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, К	773	773	773	773
The temperature in the fluidized bed , К	553	453	418	383
Coolant flow , nм^3/hour	7776	10368	12960	15552
gas flow speed in fluidized bed, nм/s	0,9	1,2	1,5	1,8
Dried middlings productivity, t/м^2·day	4,7	6,5	11,4	12,8
Boiled off water productivity, t/м^2·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.nм^3/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 ΔР – 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 , м/с	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:

V_cr > V_ev (7)

The salt rate of crystallization from the solution of the certain composition remains sustained.

V_кр = 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. - Л.: Химия, 1970. 669 p.

2 Corn G., Corn T., Mathematics guide for researchers and engineers. – M.: Nauka, 1984, 587 p.