**
**A RATE EQUATION FOR CRYSTALLIZATION OF SODIUM OXALATE UNDER BAYER
CONDITIONS

Anthony Mckinnon^{2}, Gordon Parkinson and Kevin Beckham^{1}

A.J. Parker Cooperative Research Centre for Hydrometallurgy

Curtin University of Technology

GPO Box U 1987, Perth, Western Australia 6845

^{
1Alcoa of Australia, Kwinana Alumina Refinery, Cockburn Road,
Kwinana,
Western Australia 6167
2Now located at Alcoa of Australia
ABSTRACT
During the digestion of bauxite in caustic, and subsequent operations
in a Bayer plant, entrained organic matter is degraded, much of it to the relatively
stable oxalate anion. There is consequently a continuous build up of sodium oxalate in the
Bayer liquor, and this must be removed in order to prevent unwanted crystallization during
hydrate precipitation.
In other industries, rate equations have been employed to predict the
extent of crystal growth. Although rate equations have been developed for the
crystallization of sodium oxalate in aqueous systems, no work has been published on
crystallization under Bayer conditions. This work will describe the development of a rate
equation to predict sodium oxalate crystallization in a synthetic liquor system. The
effect of supersaturation, seed charge, stirring rate and temperature on rate of crystal
growth will be discussed. From activation energy calculations it has been discovered that
the crystallization process is predominantly controlled by surface-integration and not
bulk diffusion.
A comparison of growth on blocky and acicular oxalate seed has shown
that the rate of crystallization is not a simple function of available surface area, which
suggests that some surfaces are more active than others. This will be demonstrated with
aid of SEM pictures.
KEY WORDS:
sodium oxalate, rate equation, crystallization, kinetics, Bayer
A RATE EQUATION FOR CRYSTALLIZATION OF SODIUM
OXALATE UNDER BAYER CONDITIONS
Anthony Mckinnon, Gordon Parkinson and Kevin Beckham
1.0 INTRODUCTION
During the digestion of bauxite in caustic, and subsequent operations
in a Bayer plant, entrained organic matter is degraded, much of it to the relatively
stable oxalate anion. If the sodium oxalate concentration is allowed to continually
increase in the process then it can coprecipitate with gibbsite. Coprecipitation leads to
a number of gibbsite product quality problems, including an increase in the level of fine
particles and an increase in sodium levels in the final product. It is therefore essential
that the concentration of sodium oxalate in the process stream be tightly controlled.
Although there are a number of possible ways of removing oxalate from Bayer liquors
(Gnyra, 1979), Alcoa employs a separate sidestream oxalate crystallization removal
process. Thus, the crystallization of sodium oxalate is very important to the operation of
Alcoa’s Bayer process.
The development of a rate equation for the crystallization of sodium
oxalate is an important step in understanding the factors which affect the rate at which
sodium oxalate can be removed from Bayer liquors. Once developed, rate equations can be
employed to evaluate how potential physical changes to the process will effect sodium
oxalate crystallization and how the addition of various compounds to Bayer liquor will
influence crystallization. The crystallization kinetics of sodium oxalate have been
reported in aqueous solutions (McGregor, 1995 and Xu, 1993) but to date no work has been
published on crystallization under Bayer conditions. Bayer liquors contain a multitude of
components, a number of which are known to inhibit sodium oxalate crystallization (Lever,
1983). The presence of these components means that it is impractical to develop a
fundamental model for the crystallization kinetics of sodium oxalate using process liquor.
Thus, in this study, a synthetic liquor solution was used in the development of a kinetic
expression for the crystallization of sodium oxalate.
2.0 EXPERIMENTAL
A synthetic liquor was prepared which reflected the major
characteristics of plant liquor. The final liquor composition is TA = 280 g/L, TC/TA =
0.84, Al2O3/TC = 0.28, NaCl = 40.0 g/L, Na2SO4
= 10.0 g/L, SiO2 = 0.5 g/L, P2O5 = 0.3 g/L, Sodium
Formate = 15.0 g/L, Sodium Acetate = 20.0 g/L, Sodium Malonate = 5.0 g/L, Sodium Succinate
= 15.0 g/L, Sodium Oxalate = 0.8 g/L (at 60oC) total soda (TS) = 364 g/L, and a
TS/TA = 1.3.
Crystallization experiments were carried out in a 4 L stainless
steel water jacketed reaction vessel. Typically, a 1 g/L seed charge of synthetic
acicular sodium oxalate was added to a concentrated synthetic liquor solution previously
saturated with sodium oxalate and the resulting solution was equilibrated at 60oC
for 2 hours with stirring at 200 RPM. Sufficient aqueous sodium oxalate solution (from a
35 g/L stock) was added to supersaturate the liquor to the desired oxalate concentration.
The resulting precipitation was monitored by sampling at regular intervals and analysing
for soluble oxalate by GC/MS.
Data analysis was carried out using the kinetic analysis program,
Cryskin, developed by Kevin Beckham (Beckham, 1994). This program fits desupersaturation
data and produces a growth order and rate constant of best fit. It requires input of the
seed charge with a defined surface area for each experiment and automatically adjusts the
seed area as crystal growth occurs. In order to achieve this, it requires that the seed be
well characterised and that the morphology of the seed remains constant throughout the
experiment. Well defined acicular sodium oxalate seed crystals were prepared from an
aqueous solution of sodium hydroxide and characterised by SEM. A comparison of seed
crystals prior to, and during a crystallization experiment has established that the aspect
ratio remains constant throughout the desupersaturation experiments.
3.0 RESULTS AND DISCUSSION
Rates of crystallization (R) were calculated from the experimental
curves (oxalate concentration versus time) by use of the following equation:
R = -dC/dt = k A (1)
where k is the rate constant, A is the surface area of the crystal, C
is the oxalate concentration in the solution, Cs is the equilibrium saturation
concentration and g is the growth order. To develop a kinetic expression for the
crystallization of sodium oxalate, the values for the order of growth (g) and the rate
constant (k) must be determined experimentally. The major variables which can influence
the rate equation are the supersaturation and seed surface area and these will be examined
in detail. The effect of temperature and stirring rate will also be investigated.
3.1 Effect of Supersaturation on Oxalate Crystallization
Investigations into the effect of supersaturation on oxalate growth
were carried out by varying the initial oxalate driving force (?C) whilst maintaining a
fixed seed charge (1 g/L acicular). Desupersaturation curves corresponding to initial
supersaturations from 0.75 to 2.85 g/L are shown in Figure 1.
Figure 1
The effect of varying the initial supersaturation on the
desupersaturation
of sodium oxalate in synthetic liquor at 60oC.
The desupersaturation data shown in Figure 1 have been analysed by
Cryskin, and the resulting rate constants and growth orders are displayed in Table 1. As
the value of the growth rate is strongly dependent upon the value chosen for the growth
order, it is necessary to fix the value of the growth order to compare rates under
different conditions. Tests 4 - 7, which cover a supersaturation range of 1.65 to 2.55 g/L
(oxalate concentration: 2.3 - 3.2 g/L), were used to calculate an overall growth order and
rate constant. A value of 2.45 was obtained for the overall growth order and 8.21 x
10-7 kg m-2s-1 for the overall rate constant. A growth
order of 2.45 was fixed and the rate constant for each set of data recalculated. This
yields a close agreement between the rate constants over the supersaturation range of 1.05
to 2.55 g/L. The rate constants obtained at both the extreme high and low range of driving
force (?C = 2.85 & 0.75 g/L) are also acceptable.
Table 1
Overall rate constants and growth exponents for the desupersaturation of
a solution of sodium oxalate in synthetic liquor with varying initial supersaturations at
a constant seed charge of 1 g/L acicular oxalate at 60oC
Test
Initial Supersaturation
?C
Growth Order
Rate constant k
(kg m-2s-1)
k given g = 2.45
(kg m-2s-1)
1
0.75 g/L
3.59
8.86 x 10-7
7.02 x 10-7
2
1.05 g/L
2.78
8.70 x 10-7
8.81 x 10-7
3
1.35 g/L
2.63
8.07 x 10-7
8.15 x 10-7
4
1.65 g/L
2.42
8.06 x 10-7
8.01 x 10-7
5
1.95 g/L
2.42
8.66 x 10-7
8.84 x 10-7
6
2.25 g/L
2.44
8.80 x 10-7
8.54 x 10-7
7
2.55 g/L
2.44
8.34 x 10-7
8.51 x 10-7
8
2.85 g/L
2.36
10.43 x 10-7
9.74 x 10-7
4-7
2.45
8.21 x 10-7
3.2 Effect of Acicular Seed Charge on Oxalate Crystallization
The effect of acicular seed charge on oxalate growth was
investigated by varying the acicular seed charge while maintaining a fixed sodium oxalate
concentration of 2.3 g/L. Desupersaturation curves corresponding to a range of seed
charge from 0.5 to 3 g/L are shown in Figure 2.
Figure 2
The effect of acicular seed charge on the desupersaturation of sodium
oxalate in synthetic liquor at 60oC
The desupersaturation data shown in Figure 2 have been analysed by
Cryskin and the resulting rate constants and growth orders are displayed in Table 2. These
results show an overall growth order of 2.44 and an overall rate constant of 8.43 x 10-7
kg m-2s-1. The rate constants for the data in Figure 2 were
then recalculated using a growth order of 2.45, which was obtained from the variation in
initial supersaturation experiments (Table 1) and these are shown in the last column in
Table 2. The agreement between the overall growth order obtained from the variation in
supersaturation experiments (2.45) and that obtained from the variation in acicular seed
charge (2.44) is very good.
Table 2
Overall rate constants and growth exponents for the desupersaturation of
a 2.3 g/L sodium oxalate in synthetic liquor solution with varying initial seed charges of
acicular oxalate using growth orders calculated from the variation in seed charge
experiments (Figure 2) and from the variation in initial supersaturation experiments
(Figure 1)
Test
Acicular seed charge
(g/L)
Growth Order
Rate constant - k
(kg m-2 s-1)
k given g=2.44
(kg m-2 s-1)
k given g=2.45
(kg m-2 s-1)
1
0.5
2.23
9.23 x 10-7
7.97 x 10-7
7.92 x 10-7
2
0.75
2.43
7.51 x 10-7
7.72 x 10-7
7.71 x 10-7
3
1
2.29
10.50 x 10-7
10.15 x 10-7
10.14 x 10-7
4
2
2.85
7.37 x 10-7
7.49 x 10-7
7.39 x 10-7
5
3
2.67
8.93 x 10-7
9.56 x 10-7
9.42 x 10-7
1-5
2.44
8.43 x 10-7
3.3 The effect of Stirring Rate on Oxalate Crystallization
The effect of stirring rate on the desupersaturation of sodium oxalate
in synthetic liquor was determined by carrying out crystallization experiments containing
2.3 g/L sodium oxalate with a 1 g/L acicular seed charge at stirring speeds of 200, 400
and 600 RPM. Rate constants were calculated from the data obtained, using a fixed growth
order of 2.45. The results displayed in Table 3 show that increasing the stirring speed
has only a negligible effect on the rate of oxalate growth and therefore demonstrates that
the growth of sodium oxalate is not diffusion controlled. This is confirmed by the growth
order calculations, which show that the growth of sodium oxalate follows a second order
reaction, as the value of g is approximately equal to 2 (Mullin, 1993). The slight
decrease in rate constant, with increased stirring rates, is possibly due to the attrition
of some particles which results in a slight increase in the overall surface area.
Table 3
Rate constants for the desupersaturation of a solution of 2.3 g/L
sodium oxalate in synthetic liquor with varying stirring rates, given a growth order of
2.45
Stirring Speed (rpm)
Rate constant given g=2.45
(kg m-2 s-1)
200
8.01 x 10-7
400
7.93 x 10-7
600
7.75 x 10-7
3.4 The Effect of Temperature on Oxalate Crystallization
It is expected that if the mechanism by which growth occurs is constant
over a range of temperatures, then the apparent rate constant for crystal growth will
increase with increasing temperature. Rates of crystallization were measured over a
temperature range of 25 to 80oC, while attempting to maintain a fixed initial
supersaturation (?C = 1.65 g/L) and seed charge (1 g/L acicular). As predicted, the
apparent rate constant for oxalate growth increases with increasing temperature (Table 4).
Table 4
Overall rate constants and growth exponents for the desupersaturation of
a solution of sodium oxalate in synthetic liquor, undertaken at various temperatures with
a constant initial supersaturation and seed charge of 1 g/L acicular oxalate
Temperature (oC)
Initial Supersaturation ?C
Growth Order
G
Rate constant k
(kg m-2 s-1)
k given g = 2.45
(kg m-2 s-1)
25
1.79 g/L
3.16
0.022 x 10-7
0.0809 x 10-7
32
1.58 g/L
3.03
0.081 x 10-7
0.193 x 10-7
38
1.66 g/L
2.62
0.74 x 10-7
0.893 x 10-7
44
1.64 g/L
2.60
1.52 x 10-7
1.73 x 10-7
50
1.52 g/L
2.28
4.51 x 10-7
4.17 x 10-7
55
1.74 g/L
2.73
4.48 x 10-7
5.22 x 10-7
60
1.56 g/L
2.42
8.06 x 10-7
8.01 x 10-7
65
1.35 g/L
1.98
25.2 x 10-7
25.0 x 10-7
70
1.68 g/L
2.86
17.8 x 10-7
19.4 x 10-7
75
1.29 g/L
2.30
42.9 x 10-7
46.4 x 10-7
80
1.26 g/L
2.16
65.5 x 10-7
75.4 x 10-7
The activation energy for the growth of sodium oxalate in synthetic
liquor can be calculated from the slope of a plot of ln (K) versus 1/T (Figure 3). An
activation energy of 106 kJ/mol was obtained, which is further evidence that the
crystallization of sodium oxalate is predominantly a process controlled by
surface-integration (denoted as an activation energy above 40 kJ/mol) (Mullin, 1993), and
not bulk diffusion. The linearity of the Arrhenius plot indicates that the mechanism of
crystal growth is constant over the temperature range of 25 to 80oC.
Figure 3
Arrhenius plot of the logarithm of crystallization rate constant as
a function of the reciprocal of the temperature for the crystallization of sodium oxalate
in synthetic liquor. Initial oxalate supersaturation of approximately 1.65 g/L over a
temperature range of 25 -80oC.
3.5 Growth from Blocky Seed in Synthetic Liquor
The rate of growth of blocky seed in synthetic liquor was compared to
that of acicular seed to establish whether the morphology of seed crystals influences the
rate of growth or whether growth is simply related to total surface area. If the
morphology of seed crystals is irrelevant to the rate of oxalate growth, then
desupersaturation experiments carried out with blocky and acicular seed at a constant
oxalate supersaturation and temperature should only be dependent on the surface area of
the seed. The BET surface areas of acicular and blocky seed were found to be 1.04 and
0.21 m2/g, respectively. If identical desupersaturation experiments are
carried out with 1 g/L acicular seed (total surface area 1.04 m2/L)
and 2 g/L blocky seed (total surface area 0.42 m2/L), then it is expected
that the desupersaturation experiment containing the acicular seed would proceed faster as
the total surface area is greater. The results displayed in Figure 4 show that this is not
the case, as the blocky seed desupersaturation experiment is quicker. If the blocky seed
is examined by SEM, both prior to and during crystallization (Figure 5), it is seen that
the relatively smooth faces of the control seeds show pronounced dendritic growth from the
end faces (001) after growth in synthetic liquor. Surface area analysis of the blocky
crystals at the completion of the experiment reveals a large increase in surface area
(0.96 m2/L). Thus, if blocky crystals are placed in supersaturated
synthetic liquor, dendritic growth occurs leading to an acicular like morphology. This
demonstrates that the end faces (001) of sodium oxalate grow faster in synthetic Bayer
liquor than the side faces.
Figure 4
A comparison of the effect of seed type on the desupersaturation of
sodium oxalate in synthetic liquor at 60oC, with a constant initial oxalate
concentration of 2.3 g/L
(a)
(b)
Figure 5
SEM pictures of the crystals obtained from a desupersaturation
experiment with a 1 g/L blocky seed charge and an initial oxalate concentration of 2.3
g/L: (a) initial blocky seed (Hayashi, full scale = 97 ?m); (b) after 40 mins (full scale
= 165 ?m)
Calculations of the total amount of surface area of the (001) faces
available on the blocky and acicular seed shows that the total amount of (001) face
surface area is higher for the 2 g/L blocky seed charge than for the 1 g/L acicular seed
charge. This explains why blocky seed has a higher growth rate than acicular seed (Figure
4).
4.0 CONCLUSIONS
A rate equation to predict sodium oxalate crystallization in a
synthetic liquor system has successfully been developed. The rate of growth of sodium
oxalate can be described by the following equation in the synthetic liquor system used in
this study.
R = 8.21 x 10-7 A
Investigations into the effect of temperature on oxalate
crystallization show that, with a fixed growth order, that the apparent rate constant
increases with increasing temperature. An activation energy of 106 kJ/mol was calculated
for the growth of sodium oxalate in synthetic liquor. This demonstrates that the
crystallization of sodium oxalate is predominantly a process controlled by
surface-integration and not bulk diffusion.
A comparison of rate of growth of oxalate seed with different
morphologies has shown that the rate of growth is not a simple function of available
surface area and that some crystal faces are more active than others.
ACKNOWLEDGMENTS
This research was supported by a grant from MERIWA.
REFERENCES
Beckham, K. (1994). Unpublished data.
Gnyra, B. and Lever, G. (1981). Review of Bayer organics-oxalate
control process. Light Metals. pp. 151-161.
Lever, G. (1983). Some aspects of the chemistry of bauxite organic
matter on the Bayer process: the sodium oxalate-humate interaction. Travaux.13
pp. 335-347.
McGregor, A. (1995). Sodium oxalate crystallisation kinetics. Thesis
(Honours) University of Queensland.
Mullin, J.W. (1993). Crystallization, 3rd ed.,
Oxford, Butterworth-Heinemann.
Xu, B.A.; Giles, D. and Ritchie, I.M. (1993). Report on the
crystallization of sodium oxalate. A.J. Parker Cooperative Research Centre for
Hydrometallurgy.
}