Modelling the dissolution of alumina powder in cryolite

Transcription

1 Chemical Engineering and Processing 37 (1998) Modelling the dissolution of alumina powder in cryolite R.G. Haverkamp *, B.J. Welch Department of Chemical and Materials Engineering, Uni ersity of Auckland, Pri ate Bag 92019, Auckland, New Zealand Received 11 April 1997; accepted 14 May 1997 Abstract Alumina dissolution in cryolite is a complex process at elevated temperatures. However, it is desirable to have a simple model for predictive purposes. In this study, several models for the dissolution of alumina powder in cryolite were formulated and compared with experimental results obtained using modified fast linear sweep voltammetry. As a first approximation the alumina was assumed to be smooth spheres which decrease in size as dissolution proceeds. The models were based on rate control by either first order chemical reaction at the alumina surface, heat transfer, or diffusion. The shape of the curves generated gave a reasonable fit to experimental data but the heat transfer and diffusion models appear to be the best. It is certain that these models can be used to correlate the experimental data on dissolution. It is envisioned that the actual mechanism may be a combination of both heat transfer and diffusion control. The models developed may also be applicable to other systems involving dissolving particles Elsevier Science S.A. All rights reserved. Keywords: Alumina powder; Heat transfer; Diffusion 1. Introduction In the Hall Heroult process for producing aluminium, refined alumina is added to an electrolyte of molten cryolite (Na 3 AlF 6 ). The alumina dissolves in the cryolite and is then electrolysed using carbon electrodes to produce aluminium and carbon dioxide. An important consideration in achieving maximum efficiency in the production of aluminium is in the rapid dissolution of the alumina in the cryolite bath. Rapid dissolution is necessary to prevent sludging, the formation of undissolved alumina which settles below the molten aluminium at the bottom of the cell. This sludge is undesirable since in addition to this alumina not being available for electrolysis it causes erosion of the cathode and an increase in cell resistance. The composition of the bath used in the alumina dissolution tests had a cryolite ratio (mol NaF/mol AlF 3 ) of 2.4 with 5 wt.% CaF. For this composition the NaF AlF 3 solvent is a mixture of hexafluoroaluminate, tetrafluoroaluminate and fluoride anions [1]. The predominant dissolved alumina species are Al 2 OF 6 2 and Al 2 O 2 F 4 2 in approximately equal quantities. The dissolution of alumina in cryolite may be written: * Corresponding author. 2Al 2 O 3 +2AlF 3 6 3Al 2 O 2 F 2 4 Al 2 O 3 +4AlF 4 +2F 3Al 2 OF 2 6 Two simple models for the dissolution of dispersed alumina in a molten cryolite electrolyte have been developed. The first model is one where the rate of reaction depends only on the surface area of the alumina. The dissolving alumina is regarded as shrinking smooth spheres. In this model the rate of dissolution is therefore controlled by either the rate of chemical reaction (assuming first order kinetics) or the rate of heat transfer. These two mechanisms are discussed. In the second model it is assumed that the rate of dissolution of alumina is mass transport controlled, so that the concentration of alumina in the electrolyte is important. With the second model the rate depends on the diffusion rate of alumina across a boundary layer at the surface of the alumina. The predicted shape of the dissolution curves is compared with the experimental data. This comparison is possible because of the developments in the technique of in situ measurement of alumina dissolution in molten cryolite using a modified form of fast linear sweep voltammetry [2 4]. The equations developed here are applicable to other systems of dissolving particles /98/$ Elsevier Science S.A. All rights reserved. PII S (97)

2 178 R.G. Ha erkamp, B.J. Welch / Chemical Engineering and Processing 37 (1998) Table 1 Initial mass, initial surface area and initial electrolyte alumina concentrations for alumina dissolutions Dissolution curve Alumina added, M 0 (g kg 1 ) Initial alumina concentration Surface area a, A 0 (m 2 ) C i / e (g kg 1 ) C i (g l 1 ) a Based on smooth sphere model. 2. Experimental determination of dissolution rates Alumina was added to a stirred electrolyte of cryolite in a graphite crucible 100 mm in diameter and the dissolution measured with a modified form of linear sweep voltammetry. Electrolyte velocities of cm s 1, similar to those found in commercial alumina reduction cells, were achieved. The linear sweep voltammetry consisted of a cyclic voltage applied between a graphite electrode of 3 mm diameter and 7 mm length and the graphite crucible containing the melt which acts as the counter electrode. A fast forward sweep rate is used at 20 V s 1 with a very fast the reverse sweep at 200Vs 1 and the occurrence of the anode effect is fundamental to the procedure. The position of the anode effect is repeatable and increases with alumina concentration and by various correlations the alumina concentration can be determined [3]. The scatter in individual alumina concentration measurements is 5%, however, a large number of measurements are taken for a single dissolution curve so that fast fourier transforms for noise filtering and statistical methods are used to achieve the curves shown. Temperature was measured by means of K type thermocouples positioned in the electrolyte and in the crucible wall. Thermocouples were calibrated with the melting point of NaCl and on every experiment with the liquidus of the electrolyte. Temperature accuracy of 1 C was achieved. The equipment setup and the method of dissolution rate measurement have been described more fully elsewhere [3]. Commercial grade alumina was used. This alumina was sieved and the size fraction mm was used for this work. This alumina had an alpha alumina content of 15% and a surface area, as measured by the BET method of gas adsorption, of 66 m 2 g 1. This area includes the internal surface area which is a result of the very porous nature of the alumina. A set of three dissolution curves obtained from the commercial alumina were used in this modelling work. The amount of alumina used and the electrolyte alumina concentrations are listed in Table 1. The curves obtained are illustrated in Fig. 1. These curves are typical of a large number of similar dissolution experiments performed as part of a wider experimental programme. 3. First model shrinking sphere 3.1. Deri ation of equations The first model which we propose and wish to test states that the rate of dissolution of well stirred dispersed alumina in an electrolyte of molten cryolite is proportional to its surface area. The rate is not mass transport controlled, but rather, depends on the rate of the surface dissolution process involving the endothermic reaction of the breaking of strong Al O bonds by complexing with fluoroaluminate species. The model assumes that the mass transport is fast relative to the surface chemical reaction or the heat transfer. Fig. 1. Experimental dissolution curves: 600 g electrolyte (cryolite with ratio of NaF/AlF 3 =1.50, 5% CaF2) in 100 cm diameter carbon crucible with stirrer at 200 rpm, 8 C superheat (above liquidus). Curve 1 for 1 mass% alumina addition with 0.75% initial alumina concentration, curve 2 for 1 mass% alumina addition with 1.75% initial alumina concentration, curve 3 for 1.8 mass% alumina addition with 2.75% initial alumina concentration. Alumina added through a dropper with a cone shaped spreader, addition time 2 s.

3 R.G. Ha erkamp, B.J. Welch / Chemical Engineering and Processing 37 (1998) Fig. 2. Best fit curves obtained using Eq. (7) for the first model. Fit 1, 2 curve for 1 mass% alumina, fit 3 curve for 1.8 mass% alumina. Experimental curves 1, 2 and 3 for different initial alumina concentrations and alumina additions as in Fig. 1. R=k 1 A (1) where R is the rate of dissolution, units g s 1, k 1 is the rate constant, units g s 1 m 2 and A is the surface area of the alumina, units m 2. We may suppose that the particles of alumina which are added to the cryolite electrolyte are monodisperse smooth spheres each with an initial radius r 0. In making this assumption we are supposing that although the alumina is very porous, as shown by the high BET surface area, the electrolyte does not penetrate these pores, or if it does, then there is no exchange of electrolyte from these pores to the bulk electrolyte. The initial surface area of the total alumina added is then: A 0 = 3M 0 (2) r 0 where A 0 is the initial surface area of the total amount of alumina added, M 0 is the initial mass of alumina added and is the particle density. It is readily shown that the surface area of the alumina will decrease as the mass of the undissolved alumina decreases by the relationship: A=A 0 M 2/3 M 0 where A is the surface area of all the mono-sized spheres at time t and M is the mass of alumina remaining undissolved at time t. The mass of alumina remaining undissolved can be related to the concentration of alumina in the electrolyte by the relationship: M=M 0 (C C i )V (4) where C i is the initial alumina concentration (g l 1 )in the cryolite electrolyte, C is the alumina concentration at time t, V is the volume of the electrolyte. (3) In order to simplify the equations we will call C = C C i, where C i is the initial alumina concentration, prior to each alumina addition. We therefore obtain an expression for the rate of dissolution of alumina, using the shrinking sphere model: R= dc dt V=k 1A 0 V 2/3 1 C (5) M 0 By rearranging the equation and integrating with respect to concentration and time, then obtaining the integration constant when t=0 and C =0 we get the following expression: t= 3M 0 A 0 K 1 V M 0 C 1 1/3 +1 n (6) This can be rearranged to give the concentration of alumina, C : C = M 0 V 1+ A 0 k 1 3M 0 t 1 3n (7) 3.2. Comparison with experimental Using the shrinking sphere model (Eq. (7)) a set of calculated experimental curves are plotted in Fig. 2, along with the experimental data for comparison. The density of crystalline alumina is 4.0 g 1 cm 3, however, the density of the individual alumina particles is 2 g 1 cm 3 due to the high void space within each particle. Based on the estimated median particle diameter of 76.5 m, and a density of 2 g 1 cm 3 the surface areas for the alumina additions were calculated as listed in Table 1. The rate equation is fitted to the experimental data by a non-linear regression procedure using a Marquardt Levenberg algorithm, to obtain a value of the rate constant, k 1. The values of k 1 which were found to be the best fit are listed in Table 2.

4 180 R.G. Ha erkamp, B.J. Welch / Chemical Engineering and Processing 37 (1998) Table 2 Rate constants obtained for the first model Alumina addition Rate constant k 1 (g s 1 m 2 ) The simple first dissolution model proposed above, where the rate is proportional to the surface area of the alumina supposing the alumina to be smooth spheres gives a reasonable fit to the experimental behaviour. The assumption was made that the alumina is monodisperse when in fact there is a distribution of particle sizes. Previous studies of alumina dissolution have assumed a large degree of agglomeration [7]. This may be the case in the older commercial smelting cells of the bar breaker type where infrequent large additions of alumina are made (10 20% alumina in the mixing zone). In modern point feeder cells, where conditions are similar to the laboratory apparatus used here with small additions of alumina (0.5 2% alumina in the mixing zone), it is likely that only a small amount of agglomeration will occur. Fragmentation of some alumina particles may also take place as the alumina containing 1 2% water is added to the hot electrolyte. Therefore, if the curves for the shrinking sphere model are calculated using a particle size distribution with one third by mass each of 20, 76 and 200 m diameter particles a very good fit to the experimental curves is obtained as shown in Fig Second model mass transport control 4.1. Deri ation of equations The first rate equation (Eq. (1)) can be modified by taking into account the diffusion of dissolved alumina away from the surface of the alumina into the bulk of the electrolyte. The driving force for this diffusion is the difference in concentration of dissolved alumina between that at the surface of the alumina (C sat ) and that of the bulk of the electrolyte (C). It is assumed that diffusion (diffusion coefficient D) is one dimensional through a constant thickness boundary layer,, where is invariant with respect to particle size. The rate equation may then be written: R= dc dt V=k 2A(C sat C) (8) where: k 2 D Substituting the expression for area as a function of concentration, Eqs. (3) and (4), the rate equation becomes: dc dt V=k 2A 0 V 2/3 1 C (C sat C ) (9) M 0 where C is the concentration of alumina minus the initial concentration. C sat is the saturation alumina concentration for the particular electrolyte composition used minus the initial concentration. Fig. 3. Best fit curves obtained using Eq. (6) with a particle size distribution of 1/3 each of 20, 76 and 200 m. Fit 1, 2 curve for 1 mass% alumina, fit 3 curve for 1.8 mass% alumina. Experimental curves 1, 2 and 3 for different initial alumina concentrations and alumina additions as in Fig. 1.

5 R.G. Ha erkamp, B.J. Welch / Chemical Engineering and Processing 37 (1998) Fig. 4. Best fit curves obtained using Eq. (10) for the second model. Fit 1, 2 curve for 1 mass% alumina, fit 3 curve for 1.8 mass% alumina. Experimental curves 1, 2 and 3 for different initial alumina concentrations and alumina additions as in Fig. 1. This can then be integrated, using algebraic substitution, and the integration constant found for C =0 when t=0 to yield the expression: t= Vb k 2 A 0 a 2 ln (a+u) 2 2u a a 2 tan 1 au+u 2+ 3 a ln (a+b) 2 2b an a 2 tan 1 ab+b 2 3 (10) a 3 where u= C M 0 1/3 V a= M 0 V C sat 1/3 b= M 0 1/3 V 4.2. Comparison with experimental The saturation concentration of alumina in the electrolyte used is g l 1 [8]. The initial alumina concentration in the electrolyte was 15.8 g l 1 Al 2 O 3 so that the C sat for the first second and third dissolution curves will be 150.9, and g l 1, respectively. When these values are used and Eq. (10) are plotted for each of the three dissolution runs then the curves shown in Fig. 4 are obtained. The rate constants obtained from best fits of the calculated curves with the experimental curves are listed in Table 3. The rate constants obtained are similar, as should be expected, at the three different initial alumina concentrations. As with the first model, the fit can be improved if the actual particle size range of the alumina is used in the curve fitting, rather than a single particle size. 5. A comparison of the models 5.1. Heat transfer Heat transfer has been postulated as an important process for limiting the dissolution rate of alumina [5 7]. Where this is proposed it has generally been assumed that large agglomerates of alumina form, with a frozen shell of electrolyte around the agglomerate. For the first model where the rate depends only on the surface area of the alumina, and not on the electrolyte alumina concentration, the rate may be limited by heat transfer or by the rate of chemical reaction. We will consider heat transfer in this section. The energy requirement for the dissolution of alumina is made up of three components. Firstly, the alumina must be heated from room temperature to the temperature of the bath liquidus. This will depend on the heat capacity of the alumina. The other energy requirements are the enthalpy of the phase change from -alumina to -alumina and the endothermic dissolution reaction [13]. For the initial heating of the alumina 75 kj mol 1 is required (C p T), while for the dissolution process kj mol 1, depending on the electrolyte alumina concentration [11 13], is required. Although about one fifth to one third of the energy requirements Table 3 Best fit rate constants obtained for the second model Dissolution run Initial alumina concentra- Rate constant k 2 tion C sat (g l 1 ) (m s 1 )

6 182 R.G. Ha erkamp, B.J. Welch / Chemical Engineering and Processing 37 (1998) Table 4 Calculated T using rate constants from Eq. (7) and literature values of H (Eqs. (11) and (12)) and h E (Eqs. (5) (7)) k 1 (g s 1 m 2 ) Enthalpy change H (kj mol 1 ) a Heat transfer coefficient h E (J s 1 m 2 K 1 ) b Superheat T ( C) with h E = a From Refs. [11,12] and calculation Eq. (16). b Calculation Eq. (16) with T=8 C. are for the initial heating of the alumina, this heat is supplied very rapidly compared with the remaining heat required because of the much larger temperature difference between the electrolyte and the alumina initially. The temperature of the alumina after addition to the electrolyte is given by Eq. (11): M dt C Al p W dt =h EA(T E T Al ) (11) where C p is the molar heat capacity of alumina (79 J K 1 mol 1 ). M is the mass of alumina (10 g). W is the molecular weight of alumina (102 g mol 1 ). t is time after the alumina addition. T Al is the temperature of the alumina. T E is the temperature of the electrolyte. A is the effective surface area of the alumina (0.39 m 2 ). h E is the heat transfer coefficient between the electrolyte and the alumina. This equation is applicable up to the time at which the temperature of the alumina reaches the liquidus temperature of the electrolyte. When this temperature is reached the alumina will begin to dissolve and a further heat input is required to supply the positive enthalpy of dissolution reaction. The time period for this initial alumina heating can be found by evaluating the integrals in Eq. (12). C p M W T liq T i t=diss dt Al =h E A (T E T Al )dt (12) t=0 where t=diss is the time at which the alumina begins to dissolve (when T Al reaches the electrolyte liquidus temperature). T i is the initial alumina temperature. T liq is the liquidus temperature of the electrolyte Steady state heat transfer coefficients have been reported in the range J s 1 m 2 K 1 [5 7]. Using an approximate heat transfer coefficients of 1000 Js 1 m 2 K 1 in Eq. (12), where 10 g of alumina is used with an effective geometric surface area of 0.39 m 2 (Table 1) and the liquidus temperature of the electrolyte is 975 C, and the electrolyte temperature is 983 C, gives a calculated time for alumina of 76.5 m diameter remaining out of contact with the molten electrolyte, under the conditions used, of 2.4 s. For particles of 20 and 200 m diameter times of 0.6 and 6.0 s are calculated. As the smaller particles begin to dissolve first, and these times are less than the sampling interval of 3 s, one would not expect to observe an initiation time between adding the alumina and dissolution taking place. If large agglomerates of alumina form, as is generally assumed in systems studied previously [5 7], the heat transfer would become more important because the surface area of the alumina exposed to the electrolyte is much reduced. If this were the case, one would expect to observe a large initiation time between the addition of alumina and commencement of dissolution, due to the need to remelt the frozen electrolyte formed around the agglomerate. This was not observed in these experiments thus supporting the supposition that some, if not all, of the alumina particles are well dispersed in the electrolyte by the action of the stirrer. Alternatively, it may be that heat transfer is not controlling the reaction so that the heat transfer coefficients reported are really a measure of the diffusion rate of the alumina. Once the temperature of the alumina reaches the liquidus temperature of the electrolyte dissolution would be expected to begin. If this dissolution is heat transfer controlled then the rate constant, k 1, in Eq. (1) becomes: k 1 = h E T HM 0 (13) where T is the temperature difference between the electrolyte and the liquidus temperature (which is called the superheat ). H is the enthalpy change for the dissolution reaction plus the phase change (in J g 1 ). Using this expression, the concentration as a function of time (Eq. (7)) then becomes: C = M 0 V 1+ A 0 h E T 3M 2 0 H t 1 3n (14) If the dissolution process is heat transfer controlled then the reaction will proceed at the liquidus temperature of the electrolyte at the surface of the alumina particles. The temperature gradient driving the reaction will therefore be the difference between the bulk electrolyte temperature and the electrolyte liquidus temperature. The heat flux occurs through a boundary layer of unknown thickness, this being incorporated into the heat transfer coefficient.

7 R.G. Ha erkamp, B.J. Welch / Chemical Engineering and Processing 37 (1998) Fig. 5. Relationship between alumina dissolved, temperature drop, liquidus and superheat for a 1% alumina addition. The rate constants, k 1, from the model for the dissolution of alumina powder can be compared with the values of heat transfer coefficients obtained from dissolution of alumina pellets and the enthalpy of dissolution of alumina. The enthalpy of dissolution of alumina in cryolite has been measured by Holm [12], Phan- Xuan et al. [11] and Wai-Poi et al. [13]. Wai-Poi et al. [13] observed a decrease in the enthalpy of dissolution with increasing alumina concentration. Over the range 0 6% dissolved alumina a decrease from 270 to 150 kj mol 1 was observed. Using the values of M 0 =10 g, A=0.39 m 2 for the first two additions and A=0.71, M 0 =18 g for the third, with T at 8 C the heat transfer coefficient can be calculated from Eq. (13) as listed in Table 4. These heat transfer coefficients are comparable to those obtained by other workers [5 7]. However, the change in h E with alumina concentration is larger than one would reasonably expect. This could be partly due to changes in superheat ( T) during the dissolution which were not taken into account in calculating h E or could indicate that the heat transfer model does not represent the whole mechanism of dissolution. Comparing the values for the heat transfer coefficients measured in earlier studies of Wm 1 K 1 [5 7] does not prove the validity of the heat transfer mechanism because these earlier measurements of the heat transfer coefficient were also based on the assumption that the dissolution process is heat transfer controlled. A verification of the heat transfer coefficient of the electrolyte by a method independent of the dissolution of alumina, but applicable to the system studied, is necessary to establish the validity of this assumption. An increase in concentration of 1% alumina causes a decrease in the liquidus temperature of 5 C. The superheat of the electrolyte will vary as alumina is added and then dissolves. The superheat can be calculated from the temperature and dissolution profiles as shown in the example in Fig. 5. Considering this effect on a microscopic scale, if the diffusion of the dissolved alumina away from the surface is slower than the transfer of heat to the alumina, the composition of the electrolyte adjacent to the alumina particles will be altered. Because the temperature difference driving the heat transfer is the superheat temperature, a small change in the local concentration of dissolved alumina at the particle surface will have a relatively large effect on the dissolution rate.

8 184 R.G. Ha erkamp, B.J. Welch / Chemical Engineering and Processing 37 (1998) Fig. 6. Dissolution curves based on diffusion model. k 2 = ms 1. Fit 1 curve for 1 mass% alumina addition with 0.75% initial alumina concentration, fit 2 curve for 1 mass% alumina addition with 1.75% initial alumina concentration, fit 3 curve for 1.8 mass% alumina addition with 2.75% initial alumina concentration. Experimental curves 1, 2 and 3 are experimental data for corresponding alumina additions and initial concentrations Effect of concentration If diffusion is the main process controlling the rate of dissolution over a wide range of electrolyte alumina concentrations then the dissolution rate would be expected to be less for higher initial alumina concentrations in the electrolyte. The expected dissolution curves are shown in Fig. 6 with the second model for a rate constant of ms 1. Although these differences in the predicted curves do not match precisely the measured curve the difference is probably less than the experimental uncertainty in the measurements. An indication of the validity of the concentration dependant model can be obtained by an estimation of the boundary layer thickness from rate constants and diffusion coefficient. The rate constant, k 2, for the second model is related to the diffusion coefficient, D, and the boundary layer thickness,, by the relationship: k 2 = D (15) The diffusion coefficient for alumina under the conditions used here is m 2 s 1 [9]. Therefore, a rate constant of ms 1 gives a calculated boundary layer thickness of m. Typically, in a well stirred system, boundary layers are about 10 4 m. The value obtained therefore appears to be consistent with a diffusion controlled model. Gerlach et al. [10], in dissolution experiments on alumina pellets, found that the dissolution rate was independent of alumina concentration up to 5% Al 2 O 3. This is the upper limit of alumina concentration for the experiments reported in this paper so that the lack of dependence on alumina concentration observed here is in agreement with the work of Gerlach et al. [10] Relationship between dissolution rate and stirring speed For a diffusion controlled reaction there is a boundary layer across which a dissolved alumina concentration gradient exists. Likewise, for a heat transfer controlled reaction there is a boundary layer across which a temperature gradient exists. The thickness of this boundary layer will depend upon the fluid velocities in the solvent. When the fluid velocities are in the laminar flow region it is generally found that the thickness of the boundary layer decreases with the square root of the fluid velocity. It is therefore to be expected that if the dissolution of alumina is heat transfer or diffusion controlled then the dissolution rate will increase as the square root of the stirring speed. Fig. 7 shows the results of a series of dissolution experiments at different stirring speeds. The increase in the dissolution rate is approximately a half power of the stirring speed, which supports the proposition of the existence of a boundary layer across which mass or heat transfer is taking place Relationship between dissolution rate and temperature or superheat The relationship between the dissolution rate of the alumina and the temperature of the electrolyte should

9 R.G. Ha erkamp, B.J. Welch / Chemical Engineering and Processing 37 (1998) Fig. 7. Effect of stirring speed on the dissolution rate of alumina. Fig. 8. Temperature dependence of the rate constant. provide information on the mechanism of the dissolution. In the case where the rate is controlled by chemical reaction one would expect an Arrhenius relationship, where ln k 1 is proportional to 1/T, between the electrolyte temperature and the dissolution rate. In the case where the rate is controlled by diffusion one would expect a k 2 to be proportional to T. And in the case where the rate is controlled by heat transfer one would expect k 1 to be proportional to the superheat (T T liq ). Chemical ln k 1 = K/T Diffusion k 2 =KT Heat transfer k 1 =K(T T liq ) where K is a constant. The rate constants obtained for a series of dissolution experiments at different electrolyte temperatures is shown in Fig. 8. The data is displayed in terms of superheat. The correlation of k 2 with T is also good, however, the correlation of ln k 1 verses 1/T is less good. These results on their own are inconclusive, but are consistent with the hypothesis that the dissolution of alumina in cryolite is controlled by a combination of heat transfer and diffusion.

10 186 R.G. Ha erkamp, B.J. Welch / Chemical Engineering and Processing 37 (1998) Conclusions Models for the dissolution of alumina powder in cryolite were formulated and compared with experimental results obtained using modified fast linear sweep voltammetry. The alumina was assumed to be smooth spheres which decrease in size as dissolution proceeds. The models were based on rate control by either chemical reaction at the alumina surface, heat transfer, or diffusion. The shape of the curves generated by each of the models gave a good fit to experimental data. It was not possible to state unequivocally which of the models best represents the actual rate controlling mechanism of alumina dissolution, however, these models can form the basis for further experiments. The rate control of powder alumina dissolution may vary depending on the conditions employed, namely, the size of the alumina addition and the concentration range of alumina in the electrolyte during dissolution. In modern point feeder technology small amounts of alumina, 0.5 2% in the mixing zone, are added to the alumina reduction cell at frequent intervals. This situation is quite different from the older breaker bar feeding technology, where alumina additions which amount to 10 20% alumina in the mixing zone are made. The models developed here are applicable primarily to the point feeder technology where less agglomeration of alumina takes place. However they may be modified to take account of the much larger agglomerates formed, and the greater depression of the electrolyte temperature which occurs, in the breaker bar technology. The shape of the curves generated gave a reasonable fit to experimental data but the heat transfer and diffusion models appear to be the best. Also, the relationship between the temperature and the dissolution rate is poorer for the chemical control mechanism than that predicted by heat transfer or diffusion control. However, both the heat transfer and diffusion control models match the shape of the dissolution curves well and also the temperature dissolution rate relationships. With the heat transfer control model a decrease in the rate constant occurs with increasing electrolyte alumina concentration, despite a predicted increase due to the decrease in the enthalpy of dissolution of alumina. With the diffusion controlled model, the rate constant is relatively constant, as predicted, at different electrolyte alumina concentrations. The actual mechanism may be a combination of both models with heat transfer control being important at low electrolyte alumina concentrations where the enthalpy of dissolution is high. Then at higher alumina concentrations, when the enthalpy of dissolution is lower, diffusion control may become more important. A verification of the heat transfer coefficient of the electrolyte by a method not dependent on the dissolution of alumina, but applicable to the system studied, would be helpful to clarify the relative importance of heat transfer and diffusion. These models may also be applicable to other systems involving dissolving particles. Appendix A. Nomenclature A A 0 C C i C =C C i effective surface area of the alumina (treated as mono sized spheres) at time t, m 2 initial surface area of the total amount of alumina added, m 2 alumina concentration at time t in bulk of the electrolyte, g l 1 initial alumina concentration in the electrolyte, g l 1 the relative concentration of alumina, gl 1 C sat concentration of dissolved alumina at the surface of the alumina, g l 1 C sat =C sat C i saturation alumina concentration for the particular electrolyte composition used minus the initial concentration, g C p D h E H K k 1 k 2 l 1 molar heat capacity of alumina (79 J K 1 mol 1 ) diffusion coefficient, m 2 s 1 heat transfer coefficient between the electrolyte and the alumina, J s 1 m 2 K 1 enthalpy change for the dissolution reaction plus the phase change, J g 1 a constant rate constant for the first model, gs 1 m 2 rate constant for the second model, m s 1 M mass of alumina remaining undissolved at time t, g M 0 initial mass of alumina added, g R rate of dissolution, g s 1 r 0 initial radius, m t time after the alumina addition, s t=diss is the time at which the alumina be- gins to dissolve T temperature, C T Al temperature of the alumina, C T E temperature of the electrolyte, C T i initial alumina temperature, C T liq liquidus temperature of the electrolyte, C T=T T liq the temperature difference between the electrolyte and the liquidus temperature superheat, C

11 R.G. Ha erkamp, B.J. Welch / Chemical Engineering and Processing 37 (1998) V W References volume of the electrolyte, m 2 molecular weight of alumina (102 g mol 1 ) boundary layer thickness, m particle density, g cm 3 [1] W.E. Haupin, Proc. 6th Int. Course on Process Metallurgy of Aluminium, Trondheim, 1 5 June, , [2] G.I. Kuschel, The effect of alumina properties and smelter operating conditions on the dissolution behaviour of alumina, Ph.D. Thesis, University of Auckland, New Zealand, [3] R.G. Haverkamp, B.J. Welch, J.B. Metson, An electrochemical method for measuring the dissolution rate of alumina in molten cryolite, Bull. Electrochem. 8 (7) (1992) [4] R.G. Haverkamp, Surface studies and dissolution studies of fluorinated alumina, Ph.D. Thesis, University of Auckland, New Zealand, [5] M.P. Taylor, B.J. Welch, Bath/freeze heat transfer coefficients: experimental determination and industrial applications, Light Met. (1985) [6] A.N. Bagshaw, G. Kuschel, M.P. Taylor, S.B. Tricklebank, B.J. Welch, Effect of operating conditions on the dissolution of primary and secondary (reacted) alumina powders in electrolyte, Light Met. (1985) [7] X. Liu, J.M. Purdie, M.P. Taylor, B.J. Welch, Measurement and modelling of alumina mixing and dissolution for varying electrolyte heat and mass transfer conditions, Light Met. (1991) [8] K. Grjotheim, B.J. Welch, Aluminium Smelter Technology, 2nd ed., Aluminium-Verlag, Düsseldorf, [9] K. Grjotheim, C. Krohn, M. Malinovský, K. Matias ovský, J. Thonstad, Aluminium Electrolysis, 2nd ed., Aluminium-Verlag, Düsseldorf, [10] J. Gerlach, U. Hennig, K. Kern, The dissolution of aluminum oxide in cryolite melts, Metall. Trans. 6B (1975) [11] D. Phan-Xuan, R. Castanet, M. Laffitte, J. Goret, Microcalorimetric study of alumina dissolution in cryolite baths, Light Met. (1975) [12] J.L. Holm, Thermodynamic properties of molten cryolite and other fluoride mixtures, Ph.D. Dissertation, Institute of Chemistry, NTH, Trondheim, [13] N. Waipoi, R.G. Haverkamp, S. Kübler, H. Müller-Steinhagen, B.J. Welch, Thermal effects associated with alumina feeding in aluminium reduction cells, Light Met. (1994)