9 (bottom). Considering a furnace operating at a top pressure of 15.5 pounds per square inch absolute, a t a pressure drop of 20.7 pounds per square inch absolute, when the top pressure is raised to 20, 25, and 30 pounds per square inch absolute, the corresponding pressure drops, respectively, will be 18.4, 16.2, and 14.4 pounds per square inch. Figure 10 (bottom) shows the increase in rate of blast (cubic feet per minute) for the same furnace with the increase in top pressure when operating a t a fixed
$30 0 0
20
W 3 K
8
IO
E
0
0.5
1.0
1.5
2.0
2.5
3.0
3,5
AVERAGE SIZE- IN.
40
fn 0 K 0
n
20
$
$10
a
I
I
I
I
0.3 0,4 FRACTIONAL VOID VOLUME 1
I n 1
I%
I
I
I
I 0.5
I
1
E O 15
20 TOP PRESSURE-
25 PSIA.
30
Figure 9. Effects of Size of Burden, Fractional V o i d Volume, and Top Pressure upon Pressure Drop for Fixed Rate of Blast
INDUSTRIAL AND ENGINEERING CHEMISTRY
February 1953
Table XI. True Specific Gravities, Absolute Specific Gravities, Bulk Densities, and Per Cent Void Volumes of Some Blast Furnace Cokes (7) Plant Clairton 1 2 Jones & Laughlin, 1 Bethlehem Brook1 n Gas Interde Ford Inland Republic Geneva Ironton Koppers
True Specific Gravity
1.99 1.94 1.92 1.95 1.91 1.89 1.91 1.91 1.99 1.87 1.83 1.87
Apparent Specific Gravity
v0
Bulk Density
Void Volume
27.4 27.8 24.9 24.7 27.6 23.8 25.2 23.6 26.2 2'2.9 21.5 23.1
56.4 56.5 55.7 55.9 55.8 55.6 55.9 56.0 56.9 58.0 58.9 56.5
1.01 1.02
0.90 0.90 1.00
0.86 0.91 0.86 0.98 0.87 0.84 0.85
485
ing the capacities of existing blast furnaces by controlled sizing and operation is definitely indicated. Summary
The application of a pressure drop equation to blast furnaces is illustrated. The equation was developed earlier (6) for fixed and fluidized beds and is based on fundamental theories of fluid flow. It seems probable that the present practice in blast furnace operation results in excessive channeling, reducing the heat transfer and reaction rates to almost one fourth of the maximum rates obtainable. Sizing of the charge is the most important factor in the production capacity of furnaces. By proper sizing the production rate in existing furnaces might be increased by as much as 3o070. Nomenclature
a'
= coefficient of viscous energy loss (Equation 1)
A L = free cross-sectional area of furnace a t distance L from
0
0.6
0.2
1.0
-
1.6 2.0 2.5 AVERAGE SIZE IN.
0.4 FRACTIONAL VOID VOLUME
0.3
30
0.5
tuyirre, square feet Aa = average cross-sectional area of furnace for section extending from tuyBres to stock level ( = inside volume of section divided by its height), square feet 6' = coefficient of kinetic energy loss (Equation 1) D p = particle size, inches H = height of furnace from tuyBre to stock level, feet L = distance above tuyeres, feet P = pressure, pounds per square inch absolute P, = absolute pressure a t top of furnace, pounds per square inch absolute Q = gas flow rate, cubic feet per minute = blast rate, cubic feet per minute a t 60' F. and 29.9 inches Qo of mercury t = average gas temperature, F. T = absolute gas temperature, O R. U = superficial gas velocity, feet per second-i.e., gas velocity based on empty column AP = pressure drop, pounds per square inch E = fractional void volume, dimensionless-ie., ratio of volume available for passage of gas to total internal volume of furnace between stock level and tuyeres p = absolute viscosity of gas, pounds/foot second a = density of gas, pounds per cubic foot
I I
literature Cited
60
Am. Iron Steel Inst. and Am. Coke and Coal Chemicals Inst., 0-
TOP PRESSURE
-
PSIA.
Figure 10. Effects of Size of Burden Fractional Void Volume, and Top Pressure upon Rate of blast for Fixed Pressure Drop
pressure drop. When the top pressure is raised to 20, 25, and 30 pounds per square inch absolute, the corresponding blast rates will be raised from 68,000 cubic feet per minute to 74,300, 80,200, and 85,600, respectively. I n other words, when the pressure in the furnace is raised by 10 pounds per square inch (both a t the top and a t the bottom), the corresponding increase in rate of flow will be less than 1S%. This figure is lower than those quoted in the literature ( 1 9 ) . It is seen that benefits to be gained by increasing top pressure alone are limited. The cost of compressing enormous quantities of air to higher pressures and the maintenance of higher pressures in the furnace should be considered. The calculations made above show that for a furnace operated a t a top pressure of 10 pounds per square inch gage when. charged with a burden of 2.5-inch size (Equation 6) and 5370 fractional void volume, the amount of the wind blown would be 4.62 times the normal described in the paper for the pressure drop of 20.7 pounds per square inch; if all reactions were kept in phase with the amount of blast, the capacity of the furnace would be increased by this factor of 4.62. The opportunity of greatly increas-
Report on Coke Evaluation Project, unpublished. Byrns, H. A., Proc., Blast Furnace R a w Materials Committee, Am. I n s t . Mining M e t . Engrs., 8 , 158 (1949). Dobscha, H. F., Ibid., 7, 49 (1948). Duffy, E. J., Ibid., 8, 204 (1949). Ergun, S.,Anal. Chem., 23, 151 (1951). Ergun, S., Chem. Eng. Progr., 48, 89 (1952). Ibid., p. 227. Firth, C. V., Proc., Blast Furnace R a w Materials Committee, Am. Inst. Mining M e t . Engrs., 4, 46 (1944). Furnas, C. C., U. S. Bur. Mines, Bull. 307 (1929). Ibid., Bull. 361 (1932). Johnson, H. W., Proc., Blast Furnace R a w Materials Committee, Am. I n s t . M i n i n g M e t . Engrs., 1, 12 (1941). Joseph, T. L., Blast Furnace Steel Plant, 33, 699 (1945). Joseph, T. L., Fuels and Furnaces, 6 , 635 (1928). Joseph, T. L., Trans. Am. Inst. Mining Met. Engrs., 120, 72 (1936). Joseph, T. L., and Bitsianes, G., Proc., Blast Furnace R a w Materials Committee, Am. Inst. Mining M e t . Engrs., 4, 70 (1944). Joseph, T. L., Royster, P. H., and Kinney, S. P., Proc. Engrs., SOC.West. Penn.. 41. 428 (1926). (17) Kinney, S. P., U. S. Bur. Mines, Tech. Paper 442 (1929). (18) Ibid., 459 (1930). (19) Lindgren, R. A., Proc., Blast Furnace R a w Materials Committee, Am. I n s t . Mining Met. Engrs., 3, 128 (1943). (20) Oesterle, A. A., Ibid., 8 , 132 (1949). (21) Peters, J. F., Ibid., 8, 7 (1949). (22) Saussaman, J. D., Ibid., 7, 95 (1948). (23) Voice, E. W., J.I r o n SteelInst. (London),163, 312 (1949). (24) Weed, R. C., Proc., Blast Furnace R a w Materials Committee, Am. I n s t . Mining M e t . Engrs., 9, 145 (1950). RECEIVEDfor review June 16, 1952.
ACCEPTED September 24, 1952.
