Reactor Model for Production of Aluminum Fluoride
John Karlström
Department of Chemical Engineering II, Lund University, P.O. Box 124, SE- 221 00 Lund, Sweden
A reactor model was developed to simulate the production of aluminum fluoride from
fluosilicic acid and aluminum hydroxide in a semibatch reactor. The reaction
mechanism was determined and a kinetic model was combined with the material and
energy balances to create a reactor model. The reactor model was used to study the
effects of the preheating temperature of fluosilicic acid and aluminum hydroxide, the
concentration of fluosilicic acid as well as the grain size of aluminum hydroxide.
Introduction
Aluminum fluoride is used in many industrial
processes. It is one of the minor constituents added
to the electrolytic cells during the production of
metallic aluminum. It is also used in the preparation
of white enamels, as an anti-reflection coating in
complex optical systems, as a constituent in welding
fluxes, and in the preparation of fluorine containing
glasses, (Gernes, 1962).
The present study was carried out with the aim to
investigate the reaction between fluosilicic acid and
aluminum hydroxide under the production of
aluminum fluoride and silica. The process for
production of aluminum fluoride and silica is
schematically depicted in Figure 1.
The total process of fluosilicic acid interaction
with aluminum hydroxide can be described by the
following overall reaction:
H2SiF6 + 2 Al(OH)3 → 2 AlF3 + SiO2 + 4 H2O
(I)
The reaction is exothermal and proceeds in
several steps. It can be described by the following
three reactions (Skyler, 1966; Dmitrevskij and
Semenova, 1970):
3 H2SiF6 + 2 Al(OH)3 → Al2(SiF6)3 + 6 H2O
(II)
Al2(SiF6)3+ 6 H2O → 2 AlF3 + 3 SiO2 + 12 HF (III)
12 HF + 4 Al(OH)3 → 4 AlF3 + 12 H2O
Al(OH)3
Reactor
Filter
(IV)
Crystallization
1 . The silica precipitates out in different forms,
depending on the pH of the solution. At low pH
values (<3) the readily filtered form of the silica
predominates; with increasing pH the amount of
fine and colloidal silica increases. The fine
particulate form makes filtration difficult,
therefore the pH should not exceed a certain
value (<3-4) which is determined by the method
of filtration used.
2. The reaction time plus the filtering time should
not be extended to the point that aluminum
fluoride begins to crystallize.
3. On the other hand, to obtain a good yield and
also a practically silica-free aluminum fluoride
solution, it is important that the fluosilicic acid
is converted as completely as possible.
Reaction mechanism
AlF3
H2SiF6
The production of aluminum fluoride is carried
out preferably between 70°C and 100°C. The
concentration of fluosilicic acid can be as high as 35
wt-% in a water solution. The acid concentration as
well as the particle size of the aluminum hydroxide
affect the rate of the reaction. The resulting
aluminum fluoride solution is metastable, and the
trihydrate begins to crystallize out quickly at
temperatures around 90°C. Precipitated solid silica
must therefore be removed as quickly as possible.
The main problems in the process are firstly to
carry out the reaction in such a way that the filter
cake obtained by separating out the silica exhibits
good filtering properties, and secondly to avoid the
aluminum fluoride being contaminated with silica.
This leads to the following requirement on the
conditions for carrying out the reaction (Arankathu,
1980):
SiO2
Figure 1. Process for production of aluminum fluoride
To determine the kinetics of the reactions, the
experiments and the results of Skyler (1966), and
Dmitrevskij and Semenova (1970) have been used.
When evaluating the results in the latter article, the
rate equation of the first reaction in the mechanism
above can be described as:
r1 = k1 * CA* CB2/3 * CB01/3
(1)
In this relation r1 is the rate of the first reaction
and k1 is the rate constant. CA is the concentration of
fluosilicic acid, CB is the concentration of aluminum
hydroxide and CB0 is the start concentration of
aluminum hydroxide. The first reaction is the rate
determining step of the overall reaction. The rate
constant of the first reaction is inversely proportional
to the particle size of aluminum hydroxide. Both the
second and third reactions have been calculated to be
second order reactions. The second and third
reaction can be described as:
r2 = k2 * CC * CG
(2)
r3 = k3 * CB * CD
(3)
In these equations r2 and r3 are the rates of the
reactions and k2 and k3 are rate constants. In Eq. [2]
CC and CG are the concentrations of aluminum silica
fluoride and water, respectively. In Eq. [3], CB and
C D are the concentrations of aluminum hydroxide
and hydrogen fluoride, respectively. The third
reaction should be substantially fast because of the
acidic conditions.
The activation energy for the overall reaction has
been calculated to 21,3 kcal/(K*mol) (Dmitrevskij
and Semenova, 1970). An approximation in this
model is that the activation energy for the overall
reaction is the same as the energy for each
elementary reaction step. In other words the
activation energies for the three reactions E1 = E2 =
E 3 = 21,3 kcal/(K*mol) = 89121 J/(K*mol). To
calculate the frequency factors k01, k02 and k03 for
each reaction the Arrhenius equation has been used.
The rate constants for a specific temperature were
calculated according to Eqs. [1], [2] and [3]. The
Arrhenius equations can be described as:
preheating temperature of fluosilicic acid and
aluminum hydroxide were 65° C and 35°C,
respectively. In comparison with the standard case
the temperature profile of the simulation was not
correct. In other words the frequency factors did not
resemble the real operation. The reason of the
problem was that the specific surface area of the
aluminum hydroxide used in the experiments by
Dmitrevskij and Semenova (1970) was about 100
times greater than that of the hydrates used in
commercial processes. To correct the frequency
factors they were adjusted so that the simulation
corresponded to the standard case. The result of the
simulation is depicted in Figure 2, where the
symbols represent the measured temperatures of the
standard case and the line represents the simulation.
To get values of the factors that described the real
operation k01 had to be decreased and k03 had to be
increased, while the frequency factor of the second
reaction did not have to be corrected.
The perfect match corresponded to the following
frequency factors:
k01 = 8,1 * 109 s-1*(mol/l)-1
k02 = 7,6 * 108 s-1*(mol/l)-1
k03 = 2,0 * 1011 s-1*(mol/l)-1
Kinetic model
A kinetic model has to have different kinds of
elements that easily can be separated. At first it is
important to give the components in the reactions
different symbols, due to the fact that this makes the
model easier to follow and, if necessary, to correct.
Secondly, the different elements that the model shall
include have to be determined. In this case the
model will be partly based upon the reaction
mechanism and partly upon the size of the aluminum
hydroxide particles. Finally, for the purpose of
making the model complete, material and energy
balances are used together with the kinetics.
105
k1 = k01 * exp(-E1/(R*T))
(4)
100
k2 = k02 * exp(-E2/(R*T))
(5)
k3 = k03 * exp(-E3/(R*T))
(6)
In these equations T is the temperature in Kelvin
and the gas constant R = 8.31 J/(K*mol). The
calculated frequency factors were used for
calculation of the rate constants when the
temperature of the reactor was varied. The results of
several simulations were compared with a standard
case. The standard case corresponded to an acid
concentration of 28.3 wt-%, a particle diameter of
100 µm and stoichiometrical amounts of fluosilicic
acid and aluminum hydroxide. Furthermore, the
)
C
(
e
r
u
t
a
r
e
p
m
e
t
simulation
95
90
85
80
75
70
65
60
0
100
200
300
400
500
600
reaction time(s)
Figure 2. Simulation of the standard case
700
800
900
1000
As mentioned earlier the overall reaction is
divided into three steps. With symbols the schedule
of the reaction becomes a bit easier to follow. With
the symbols A=H2SiF6, B=Al(OH)3, C=Al2 (SiF6)3,
D=HF, E=SiO2, F=AlF3 and G=H2O the reaction can
be described in another way:
3 A + 2 B→ C + 6 G
(II)
C + 6 G → 2 F + 3 E + 12 D
(III)
12 D + 4 B → 4 F + 12 G
(IV)
As mentioned earlier the rate equations of the
reaction can be described as:
r1 = k1 * CA * CB2/3 * CB01/3
(1)
r2 = k2 * CC * CG
(2)
r3 = k3 * CB * CD
(3)
The rate constant of the first reaction has to be
adjusted for different particle sizes. The standard
case corresponds to a size of 100µm, which in this
model is called dp0N. This size gives the value k1N for
the rate constant of the first reaction. To calculate
the rate constant k1 for a different grain size dp0 the
following equation can be used:
k1=(dp0N/dp0)*k1N
(7)
Material balances
The reaction cycle of the model has been the
basis of the whole investigation. In this model
fluosilicic acid is pumped into the reactor initially, at
the time t0, with a constant flow. At the time t1 the
start of pumping aluminum hydroxide into the
reactor with a certain flow takes place. The flow of
aluminum hydroxide is decreased at t2, the so called
fine feeding is started. At the times t3 and t4 the feed
of aluminum hydroxide and fluosilicic acid,
respectively, are stopped. At the latter time the
double amount of aluminum hydroxide in relation to
fluosilicic acid has been pumped into the reactor. In
other words the reaction is performed
stoichiometrically. After the time t4 the reaction
proceeds until emptying of the reactor takes place at
t5. In Table 1 all the time points of the different
moments are presented.
For material and energy balances general
equations have been used. The equations for the
rates of the reactions can be transformed from terms
of reactions into terms of species.
rA = –3 * r1
rB = – 2 * r1 – 4 * r3
rC = r1 – r2
rD = 12 * r2 – 12*r3
rE = 3 * r2
rF = 2 * r2 + 4*r3
rG = 6 * r1 – 6 * r2 + 12 * r3
(8)
(9)
(10)
(11)
(12)
(13)
(14)
In these equations rA through rG are the rates of
change of the elements in mole/(l*s) according to
the symbols presented earlier.
Finally, material balances can be presented.
These balances will calculate the change in the
amount of moles related to the reactions.
dnA/dt = rA*V + FA
dnB/dt = rB*V + FB
dnC/dt = rC*V
dnD/dt = rD*V
dnE/dt = rE*V
dnF/dt = rF*V
dnG/dt = rG*V + FG
(15)
(16)
(17)
(18)
(19)
(20)
(21)
In these equations V is the volume in liters in the
reactor. FA , FB and FG are the feed flows in moles
per second of fluosilicic acid (100%), aluminum
hydroxide and water in the acid solution,
respectively. The volume will increase as long as
either fluosilicic acid or aluminum hydroxide still is
pumped into the reactor. Therefore, a balance of the
change of volume in the reactor has to be
implemented in the model:
dV/dt = (m1/DA) + (m2/DB)
(22)
In this equation m1 is the mass flow of acid and
water and m2 is the mass flow of aluminum
hydroxide. Both in kg/s. D A is the density of
fluosilicic acid in kg/l and it varies proportionally
with the concentration of the acid in the solution.
This according to the next equation:
DA = 0.878*(acid conc. (%/100)) + 1.00 kg/l
(23)
DB is the density of the aluminum hydroxide and
it has a value of 2.4 kg/l.
Table 1. Different operations during one reaction cycle
Operation
Start of acid filling, t0
Start of hydrate filling, t1
Start of fine feeding of hydrate, t2
Stop of fine feeding of hydrate, t3
Stop of acid filling, t4
Emptying of reactor
Time
0s
37 s
78 s
90 s
128 s
700-800 s
Thermodynamic data
In the model ∆H f-values of the components are
used to calculate the heat of reaction of the three
reactions. Although the temperature increases during
the reaction the ∆H f-values at 25°C will be used.
The ∆Hf- and Cp-values of the components are
presented in Table 2.
Table 2. ∆Hf- and Cp-values at 25°C (SI Chemical Data)
Component
H2SiF6 (aq)
Al(OH)3 (s)
Al2(SiF6)3 (aq)
HF(aq)
SiO2 (s)
AlF3 (aq)
H2O (aq)
∗
∆Hf (J/mol)
-2331300, HA
-1276000, HB
-8066300∗, HC
-333000, HD
-847300, HE
-1510000, HF
-286000, HG
Cp (J/(K*mol))
94∗, Cp1
93, Cp2
-107
44
75
75
estimated value
The only two Cp-values that are used in the
model are that of aluminum hydroxide and the
assumed one of fluosilicic acid. A mean value for
the Cp-value of the mixture in the reactor during the
reaction has been assumed through adjustment
between the temperature in the simulations with the
temperature of the standard case. The Cp-value of
the mixture, Cpm i x , has been estimated to 94
J/(K*mol).
Energy balance
The heat of the reactions are represented as ∆H1
for the first reaction, ∆H2 for the second reaction and
∆H3 for the third reaction in the following equations:
∆H1 = 6*HG + HC – 2*HB – 3*HA
(24)
∆H2 = 12*HD + 3*HE + 2*HF – 6*HG – HC
(25)
∆H3 = 12*HG + 4*HF – 4*HB – 12*HD
(26)
Finally, the energy balance can be derived. The
following equation describes the enthalpy change of
the system during the reaction:
dH/dt = (–r1*∆H1 – r2*∆H2 – r3*∆H3)*V – (FA + FG)*
*Cp1*(273.15 – T10) – FB*Cp2*(273.15 – T20) (27)
In Eq. [27] T10 and T20 are the temperatures of
the feed of fluosilicic acid and aluminum hydroxide,
respectively. Before aluminum hydroxide is pumped
into the reactor, which in this model is before 37
seconds, no reaction takes place. Then the energy
balance has to be described in another way:
dH/dt = – (FA + FG)*Cp1*(273.15 – T10)
(28)
The enthalpy in the reactor varies with the
temperature according to:
G
H = Cpmix*
∑ ni * T
A
(29)
The first thing to do is to take the derivative of
Eq. [29]. Then the temperature T is solved from the
equation. The result is an equation that describes the
temperature derivative in the reactor:
dT/dt = (dH/dt – (T – 273.15)*Cpmix*∑dni/dt) /
(Cpmix * (nA+nB+nC+nD+nE+nF+nG))
(30)
Equation [30] is used to calculate the
temperature in the reactor during the reaction.
Before the reaction takes place the temperature is
assumed to be constant, and then the temperature of
the preheated fluosilicic acid gives the temperature
in the reactor. When the reaction starts the
temperature increases adiabatically until 102°C,
which is the boiling point of fluosilicic acid. The
concentration of the acid affects the boiling point.
Into this effect the model does not take any
consideration. When the boiling point has been
reached the temperature in the reactor in stays
constant. In other words the temperature derivative
is held constantly at zero both before aluminum
hydroxide is pumped into the reactor and after that
time when the boiling point of fluosilicic acid has
been reached.
Results
The investigation was based upon how a few
different parameters affect the reaction. These
parameters were the preheating temperature of both
fluosilicic acid and aluminum hydroxide, the particle
size of aluminum hydroxide, the acid concentration
and a possible excess or deficit of aluminum
hydroxide. The results were evaluated in terms of
increased or decreased conversions, temperature
profiles and enthalpy profiles in comparison with the
base case.
Simulation of the base case was, as mentioned
earlier, performed with the following values of the
parameters. The acid concentration was 28.3 wt-%,
the particle diameter 100µm and there were
stoichiometrical amounts of fluosilicic acid and
aluminum hydroxide at a mole ratio of 1:2.
Furthermore, the preheating temperature of
fluosilicic acid and aluminum hydroxide was 65°C
and 35°C, respectively. According to commercial
processes the emptying of the reactor is carried out
after approximately 700-800 seconds. This fact can
be of great interest when the parameters vary. The
conversions of the reactants can be compared with
the conversions of the base case. When the degree of
the conversion increases, emptying of the reactor can
be performed earlier, while higher concentrations of
the products are received earlier. This could lead to a
more efficient production. The concentration profiles
for the base case are shown in Figure 3.
Concentrations of the components
6
H2SiF6
Al(OH)3
Al2(SiF6)3
HF
SiO2
AlF3
5
Time (s)
4
Conversion of fluosilicic acid
3
2
2200
2000
1800
1600
1400
1200
1000
800
600
400
200
0
50% conversion
95% conversion
45
50
55
60
65
70
75
80
85
90
Preheating temperature of H2SiF6 (C)
1
0
0
100
200
300
400
500
600
reaction time(s)
700
800
900
1000
Figure 4. Variation of conversion of fluosilicic acid with
the preheating temperature of fluosilicic acid
Figure 3. Concentration profiles for the base case
The preheating temperature of fluosilicic acid
and the acid concentration have the largest effects on
the reaction. An increased temperature of the
fluosilicic acid leads to a faster reaction and greater
heat production. Even if measures like this could
lead to a more efficient process the heat production
causes some problems. An excess of enthalpy is
supplied to the reactor which could cause the reactor
content to violently boil and foam. Accordingly, a
decrease in the preheating temperature gives a
slower reaction and a temperature profile that
finishes below 102° C. An increased acid
concentration affects the reactor in principle the
same way as an increased temperature of fluosilicic
acid. This fact gives reason to lower the preheating
temperature of fluosilicic acid when the acid
concentration is higher than the normal case.
Accordingly a higher preheating temperature is
necessary when the acid concentration is well below
28.3 wt-%. The reaction times, when 50% and 95%
conversion of fluosilicic acid are reached, variation
with the preheating temperature of fluosilicic acid
and the acid concentration are shown in Figures 4
and 5, respectively. In these diagrams the other
parameters have the same values as the base case.
The preheating temperature of aluminum
hydroxide does not affect the reaction much. An
increase in this temperature makes the reaction a bit
faster, but not much. The particle size of aluminum
hydroxide affects the reaction much more. With a
smaller particle diameter the rate of the first reaction
increases, which affects the total reaction. Smaller
particles however give only a small excess of
enthalpy. In other words a more fine material could
give a more efficient production. Bigger particles
lead to the opposite effect. The concentration
profiles of a decreased particle diameter with 50% to
50 µm are shown in Figure 6.
Conversion of fluosilicic acid
1600
1400
1200
Time (s)
)
l
/
l
o
m
(
n
o
i
t
a
r
t
n
e
c
n
o
c
1000
50% conversion
800
95% conversion
600
400
200
0
15
20
25
30
35
40
Acid concentration (%)
Figure 5. Variation of conversion of fluosilicic acid with
the acid concentration
)
l
/
l
o
m
(
n
o
i
t
a
r
t
n
e
c
n
o
c
Concentrations of the components
6
H2SiF6
Al(OH)3
Al2(SiF6)3
HF
SiO2
AlF3
5
4
3
2
1
0
0
100
200
300
400
500
600
reaction time(s)
700
800
Figure 6. Concentration profiles for a 50% decrease of the
particle diameter
900
1000
An excess of aluminum hydroxide could in the
future be of interest due to the fact that it leads to a
higher pH-value without giving a filter cake that is
more difficult to handle. This measure could give a
better production because the aluminum fluoride
might be produced in a more pure form, free from
phosphorus. In other words a more phosphorus
containing fluosilic acid into the reactor would not,
with a pH-value at about 4 when the reaction is
completed, give a less pure aluminum fluoride. The
results of an excess of hydrate show that this would
lead to some what of a faster reaction without any
direct problems. A deficit of aluminum hydroxide on
the other hand leads to unwanted effects on the
process. The production of both aluminum fluoride
and silica decreases and large amounts of hydrogen
fluoride are produced.
Literature cited
1. Donald C. Gernes, Producing aluminum fluoride, patent
US 3,057,681, Oakland, California, 1962.
2. Arankathu Skaria, Felix Hartmann, Process for
producing aluminum fluoride, patent GB 2,049,647,
London, England, 1980.
3. L. D. Skrylev, Kinetics and mechanism of interaction of
fluosilicic acid with aluminum hydroxide, Zh. Prikl.
Khim, 1966 , 39(1), 58-64. Journal written in Russian.
4. G. E. Dmitrevskij, E. B. Semenova, Kinetics of
fluosilicic acid interaction with aluminum hydroxide,
Odess. Gos. Univ. im. Mechnikova, Odessa, USSR.
Izv. Vyssh. Ucheb. Zaved., Khim. Khim Tekhnol,
1970, 13(7), 960-962. Journal written in Russian.
Received for review April 22 2002