Kinetic model for the reaction of ilmenite with sulphuric acid

Article abstract of DOI:10.1023/A:1012405826498

The kinetic of the reaction ilmenite with sulphuric acid was studied using non-adiabatic and non-iso-thermic calorimetric device system. The kinetic model based on interphase surface and kinetic models round in literature which are usually applied were te

Full text of DOI:10.1023/A:1012405826498

Journal of Thermal Analysis and Calorimetry, Vol. 65 (2001) 583–590
KINETIC MODEL FOR THE REACTION OF
ILMENITE WITH SULPHURIC ACID
M. JabÓoÕski and A. Przepiera
Technical University of Szczecin, Institute of Chemistry and Environmental Protection,
Laboratory of Material Chemistry and Environmental Protection, Szczecin, Al. Piastów 42, Poland
Abstract
The kinetic of the reaction ilmenite with sulphuric acid was studied using non-adiabatic and non-iso-
thermic calorimetric device system. The kinetic model based on interphase surface and kinetic mod-
els found in literature which are usually applied were tested.
The best agreement between experimental and calculated values was found with model based
on first order of reaction and model of contracting volume.
Keywords: calorimetry, ilmenite, interphase surface, kinetics, model
Introduction
In the process of obtaining titanium dioxide by sulphate method, titanium raw materi-
als, ilmenites or titanium slags are digested at high temperature and in the concen-
trated solution of sulphuric acid. As a result of an exothermic reaction, the tempera-
ture of the reacting mixtures grows up to about 200°C. The reaction product is a
mixture of sulphate of titanium(IV), iron(II), iron(III), magnesium and other metals,
which are present in raw material.
Thermal power of the reactor, in which titanium raw material is digested, in the
period of the main run of the reaction can reach about 10 MW. The uncontrolled run
of the reactor creates a dangerous possibility of explosion of the reaction mixture.
The aim of the presented investigations was the research of the rate of reaction
of Norwegian ilmenite with sulphuric acid by the method of non-isothermic calorim-
etry and the determination the kinetic model of this process.
Experimental
Natural ilmenite is a concentrate most often received by the method of flotation from
solid magma rocks or from alluvial sands. These raw materials are characterised by
high content of titanium dioxide and oxides of iron, magnesium and other metals such
as manganese, chrome, niobium.
1418–2874/2001/ $ 5.00
Akadémiai Kiadó, Budapest
© 2001 Akadémiai Kiadó, Budapest
Kluwer Academic Publishers, Dordrecht

584
JAB£OÑSKI, PRZEPIERA: REACTION OF ILMENITE WITH SULPHURIC ACID
Ilmenite from the south of Norway was applied in the investigations of the reac-
tion of ilmenite with sulphuric acid. The elemental composition of ilmenite deter-
mined by spectrometer of X-ray fluorescence XRF PHILIPS PW1480 was as fol-
lows: TiO2 – 44.4%, FeO – 34.8%, Fe2O3 – 11.6%, MgO – 4.1% and SiO2 – 2.1%.
Investigations of phase composition on X-ray diffractometer PHILIPS with
goniometer PW 1820 and with controller PW 1710 showed, that the main crystallo-
graphic phase of ilmenite is iron - titanic oxide FeTiO3.
Ilmenite before measurement was dried at 105°C to constant mass, and then
grounded in Fritsch sphere mill to the moment when the remainder on 40 µm sieve
was 15%.
Ilmenite reaction with sulphuric acid was investigated in non-isothermic and
non-adiabatic calorimeter. The main unit of the apparatus was a calorimetric vessel
volume about 0.6 dm3, equipped with a heater, a stirrer and a temperature Pt 100 sen-
sor. The calorimetric vessel was placed in thermostatic jacket. Schematic diagram of
apparatus was presented in Fig. 1.
Fig. 1 Apparatus used for thermokinetic investigations. 1 – calorimetric vessel,
2 – thermostat, 3 – dosage vessel, 4 – temperature sensor, 5 – heater, 6 – stirrer
The calorimetric vessel was connected with the feeder of ilmenite. The reaction
begins when ilmenite was introduced into the calorimetric vessel filled with sulphuric
acid.
The installed electric heater served to calibrate the calorimeter (determination of
calorimetric constant, time constant and heat transfer coefficient).
The used sample of ilmenite was about 100 g and mass of sulphuric acid of con-
centration 84% was about 400 g.
In Fig. 2 was presented the temperature run of reaction ilmenite with sulphuric
acid in calorimeter at the starting temperature 80°C and in concentration of sulphuric
acid 84%.
J. Therm. Anal. Cal., 65, 2001

JAB£OÑSKI, PRZEPIERA: REACTION OF ILMENITE WITH SULPHURIC ACID
585
Fig. 2 Temperature changes in calorimeter during reaction ilmenite with sulphuric acid
After the beginning of the reaction the temperature began growing quickly in the
calorimetric vessel. At the moment when almost all mass of ilmenite was reacted, the
diminution of the heat stream takes place, which is visible as a slight maximum on the
graph. When the maximum of the temperature was reached, the amount of the heat re-
action was smaller than the heat losses and the temperature decreases.
Theoretical
Reaction of ilmenite with sulphuric acid, solid–liquid system, proceed on an interphase
surface. Processes of mass transport to and from interphase surface, inflow of sulphuric
acid to the area of the reaction and outflow dissolution product of the reaction from the
reaction area play an important role in this reaction. Driving module of this processes is
difference of concentrations among area of reaction and environment.
It can be assumed, that products of the reaction dissolve partly, and remainders
create porous structure, which is not a barrier for processes of mass transport. As the
reaction is carried on with excess of sulphuric acid, it can be accepted, that the con-
centration of sulphuric acid is constant during the reaction.
This reaction is exothermic, the heat of reaction is the reason for the increase of
the temperature of the reactionary mixture. The increase of the temperature influ-
ences the expansion of the reaction rate. On constructing a kinetic model the follow-
ing assumptions were accepted; all particles are of identical dimension and shape, the
enthalpy of the reaction is constant and is not dependent on temperature, the heat con-
duction of the reaction mixture is sufficiently high, that temperature is identical in
given moment in all sample, and specific heat of the reaction mixture is constant and
does not depend on temperature.
The reaction rate according to this assumption can be expressed with equation:
dα
dt
E
= Aexp −
f (α )
(1)
RT
where: α – degree of transformation, A – pre-exponential coefficient, E – activation
energy.
J. Therm. Anal. Cal., 65, 2001

586
JAB£OÑSKI, PRZEPIERA: REACTION OF ILMENITE WITH SULPHURIC ACID
The reaction temperature is not constant and the second equation is necessary in
order to describe this dependence. In case of calorimetric systems we can use balance
equation of heat flow:
dT dQ
=
K
−βT (t)
(2)
dt dt
where: K – calorimetric constant, Q – heat amount generated during reaction, β – co-
efficient of heat losses.
In Eq. (2) the left side determines heat accumulation in calorimetric system, and
the right side determines the difference between heat of stream generated in calori-
metric vessel and heat losses to environments. We receive in consequence the follow-
ing system of differential equations:
dT
dt
dα
dt
K
=∆Hr
−βT (t)
(3)
dα
dt
E
= Aexp −
f (α )
RT
The solution of the equation system (3) requires a kinetic equation. In literature
series of kinetic models with different factors influencing the reaction rate was de-
scribed [1]. Models describing phenomena of nucleation belong to popular kinetic
models. Avrami equations [2] take into account this type of process. To reactions in
which occur process of diffusion, belongs oxidising of metals (gas+solid), reactions
between solids and reactions in liquid–solid system. The simpliest equation taking
into account diffusion processes is the parabolic equation [3].
Kinetic models taking into account influence of surface change on rate of reac-
tion are qualified as models of disappearing geometry. Example of this kinetic type is
reaction of solid in sphere form, which decrease during reaction until complete disap-
pearances.
In heterogeneous systems quantity of interfacial surface plays an essential role.
The surface of the reaction is closely connected with the degree of transformation.
Degree of transformation is defined by
m0 −m
α =
(4)
m0
where: m – mass present, m0 – initial mass.
For spherical particles dependence of interfacial surface on degree of transfor-
mation we get by substituting mass and surface of particle:
S=S0 (1−α )2/3
(5)
This equation was presented in paper [4].
We can use similar considerations for particles of simple regular solids, for ex-
ample, particles in shape of cylinder.
J. Therm. Anal. Cal., 65, 2001

JAB£OÑSKI, PRZEPIERA: REACTION OF ILMENITE WITH SULPHURIC ACID
587
Substituting mass of particle in shape of cylinder
ρπD2L
m=
(6)
(7)
4
and surface
πD2
S=πDL+
2
into Eq. (4) we receive
1
2
πD02L(1−α )
L(1−α )
S= πD0 L
+
(8)
L0
2L0
For the case when the cylinder shape nears to needles i.e. L>>D and the length of
this needles does not change in time of reaction i.e. L=L0, Eq. (8) will simplify and we
obtain:
S=S0 (1−α )1/2
(9)
For the case of particles in shape of cylinder when both diameter and length
change in time of reaction in the following way
D
=const.
(10)
L
we obtain
S=S0 (1−α )2/3
(11)
This equation is identical with Eq. (5) obtained for spherical particles.
Next shape in our consideration is particle of rectangular prism of edges A, B
and C. We assumed, this dimension in time of reaction changes in following way
A
= const.
B
(12)
B
= const.
C
After transformation we obtain Eq. (11).
From this considerations it can be concluded that for reaction of ilmenite (irreg-
ular shape of particles) with sulphuric acid we can take the kinetic equations into ac-
count
f (α )=(1−α )1/2
(13)
and
f (α )=(1−α )2/3
(14)
J. Therm. Anal. Cal., 65, 2001

588
JAB£OÑSKI, PRZEPIERA: REACTION OF ILMENITE WITH SULPHURIC ACID
In [1] we found rate equations used in kinetic analyses of solid state reactions.
These kinetic models take geometric factors, chemical controls and diffusion into
consideration and are used to describe processes of thermal transformations.
Substituting this kinetic equations to system of Eq. (3), we can calculate the
value of the pre-exponential factor and activation energy and determine the best fit-
ting model.
Results and discussion
To find the value of parameters in the equation system (3) the experimental data and
non-linear regression were used. This is an iterative procedure to find out the mini-
mum of sum of square deviations.
Σ(Ti exp −Ti cal )2 =min
(15)
To solve this function the algorithm on the basis of Marquart method was ap-
plied. In this algorithm during each iteration the system of differential Eq. (3) by the
Runge–Kutta method was solved.
Calculations were carried out for experimental data of ilmenite with sulphuric
acid and for kinetic models. Results of calculations are in Table 1.
Table 1 Results of calculation
Σ(Ti exp–Ti)2
f(α)
(1–α)[–ln(1–α)]2/3
1288.2
27832.9
179.4
α(1–α)
(1–α)1/2
(1–α)2/3
104.7
(1–α)
51.2
(1–α)2
178.8
1/α
[–ln(1–α)]–1
(1–α)2/3[1–(1–α)1/3
[(1–α)–1/3–1]–1
42207.9
16321.5
10485.2
10486.5
–1
]
In Table 1 we present the sum of squares deviations for kinetic model.
The best fitting of experimental data we received for the kinetic models of con-
tracting volume and for model of chemical reaction of first order. In both cases lowest
value of sum of squares deviations was received. The activation energy for the kinetic
model of contracting volume Eq. (11) was E= 41.44 kJ mol–1 and for reaction of first
order was E=49.54 kJ mol–1.
J. Therm. Anal. Cal., 65, 2001

JAB£OÑSKI, PRZEPIERA: REACTION OF ILMENITE WITH SULPHURIC ACID
589
Remaining equations taking into account diffusion show considerably worse fit-
ting to given experimental. Equations taking into account occurrence of nuclei
(Avrami equation) do not give a good fitting, either.
The calculations show, that diffusion processes and transportation of mass from
and to interfacial surface do not decide about the reaction rate. The main units having
influence on the reaction rate are the interfacial surface and chemical kinetics in reac-
tion of ilmenite with sulphuric acid. The obtained results confirm earlier assumptions
accepted.
The experimental value of heat of reaction ilmenite with sulphuric acid was ob-
tained from the experiment. Taking into account suitable corrections we received the
value of 1.12 kJ g–1.
During reaction of ilmenite with sulphuric acid, the chemical reaction can be as-
sumed and presented below:
TiO2+H2SO4 → TiOSO4+H2O
Fe2O3+3H2SO4 → Fe2(SO4)3+3H2O
FeO+H2SO4 → FeSO4+H2O
MgO+H2SO4 → MgSO4+H2O
On the basis of these reactions it is possible to calculate the theoretical value of
heat reaction. The result of heat calculation for ilmenite is 0. 997 kJ g–1.
Conclusions
Presented results of calculations and theoretical considerations lead to the conclusion
that the reaction rate of ilmenite with sulphuric acid mainly depends on the quantity
of interfacial surface and chemical reaction. In this case process of mass transport
does not influence on the reaction rate. It confirms the assumption, that products of
reaction dissolve partly, and the remainders create a porous structure which in not a
barrier for process of mass transport.
Theoretical considerations about particles shape of solids lead to the conclusion,
that kinetic Eq. (11) could be used to particles in a more complicated shape, together
with particles in an irregular shape. The assumption about the constant ratio of main
dimensions of particles in time of reaction could be applied to the particles in irregu-
lar shapes. Experimental results confirm this assumption.
The assumption about constant specific heat of reaction mixture in time of reac-
tion is close to real conditions. The measured specific heat of substrate and the prod-
uct of reaction was on the same level about 1.5 J g–1 K–1.
Differences from real conditions were in the assumption about identical dimen-
sions of particles in reaction mixture. It is very difficult to fulfil this assumption, in
our experiment the dimensions of particles were in the range from 1 to 40 µm.
The rest of assumptions are consistent with real condition of reaction.
The tested kinetic model of reaction of ilmenite with sulphuric acid is very sim-
ple and could be used in simulation of production technology, especially to determine
conditions for safety run of reaction.
J. Therm. Anal. Cal., 65, 2001

590
JAB£OÑSKI, PRZEPIERA: REACTION OF ILMENITE WITH SULPHURIC ACID
References
1 Handbook of Thermal Analysis and Calorimetry. Vol. 1. Principles and Practice,
Ed. M. E. Brown, Elsevier Science 1998.
2 M. Avrami, J. Chem. Phys., 7 (1939) 1103; 8 (1940) 212; 9 (1941) 177.
3 M. E. Brown, D. Dollimore and A. K. Galwey, Comprehensive Chemical Kinetics, Vol. 22,
Elsevier, Amsterdam 1980.
4 A. Przepiera, M. Jab³oñski and M. Wiœniewski, J. Thermal Anal., 40 (1993) 1341.
J. Therm. Anal. Cal., 65, 2001