THERMODYNAMIC CHARACTERISTICS OF REACTIONSIN METAL–SLAG–GAS SYSTEMS
M. P. Shalimov1, M. I. Zinigrad2 and V.L. Lisin3
1Ural State Technical University–Ural Polytechnic Institute, Russia
2College of Judea and Samaria, Israel
3Institute of metallurgy, Ural’s Division of Russian Academy of Science, Russia
ABSTRACT. The investigation and mathematical modeling of real metallurgical processes requires knowledge of the parameters and characteristics that determine the thermodynamic state of the system.
This paper examines the application of theoretical and experimental methods for estimating the thermodynamic characteristics in metal–slag–gas systems for a series of components.
Method for calculating the equilibrium concentration distribution
of elements in multicomponent systems
Methods for calculating the values of equilibrium concentrations are most often based on the use of the equilibrium constants of the reactions that are possible in the system under investigation as starting data [1, 2]. At the same time, the use of equilibrium constants expressed in terms of concentrations, rather than in terms of the activities of the components, can lead to errors in the calculations.
Let us consider the following method as one of the possible methods for calculating the equilibrium concentrations of the elements in a multicomponent carbon-containing molten metal and a multicomponent slag [3] using the reactions
[C] + 2 [О] = {CO2}(1)
[C] + [О] = {CO}(2)
n[Ei] + m[O] = (EinOm), (3)
where Ei denotes Fe, Ni, Al, Si, B, etc.
Oxidation reactions are chosen because they have been studied in fairly great detail and the equilibrium constants of most reactions have been expressed in terms of the activities of the components [4]
(4)
(5)
(6)
Here fi is the Wagner interaction parameter.
We express the temperature dependence of the equilibrium constants of reactions (1)–(3) as
log Keq = A/T + B(7)
We perform several transformations with Eqs. (4) and (5), taking into account that PCO = 1 – . We assume that the equilibrium concentrations of all the elements in the melt apart from carbon are insignificant, and, therefore, their influence on fC can be neglected. Then f = fCc and PCO can be found for assigned values of the temperature and the carbon concentration in the metal.
Knowing PCO, we can easily obtain
(8)
For the reaction of the main component of the alloy (for example, iron) with oxygen, we write
.(9)
To calculate the equilibrium concentrations of the elements, we assign the temperature, the slag composition respect to all the components apart from FeO, and the concentration of carbon in the metal.
Let us examine the sequence of calculations in the example of a system consisting of an iron–carbon alloy and an oxide slag.
We first find the concentration of iron in the alloy:
[Fe] = 100 – [C].(10)
We determine the values of PCO and D, and from Eq. (9) we obtain the activity of ferrous oxide. Taking into account that FeO = 0 [5], we can write
(11)
Since all the remaining concentrations of the components in the original slag are assigned, the mole fraction (wt. %) can be expressed as follows:
(12)
whence the mass concentrations are easily found.
Taking into account the FeO content, we find new values of the concentrations of the remaining components in the slag. Knowing the composition of the slag, we can use the equations of the theory of regular solutions to calculate the activities of the components in the slag [6]. When there are complex-forming ions in the slag, we recalculate the activities using the relations that were presented in [6].
Using equations similar to (9), we find the values of the concentrations of all the components in the metal [Ei] apart from iron and carbon. We then calculate the Wagner interaction parameters for each of the i components from the relation
(13)
From relation (8) we find the concentration of oxygen in the metal, assuming that
(14)
This completes the first calculation cycle.
The second calculation cycle starts with determination of the Wagner interaction parameter for carbon with allowance for the influence of oxygen and all the components in the metal.
These calculations are performed according to the procedure described. Here the concentration of iron in the metal is determined from the equation
[Fe] = 100 – [C] – [О] - [Ei].(15)
The calculation is repeated until the values of all the concentrations of the elements in the metal coincide (with an assigned error) in two successive iterations.
The accuracy of the results obtained by this calculation method is determined by the completeness of the data on the Wagner interaction parameters for different temperatures and melts with different carbon concentrations, including a carbon concentration close to saturation, as well as by the heats of mixing of the oxides.
Using the data in [7], we estimate the values of Qij for systems in which these values have not been determined experimentally.
Let us examine the application of the method described to the calculation of equilibrium concentrations of components in the case of concrete systems.
Distribution of boron, aluminum, and phosphorus
between the metallic and slag phases
An oxide phase similar in composition to the phases used in non-furnace steel working and the AN-28 and AN-30 reference fluxes. The basic oxide melt had the following composition (wt. %): 51Al2O3, 43CaO, 6MgO. Up to 15 wt. % B2O3 or up to 10 wt. % P2O5 were added to it. An Fe–C melt with a carbon content equal to 0.5–3 wt. % was also employed as the starting melt.
The method described was used to calculate the equilibrium concentrations of the components in the metal and the slag [3].
Published values of the Wagner interaction parameters [1, 4], heats of mixing [6, 7], equilibrium constants [4, 8], and distribution constants (Li) [9, 10] were used in the calculation.
The calculation results demonstrate the non-monotonic character of the dependence of the boron and aluminum concentrations in the metal on its carbon content. This is because carbon in a concentration greater than 2 wt. % in the metal is a stronger reducing agent than boron and aluminum at corresponding concentrations. Since the oxygen concentration passes through a minimum at [C] 2 wt. %, the concentrations of boron and aluminum accordingly pass through a maximum. According to the data in [4], the carbon concentration which ensures the minimal oxygen content in iron at 1873K equals 2.25 wt. %. This value is fairly close to the value that we obtained.
Let us analyze the dependence of the metal-slag distribution coefficients of boron and aluminum, which equal
(16)
on various parameters.
They depend on temperature and on the carbon concentration in the metal. In addition, in analogy to [8], we assume that they are linearly dependent on the concentration of the oxide in the slag:
LB = a + b (B2O3), LAl = a1 + b1 (Al2O3)(17)
Treatment of the data obtained yielded equations for calculating LB and LAl and the limits for their use:
(18)
(19)
These equations allow us to calculate the values of LB and LAl in the 1723–1973 K temperature range for concentrations of B2O3 in the slag up to 25 wt. % and concentrations of Al2O3 in the slag up to 55 wt. %.
It is noteworthy that similar results with respect to the values of the equilibrium concentrations of aluminum and their dependence on the carbon content in the metal for slag and metallic systems not containing boron were obtained in [11].
At low concentrations of (B2O3) in the slag, Eq. (18) undergoes a slight transformation. At (B2O3) ≤ 3 wt. %, LB is scarcely dependent on the concentration of boron oxide in the slag and can be calculated using the following expression
(20)
To test the calculated data obtained, we undertook the experimental determination of the equilibrium distribution coefficients of boron. The compositions of the metal and the slag in the experiments were similar to those used in the calculations. The metals were prepared by fusing powders of carbonyl iron, spectroscopically pure graphite, and amorphous boron; the slag was prepared from CaO, Al2O3, MgO, and B2O3. The carbon concentration in the metal was 1.0, 1.5or 2.0 wt. %, and the boron concentration ranged from 0 to 0.3 wt. %.
Three series of experiments were performed to ensure approach to the equilibrium position from both sides. In the first series, the boron content in the metal significantly exceeded the equilibrium concentration, and there was no B2O3 in the original slag. Conversely, in the second series, the metal did not contain boron, and the concentration of B2O3 in the slag was 5, 10, or 15 wt. %. In the third series, boron was present in both the metal and the slag.
Equal Weighed portions of the preliminarily ground metal and slag of equal weight were taken and mixed. The contact surface between the phases was thus maximized for the purpose of shortening the time needed for the system to achieve an equilibrium state and of eliminating the influence of the mass of the metallic and slag phases on the distribution coefficient of boron. The mixture was placed in the isothermal zone of a carbon resistance furnace and held at a constant temperature for 60 min. The temperature was monitored by a platinum–rhodium thermocouple. To eliminate any possibility of the components of the metal interacting with the gaseous phase, the heating zone was isolated from the carbon heating element by a corundum covering and purged with argon. The purging was discontinued after the phases melted, because an air atmosphere does not have an appreciable influence on the composition of the reacting melts [11].
The experimental data allow us to conclude that equilibrium with respect to boron does not always manage to be established under the conditions of our experiments. However, the character of the variation of its concentrations in the metal and the slag is such that convergence of the experimental points on the calculated curve can be expected.
Therefore, the method described can be used to calculate the equilibrium concentrations in a system consisting of an iron–carbon metal and an oxide slag.
Expressions for calculating the ratios between the equilibrium concentrations for the following reactions were also derived on the basis of the data obtained:
2/3(BO1,5) + [C] =2/3[B] + {CO}(21)
2/3(BO1,5) + [Fe] =2/3[B] + (FeO)(22)
2/3(AlO1,5) + [C] =2/3[Al] + {CO}(23)
2/3(AlO1,5) + [Fe] =2/3[Al] + (FeO)(24)
(25)
(26)
(27)
(28)
Expressions (25)–(28) were used in our work both for carrying out the kinetic analysis of multicomponent systems containing boron and aluminum and for developing mathematical models of technological processes.
We similarly presented calculations for the distribution of phosphorus between a metal and a slag. In this case, instead of reaction (3), for phosphorus we considered the following equation
(29)
whose equilibrium constant is described by the expression [4, 5]
(30)
The results of the calculations are presented in Table 1.
Table 1. Equilibrium concentrations of components in the metal and slag
T,K / (P2O5), wt. % / [С], wt. % / [Р], wt. % / LP=(P2O5)/[P]1873 / 5 / 1.0 / 0.27 / 18.5
10 / 0.5 / 0.15 / 66.7
1.0 / 0.49 / 20.4
1.5 / 0.75 / 13.3
1923 / 10 / 1.0 / 0.92 / 10.9
The data obtained allow us to draw some conclusions.
The distribution coefficient depends weakly on the concentration of (P2O5) in the slag, in agreement with the data in [12]. At the same time, LP depends to a considerable extent on the concentration of carbon in the metal. A decrease in the carbon concentration results in an increase in LP to values close to the values obtained in [12] for a carbon-free metal and to nearly complete constancy of the distribution constant of phosphorus.
To test the calculated data, we performed experiments to determine the distribution coefficient of phosphorus between the metal and slag. In particular, it was found for T = 1973 K and a carbon content in the metal equal to 0.3 wt. % that LP = 28.6 when equilibrium is approached form the slag side. When equilibrium is approached from the metal side, LP = 4.3. At the same time, LPcalc for these conditions equals 25.5.
Treatment of the results yielded the following expressions for the distribution constant of phosphorus between the metal and slag:
for (P2O5) > 0.5 wt. %
(31)
for (P2O5) ≤ 0.5 wt. %
(31)
Expression for calculating the ratio between the equilibrium concentrations for reactions involving phosphorus were also obtained:
2/5 (PO2,5) + [C] = 2/5 [P] + {CO},(33)
(34)
2/5 (PO2,5) + [Fe] = 2/5 [P] + (FeO),(35)
(36)
Equilibrium Distribution of Tungsten between Liquid Metallic and Slag Phases
When a tungsten-containing metal comes into contact with an oxide melt, the main process determining the distribution of tungsten between the interacting phases can be represented by the reaction
1/3[W] + (FeO) = 1/3(WO3) + [Fe],(37)
where KW is the ratio between the equilibrium concentrations.
The direction of the reaction for phases with assigned compositions can easily be determined from the value of KW. Moreover, this constant is needed for calculations of the chemical composition of the metal and slag during their interaction with tungsten. However, there are no experimental values of this ratio for phases with compositions close to the compositions observed in the oxidative smelting of tungsten-containing scrap.
It is virtually impossible to use theoretical methods to find the equilibrium concentrations of the components since the literature data on the thermodynamic parameters of reaction (37) are very sparse and contradictory. According to the data in [13, 14], the difference between the values of KW found by theoretical and experimental methods is as high as 150%. Therefore, we shall use only experimental methods to determine the equilibrium concentrations for this system.
It should be noted that the presently available data on the distribution of tungsten between a metal and a slag [13–18] refer to oxide systems containing at least 30 wt. % ferrous oxide. At the same time, there are no data on the distribution of tungsten between a metal and a slag for FeO concentrations smaller than 20 wt. %, which are typical of steel-smelting slags.
The equilibrium distribution of tungsten between a carbon-containing metal and slag was studied experimentally at 1773–1873K in [19] according to the method described.
The starting materials used were a slag based on the low-melting eutectic composition (wt.%) 51Al2O3 + 43CaO + 6MgO with additions of 0.5–20.0 wt. % FeO and 5–20 wt. % WO3 and a metal based on iron containing 0.5–3 wt.% carbon and up to 6 wt.% tungsten.
For the purpose of determining the time during which the metal must be held with the slag for the system to achieve an equilibrium state, we performed experiments that permitted estimation of the dependence of the reactant concentrations on the interaction time of the molten phases.
Experiments were performed at 1823 K with initial concentrations of ferric oxide in the slag and of carbon and tungsten in the metal equal to 10, 1.1, and 6 wt.%, respectively. These experiments showed that the composition of the metal and slag scarcely varies with time after 10–15 min of holding. This time is probably sufficient for the system to achieve a state close to equilibrium. Experiments employing phases with other compositions were carried out with a holding time of 30 min.
It follows from the results obtained that an increase in the concentration of FeO in the final slag leads to significant lowering of the values of LW = [W]/(WO3). When (FeO)> 7.0 wt.%, variation of the temperature and increases in the concentration of ferrous oxide in the slag have scarcely any influence on LW. Fairly similar results were obtained in [14, 16, 17]. At the same time, the values of LW for FeO concentrations in the slag less than 3 wt.% were obtained for the first time. Under these conditions, LW exhibits strong temperature dependence, and the values of the distribution coefficient are significantly higher than the previously known values.
It is noteworthy that the concentrations of the components vary in the experiments because of the interactions with carbon and FeO. The experimental data suggest that reaction (37) reaches a state close to equilibrium at the end of each experiment. In fact, it follows from the experimental data that KW remains essentially constant at an assigned temperature in the range of phase compositions obtained after each experiment. The experimental data were used to estimate the dependence of the mean values of KW on the temperature at which the phases interacted. It can be linearized in logKW versus 1/T coordinates and described by the expression
.(38)
It follows from (38) that raising the temperature results in displacement of the equilibrium of reaction (37) to the left, in agreement with the conclusion drawn in [14, 16, 17] that this process is exothermic.
The literature offers practically no data on the influence of carbon on the distribution of tungsten. It is only known [14] that raising the carbon concentration results in an increase in KW.
The experimental data in [14] yield the following dependence of LW on the carbon content in the metal:
LW = A [C]b,(39)
where b = 0.7–0.85.
The experimental dependence of LW on [C] derived from the data obtained in our experiments is described by Eq. (39), in which b = 0.5–0.6.
In our opinion, the dependence of LW on the initial concentration of carbon in the metal is interesting. This dependence, which can be used for approximate calculations, has the form
(40)
where [C]0 is the initial concentration of carbon in the metal, wt.%.
The value of A1 can be estimated from the following data:
- If the initial value of (FeO) in the slag is greater than 7.0 wt.%, A1 = 8.88 at 1673–1973K.
- If the initial value of (FeO) in the slag is less than 4 wt.%, A1 can be calculated from the expression
(41)
Theoretical and Experimental Determination of the Equilibrium
Distribution Coefficients of Sulfur
The equilibrium distribution of sulfur between immiscible oxide and metallic phases is often described by the ratio of equilibrium concentrations
LS = (S)/[S].(42)
When the composition of the interacting phases remains constant, the coefficient LS is proportional to the equilibrium constant of the desulfurization processes.
For a system consisting of an iron–carbon melt and an oxide slag, the desulfurization reaction is written [20] in the form
[FeS] + (CaO) + [C] = (CaS) + [Fe] + {CO},(43
)
or in the ionic form
[S] + (О)2- +{C} = (S)2- + {CO}(44)
The expression for the equilibrium constant of process (43) can be written in the form
.(45)
We assume that the equilibrium partial pressure of carbon monoxide (PCO) equals unity. This assumption is valid if CO bubbles form on the metal–oxide boundary when the external pressure equals 1 atm. In addition, we assume that the activity coefficients of sulfur and oxygen in the slag are equal to 1, and we express the activities of sulfur and carbon in the metal using the Wagner interaction parameters. Equation (45) is then simplified.
Let us express the equilibrium distribution coefficient of sulfur LS on the basis of Eq. (45).
We assume that N(S2-) = N(S). This assumption is fully permissible at a low (less than 3 wt.%) sulfur content in the slag. Then the expression for LS can be written as