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BF PROCESSING 1 - THE GENERAL RATE EQUATION
The general Rate Equation can be written in words as:
n
RATE = CONDUCTIVITY x (DRIVING FORCE) (1.1)
Or in symbols:
n
RATE = K x (F) (1.2)
Note that there is an exponent (n) for the Driving Force. It can range from -1 to +4.
It many books it is generally not included. This is because many rates are first order, or n =
1, and, of course, we never put 1.0 as an exponent!
Common examples of rates for n 1 are:
n = -1 Dissolution of solids (Reciprocal shrinkage).
n = 0 Discharge of solids from bins and silos.
n = Discharge of liquids from storage bins.
n=2 Fermentations.
n=4 Radiation heat transfer.
For n = 1, a very common example is the Ohms law.
RATE OF FLOW OF ELECTRONS = CONDUCTIVITY x (DRIVING FORCE)1
And since Rate of Flow of electrons is called Current (I) and Conductivity is reciprocal of
resistance I, or 1/R, then:
I = 1/R x (V)
V = IR
Because of its importance in the BF Plant lets derive the rate for n = 1/2.
In a column of liquid of height h (Fig 1.1) we focus on a small
mass of liquid at the surface at h with PE = mgh and the same
small mass of liquid flowing out the exit with KE = 1/2mv2.
According to the Law of the Conservation of Energy PE = KE.
Therefore:
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PE = KE
mgh = 1/2mv2
h = 1/2gv2
v2 = 2gh
v = 2g h = C(h)1/2
Fig. 1.1
So the rate of flow = Conductivity x (F)1/2 = 2g (h)1/2 (1.3)
If the column is filled with granular materials then:
The rate of flow = Conductivity x (F)0 = Conductivity (h)0 = Conductivity (1.4)
So, the rate of flow of granular materials from bins and silos
IS INDEPENDENT OF HEIGHT!
This is why bins and silos are tall for granular materials!
If it is a liquid inside, then at the bottom of a tall tank the pressure would be very high and
the bottom would need reinforcing to prevent the dam from collapsing.
This is why dam walls are wide at the bottom and narrow at the top.
OXIDE REDUCTION
The iron blast furnace (BF) makes iron (Fe). There are also copper, zinc and lead blast
furnces and they make Cu, Zn and Pb, respectively. The processes in all blast furnaces are
based on CHEMISTRY. In the IRON BF it is the reduction of oxides. (In the others - oxides
and sulphides.)
The simplest chemical equation for the making of iron by reduction is:
FeO + CO = Fe + CO2 (1.5)
Equation (1.5) states that to make Fe there must simultaneously be:
1. IRON OXIDE and CO, and
2. The two MUST CONTACT EACH OTHER.
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If either of the two is not present then no iron will be made!
Thus,
1. If no FeO exists, or if it is mixed with other oxides, then:
EITHER NO IRON WILL BE MADE, OR IT WILL BE MADE INEFFECTIVELY!
and
2. If no contacting (given by the + sign) exists, or contacting is poor, then:
EITHER NO IRON WILL BE MADE, OR IT WILL BE MADE INEFFECTIVELY!
(In the blast furnace contacting is determined by the BURDEN DISTRIBUTION.)
So, from the above:
1) Make sure the ferrous burden (sinter, pellets and lump ore) has the highest possible
content of Fe and the lowest possible contents of others, especially Al2O3, but also
SiO2, and, of course S, P, Na and K.
2) The above ferrous burden has the correct properties (size, strength, LTD and
reducibility) and is DISTRIBUTED CORRECTLY ON THE SL (Stock Line)
IRON OXIDES
Table 1.1 gives the properties of iron oxides.
Table 1.1. Properties of pure iron oxides.
Compound MW ( - ) % Fe SG ( - ) MP (oC) O/Fe
Iron (Fe) 55.85 100% 7.86 1535 0.0
Hematite (Fe2O3) 159.70 70% 5.24 1565 1.5
Magnetite (Fe3O4) 231.55 72% 5.18 1538 1.33
Wustite (FeO)* 71.84 78% 5.71 1420 1.0
*Actually (Fe1-xO) where 0.833 x 0.957
Because of phase equilibria*, reduction of Fe2O3 must proceed stepwise from hematite to
Fe, namely:
Fe2O3 Fe3O4 FeO Fe (1.6)
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*A common example of phase equilibria is ice water steam
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Fig.1.7. Illustration of stepwise reduction.
This kind of reduction is called topochemical, and you can think of it as onion-like.
Thus, Fe2O3 is contacted with CO to form Fe3O4 and CO2 , then Fe3O4 is contacted
with CO to form FeO and CO2 and finally FeO is contacted with CO to form Fe and
CO2 .
An illustration of Rate Controlling Steps in reduction is shown in Fig 1.8.
Fig.1.8. Illustration of Rate Controlling Steps in reduction.
Usually, in practice, gas velocity is always high enough not to have Gas Film Resistance.
Also, at the high temperatures in the BF as soon as the CO molecule arrives at the reaction
surface it is consumed.
So, the Rate Controlling step is usually the DIFFUSION OF CO THROUGH THE SOLID TO
THE REACTION SURFACE.
And here is where the particle size becomes important, because diffusion is (particle size)2 !
For example, if the time for complete reduction of a 6mm FeO particle is 3 hrs, it is 27 hrs
for a 18 mm particle!!!
THIS IS WHY THE BLAST FURNACE IS TALL AND IN ALL COUNTRIES OUTSIDE
ENGLAND IS CALLED TALL FURNACE. (Hochoffen, Haut Furneau, Altos Hornos, Visoka
Pec, Koro, and TANUR TINGGI)
The above was very important in the old days, when just lump ore was used.
Please look again at Table 1.1 carefully. What do you see?
Fe2O3 Fe3O4 FeO Fe
Oxygen to be removed: 10% 23% 67%
Can you see this? Make sure you can!
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So, the step FeO Fe removes 67% or 2/3rd of all the Oxygen THATS A LOT!
But thats not all! Why not? What else is there?
Because of thermodynamics (see Figs 1.9 and 1.10) the concentration of CO required for
each step is at 1000oC:
Fe2O3 Fe3O4 FeO Fe
CO strength required: 1% 26% 73%
Can you see this? Make sure you can!
Fig. 1.9. CO - T graph for iron oxides. Fig. 1.10. Same with C-CO- CO2 line.
So, the step FeO Fe must not only remove the most oxygen (2/3rd), but the CO
strength must also be the highest of all (73%)!!!!
No wonder the blast furnace must be high so the lump iron ore, especially the big size ones,
will have long residence/cooking time to become matang!
Figure 1.10 includes the C-CO-CO2 line which is very important in blast furnaces where the
CO2 from reduction of FeO is regenerated (CO2 + C = 2CO) to CO to increase the CO
concentration to reduce more FeO and keep up the high production rate of the hot metal.
Without this regeneration, also known as Boudouard reaction mainly in universities, and
seldom as SOLUTION-LOSS REACTION, which I strongly recommend be always used!
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