28
Tolentino S. y Caraballo S. Simulación numérica del ujo de aire.
UNIVERSIDAD, CIENCIA y TECNOLOGÍA Vol. 21, Nº 82 Marzo 2017 (pp. 4-15)
ISSN 2542-3401
28
28
Juan Segura1, Franyelit Suàrez2, Juan Casierra2 .
Salomón et al., Productividad del proceso minero, mas allá de la producción
.
Echegaray et al., Energy balance formation of subeutectoide fayalita
ATHENEA JOURNAL IN ENGINEERING SCIENCES Vol. 2, Nº 6 December 2021 (pp.2842)
ISSN 27376419
Energy balance formation of sub-eutectoide fayalita at high pressures
in particle separators
Recibido (15/10/21), Aceptado (18/11/21)
Abstract:
This article presents an approach to the problem of ceramic types adhesion, applying energy
and matter balance to the established control volume (cyclone) with the use of mathematical formulas
that are interrelated to develop mathematical calculations and establish a new mathematical model The
rst results are obtained by operating the energy balance considering the collision of particles, using the
principle of conservation of energy, the rst law of thermodynamics, in order to obtain information that
allows describing the phenomena of thermoplasticity and creep, in the formation of adhesions, from a
physicochemical and kinetic point of view, which will serve as the basis for understanding their effect.
As a result, an energy value of 660 kJ / mol was obtained, sufcient energy to start the transformation
of the solid particles to a state of thermo-ow that allows the adhesion phenomenon to be started.
Keywords:
Adhesion, energy balance, cyclones, elutriation, eutectoid, fayalite, thermoplasticity.
Balance de Energía formación de fayalita Sub-
eutectoide a altas presiones en separadores de partículas
Resumen:
En este artículo se presenta una aproximación al problema de las adherencia tipos cerámicas,
aplicando balance de energía y materia al volumen de control establecido (ciclón), con la utilización
de fórmulas matemáticas que se interrelacionando entre sí para desarrollar los cálculos matemáticos
y establecer un nuevo modelo matemático. Los primeros resultados se obtienen operando el balance
energético considerando la colisión de partículas, utilizando el principio de conservación de energía,
la primera ley de la termodinámica, con el n de obtener información que permita describir los
fenómenos de termo-plasticidad y uencia, en la formación de adherencias, a partir de un punto
de vista sicoquímico y cinético, que servirá de base para comprender su efecto. Como resultado
se obtuvo un valor energético de 660 kJ/mol, energía suciente para iniciar la transformación de
las partículas sólidas a un estado de termo-uencia que permite iniciar el fenómeno de adhesión.
Palabras Clave:
Adhesión, balance energético, ciclones, elutriación, eutectoide, fayalita, termoplasticidad.
Echegaray Alberto
echegaray,alberto@gmail.com
https://orcid.org/0000- 0003-4234-0452
Universidad Nacional Experimental Politécnica
Antonio José de Sucre
Puerto Ordaz- Venezuela
doi: https://doi.org/10.47460/athenea.v2i6.31
29
Juan Segura1, Franyelit Suàrez2, Juan Casierra2 .
Salomón et al., Productividad del proceso minero, mas allá de la producción
I.INTRODUCCTIÓN
Indirect reduction processes that use the uidized bed, such as the Finmet process, which operate at pressures
greater than 5 bar and temperatures greater than 600 ° C, it is made up of a sequence of reactors that are inside each
one of them. Four particle separators known as cyclones are located, as can be seen in gure 1.
Fig 1: reactors with cyclones of the FINMET plant in Venezuela. Turmero Ruben 2010.
These cyclones for separating particles smaller than 50 µm (microns), are used for their simplicity of operation
and low maintenance cost due to the absence of moving parts, avoiding effects of dissipation of mechanical energy
in the discharge of a hydrocyclone (Bustamante, 2013), [1] the relationship of these variables are of empirical ori
-
gin and are limited to the development of correlations using experimental data, taking into consideration the design
of the device considered as a “Black Box” with the use of empirical models that are still unknown. [2], [3]. These
models do not consider the phenomena that occur inside the cyclone. Currently, these models are based on the
physics of the uid that has allowed them to be used in circulating uidized bed processes (CFD), therefore a large
number of numerical solutions are required that make it difcult to process the data generated inside the container.
The latest approximations obtained to seek a better understanding of the separation of the size of the particles as
the only consequence of the movement of the uid, for this reason, it allows to optimize the performance and the
operating conditions by examining only the ow of the gas with solid.
The literature does not report the relationships between some variables associated with the number of solids
at discharge to maintain the correct operation of the equipment, without taking into account the eld of internal
velocity on the discharge in an incipient manner [4], [5]. From the aforementioned, it can be established that even
though there is evidence of the inlet and discharge ow, it has not been included in the performance of the equi
-
pment operation. For this reason, with the aim of coupling the separation dynamics by particle size, the energetic
conditions that can be used to understand these phenomena inside the cyclone separator are considered.
These considerations generate lines of research that allow giving answers to the balance of internal energies
associated with the phenomenon of adhesions in the cylindrical zone of the particle separators used in circulating
uidized beds.
This article has been divided into sections, as follows: a rst approach to the balance of matter to explain the
phenomenon of the interaction of the particle size when it enters the cyclone separator, then a theoretical approxi
-
mation of the balance of mechanical energy inside the separator is presented cyclonic starting from Cauchy's law
to later nish with the validation of the calculation that allows explaining the phenomenon of adherence and ope
-
rability from the energetic aspects related to the conditions of formation of the shells on the walls.
ACTUAL WORK
Concept of thermal plasticity
Few authors have introduced the concept of thermoplasticity in particle sizes that go into motion in a cyclone
Echegaray et al., Energy balance formation of subeutectoide fayalita
ATHENEA JOURNAL IN ENGINEERING SCIENCES Vol. 2, Nº 6 December 2021 (pp.2842)
ISSN 27376419
30
Tolentino S. y Caraballo S. Simulación numérica del ujo de aire.
UNIVERSIDAD, CIENCIA y TECNOLOGÍA Vol. 21, Nº 82 Marzo 2017 (pp. 4-15)
ISSN 2542-3401
30
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Juan Segura1, Franyelit Suàrez2, Juan Casierra2 .
Salomón et al., Productividad del proceso minero, mas allá de la producción
separator that is subjected to temperatures above 600 ° C. However, from the perspectives of the operation of the
equipment, which involves the heat generated by the impact, heat by inelastic shock, heat by chemical reactions,
differentiation from signicant pressures, this could be denitely decisive inefciency.
From a thermodynamic approach, the physical meaning of the energy released by a dened particle size within
the separated particle could be established. As explained in [6] that starting from Cauchy's rst law and multipl
-
ying both sides by the viscosity (v).
(1)
If the body force is expressed as the gradient of a potential it can be written as , and equation (1) can
be rewritten like this:
(2)
Rearranging the terms, we nally get that:
(3)
The product represents the viscous dissipation .
Cyclone mass balance
To perform the energy balance in a circulating uidized bed reactor made up of a battery of cyclones arranged
in a conical shape that internally allows the maximum separation of the solid particles found in the reducing gas
stream, coming from the entrained gas bed. iron ore in wustitic thermodynamic stgte (FeO). (see gure 2) there is
a schematic of the particle separator.
Fig 2: Schematic diagram of a particle separator (cyclone) Source: author 2020.
Echegaray et al., Energy balance formation of subeutectoide fayalita
ATHENEA JOURNAL IN ENGINEERING SCIENCES Vol. 2, Nº 6 December 2021 (pp.2842)
ISSN 27376419
2
=
∇
.
.
+
.
= −
∇
φ
2
=
∇
.
.
+
.
+
=
∇
.
.
+
:
∇
:
∇
31
Juan Segura1, Franyelit Suàrez2, Juan Casierra2 .
Salomón et al., Productividad del proceso minero, mas allá de la producción
Data from the cyclones used in the FINMET process plant (Venezuela). See table I where the data used for the
mathematical calculations in the cyclone is shown.
Table 1
.
Source: Orinoco Iron cyclone plans.
For the calculations, the control volume is established, in this case the cylindrical zone of the cyclone is selec
-
ted in which the mass and energy balances necessary to demonstrate its inuence on the mechanism of adherence
of the particles on the metallic surface of the cyclone walls, which causes the generation of shells that affect the
operation of the particle separator.
Flow Characteristics
In the cylindrical zone of the cyclone a forced rotational ow is generated, causing the particles that enter the
gas stream through the inlet, generating a friction force against the walls of the equipment, said inlet and outlet
head loss is usually proportional to the square of the speed of the gas that circulates through the cyclone, through
the Euler number (Eu) this magnitude can be related to equation 4.
(4)
Where
∆P is the pressure drop between inlet and outlet.
gas is the density of the gas.
U is the velocity of the gas as it enters.
This velocity of the gas entering the cyclone is the supercial velocity based on the internal diameter of the
cyclone. (see equation 5).
Echegaray et al., Energy balance formation of subeutectoide fayalita
ATHENEA JOURNAL IN ENGINEERING SCIENCES Vol. 2, Nº 6 December 2021 (pp.2842)
ISSN 27376419
SimbolSignificado
Unidad
Valor
D
Cyclone diameter
mts1,423
De
Cylinder diameter
mts0,508
B
Lower outlet diameter
mts-
H
Cylindrical zone height
mts-
h
Cylinder height
mts1,391
S
Height of outlet cylinder
mts25,57
a
Inlet height
mts0,880
b
Inlet mouth width
mts0,278
=
∇
.
2
2
ρ
32
Tolentino S. y Caraballo S. Simulación numérica del ujo de aire.
UNIVERSIDAD, CIENCIA y TECNOLOGÍA Vol. 21, Nº 82 Marzo 2017 (pp. 4-15)
ISSN 2542-3401
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Juan Segura1, Franyelit Suàrez2, Juan Casierra2 .
Salomón et al., Productividad del proceso minero, mas allá de la producción
.
(5)
Where
q is the volumetric ow rate
D is the internal diameter of the cylindrical zone.
The Euler number that relates pressure forces to inertial forces is practically constant for a cyclone of dened
geometry.
Figure 4a describes how the particles that enter the cyclone make a circular movement towards the walls of the
equipment. The net ow of the gas is radial towards the center of the tube, this force acting on the particles as des
-
cribed in gure 4b for a given radius of the orbit of movement, these particles are dragged (Fb), those of thrust (Fu)
and the centrifuge (Fc), The drag forces occur towards the interior of the uid, this is due to the fact that the gas
ows into the cyclone, generating two components, the tangential velocity (Utang) and the radial velocity (Urad).
Fig 4 diagram of particle motion in a cyclone adopted by Rhodes 1998
The forces breakdown currently be considered are show in gure 4a, regarding the movement of the particles
in the cylindrical zone are shown below.
Fig 4 b balance of force on a particle adopted by Rhodes (1998).
Echegaray et al., Energy balance formation of subeutectoide fayalita
ATHENEA JOURNAL IN ENGINEERING SCIENCES Vol. 2, Nº 6 December 2021 (pp.2842)
ISSN 27376419
=
4
∗
+
2
33
Juan Segura1, Franyelit Suàrez2, Juan Casierra2 .
Salomón et al., Productividad del proceso minero, mas allá de la producción
The centrifugal acceleration (ac) generated by the particle inside the cyclone when it makes a turn, is to provide
the square of the tangential speed and inversely to provide the radius of the turn, see equation 6.
(6)
Considering that Fc = mp. ac, where mp is the mass of the particle x is the diameter of the particle, it results:
(7)
Similarly the pushing force can be written as:
(8)
The drag force if we assume Stokes's law is valid and can be expressed as:
F
d
=3*π*μ*U
rad
*r (9)
As the particles move inward or outward until the force is swinging, at this point we can assume that the parti
-
cles are in equilibrium in their orbit. In this you can verify.
(10)
(1
1)
(12)
Equation (12) indicates that small particles will be in equilibrium at radii close to the center of the cylinder,
while the larger particles will be in equilibrium at larger radii. For this reason, the larger ones tend to be collected
and the smaller ones carried away by the gas.
On the other hand, if the gas ow circulates radially as shown in gure 4a, it results:
Echegaray et al., Energy balance formation of subeutectoide fayalita
ATHENEA JOURNAL IN ENGINEERING SCIENCES Vol. 2, Nº 6 December 2021 (pp.2842)
ISSN 27376419
=
2
=
∗
3
6
∗
∗
2
=
∗
3
6
∗
∗
2
F
c
=F
d
+F
u
∗
3
6
∗
∗
2
=3
∗∗∗
+
∗
3
6
∗
∗
2
2
=
18
∗∗
−
∗
2
∗
34
Tolentino S. y Caraballo S. Simulación numérica del ujo de aire.
UNIVERSIDAD, CIENCIA y TECNOLOGÍA Vol. 21, Nº 82 Marzo 2017 (pp. 4-15)
ISSN 2542-3401
34
34
Juan Segura1, Franyelit Suàrez2, Juan Casierra2 .
Salomón et al., Productividad del proceso minero, mas allá de la producción
(13)
Where q is the volumetric ow rate of the gas, L is the height of the cylindrical section of the cyclone, r and R
represent the radial coordinate evaluated at any r and D/2, while Urad and UR represent the velocity of the gas at
any radius and at the area near the wall, respectively.
Substituting expressions (10) and (11) in (12) is obtained in equation 14.
(14)
Rearranging the terms, it is as follows:
(15)
Where r is the equilibrium orbit of the particle of size x, in case the particles are not spherical, x is the dv. If it
is assumed that the particles that can be collected are those that are close to r = R, it results:
(16)
xcrit represents the critical size; if the particles are smaller than xcrit they will not be collected and will be ca
-
rried by the gas, otherwise they will be collected at the bottom of the cyclone. If the cyclone operation complied
with all the hypotheses made to conclude in equation 16, the efciency per class should be 0 for all particles sma
-
ller than xcrit and 1 for those with a diameter greater than xcrit .
III RESULTS ANALYSIS
ENERGY BALANCE IN THE CYCLONE
The algorithm to determine the energy balance is presented in several steps as shown below, for this reason it
will start with the energy balance that acts inside the particle separator where the different energies will be studied:
Qimpacto; Qvacancia; Qpotential; Inelastic collision.
Identifying the input data in Table 2 to carry out the energy balance is to know how to see gure 5 where the
diagram of the energy balance in the cyclone is shown table 2.
Echegaray et al., Energy balance formation of subeutectoide fayalita
ATHENEA JOURNAL IN ENGINEERING SCIENCES Vol. 2, Nº 6 December 2021 (pp.2842)
ISSN 27376419
=2
∗∗∗∗
=2
∗∗∗∗
2
=
18
∗
∗
−
∗
2
2
∗
∗
∗
2
=
18
∗∗
−
∗
2
∗
2
=
18
∗
−
∗
2
∗
∗
35
Juan Segura1, Franyelit Suàrez2, Juan Casierra2 .
Salomón et al., Productividad del proceso minero, mas allá de la producción
Table 2 variable inputs
Flow diagram for the energy balance in the cylindrical zone
Fig 5 diagram to explain the energy balance in the cyclone. Source the author 2020.
Echegaray et al., Energy balance formation of subeutectoide fayalita
ATHENEA JOURNAL IN ENGINEERING SCIENCES Vol. 2, Nº 6 December 2021 (pp.2842)
ISSN 27376419
SimbolSignificado
Unidad
Valor
ρ
lecho
Wustite
beddensity
kg/cm
3
1
.543
P
Work
pressure
bar
10
H
2
Hydrogen
%
57
CO
Carbon
monoxide
%
8
,95
CO
2
Carbon
dioxide
%
3
,30
CH
4
Methane
%
25
,57
N
2
Nitrogen
%
4
,13
T
entrada
Inlet
temperature
°
C
700
T
salida
Outlet
temperature
°
C
600
ρ
Fe
Iron
density
kg/m
3
2
,461
ø
Reactor
diameter
mts
4
,5
36
Tolentino S. y Caraballo S. Simulación numérica del ujo de aire.
UNIVERSIDAD, CIENCIA y TECNOLOGÍA Vol. 21, Nº 82 Marzo 2017 (pp. 4-15)
ISSN 2542-3401
36
36
Juan Segura1, Franyelit Suàrez2, Juan Casierra2 .
Salomón et al., Productividad del proceso minero, mas allá de la producción
Calculation of the molecular weight of the gas
Calculation of the molecular weight of the reducing gas (Kg/mol) Molar ow
.
This is calculated by the percentage of the element times the molecular weight and divided by 100.
H2 = 57gr / mol; CO = 8,95gr/mol; CO2 = 3,30 gr/mol; CH4 = 25,57gr / mol and N2 = 4,13 gr/mol.
The molecular weight of the reducing gas is 10,37 gr/mol.
Calculation of the gas density using operational data
The reducing gas density kg / m3 is determined, applying the ideal gas law P * V = n * R * T, we can substitute
the number of moles that is equal to the mass over the molecular weight of the gas. Then we have the equation of
the following form P*V= m/Pm*R*T, now if we can clear the density of this equation, remembering that the den
-
sity is equal mass over the volume, the mathematical equation is: m/V=P*PM/R*T we already have the formula to
calculate the density, for this we have the input data.
The molecular weight of the reducing gas that was calculated in step two is 10.37 gr/mol, the outlet gas tempe
-
rature is 600°C, and the working pressure is 10 atm.
I convert 600 degrees centigrade to kelvin = 873 K
Calculation of bed density
The density of the bed is calculated, for this the pressure data measured by the instrument pdi xy.18.733 is
taken, which censes the density of the bed in a wustite reactor, in this case the value of 108 mbar, then it was trans
-
formed to density obtaining a value of of 1,542 kg/m3.
Calculation of real velocity of the gas entering the cyclone separator
The speed of the gas that is entering each of the cyclones is determined, the inlet ow is assumed to be 200,000
Nm
3
/h, total ow that enters the reactor, from the bottom, this ow is divided by four since it is the amount of
cyclones that make up the system, in order to have a uniform distribution.
.
working pressure 10 atm and temperature of 600°C.
It is important to calculate the actual ow that is entering the cyclone.
Qreal is calculated with the following equation.
Echegaray et al., Energy balance formation of subeutectoide fayalita
ATHENEA JOURNAL IN ENGINEERING SCIENCES Vol. 2, Nº 6 December 2021 (pp.2842)
ISSN 27376419
=
10
,
7
∗10
0
,
0821
∗
∗
∗97
;
ρ
=
0,1715gr/lts=1,75kg/m
3
=
200
.
000
4
;
50.000
ρ
37
Juan Segura1, Franyelit Suàrez2, Juan Casierra2 .
Salomón et al., Productividad del proceso minero, mas allá de la producción
Divide by 4 to determine the actual ow entering each cyclone.
This is actual ow that should enter the rectangular mouth of each cyclone.
Calculation of the theoretical entering gas velocity
We then proceed to calculate the velocity of the gas entering the cyclone, with the following ow equation, in
which the velocity is cleared.
Q=V*A; V=Q/A
Where
V is the velocity m/s
Q is the ow rate m3/h
A is the area of the rectangular = 0,245m2
The theoretical and actual speed is determined.
Theoretical V = 56,77m/seg (very high)
Real speed = 16,69 m/seg (Real speed)
Volume calculation of particle separation in the cylindrical zone
The cyclone volume calculations were made to determine the mass with which the wustite mineral particles are
impacting the cyclone wall.
For this reason, it is necessary to know the material of manufacture of the barrel or cylindrical area, in this case
it is 304 stainless steel with the density of austenitic stainless steel AISI-304 whose density ρsteel 7,980 Kg / m3
these plates have a thickness of 15 mm, height 1,391 m, diameter of the cyclone 1,423 m (D) radius 0,712 m.
Calculation of the cyclone perimeter
P = 2 * 3,1416 * 0,712 m
P = 4,470mts
Volume calculation h * e * P
h is the height mts
e is the thickness mts
Echegaray et al., Energy balance formation of subeutectoide fayalita
ATHENEA JOURNAL IN ENGINEERING SCIENCES Vol. 2, Nº 6 December 2021 (pp.2842)
ISSN 27376419
=
200.000
3
ℎ
+
1,013
10
+1,013
∗
273,15+600°
273,15
°
=58.806
3
ℎ
=14.701
3
ℎ
38
Tolentino S. y Caraballo S. Simulación numérica del ujo de aire.
UNIVERSIDAD, CIENCIA y TECNOLOGÍA Vol. 21, Nº 82 Marzo 2017 (pp. 4-15)
ISSN 2542-3401
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Juan Segura1, Franyelit Suàrez2, Juan Casierra2 .
Salomón et al., Productividad del proceso minero, mas allá de la producción
P is the perimeter mts
V = 0,093 m
3
Calculation of inlet wall mass
M = Volume * Steel density
M = 744,53kg
.
Calculation of particles impact released energy
The impact energy is calculated with the following equation
Ec = ½ M * V2
Ec = 103,707 K J / mol
Calculation of energy for vacancies
The reduction chemistry is calculated: During the transition from wustite to metallic iron, 2 vacancies are ge
-
nerated, with this the amount of energy associated with the reduction mechanism is determined.
1(□) = 28 cal/mol ;1 J = 0,238 cal /mol; 1(□)=235,29 J
The energy per vacancy product of the reaction of wustite with oxygen is calculated.
A vacancy is equal to 28.38 Kcal/mol Tesis Dr Oscar Dam [7].
During this process, two vacancies arise
Evac. = 4 * 28,38 Evac. 113,20 Kcal/mol
Evac = 473,63K J/mol
Determination of associated chemical reactions to calculate heat capacity.
Applying the rst law of thermodynamics to explain the energy of formation of iron ferrosilicate in the propo
-
sed system.
For the formation of fayalite as expressed in the following reaction.
Next, in table III, we have the elements to be used to carry out the thermodynamic calculations
Echegaray et al., Energy balance formation of subeutectoide fayalita
ATHENEA JOURNAL IN ENGINEERING SCIENCES Vol. 2, Nº 6 December 2021 (pp.2842)
ISSN 27376419
2FeO
Fe
+2
+2O
-2
+ 2
□
2‹
FeO
›+‹ SiO
2
›
2‹FeSiO
4
›
39
Juan Segura1, Franyelit Suàrez2, Juan Casierra2 .
Salomón et al., Productividad del proceso minero, mas allá de la producción
Table 3
Source the author 2020
CpFe(α)= 37,12+6,147x10-3T-0,5 J/K ; CpFe(γ)= 24,48+8,45x10-3T J/K
Thermodynamic reaction
SiO2 ∆H
0
298=-910.900 cal/mol
When the two reactions are combined:
Explains Eli Ringdalen, (2016) [8] Quartz (SiO
2
) is the main source of silicon for the production of metallurgi
-
cal grade silicon in submerged arc furnaces and with softening temperatures in the range of 1675 °C to 1800 °C,
and melting temperatures in the range of 1790 °C to 1900 °C were recorded.
For the formation of fayalite David R Gaskell (2003) [9] in introduction to thermodynamics so that 2FeO.SiO
2
is a compound formed from FeO with SiO
2
at a pressure of 1 atmosphere, the free energy Gibbs, the following
reaction is obtained.
The molecular weight is 203,73 gr/mol
∆G
o
1200K = 54 KJ/mol
Therefore, 599 KJ/mol plus 54 KJ/mol are required to start the fayalite formation process; this gives a total of
653 KJ/mol.
Calculation of the heat capacity using the rst law of thermodynamics
The heat of reduction reaction: It is the net heat in the passage from wustite to metallic iron, when the phase
Echegaray et al., Energy balance formation of subeutectoide fayalita
ATHENEA JOURNAL IN ENGINEERING SCIENCES Vol. 2, Nº 6 December 2021 (pp.2842)
ISSN 27376419
Element
Molecular
Weight
(gr/mol)
Density
(gr/cm
3
)
Melting point
(
°
C)
SiO
2
602,65-
FeO
725,751.377
Fe
2
O
3
1605,24-
Fe
3
O
4
2325,171.597
2FeO.SiO
2
203,78
(3,58 a
4,32)
1.205
2FeO(
s
)+SiO
2
(
s
)
2FeOSiO
4
(
s
)=
∆H
0
2000
=599kJ/mol
‹Si›+(O
2
)
‹SiO
2=
∆
H
0
298=
-907.100+175Tcal/mol
‹Fe›+1/2(O
2
)
‹FeO›
2‹FeO›+‹SiO
2
›
2‹FeSiO4›=
∆
H
0
298=-263.700+53,68Tcal/mol
SiO
2
(s,l)+Si(l)
2SiO(g)
ΔG
o
2000K=599kJ/mol
2FeO(s)+SiO
2
(s)
2FeO.SiO
2
(s)is-
11.070 J
40
Tolentino S. y Caraballo S. Simulación numérica del ujo de aire.
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Juan Segura1, Franyelit Suàrez2, Juan Casierra2 .
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transformation occurs Iron( ): This occurs after the impact of the particle with the metallic surface of the
separator barrel mechanical cyclone, in this case the inlet gas temperature 600ºC and outlet gas temperature 700ºC
are known, particle diameter Ø particle 4,31 E-04mm and the heat capacity is calculated with the following equa
-
tion. The amount of energy transferred by heat between a sample of mass m of a material and its surroundings by
a change in temperature from T
1
to T
2
is:
.
The energy transferred is calculated by applying the following equation ∆Q = Cp * m * ∆T to determine the
amount of heat transferred.
Where
∆Q = Net heat transfer from gas;
Cp:=Specic heat
m = Mass
The amount of energy released is determined.
Cp=37,12*(993,15K-873,15K)+(6,17*10^-3*(993,15K^2-873,15K^2))+56,92*(993,15K^0,5-873,15K
^0,5)+24,48*10^3*(1664^-3-1187^-3)
Cp=5.948 J/K
Calculation of particle volume
Particle = 4/3 * (1) * 3,1416
Varticle = 4,188 cm3
Mass = Density * Vparticle
Mass = 4,32 gr / cm3 * 4.188 cm3
Mass = 18,096 gr = 0.018096 kg
The density of FeO 5,77gr / cm3 and the density of SiO2 2,62 gr / cm3 are known
Inlet temperature 600ºC outlet temperature 700ºC
The temperature in Kelvin 273,15 + ºC
Tempted = 873,15 K
Tsalida = 973,15 K
Q = m * Cp * ∆T
Q = 12,92 KJ / mol
Creep temperature when working with 600 °C,
TC = 873/1808 = 0,478
Tc = 0,478 * Tf
Where
Tc is the critical temperature; Tf is the melting temperature of iron.
IV RESULTS
To carry out the energy balance, the composition of the gas that enters the wustite reactor with the following
molecular weight 10,37 g/mol and working temperature of 600°C to 800°C with working pressures of 10 bar was
taken.
Next, table 4 of the results of the energy balance that acts in the internal part of the cyclone separator is shown,
in order to explain the adhesion formations and therefore the generation of the fayalite is possible.
Echegaray et al., Energy balance formation of subeutectoide fayalita
ATHENEA JOURNAL IN ENGINEERING SCIENCES Vol. 2, Nº 6 December 2021 (pp.2842)
ISSN 27376419
Iron(
α −γ
)
41
Juan Segura1, Franyelit Suàrez2, Juan Casierra2 .
Salomón et al., Productividad del proceso minero, mas allá de la producción
Table 4
Source: the author 2020
V.CONCLUSIONS
For the fusion of quartz in a liquid state at 2,000K, 599KJ/mol is required and for the fusion of fayalite at
1200K, 54 KJ/mol is required, the sum of energy gives a total of 653 KJ / mol with this amount of energy being
is guaranteeing the formation of this ferrosilicate, by energy balance it was determined that 660 KJ/mol enough
energy is generated to guarantee the softening point of the particles inside the cyclone separator.
The formation of adhesions in the form of shells in the cylindrical zone in the temperature range greater than
600 ° C and pressures greater than 10 bar, is possible in uidized bed processes when they work with molecular
weights in the gas of 10 gr/mol.
Thermoplasticity in the studied temperature range 600 ° C (873K) to reach the melting point of iron requires
the following factor 0.478, obtaining the following equation Tc = 0.478 * Tf.
The results shown in the summary table of the summation of the energies released inside the cyclone separator
is 660 KJ/mol higher than the 599 KJ / mol that is required to melt the silicon oxide at 2000 ° C.
RECOGNITION
The authors are especially grateful to the Directorate of Postgraduate Research at UNEXPO for the opportuni
-
ty to write a research article related to the energy balance to explain the formation of fayalite inside the cyclonic
separator that occurs at temperatures below the point eutectic.
REFERENCES
[1]O. Bustamante. “Dissipation of mechanical energy in the discharge of a hydrocyclone”. (Dyna, Ed.) The ne
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twork of Scientic Journals of Latin America, the Caribbean, Spain, and Portugal, vol. 80 (181), Pages 136-
143,2013
[2]K.Petersen, P.Aldrich, and D.Van.,”Hydrocyclone underow monitoring using image processing methods. Mi
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nerals Engineering”, pp. 301-315,1996
[3]M. Farghaly,” Controlled Wash Water Injection to the hydrocyclone underow” [Ph.D. Thesis]. Erlangen,
FAU,2009
[4]M, Schneider, and T. Neesse. “Overow-control system for a hydrocyclone battery. Int. J. Miner. Process". 74,
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[5]J.Bergström., “Flow eld and ber fractionation studies in hydro cyclones” [Ph.D. Thesis] Stockholm, Sweden,
Royal Institute of Technology,2006
[6]C, Liu, L. Wang, and Q. Lui., “Investigation of energy loss mechanisms in cyclone separators”. Chemical En
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gineering Technology 28, pp. 1182-1190,2005
[7]O.Dam. & E.Jeffes.,.”Model for detailed assessment of chemical composition of reduced iron ores from single
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[8]E. Ringdalen., “Softening and melting of SiO2 an important parameter for reactions with quartz in Si produc
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tion” pp 43-44,2016
Echegaray et al., Energy balance formation of subeutectoide fayalita
ATHENEA JOURNAL IN ENGINEERING SCIENCES Vol. 2, Nº 6 December 2021 (pp.2842)
ISSN 27376419
M
EANING
U
NIT
(KJ/
MOL
)
U
NIDAD
(K
CAL
/
MOL
)
Energy
perimpact
103,7129,79
Energy
pervacancy473,63113,20
Energy
perparticlecollision12,923,09
Energy
duetoinelasticcollision69,7516,67
Total
Energy660,01157,74
42
Tolentino S. y Caraballo S. Simulación numérica del ujo de aire.
UNIVERSIDAD, CIENCIA y TECNOLOGÍA Vol. 21, Nº 82 Marzo 2017 (pp. 4-15)
ISSN 2542-3401
42
42
Juan Segura1, Franyelit Suàrez2, Juan Casierra2 .
Salomón et al., Productividad del proceso minero, mas allá de la producción
[9]R. Gaskell., “Introduction to the Thermodynamics of Materials. New York: Taylor & Francis” pp 614-616,2003
.
CURRICULUM SUMMARY
Echegaray et al., Energy balance formation of subeutectoide fayalita
ATHENEA JOURNAL IN ENGINEERING SCIENCES Vol. 2, Nº 6 December 2021 (pp.2842)
ISSN 27376419