Viscosity and viscosity estimation model of fully liquid slags in TiO 2 –Al 2 O 3 –CaO–SiO 2 and TiO 2 –Al 2 O 3 –CaO–SiO 2 –MgO systems with high TiO 2 concentration and low mass ratio of CaO to SiO 2

Abstract

The present paper focuses on the viscosity of high titanium containing slags in the process of titanomagnetite smelting by taking the TiO₂–Al₂O₃–CaO–SiO₂ quaternary system with TiO₂ in the range from 23 to 43%, Al₂O₃ in the range from 3 to 12% and basicity (mass ratio of CaO/SiO₂) in the range from 0·3 to 0·7 as the object. Experimental determinations of the viscosity were carried out in the temperature range from 1573 to 1873 K using the rotation cylinder method. The effects of TiO₂, Al₂O₃, basicity and temperature on viscosity were studied. The experimental results indicated that the viscosity decreased with increasing TiO₂ concentration and basicity, and increased with increasing Al₂O₃ concentration. Based on the experimental data of the TiO₂–Al₂O₃–CaO–SiO₂ quaternary system, a new viscosity model was proposed by modifying the Urbain model. The new model was applied successfully to predict the viscosity of TiO₂–Al₂O₃–CaO–SiO₂ and TiO₂–Al₂O₃–CaO–SiO₂–MgO systems in the fully liquid condition with high TiO₂ concentration and low basicity over a wide range of composition and temperature using one set of model parameters.

Introduction

Titanium is the ninth most abundant element in the earth’s crust and the seventh most abundant metallic element. The titanium reserves in China accounts for one-third of the world total and mainly exists as titanomagnetite located in Panzhihua.^1,2 Currently, the titanomagnetite concentrates are smelted in the blast furnace, from which it is difficult to recover the titanium component. In order to make use of the titanomagnetite concentrates, a new process using a rotary hearth furnace–electric arc furnace process has been developed for recovering the iron, titanium and vanadium.³ In comparison with blast furnace slag, the slag in the pellets used in the process is of low basicity (about 0·5) and high TiO₂ concentration (35–40%). Over recent years, several researchers have reported the properties of the TiO₂–Al₂O₃–CaO–SiO₂ slag system,^4–9 most of whom investigated the slags with basicity 0·8–1·1 and the concentration of TiO₂ <30%. However, the properties of high titanium concentration slag with low mass ratio of CaO to SiO₂ have not been investigated to date. Viscosity is one of the key properties of industrial slags and is very sensitive to compositional and temperature changes. It is difficult to measure accurately, requires the use of sophisticated apparatus and is time consuming as well as expensive. In the last decades, various mathematical models have been developed by Urbain,¹⁰ Riboud,¹¹ Zhang and Jahanshahi,¹² Iida et al.,¹³ Mills and Sridhar,¹⁴ Ray and Pal,¹⁵ Seetharaman and Du,¹⁶ Nakamoto et al.,¹⁷ Shu¹⁸ and Ghoshu et al. ¹⁹ to describe the viscosity of metallurgical, coal ash and geological silicate slags, but the accuracy to predict the slag with high TiO₂ concentration and low basicity is not accessible.

In the present work, the viscosity of the TiO₂–Al₂O₃–CaO–SiO₂ system with TiO₂ between 23 and 43%, Al₂O₃ between 3 and 12% and CaO/SiO₂ between 0·3 and 0·7 is measured. Moreover, a new model based on these data is proposed. The new model has been applied successfully to predict viscosity of the TiO₂–Al₂O₃–CaO–SiO₂ and TiO₂–Al₂O₃–CaO–SiO₂–MgO systems in fully liquid with a wide range of temperature and slag composition using one set of model parameters.

Experimental

Apparatus for viscosity measurement

In the present work, viscosity was measured by the rotating cylinder method using a Brookfield digital viscometer. The experimental equipment for the viscosity measurement, which consists of a rotating system, a heating system and a measuring system, is shown in Fig. 1a . MoSi₂ heating elements were used to ensure that the electric resistance furnace could be stabilised at 1873 K. The experimental temperature was controlled by two Pt–6%Rh&Pt–30%Rh thermocouples inserted into the furnace with an error less than ±1 K. The crucible and bob, both made of molybdenum, were employed for the viscosity measurement, and the dimensions of the crucible and the bob are shown in Fig. 1b . The viscometer was calibrated using standard silicone oil at 298±1 K.

a viscometer; b dimension of crucible and bob

Sample preparation

The compositions of synthetic slags for viscosity measurement are listed in Table 1. The slags were prepared by mixing reagent grade oxides of SiO₂, A1₂O₃, TiO₂ and CaO. The reagents were calcined at 1273 K in a muffle furnace under argon atmosphere to decompose any carbonate or hydroxide present, and then powders were mixed in an agate mortar with desired proportions. Then, the mixtures were packed in a molybdenum crucible and premelted in an induction furnace at 1873 K for 1 h. Once premelted, the slag was poured into a steel mould and cooled naturally under argon atmosphere. The obtained premelted slag was crushed into powder and used for viscosity measurement.

Table 1.

Slag composition for viscosity measurement/wt-%

Slag	CaO	SiO₂	Al₂O₃	TiO₂	Basicity (CaO/SiO₂)
Ti43	16·0	32·0	9·0	43·0	0·5
Ti38	17·7	35·3	9·0	38·0	0·5
Ti33	19·3	38·7	9·0	33·0	0·5
Ti28	21·0	42·0	9·0	28·0	0·5
Ti23	22·7	45·3	9·0	23·0	0·5
Al12	18·3	36·7	12·0	33·0	0·5
Al6	20·3	40·7	6·0	33·0	0·5
Al3	21·3	42·7	3·0	33·0	0·5
R0·7	23·9	34·1	9·0	33·0	0·7
R0·6	21·8	36·2	9·0	33·0	0·6
R0·4	16·6	41·4	9·0	33·0	0·4
R0·3	13·4	44·6	9·0	33·0	0·3

Viscosity measurement

The molybdenum viscometer crucible, filled with 140 g of the prepared slag sample, was placed in the furnace and heated up to 1873 K under argon gas flowrate of 5 L min⁻¹. After melting, the height of the slag is ∼40 mm. Then, the bob was lowered and kept at a distance of 10 mm above the crucible bottom. The crucible and bob were properly aligned along the axis of the viscometer. This is very important because a slight deviation from the axis can cause a big experimental error. The molten slag was held at 1873 K for 1 h, and then the viscosity value was measured.

The measurements were carried out at three different rates of rotation (100, 150 and 200 rev min⁻¹) at each temperature, and the average of the measured values was adopted as the viscosity value at each temperature. At each rotational speed, the measurement time was 2 min. After each measurement, the temperature was lowered by 20 K and held for 10 min for the next measurement until the value of viscosity was beyond 4 Pa s. In order to estimate the reproducibility of the experimental results, selected slags, namely, Ti23, Al3 and R0·3, were chosen for repeat measurement, and the results shown in Fig. 2 illustrate good repeatability with an error <5%.

Repetitive experiments of Ti23, Al3 and R0·3

Results

The viscosity of 12 different slag compositions within the TiO₂–Al₂O₃–CaO–SiO₂ system were measured based on different levels of TiO₂, Al₂O₃ and CaO/SiO₂ ratio. The range of TiO₂ was varied between 23 and 43%, Al₂O₃ was varied between 3 and 12% and the CaO/SiO₂ between 0·3 and 0·7. The viscosity measurements were performed at a wide temperature range from 1873 K to the temperature at which viscosity was beyond 4 Pa s. The obtained viscosity values for each slag composition are shown in Table 2.

Table 2.

Measured viscosity

Slag	Viscosities/Pa s
Slag	1873	1853	1833	1813	1793	1773	1753	1733	1713	1693	1673	1653	1633	1613	1593
Ti43	0·25	0·26	0·33	0·45	0·80	1·42	2·09	3·10	4·00
Ti38	0·33	0·35	0·40	0·44	0·49	0·53	0·60	0·93	1·37	1·91	2·55	4·11
Ti33	0·37	0·43	0·48	0·53	0·58	0·66	0·77	0·91	1·13	1·41	2·28	3·15	4·37
Ti28	0·47	0·50	0·54	0·62	0·70	0·76	0·85	0·92	0·99	1·20	1·42	2·00	4·01
Ti23	0·66	0·64	0·69	0·79	0·91	1·00	1·10	1·22	1·36	1·55	1·81	2·12	2·56	3·21
Al12	0·56	0·59	0·64	0·69	0·74	0·82	0·91	1·08	1·34	1·74	2·90
Al6	0·24	0·27	0·29	0·30	0·34	0·35	0·40	0·45	0·52	0·60	0·70	1·20	3·04	5·06
Al3	0·15	0·17	0·18	0·20	0·21	0·25	0·29	0·33	0·39	0·45	0·51	0·66	1·15	3·36	5·57
R0·7	0·16	0·17	0·19	0·19	0·19	0·21	0·23	0·27	0·33	0·37	0·41	0·47	0·55	0·66	3·32
R0·6	0·23	0·24	0·28	0·31	0·37	0·38	0·41	0·49	0·56	0·61	0·67	0·79	1·11	2·07	4·11
R0·4	0·53	0·58	0·65	0·69	0·76	0·85	1·01	1.62	2·34	3·53
R0·3	0·95	0·95	1·08	1·27	1·59	2·77	5·31

Effect of TiO₂ on viscosity

Figure 3 shows the effect of TiO₂ on the viscosity of the TiO₂–Al₂O₃–CaO–SiO₂ slags, and it shows that TiO₂ decreased the slag viscosity at high temperature. According to the ionic theory of slag, the viscosity of slag depends on the complexity of Si–O ionic group. The more complex the Si–O structure, the greater the viscosity. The size of Si–O ionic group is determined by the oxygen/silicon ratio, and it is of the simplest structure with O/Si = 4.^20,21 The ionic radius of Ti⁴⁺ (0·68×10⁻¹⁰ m) is bigger than that of Si⁴⁺ (0·41×10⁻¹⁰ m), and the electrostatic potential of Ti⁴⁺(1·85 I) is smaller than that of Si⁴⁺(2·51 I), so the bond between Ti⁴⁺ and oxygen is weaker than that between Si⁴⁺ and oxygen. Therefore, the bond of oxygen will be weak with increasing concentration of Ti⁴⁺, leading to the depolymerisation of the oxygen ion. Moreover, Ti⁴⁺ is not the same as Si⁴⁺, which tends to form a complex anion group, contributing to the simpler structure with consequent decrease in the viscosity.

Effect of TiO₂ on viscosity of TiO₂–Al₂O₃–CaO–SiO₂ slags

Effect of Al₂O₃ on viscosity

Figure 4 shows the effect of Al₂O₃ on the viscosity of the TiO₂–Al₂O₃–CaO–SiO₂ slags, and it shows that Al₂O₃ increased the slag viscosity. Generally, Al³⁺ is classified as intermediate in the (SiO₄)⁴⁻ network, because it either joins to the network or occupies the holes between the (SiO₄)⁴⁻ tetrahedron in the same way as Ca⁺ or Mg²⁺, which is according to the ratio of to ,^22,23 where is the sum molar fraction of the basic oxides. In the present study, it is obvious that , so the Al³⁺ will substitute for Si⁴⁺ to form the network, increasing the degree of polymerisation. Thus, the longer chain is formed, leading to lesser mobility of the species in the system with consequent increase in the viscosity.

Effect of Al₂O₃ on viscosity of TiO₂–Al₂O₃–CaO–SiO₂ slags

Effect of basicity on viscosity

Figure 5 shows the effect of basicity (mass ratio of CaO/SiO₂) on the viscosity of high titanium slag. It can be seen clearly from the figure that the viscosity decreased with increasing basicity. The viscosity of slag depends on the complexity of oxygen/silicon ratio. The increase in basicity can break oxygen bonds and improve the proportion of free oxygen O²⁻ and the dissociated free oxygen O²⁻, leading to the increase in oxygen–silicon ratio.²⁴ Once the oxygen–silicon ratio increased, the connect type of the (SiO₄)⁴⁻ tetrahedral transforms from skeleton (O/Si = 2·16, R0·3) to layer, chain or ring (O/Si = 2·67, R0·7). The oxygen–silicon ion group shifting towards simpler structure leads to a decrease in the slag viscosity.

Effect of basicity on viscosity of TiO₂–Al₂O₃–CaO–SiO₂ slags

Effect of temperature on viscosities

It can be seen clearly that the viscosity of slags increases with temperature decreasing. Mills²³ found that the activation energy Q would be expected to be constant at temperatures above the liquidus temperature, but Q will increase sharply in the vicinity of the liquidus temperature. This means that the first derivative of activation energy against temperature (∂Q/∂T) should show a corresponding change. Consequently, the second derivative ∂Q ²/∂T ², as equation (1), should start from zero at high temperature and then decrease at the liquidus temperature. So, the temperature that the second derivative deviates sufficiently from zero is the liquidus temperature, T _L.²⁵ Considering viscosity measurement with the temperature interval 20 K, the error of the calculated liquidus temperature is ±10 K. R0·7 is taken as the example in Fig. 6 1 where Q is the activation energy for viscous flow (J mol⁻¹), η is viscosity value (Pa s), T is absolute temperature (K) and R is the gas constant (8·14 J mol⁻¹ K⁻¹). The liquidus temperatures of slags calculated from the viscosity are listed in Table 3. The liquidus temperatures increase with the increasing TiO₂ and Al₂O₃ concentration. This is mainly due to the high melting point of TiO₂ and Al₂O₃, but decreases with the increase in basicity. With the analysis of the phase diagram,²⁶ it is found from Fig. 7 that the increase in basicity leads to the transition from area (a), corresponding to R0·3, to area (b) corresponding to R0·7. The area of (b) is the CST area (CaO.SiO₂.TiO₂: 1655 K) and (a) the low melting point area.

Second derivatives of activation energies for viscous flow with respect to temperature as functions of temperature for slag R0·7

Liquidus surface and compatibility relations in CaO–SiO₂–TiO₂ system

Table 3.

Liquidus temperatures calculated from viscosity

	Ti23	Ti28	Ti33	Ti38	Ti43	Al3	Al6	Al12	R0·3	R0·4	R0·6	R0·7
T _L/K	1653	1673	1733	1773	1833	1653	1673	1753	1833	1773	1733	1633

Viscosity model

Classification of TiO₂

Considering the complexity of TiO₂, there is no unified view of classifying TiO₂ to acid oxide or basic oxide. In this paper, the method²⁷ based on ion theory is used to classify the properties of TiO₂ by calculating the sulphur partition coefficient of the slag in the electric furnace melting process (Table 4), providing a solid foundation for the model building.

Table 4.

High titanium slag composition in electric furnace melting process of vanadium–titanium magnetite (per 100 g)

	TiO₂	FeO	SiO₂	Al₂O₃	CaO	MgO	S
Mass/g	33·25	37·80	8·80	9·09	4·08	6·97	0·037
n/mol	0·4161	0·5261	0·1445	0·0892	0·0728	0.1729	0·0001

TiO₂ is classified as acid oxide

According to the phase diagram of TiO₂–Al₂O₃–CaO–SiO₂ system and subsystems, it is known that SiO₂, Al₂O₃ and TiO₂ exist in the form of , and 2 3 4 According to chemical equations (2)–(4), it is possible to calculate , , and , , , where , and are the molar of , and and , and are the molar of the free oxygen occupied in the three equations respectively.

For slags in present paper, the following is obvious where , , , and are the molar sum of the free oxygen provided by basic oxides, the free oxygen occupied to form tetrahedron, the free oxygen remaining in the slag, and the anion and cation in slag respectively.

For the acid slag, the following equations exist based on the studies of desulphurising powers of the slag with high SiO₂ concentration (SiO₂ concentration >30%) and low basicity²⁸ where and are the activity of Fe²⁺ and S²⁻, is ratio of the free oxygen remaining in the slag to total anion and Ls is the equilibrium constant of FeS distribution reaction equation respectively.

Considering that the concentration of impurity is very low, it can be ignored, except for carbon [%C] = 6. So the sulphur activity coefficient can be calculated as , where and are the interaction coefficients.

Based on the above, the sulphur partition coefficient²⁹ is calculated as

TiO₂ is classified as basic oxide

If TiO₂ is classified as basic oxide, 1 mol TiO₂ will provide 1 mol Ti⁴⁺ and 2 mol O²⁻. The forms of SiO₂ and Al₂O₃ act the same way as above. In this case, the following calculations exist. For the basic slag, the following equations exist²⁷ where is the ratio of the molar of to total anion.

Based on the above, the sulphur partition coefficient is calculated as follows It is known that the sulphur partition coefficient for ordinary titanium slag produced by the blast furnace is between 30 and 40, and that of the high titanium slag is between 4 and 6.³⁰ Thus, by comparing the two sulphur partition coefficients, TiO₂ can be divided into acid oxide in the present study.

Model building

The present paper uses a modified Urbain method.^10,31–33 The new model further modifies the formalism developed by Urbain in order to describe viscosity behaviour of fully liquid slags over a wide range of composition with high TiO₂ concentration and low basicity. Three classes of oxides, named glass formers, modifiers and amphoterics, are introduced in the Urbain model. Considering that there are no corresponding parameters for high TiO₂ slag system, the new model extends the Urbain model, reclassifies the oxides and redefines viscous activation energy B, a function of composition calculated by the three classes of oxides 5 6 7 Glass formers Modifiers Amphoterics where η is viscosity value (0·1 Pa s), A is the preexponential, B is viscous activation energy (J mol⁻¹ K⁻¹), m and n are empirical parameters; X _G, X _M and X _A are the mole fractions of glass former oxides, modifier oxides and amphoteric oxides; and a _i, b _i and c _i (i = 1, 2, 3) are the coefficients by fitting experimental data listed in Table 5. Since m and n proposed by Urbain cannot provide an accurate description of experimental values of A and B in the TiO₂–Al₂O₃–CaO–SiO₂ system, the new model adopts m = 0·35 and n = 10·08 by linear fitting, according to this system and its subsystems. The fitting curve is shown in Fig. 8.

Relationship between –ln A and B

Table 5.

Model parameters

	a _i	b _i	c _i
0	−13 730·50	−17 514·50	19 993·56
1	53 426·01	5747·51	−27·76
2	−87 981·70	−25 200·20	3873·84
3	48 351·05	36 976·71	−23 829·00

The differences between the experimental data and the estimation by the Urbain model, NPL model and the new model are compared in Fig. 9. It is obvious that the new model provides reasonable estimation of the viscosity for a wide range of slag composition. The uncertainties in estimation with the new model (the deviation being round 11%) are less than those in estimation obtained with the Urbain (the deviation being round 43%) and the NPL (the deviation being round 57%) models.

Comparison of experimental data and date predicted by new model, NPL model and Urbain model

Viscous activation energy of pure oxides

Owing to the high melting point of pure SiO₂, Al₂O₃ and CaO, their viscous activation energies are not accessible to measurement, and the activation energy of pure SiO₂, Al₂O₃ and CaO can be obtained from the new model by the extrapolation of B. The extrapolated values of B in Table 6 are in good agreement with the theoretical values given by the Urbain model through extrapolating the value of B obtained from binaries and by Bockris and Reddy³⁴ using the ‘hole’ method.

Table 6.

Viscous activation energy

	B(SiO₂)/kJ mol⁻¹	B(Al₂O₃)/kJ mol⁻¹	B(CaO)/kJ mol⁻¹
New model	64·80	10·67	9·57
Urbain	64·10	8·60	10·70
Bockris J.O.M.	…	13·20	…

Viscosity prediction

Good agreement was achieved between the new model and the experimental data of the TiO₂–Al₂O₃–CaO–SiO₂ quaternary system in fully liquid over wide composition ranges. To widen the use to a multisystem, the new model using one set of parameters was applied to the TiO₂–Al₂O₃–CaO–SiO₂–MgO quinary system with low basicity and high TiO₂ concentration. Considering the locking of the data of TiO₂–Al₂O₃–CaO–SiO₂–MgO quinary system with high TiO₂ concentration and low basicity, the chemical compositions of the slags in Table 7 were studied in the fully liquid condition. Figure 10 shows the effect of MgO on the viscosity of the TiO₂–Al₂O₃–CaO–SiO₂–MgO slags.

10.

Viscosity experiments of TiO₂–Al₂O₃–CaO–SiO₂–MgO quinary system

Table 7.

Slag composition for viscosity experiments of TiO₂–Al₂O₃–CaO–SiO₂–MgO quinary system/wt-%

Slag	TiO₂	Al₂O₃	SiO₂	CaO	MgO	(CaO+MgO/SiO₂)
Mg2	33·0	9·0	38·7	17·3	2·0	0·5
Mg6	33·0	9·0	38·7	13·3	6·0	0·5
Mg10	33·0	9·0	38·7	9·3	10·0	0·5
Mg14	33·0	9·0	38·7	5·3	14·0	0·5

The calculated results are shown as a function of the experimental viscosity values in Fig. 11. It can be seen that the new model provides a reasonable prediction, the deviation being ∼20%. The values predicted by the Urbain (the deviation being ∼72%) and NPL (the deviation being ∼106%) models are also shown in Fig. 11. It can be seen that the results calculated by the new model are better than those by Urbain and NPL models. Thus, it is appropriate to apply the new model to predict the viscosity in the fully liquid of TiO₂–Al₂O₃–CaO–SiO₂–MgO quinary system with low basicity and high TiO₂ concentration, and the concentration of MgO ranges from 0 to 14%.

11.

Comparison of experimental data about TiO₂–Al₂O₃–CaO–SiO₂–MgO quinary system and date predicted by new model, NPL model and Urbain model

Conclusions

The viscosity of the TiO₂–Al₂O₃–CaO–SiO₂ system with TiO₂ between 23 and 43%, Al₂O₃ between 3 and 12%, and CaO/SiO₂ between 0·3 and 0·7 was measured at temperatures ranging from 1573 to 1873 K. The viscosity decreased with increasing TiO₂ concentration and basicity, and increased with increasing Al₂O₃ concentration.

The new model further modified the formalism developed by Urbain and was applied successfully to describe the viscosity behaviour of TiO₂–Al₂O₃–CaO–SiO₂ and TiO₂–Al₂O₃–CaO–MgO–SiO₂ systems in the fully liquid condition with the low basicity and high TiO₂ concentration over a wide range of composition and temperature using one set of parameters.

The activation energies of pure SiO₂, Al₂O₃ and CaO obtained from the new model by the extrapolation of B are 64·3, 10·67 and 9·57 kJ mol⁻¹ respectively.

Footnotes

Acknowledgement

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (grant no. 51090381).

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Viscosity and viscosity estimation model of fully liquid slags in TiO 2 –Al 2 O 3 –CaO–SiO 2 and TiO 2 –Al 2 O 3 –CaO–SiO 2 –MgO systems with high TiO 2 concentration and low mass ratio of CaO to SiO 2

Abstract

Introduction

Experimental

Apparatus for viscosity measurement

Sample preparation

Viscosity measurement

Results

Effect of TiO2 on viscosity

Effect of Al2O3 on viscosity

Effect of basicity on viscosity

Effect of temperature on viscosities

Viscosity model

Classification of TiO2

TiO2 is classified as acid oxide

TiO2 is classified as basic oxide

Model building

Viscous activation energy of pure oxides

Viscosity prediction

Conclusions

Footnotes

Acknowledgement

References

Effect of TiO₂ on viscosity

Effect of Al₂O₃ on viscosity

Classification of TiO₂

TiO₂ is classified as acid oxide

TiO₂ is classified as basic oxide