Process for estimating particle size segregation of burden layer in blast furnace top

A process for estimating a particle size segregation in a burden layer at a blast furnace top is disclosed, which comprises measuring a particle size distribution of a burden material before the charging and a layer thickness distribution of the burden layer after the charging, and estimating a particle size distribution at every position in the burden layer charged at the furnace top on the basis of the above measured values, charging conditions and furnace operating conditions according to a simulation model of particle size segregation.

This invention relates to a process for estimating a state of a particle 
size segregation in a burden layer at a top portion of a blast furnace, 
and more particularly to a process for estimating a particle size 
distribution of a burden layer charged in the top portion of the blast 
furnace at each position toward the radial direction of the furnace throat 
from the particle size distribution of the burden material before the 
charging, the charging conditions and the furnace operating conditions 
according to a particle size segregation model. 
In order to achieve the reduction of fuel rate and the stabilization of 
blast furnace operation, it is important to optimize a radial distribution 
of gas flow in the furnace by controlling the burden distribution in the 
furnace top portion. The term "burden distribution in the furnace top 
portion" used herein mainly means a layer thickness distribution for ore 
layer and coke layer and a particle size distribution in each layer. In 
general, the gas flow in the furnace is distributed according to the 
radial distribution of gas flow resistance of the burden layer, which is 
determined from the layer thickness distribution and particle size 
distribution, so that it is necessary to know both the distributions. In 
this connection, there are many measurements for the layer thickness 
distribution, but no means actually measuring and estimating the particle 
size distribution have been developed. 
In general, the burden distribution at the top of the blast furnace are 
influenced by various factors complicatedly entangled with each other. The 
main factors are as follows: 
(1) Physical properties of burden material such as density, particle size, 
coefficient of internal friction and so on; 
(2) Charging speed; 
(3) Charging conditions such as coke base, ore/coke ratio (hereinafter 
referred to as O/C), stock line level and so on; 
(4) Falling trajectory of burden flow, which fundamentally depends on a 
notch position of a movable armor in a bell-type blast furnace or a 
tilting angle of a distributing chute in a bell-less top blast furnace; 
(5) Charging sequence; and 
(6) Gas flow rate in the furnace. 
Besides, a geometrical arrangement between the throat of the furnace and 
the charging equipment is considered to be one of the fundamental factors 
in the formation of burden distribution, but it is not an operational 
factor in the specified blast furnace. Therefore, when the burden is 
charged into the specified blast furnace through the specified charging 
equipment, the burden distribution is determined under an influence of the 
above mentioned factors. Particularly, layer thickness distribution and 
particle size distribution of the burden in the radial direction of the 
furnace are significant in order to achieve the reduction of fuel rate and 
the stabilization of furnace operation. 
In the conventional operation of blast furnaces, the concept for 
controlling the burden distribution is based on the control of the layer 
thickness distribution and lies in optimizing the radial distribution of 
the thickness ratio of ore layer to coke layer (L.sub.o /L.sub.c) or of 
O/C explained by a product of this ratio with a bulk density ratio 
(.rho..sub.o /.rho..sub.c). For instance, it is experimentally known that 
when the horizontally sectional area of the throat in the blast furnace is 
equally divided into a central part (C), a middle part (M) and a 
peripheral part (P), if the relation of the layer thickness ratio (L.sub.o 
/L.sub.c) in these parts is given by the following equation (1): 
EQU (L.sub.o /L.sub.c).sub.M &gt;(L.sub.o /L.sub.c).sub.P &gt;(L.sub.o 
/L.sub.c).sub.C( 1), 
the stable operation with low fuel rate can be achieved. However, the 
control of burden distribution aims at optimizing the radial distribution 
of gas flow resistance of burden layer and radial gas flow distribution 
accompanied therewith. For this purpose, there must be known the particle 
size distribution of burden material at each position in the radial 
direction of the furnace in addition to the above layer thickness 
distribution. The thickness of the burden layer can be measured directly 
or indirectly. The techniques of direct measurement are based on the use 
of an electrode or a magnetic censor. The indirect method is based on the 
procedure of determining the layer thickness from the difference of the 
burden surface level measured before and after charging the said burden 
materials by means of a transversely movable sounding device or microwave 
device or a layer-measuring system. On the other hand, a method of 
measurement of particle size distribution is not established at all 
because the quantity required for exactly determining the particle size 
distribution of the burden cannot be sampled from the inclined burden 
surface at given local positions in the radial direction of the operating 
furnace. In order to optimize the gas flow distribution in the blast 
furnace, it is essential and important to know the particle size 
distribution of the burden at given positions in the radial direction of 
the furnace. 
With the foregoing in mind, the inventor has made various studies and 
experiments and as a result, the invention has been accomplished. 
According to the invention, there is the provision of a process for 
estimating a particle size segregation in a burden layer stacked at a top 
portion of a blast furnace, which comprises measuring a particle size 
distribution of a burden material before the charging and a layer 
thickness distribution of said burden layer after the charging, and 
estimating a particle size distribution at every position in said burden 
layer charged at the furnace top on the basis of said measured values, 
charging conditions and furnace operating conditions according to a 
simulation model of particle size segregation given by the following 
equation: 
EQU log{X.sub.n /(1-X.sub.n)}=-.alpha..multidot.l+log{X.sub.n.sup.o 
/1-X.sub.n.sup.o)} 
wherein X.sub.n is a cumulative weight fraction of particles having smaller 
size than n-th sieve opening, .alpha. is a size segregation constant and l 
is a distance from a collision point of main falling trajectory against 
burden surface to the flowing direction, that is, to center and to the 
wall. The suffix `o` means the value of X.sub.n at l=o.

In FIG. 1 is schematically shown a state of particle size segregation in a 
burden layer stacked upwardly at a top portion of a blast furnace. A 
burden flow 2 discharged from a charging equipment 1 falls in a spaced 
bordered with an upper side 3 and a lower side 4 of a falling trajectory 
and comes into collision with a previously charged burden 5 to stack it 
thereon. In this case, when the profile of burden distribution as shown in 
FIG. 1 is M-shape, the burden flow is divided at a position of peak 6 
appeared in the burden distribution into a stream directing to the center 
of the furnace and a stream directing to the wall of the furnace. With the 
advance of the stacking, the position of peak 6 is shifted upward along a 
main falling trajectory 7 of the burden flow as shown in FIG. 1. The main 
trajectory 7 is regarded as the curve passing through the points inside 
the burden flow 2, at which the cumulative weight fraction of burden 
materials integrated in a certain hortizontal plane from the upper side of 
the falling burden flow toward the lower side reaches 50%. When each of 
the two streams directing to the furnace center and furnace wall flows 
with a certain layer thickness, a void between large-size particles plays 
the same role as a sieve opening in the sieving operation. Under such a 
role of the void, small-size particles in the burden material is 
percolated into a lower-side portion having a small flow rate and then 
left in a portion near the falling point as they are, while large-size 
particles go on rolling toward the furnace center downward. As a result, 
the particle size in case of the M-shape profile is maximum at the central 
part of the furnace, and becomes smaller toward the furnace wall, and is 
minimum near the collision portion of the burden flow against the 
previously charged burden. When the profile of burden distribution is 
V-shape, there is obtained such a particle size segregation that the 
particle size gradually increases in a direction of from the furnace wall 
to the furnace center. 
Now, such a phenomenon of particle size segregation in the radial direction 
of the furnace may be simulated by an equation as expressed below. When a 
horizontal distance from the position of peak or the collision point (R*) 
of main falling trajectory against burden surface to an optional 
downstream point is l (m) and the cumulative weight fraction of particles 
having smaller size than n-th sieve opening is X.sub.n, if the burden 
stream flows from l to l+dl, a percolation rate of particles having the 
above mentioned particle size (-dX.sub.n /dl) is given by the following 
equation (2), as a result of investigations by the inventor. 
EQU -dX.sub.n /dl=.alpha..multidot.X.sub.n .multidot.(1-X.sub.n)(2) 
That is, the equation (2) means that the percolation rate of fine particles 
is proportional not only to the weight fraction of fine particles but also 
a weight fraction of coarse particles acting as a sieve in the 
percolation. In this equation, .alpha. is a constant indicating a degree 
of particle size segregation in the flowing direction of the burden, which 
is called as a size segregation constant. The value of .alpha. depends 
upon the properties of the burden material, charging speed and gas flow 
velocity in the furnace and the like. 
The integration of equation (2) gives the following equation (3): 
EQU log{X.sub.n /(1-X.sub.n)}=-.alpha..multidot.l+log{X.sub.n.sup.o 
/1-X.sub.n.sup.o)} (3) 
In the equation (3), the second term on the right-hand side means the value 
of {X.sub.n /(1-X.sub.n } at l=0. That is, the equation (3) is a 
simulation model of particle size segregation for a particle size 
distribution of the burden layer charged at every position of the furnace 
top toward the radial direction of the furnace. 
In order to estimate X.sub.n (i.e. cumulative weight fraction of particles 
having smaller size than n-th sieve opening) at every position in the 
radial direction, the value of the second term on the right hand side of 
the equation (3) must first be determined, which may be given as follows. 
That is, the averaged value of cumulative weight fraction of particles 
having a particle size smaller than n-th sieve opening, which are 
distributed radially from the furnace center to the furnace wall, should 
be equal to a value X.sub.n.sup.f of the burden material before the 
charging. Assuming that the bulk density of the burden layer is constant 
at each position, X.sub.n.sup.o is strictly given by the following 
equation (4): 
##EQU1## 
wherein .alpha. is a size segregation constant at r=o.about.R*, .beta. is 
a size segregation constant at r=R*.about.R, r is a distance from the 
furnace center, h(r) is a function indicating the layer thickness 
distribution and requires a found value, R is a radius of the furnace 
throat, and R* is a radial position from the furnace center at l=0 and 
corresponds to a collision point of the main falling trajectory against 
the previously charged burden. In order to obtain the value of R*, it is 
necessary to measure the profile of burden distribution. 
The equation (4) means that an average value derived from the integration 
of the equation (3) between the furnace center and the furnace wall is 
equal to the value before the charging. Therefore, the particle size 
distribution at l=0, i.e. the value of the second term on the right-hand 
side of the equation (3) is calculated from the equation (4) considering 
the found values for the particle size distribution X.sub.n.sup.f before 
the charging and the layer thickness distribution h(r) as well as the 
position R* of peak of the burden distribution profile, so that the 
particle size distribution at an optional distance l can be arithmetically 
estimated by the equation (3). 
As apparent from the equation (4), the value of X.sub.n.sup.o cannot be 
calculated explicitly. Now, by using the assumed X.sub.n.sup.o, the 
integration on the right hand side of the equation (4) is first performed 
and then the value of X.sub.n.sup.o satisfying the equation (4) must be 
determined by trial and error method, which can easily be performed by 
means of an electronic computer. 
The equation (4) gives a strick value of X.sub.n.sup.o, but if this value 
is accepted to have an error of few percents, X.sub.n.sup.o can be 
estimated by the following equation (5): 
##EQU2## 
By using the equation (5), the calculation can somewhat be simplified 
because it is not necessary to perform the trial and error method as in 
the equation (4). 
In the actual operation, the particle size segregation constant .alpha. of 
the equation (3) must first be determined. In this case, the burden 
material in an actual or laboratory furnace are sampled at two positions 
spaced only by a distance .DELTA.l(m) in the radial direction of the 
burden level in the furnace. Then, the particle size analysis for the two 
samples is performed to determine a difference .DELTA.log{X.sub.n 
/(1-X.sub.n)} between two positions, from which .alpha. is calculated 
according to the equation (6) as follows: 
##EQU3## 
Moreover, when the sampling of the burden material is carried out at three 
or more positions, .alpha. and log{X.sub.n.sup.o /(1-X.sub.n.sup.o)} are 
calculated by the least squares method using the equation (3). 
Then, there was made a comparison between the found value and the estimated 
value for particle size distribution in burden layer at every position 
toward radial direction according to the process of the invention to 
obtain a result as shown in the following Table 1. 
TABLE 1 
__________________________________________________________________________ 
Weight fraction of each particle size X.sub.n (%) 
Distance from furnace center in radial direction 
Weight 
4.62 m 4.0 m 3.0 m 2.0 m fraction 
Particle Esti- Esti- Esti- Esti- 
before 
size Found 
mated 
Found 
mated 
Found 
mated 
Found 
mated 
the charging 
n (mm) value 
value 
value 
value 
value 
value 
value 
value 
X.sub.n.sup.f (%) 
__________________________________________________________________________ 
1 0-5 22.8 
22.2 
17.3 
15.4 
7.9 8.1 5.1 4.1 15.9 
2 5-7.5 
23.5 
17.7 
38.2 
33.7 
28.4 
24.7 
19.1 
14.4 
28.3 
3 7.5-9.5 
9.7 9.4 15.3 
15.8 
18.2 
14.5 
12.9 
11.8 
14.2 
4 9.5-13.5 
19.3 
20.8 
18.2 
20.7 
27.0 
26.9 
26.8 
28.0 
22.1 
5 13.5-18.5 
17.5 
20.0 
7.8 10.1 
12.5 
17.3 
24.0 
25.6 
13.6 
6 18.5-26.0 
6.4 8.4 2.5 3.3 3.8 6.4 10.2 
12.0 
4.6 
7 26.0-36.0 
0.5 0.7 0.4 0.5 0.8 1.1 1.2 2.0 0.6 
8 36.0-50.0 
0.3 0.8 0.1 0.5 0.2 0.5 0.3 1.4 0.2 
9 50.0-65.0 
0 0 0 0 1.1 0.5 0.4 0.7 0.5 
Average 
particle 
size 9.4 10.3 
8.0 8.7 10.2 
10.9 
12.1 
13.4 
9.4 
__________________________________________________________________________ 
In the blast furnace with the throat radius of 5.25 m, the boundary between 
ore layer and coke layer and the surface of ore layer were measured by 
means of a layer thickness measuring device utilizing the electrodes. Both 
radial profiles are shown in FIG. 2. And also, the ore layer thickness 
h(r) was obtained from the difference of both the levels of radial profile 
as shown in FIG. 2. 
The particle size analysis was made with respect to four samples of the ore 
layer, each of which being sampled at a distance of 2.0, 3.0, 4.0 or 4.62 
m from the furnace center, to obtain a result as shown in a column "Found 
value" of Table 1. From these found values is obtained log{X.sub.n 
/(1-X.sub.n)}, which is plotted in FIG. 3 with respect to the radial 
position. As a result, R* is 4 m, .alpha. is 0.314 (1/m) on the average 
and .beta. is 0.65 (1/m). In this case, the reason why the average value 
of 0.314 is selected as .alpha. value is due to the face that the .alpha. 
value is 0.310, 0.314, 0.308, 0.317 and 0.321 for X.sub.1, X.sub.2, 
X.sub.3, X.sub.4 and X.sub.5, respectively, which means that these .alpha. 
values are not substantially dependent upon the particle size. 
Further, the particle size distribution of ore before the charging 
X.sub.n.sup.f (%) is shown in the most right-hand column of Table 1. On 
the other hand, the particle size distribution at a distance of 2.0, 3.0, 
4.0 or 4.62 m from the furnace center is estimated according to the 
equations (3) and (5) using the above mentioned values and also shown in a 
column "Estimated value" of Table 1. 
As apparent from Table 1, the estimated value is well coincident with the 
found value, which proves that the particle size distribution in the 
burden layer at every position in the radial direction is adequately 
estimated by the process according to the invention. 
Although this example shows the case that the value of .alpha. is not 
dependent upon the particle size and is substantially constant, the 
invention is applicable without troubles even when the .alpha. value 
varies with the particle size. 
According to the invention, the operation of determining the size 
segregation constant by sampling the burden material may be omitted by 
measuring beforehand a relationship between the size segregation constant 
and each factor influencing thereupon. For instance, a relation between 
the size segregation constant and the gas flow velocity in a bell-less top 
blast furnace is shown in FIG. 4, wherein the charging speed of the burden 
material is 0.7 m.sup.3 /sec. As apparent from FIG. 4, the flowing rate of 
the burden material on the old burden surface toward the furnace center or 
wall becomes higher with the increase in gas flow velocity, so that the 
degree of size segregation becomes smaller. Thus, sich a relation is 
sufficient to be measured beforehand in each of blast furnaces under 
various conditions. 
In this way, the invention first makes possible not only to estimate a 
particle size segregation state of a burden layer in the top portion of 
the blast furnace, but also to quantitatively examine a charging method 
for optimizing the burden distribution inclusive of layer thickness 
distribution and particle size distribution. In the latter case, the 
burden distribution can be controlled so as to always hold at an optimum 
state, so that the reduction of fuel rate and the stabilization of furnace 
operation can effectively be achieved in the blast furnace. 
Moreover, a fundamental physical phenomenon aiming at the invention 
consists in the particle size segregation of the burden layer toward the 
flowing direction on the inclined burden surface. Similarly, such a 
phenomenon occurs in the supply of particulate matters, granules or the 
like into a storing apparatus, reaction vessel or the like. In iron-making 
process, there are (a) particle size segregation in the layer thickness 
direction during the supply of raw material onto a pallet for sintering, 
(b) particle size segregation in radial direction of a banker for raw 
sintering material or an ore stock yard, the the like. In any case, the 
estimation according to the invention can be applied to such particle size 
segregation phenomena.