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Yunusov Bokhodir, senior teacher chair «Informatics, automation and managements», Tashkent chemical institute of technology, Tashkent, Uzbekistan E-mail: Ulug85bek77@mail.ru
Theorethical bases of process of an air separation of loose materials in a fluidizated layer
Abstract: In this work on the basis of the multistage system analysis the computer model of process of an air separation of loose materials in a fluidizated layer is constructed. The recommended technique allows to investigate separation conditions in a fluidizated layer of easy and heavy components of loose materials.
By consideration of the criteria! equations of Archimedes and Reynolds, options of creation of a fluidizated layer and questions of determination of speed of ablation of particles are defined. The interrelation of distribution of density of a separated material from diameter of particles that allowed to define a air separation zone with use of a fluidizated layer is defined.
On computer model calculations of an air separation of a loose material with various density are made.
Keywords: multistage system analysis, mathematical model, computer model, air separation, speed fluidization beginning, speed of ablation.
Process of enrichment of non-ferrous ores, precious and rare metals, is an important link in production of metals. The researches which have been carried out in recent years showed on possibility of realization of more economic and simple way of air separation of loose materials [1; 2].
Emergence of computer programs allowed to carry out exact modeling of technological process of an air separation, to reveal the narrow ranges of modes providing the best separation of a material. It is known that ore consists of joints of a set of minerals which have various density. By research ofprocess of an air separation ofloose materials on its mathematical model it is possible to define the dependences reflecting nature ofchange ofthe sizes of particles at various design data of a separator, to determine consistent patterns of change of target concentration of useful components as a part of ore depending on the geometrical sizes and density of particles, and also the constructive sizes of the device [3-5].
Development of theoretical bases of an air separation allowed to investigate process of an air separation of loose materials on its mathematical model and to define regularities of change of target concentration of useful components as a part of ore depending on the geometrical sizes and density of particles, and also the constructive sizes of the device.
Installation ofa fluidizated separating (Fig. 1.) consists of the following several elements: the compressor 1, the needle gate 2, rotameter 3, the device of a fluidization 6,
cyclones 8 and collections for the besieged materials 9. In the bottom flange 5 the grid previously is established. The capacity of an air separation is connected to the cyclones 8, serving for catching of easy components of ore.
Installation works as follows: test of a separated material, load into the device of a fluidization and then the upper flange 5 is densely closed with the help of rubber laying, bolts and nuts (4 and 7). At the closed needle gate 2 the compressor 1 turns on and slowly opening by means of the gate 2 air in the device of a fluidization 6, the consumption of air on parameter 3, the beginning of a fluidizated corresponding to speed for particles with certain sizes and density of particles is established.
Fig. 1. Scheme of an air separation of loose materials
The material under the influence of air is given in a condition ofa boiling layer. From a boiling layer consistently are carried away in cyclones 8, easy components, and in a fluidizated layer there are heavy components.
The main device here is the device with a fluidizated layer. If at the first stage of the multistage system analysis the system is dismembered on the elements considered above, and the device with a fluidizated layer also is dismembered on a number of elements: gas supply, grid, zone of a fluidization and ablation zone. The zone of a fluidization is divided into two components: gas and firm phases. In turn, the firm phase consists of particles of the first, the second, the third etc. components (fig. 2).
Let's consider, what parameters are entrance, and what parameters define a condition of elements of installation, i. e. are target parameters.
Input parameters of object are: an expense of a firm material, concentration of a loose material, the sizes of firm particles, a consumption of gas, pressure in the device, concentration of studied components on an entrance. Target parameters: an expense of the enriched material, concentration of a component in the enriched material, a consumption of gas, concentration of studied components in gas.
In precisely the same way it is possible to define input and target parameters for each element of installation. Let's say for the compressor an input parameter is energy, and days off — an expense and pressure of gas.
Input parameters of a fluidizated layer are: expense of a firm loose material, concentration of a loose material, sizes of a loose material. Target parameters is the expense of the enriched material.
Entrance parameters of gas phase of a fluidizated layer: consumption of gas, concentration of a valuable component. Target parameters: consumption of gas, concentration of a valuable component and pressure.
The firm phase of a fluidizated layer is characterized: expense of a firm phase, concentration of a valuable component, in diameter of particles. As target parameters here act: an expense of the enriched material, concentration of a valuable component in the enriched material, an expense of the easy component which is carrying away with gas.
When modeling by input parameters ofparticles are: consumption of gas, speed of gas, density of particles and diameter. Target parameter of object is speed of particles [3].
Installation of an air
separation in fluidizated layer
Compressor
Apparatus of fluidzated layer
The device of inputting of solid material
The device of diversion of solid materiel
The device of diversion of light weight material
-1- -1-
Inputting of gaz Coips Net Fluidizated layer Asportation zone
Gaz phase Solid phase
1
Particle 1 Particle 2 Particle 3
Fig. 2. Components and knots of installation of an air separating of loose materials in a fluidizated layer
Thus, having considered consistently all phenomena and the effects which are taking place in studied installation, it is possible to make mathematical model of process of an air separating of particles of a loose material in a fluidizated layer.
If to present that each particle of the crushed material has a sphere form, with the identical sizes, but different masses, the task consists in removal by means of an air stream of easy particles from a mix.
Each particle is influenced by the following two forces:
Force of weight of the spherical particle, operating with top down is equal:
F = mP *g (1)
where mp — mass of a particle, g — acceleration of a free fall.
The force created by an air stream, lifting a particle from below up is equal:
W2
F2 =1*S* Pa *— (2)
Where, Я — the factor expressing a turbulent or laminar mode, W — speed air a stream, Pa — density of air, S — the area of a spherical particle which the stream affects.
If the forces operating on particles, are equal each other, particles are in balance. Mathematical expression of this condition looks as follows:
F = R
W2
mng = X*S*P *-
a 2
(3)
Where mp — it is possible to replace mass of a particle m with the following equation:
mp = pp * V (4)
Where Pp particle density, V — particle volume. It was accepted that the particle has a form of a sphere and, considering that the volume of a particle is equal:
= 4 r3 =1 d3 (5)
3 6
And having substituted value V in the equation (4), and the received expression in the equation (3), we find:
Pp V ^ g = ** n^* Pa * W2 (6) Solving this equation of ratherequilibrium speed W, it is possible to receive the well-known equation [6]:
w = -
14* Pp
* dp * g
(7)
.3 A* pa
The form of particles of real disperse materials usually differs from the spherical. Such difference at mathematical modeling of technological processes is considered by means of geometrical factor of a form.
The maximum limit of this speed should not reach the speed deducing particles with heavy weight, i. e.
w, < w < w
l s
Thus, having calculated speed for the established border it is possible to carry out an air separation process.
Essential indicator of process of an air separation of ores of non-ferrous metals at enrichment is the office of heavy particles from a stream. It is reached by change of speed of a stream. Therefore it is necessary to know, at what speeds particles of heavy fraction are besieged. It depends on diameter of particles and their density.
At smooth increase in speed of a stream from 0 to some first critical value there is a usual process of filtering at which firm particles are not mobile.
To transition from a filtration mode to a mode of a fluidization there corresponds critical speed of a fluidization of Wfl called in the speed of the beginning of a fluidi-zation. At the moment of the fluidization beginning the weight of the granular material falling on unit of area of cross-section section of the device, is counterbalanced by force of hydraulic resistance of a layer.
Since speed of the beginning of a fluidization and above, pressure difference in a layer < keeps almost constant value. This results from the fact that with growth of speed of the fluidization agent contact between particles decreases, and they receive a great opportunity for chaotic hashing in all directions. The average distance between particles thus increases, that is the fenestration of a layer г and, therefore, its height of h increases г.
For determination of the size W' there is rather large number of semi-empirical and theoretical dependences. At a formula conclusion the fenestration of a layer of motionless spherical particles can be accepted equal 0,4.
The top border of a fluidization condition corresponds to speed of a free ablation of single particles. It is obvious that at the speed of a stream surpassing speed of a ablation, Wa> Wf ,will be there is an ablation of particles from a layer of a granular material.
On the other hand it is possible to consider classical methods of formalization of descriptions for calculation of process of an air separation of a loose material in a fluidizated layer
Processes of interaction of a gas phase with particles of a firm phase have special value. Considering disorder of the sizes of particles, the concept of equivalent diameter of particles is entered. It is supposed that particles have various values of diameters, changing from the minimum value of diameter to the maximum value. Proceeding from a percentage ratio of the sizes of the particles, equivalent diameter decides on the help of the equation
d=
100
z
(S)
Re = Ar
f 18 + 0.5754Är
(12)
If equivalent diameter is known, for determination of speed of the beginning of a fluidization it is necessary to determine Archimedes criteria by the equation:
g*Ps - P
Taking into account the equation (12), according to the classical equation of criterion of Reynolds, it will be possible to define speed an ablation of particles, that is speed of ablation of a particle.
Ar =
p
(9)
V P
Knowing Archimedes criterion, it is possible to define Reynolds's criterion for a fluidizated layer.
Ar
wf =
Ref * ^ d * p
(1З)
Refl 1400 + 5.22JAr
(1O)
It is also known that Reynolds's criterion for a particle is defined by the classical equation on which it is possible to determine speed of a fluidization of gas by the equation:
Re =
w,
d * p
wß =
Re * p
(11)
¡j d * p Also settlement equation of criterion of Reynolds for a case of an ablation of particles is known:
This equation gives the chance to define speed and a consumption of gas for providing a fluidization, or ablation of particles. Varying diameters of particles it is possible to define a consumption of gas for material separation with various density.
Using the known equations of calculation of criteria of Archimedes, Lyashchenko and Reynolds the equations for calculation of speeds the fluidization and ablation beginning for particles of different density and are chosen the sizes and on their basis the computer model of process of an air separation of firm particles in a fluidizated layer, with use of a package of the MATLAB program (the Fig. 3 is constructed.).
0.052"10"-3
d(ekui"'a I e ni)
R ijl i.iijzd и h)
ад —к. 44.141
Nachalnaya skorost
□ .0025ST]
ад >> 1 1 .515е+С105 |
Display
ад —^ 626.41
Reynolds
Displayl
ад 0.03635 I
skorost un osa
Displays
Fig. 3. Computer model of process of an air separation of firm particles in a fluidizated layer.
Calculations of speeds depending on diameter and density of particles carried out the fluidization and ablation beginning for minerals of SiO2, Al2O3, K2O, CaO, MgO, TiO2, FeO and Fe2O3 being in ore. In the crushed ore each particle too consists of joints of minerals. In particles it is more than one mineral and it is less than other minerals. Therefore, the particles containing heavy components will be heavier. With reduction of the sizes
of particles, influence of minerals of heavy components on all of a particle will be more.
On computer model (fig. 3) changes of speeds the fluidization beginning (fig. 4) and ablation (table 2) depending on the size of particles of a separated loose material and density are calculated.
The analysis of the received results shows that at the big sizes of particles 0.060^0.080 mm, the limiting sizes
of particles providing a good separating increase till seven and nine sizes of particles. It is possible to note that for ore enrichment with the sizes of particles in a range 0.010^0.030 mm, the limiting sizes of particles providing a good separation are in limits of one, two and three sizes of particles. On the other hand, at smaller diameters of particles of influence of the maintenance of an enriched material (heavy components) on particle density it is more than at big diameters of particles.
On computer model calculations of speeds the flu-idization and ablation beginning depending on diameter
Table
are made and density of particles for ore test which structure is presented in table 1.
Considering it, we recommend to carry out ore enrichment in a range of the crushed particles from 0.030 mm till 0.050 mm (fig. 5) where the limiting sizes of particles providing a good separation are in limits from 0.030 mm till 0.034 mm, from 0.034 mm till 0.039 mm, from 0.039 mm till 0.044 mm and from 0.044 mm till 0.050 mm. Thus, ore enrichment in this range will need four installations with a fluidizated
layer.
№ Component Mass fraction of % Densi-tyKg/m3 № Component Mass fraction of % Density Kg/m3
1. M2O3 13,31 3990 8. K 0 3,97 2320
2. SiO2 67,52 2650 9. Na2O 0,14 2390
3. TiO2 0,41 4505 10 CaO 1,55 3370
4. Fe2O3 4,49 5240 11 PA 0,19 2390
5. MgO 0,60 3580 12 3,45
6. MnO 0,06 5460 13 H2° 0,42
7. FeO 1,62 5700 14 n. n.n 2,52
Dependence of speed of ablation on diameter and type of particles
Table 2.
Diameter of particles Speed of ablation depending on diameter and a type of particles
Au FeO FeA TiO2 Al2O3 MgO CaO SiO2 K20
0.000030 0.301 0.092 0.085 0.073 0.065 0.058 0.055 0.044 0.038
0.000031 0.319 0.098 0.090 0.078 0.069 0.062 0.059 0.046 0.041
0.000032 0.339 0.104 0.096 0.083 0.073 0.066 0.062 0.049 0.043
0.000033 0.358 0.110 0.102 0.088 0.078 0.070 0.066 0.052 0.046
0.000034 0.378 0.117 0.107 0.093 0.083 0.074 0.070 0.055 0.049
0.000035 0.398 0.123 0.114 0.098 0.087 0.079 0.074 0.059 0.051
0.000036 0.419 0.130 0.120 0.103 0.092 0.083 0.078 0.062 0.054
0.000037 0.440 0.137 0.126 0.109 0.097 0.087 0.082 0.065 0.057
0.000038 0.462 0.144 0.133 0.115 0.102 0.092 0.087 0.069 0.060
0.000039 0.484 0.151 0.139 0.120 0.107 0.096 0.091 0.072 0.063
0.000040 0.506 0.158 0.146 0.126 0.112 0.101 0.095 0.076 0.067
0.000041 0.528 0.166 0.153 0.132 0.118 0.106 0.100 0.079 0.070
0.000042 0.551 0.173 0.160 0.138 0.123 0.111 0.105 0.083 0.073
0.000043 0.575 0.181 0.167 0.145 0.129 0.116 0.109 0.087 0.076
0.000044 0.598 0.189 0.174 0.151 0.134 0.121 0.114 0.091 0.080
0.000045 0.622 0.197 0.182 0.157 0.140 0.126 0.119 0.095 0.083
0.000046 0.646 0.205 0.189 0.164 0.146 0.132 0.124 0.099 0.087
0.000047 0.670 0.213 0.197 0.171 0.152 0.137 0.129 0.103 0.090
0.000048 0.695 0.226 0.205 0.177 0.158 0.143 0.135 0.107 0.094
0.000049 0.720 0.230 0.213 0.184 0.164 0.148 0.140 0.111 0.098
0.000050 0.745 0.239 0.221 0.191 0.170 0.154 0.145 0.115 0.102
Diameter of particles (m) Fig. 4. Dependence of speed of the beginning fluidization from diameter and a type of particles
Fig. 5. Dependence of speed of ablation from diameter and a type of particles The technological scheme on processing of ores 0.039 mm, from 0.039 mm till 0.044 mm and from 0.044 mm according to the scheme of preliminary enrichment and till 0.050 mm, moves in four separate capacities. Further, sandy separation in a psevdoozhizhenny layer is offered. pumps, the loose material moves in separate installations of a
Crushed till certain sizes and the ore sifted on sets, in multistage air separation in a fluidizated layer where there is limits from 0.030 mm till 0.034 mm, from 0.034 mm till a separation ofa loose material.
References:
1. Lebedev I. F. Research of processes of division of minerals of various density in an air-sand stream and development of new devices of an air separation the dissertation Author's abstract on competition of a scientific degree of Candidate of Technical Sciences. - M. - 2008.
2. Matveev A. I., Vinokurov V. P., Fedorov V. M. Prospects of application of modular mobile ore enrichment installations. - Yakutsk: Publishing house of YaNTs of the Siberian Branch of the Russian Academy of Science, 1997. -120 p.
3. The system analysis of a pnevmoseparirovaniye of loose materials in fluidizated layer/Yunusov B. I., Kara-bayev D. T., Artikov A. A./TamrTy Chemical technology. Control and management. 2/2011.
4. Determination of speeds of fluidization separation of loose materials./Yunusov B. I., Karabayev D. T., Artikov A. A./TamrTy Chemical technology. Control and management. 2/2011.
5. Kasatkin A. G. Main processes and devices of chemical technology. - M: Chemistry, 1971. - 784 p.
