Komkov N.M., Kokaeva G.A.
The East-Kazakhstan State Technical University
Ust-Kamenogorsk, the Kazakhstan Republic
Granulation
thermodynamics from
sulphide
middlings’ pulp
Thermal dehydration of
different middlings allows to involve stripping products into metallurgical
processing. These products contain rich elements, which contribute into
significant increase of mineral raw materials utilization complexity.
Granulometric
composition of stripping products of pulp in a furnace has a great importance
both for the next thermal metallurgical processing and for the stripping
process itself. Hydrodynamical, heat exchange and mass exchange, mode of
stripping process depends on fluidized bed of granulometric composition. This
is the reason why it is necessary to study thermodynamical characteristics which
give an opportunity to control the process. Stripping products quality and
process effectiveness depends on pellet formation mechanism, which is
determined by thermodynamical characteristics.
Define the number of elements, going through the fluid-bed apparatus per unit of time [1]:
(1)
where G – fluid-bed furnace productivity per
unit of time kg/s;
d – equivalent diameter of the
dryable material, m;
p – the dryable material density
kg/m3.
The equation (1)
illustrates that at fixed displacement the number of elements n and equivalent diameter d are in inverse proportion to each
other.
Table 1 – Technological parameters
of stripping process
Parameters |
Modes |
|||
1 |
2 |
3 |
4 |
|
Pulp
density |
1,83 |
1,79 |
1,8 |
1,74 |
Solids
content in the pulp, % |
61 |
59 |
58 |
55 |
Air-blast temperature, Ê |
773 |
773 |
773 |
773 |
The
temperature in the fluidized bed , Ê |
553 |
453 |
418 |
383 |
Coolant flow , nì3/hour |
7776 |
10368 |
12960 |
15552 |
gas
flow speed in fluidized bed, nì/s |
0,9 |
1,2 |
1,5 |
1,8 |
Dried
middlings productivity, t/ì2·day |
4,7 |
6,5 |
11,4 |
12,8 |
Boiled
off water productivity, t/ì2·day |
3 |
4,52 |
8,1 |
10,5 |
Emersion of dried middlings dust fraction, % |
21,5 |
19,6 |
20 |
11,7 |
Moisture
content of middlings pellets, % |
0,1 |
1 |
3,5 |
3 |
1
t of dried middlings coolant flow,
thousand.nì3/hour |
35 |
27 |
15,4 |
10 |
Blast pressure ,
mm H2O |
1100-1200 |
1100-1200 |
1100-1200 |
1100-1200 |
Blast pressure, kPa |
11
- 12 |
11
- 12 |
11
- 12 |
11
- 12 |
In order to determine
pellet formation mechanism, it is necessary to define how granulation centers
formation from dust particles (potential granulation centers) depends on stripping
process parameters.
For solution of the
given problem we used the data retrieved in stripping stationary mode, i.e. at
normal supplying of the fluid-bed furnace with pulp; and in stripping
nonstationary mode, when supplying of the fluid-bed furnace with pulp stopped
and supply of fluidized agent continued. Thus we studied dynamics of pellet
breakdown on dust fraction growth in stripping products, and determined the
probability of granulation centers formation from dust particles.
We also determined pellet
breakdown speed in nonstationary mode. As the supply of the fluid-bed furnace
with pulp stopped, so the growth of pellets in this mode lacked and couldn’t
distort the picture of their breakdown. Samples were selected in 0,1 average
time of particles being in fluidized bed for defining the changes of dust
fraction part (Table 1).
Then with the help of the retrieved
data we defined speed of dust fraction growth (table 1) and thus we defined
quantity of dust which is formed every second:
(2)
where ΔÐ – Changes of dust fraction part, %;
m – the mass of fluidized bed, kg.
Knowing the dust
quantity we can define minimum amount of dust particles n , emerging every second at the certain modes. For this matter we
use the equation (1) with the corresponding changes in physical significance of
the parameters:
(3)
where Q – the quantity of the emerging dust, kg;
d – diameter of a dust particle.
Every dust particle,
emerging in the result of pellets detrition, can become the granulation centre,
i.e. pellet embryo. But every particle can’t become the granulation center, as
a pellet can’t emerge from any potential granulation center. We can define the number
of the dust particles, which became the granulation centers at stationary modes
of the stripping by the number of received pellets:
(4)
where N –
the number of pellets;
G – amount of a substance contained in the
received pellets, kg;
d – equivalent diameter of the pellets, m;
p – density of pellets’ substance, kg/m3.
Knowing the number of
the dust particles, which can become the granulation centers and the dust
particle, which really became these centers, we can define probability of
pellet formation in every separate mode:
p = N/n (5)
where p
– the probability of pellet formation;
N – the number of real granulation centers;
n – the number of dust particles, potential granulation centers.
According to the probability of
pellet formation, we can find entropy of this process in every mode.
H(x) = - Σ p (x) log2 p (x) (6)
If the fluidizing
velocity increases, the entropy of the pellet formation raises (picture 1), it
means that randomness of pellet formation process increases, as entropy serves
as a randomness measure of the stochastic process. This is the reason why the
randomness increase leads to increasing probability of emerging the real
granulation centers and decreasing size of stripping products pellets. (picture
2).
If the fluidizing velocity increases
from 0,9 to 1,8 m/s , the entropy of the pellet formation raises from 21,98 *
10-4 to 551,04 * 10-4, and this contributes to increase
of the pellet formation probability from 1,76 * 10-4 to 78,88 * 10-4
. This in its turn provides the increase of the emerging pellets number from 54
to 6705 it./s and it leads to decrease of a pellet equivalent diameter, got in
the stripping process from 0,01 to 0,003 m.
Table 2 – Thermodynamic parameters
of the pulp stripping in fluid-bed furnace
Parameters |
Modes |
|||
1 |
2 |
3 |
4 |
|
Increase
of the dust fraction part for 0,1 of the average time in fluidized bed, % |
11,72 |
12,57 |
13,3 |
14,8 |
Average
stay period of the material in the fluid-bed furnace, s |
152861,5 |
91733,33 |
42000 |
30400 |
The
increase speed of emersion dust
fraction, %*10-4/s |
7,67 |
13,7 |
31,7 |
48,9 |
The
mass of the fluidized bed, kg |
19872 |
16512 |
13440 |
10944 |
The
number of emerging: |
|
|
|
|
dust, kg/s |
5,9E-06 |
7,61E-06 |
9,9E-06 |
1,35E-05 |
dust
particles, 1/s |
306355,5 |
422776,9 |
590913,6 |
850028,8 |
Granulation
centers, 1/s |
54 |
190 |
1223 |
6705 |
Probability
of pellet formation |
0,000176 |
0,000448 |
0,00207 |
0,007888 |
Equivalent
diameter of the received pellets, m |
0,01 |
0,0075 |
0,005 |
0,003 |
Fluidizing velocity , ì/ñ |
0,9 |
1,2 |
1,5 |
1,8 |
Entropy
of the pellet formation |
0,002198 |
0,004988 |
0,018453 |
0,055104 |
The received results prove that
pellets grow in the fluidized bed layer by layer (picture 3).
Getting
on the pellet, a solution drop vapors; the salt contained in the solution
crystallizes on its surface and thus a solid layer appears. In order to have
the stable bond between the pellet and the layer, it is necessary to achieve
the complete crystallization process ending on the pellet surface. So, we may
say that rate of crystallization must be higher than the evaporating rate:
Vcr > Vev (7)
The
salt rate of crystallization from the solution of the certain composition
remains sustained.
Vêð = const (8)
Entropy of the pellet
formation
Fluidizing velocity
Picture 1 – The
entropy of the pellet formation dependence of fluidizing velocity
Evaporating
rate of the solution depends on the energy quantity given to the pellet,
because evaporation is accompanied with its great input and goes on in the
isothermal mode. Thus increasing the temperature of the fluidized bed (by means
of external power supply), it is possible to decrease the energy quantity given
to the pellet, and so to slow down evaporation at the constant rate of
crystallization (isothermal crystallization).
Equivalent diameter of the
pellets
Entropy of the pellet formation
Picture 2 – Equivalent diameter of
the pellets dependence of pellet
formation entropy
Picture 3 – A pellet section
received in the result of middlings pulp stripping
If the
temperature of the fluidized bed increases, evaporating rate decreases, and
this contributes to the process in which salt contained in the solution and
getting on the pellets’ surface, forms stable bond with their surface during
crystallization.
If the
temperature of the fluidized bed decreases, then the energy quantity given to
the pellet increases, and also evaporation speeds up at the constant
evaporating rate. In this case the condition (7) violates, as not all the salt
contained in the solution and covering the pellet is able to fix on its surface
and become the whole. This part of the salt is rubbed off them under the action
of frictional force between the pellets. In the result the dust is formed, i.e
new granulation centers, and so the growth of pellets slows down. When the
number of centers increases, and due to pellets growth slowing down their size
diminishes.
In the mode 1, at
fluidizing velocity 0.9 m and temperature of fluidized bed 553 K, at air-blast
temperature 773 K, pellet formation entropy is 21,98 * 10-4. As this
takes place pellets equivalent diameter comes up to 0,01 m.
In the mode 4, at
fluidizing velocity 1.8 m and temperature of fluidized bed 383 K, at air-blast
temperature 773 K, pellet formation entropy is 551,04 * 10-4. As
this takes place pellets equivalent diameter comes up to 0,003 m.
Generally in the modes
with higher fluidizing velocity, pellet formation entropy is higher too. If
pellet formation entropy is high, there is a high probability of granulation
centers formation, and this leads to pellets equivalent diameter diminishing.
Thus changing the
temperature of fluidized bed and fluidizing velocity it is possible to achieve
wanted pellets’ size. It has great importance for the processes of heat
exchange and mass exchange.
REFERENCES:
1 Pavlov K.F., Romankov P.G., Noskov A.A. Examples and problems for the
course of chemical engineering processes and devices. - Ë.: Õèìèÿ, 1970.
669 p.
2 Corn G., Corn T., Mathematics guide for researchers and engineers. –
M.: Nauka, 1984, 587 p.