3. Materials and method
3.5 Thermodynamic modelling methodology
Thermodynamic equilibrium modelling was performed with a commercial software package FactSage, version 6.2 [64].
Thermodynamic modelling (FactSage) approach
The analysis of chemical reactions forms the central part in any chemical/metallurgical engineering environment. There is an infinite amount of products and arrangements that can be formed from a certain set of reactants. Therefore it is important to determine which products are favoured given specified elemental composition, temperature and pressure. This phenomenon is known as chemical
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reaction equilibria and will form the basis during the reduction of all metal oxides. The constraints [6] associated with reaction equilibria need to be considered at all times since it will determine if a metal oxide will be reduced or not. During the reduction of any concentrate or ore the final product will be a combination of product species with the lowest Gibbs energy from a reactant input [6, 64]. FactSage equilib module employs the Gibbs energy minimization algorithm for treating complex heterogeneous equilibrium using compound and solution databases.
System selection
Within the FactSage equilib module, it is possible to calculate equilibrium according to a normal and open system. The normal system calculates equilibrium products of the entire input feed streams, including gaseous, liquid and solid. The open system allows for the gaseous products to be continually removed in a number of steps and a new gas addition is done upon which equilibrium is calculated again. The equilibrium products, with the exception of the gas phase, are seen as the feed to the next step, with the number of steps being specified.
However, in this evaluation, a normal system is a suitable selection to calculate equilibrium compositions, since the concentrate and reductant is feed into a furnace and contained, with the gas phase being slowly extracted. Therefore, only one equilibrium state could be calculated.
Databases description used in the thesis
The FactSage databases utilized in this study are the largest set of evaluated and optimized thermodynamic databases for inorganic systems in the world and used extensively in metallurgical and chemical applications. The solution databases (for solutions of oxides, salts, metals, etc.) have all been developed by evaluation and optimization obtained from literature.
Based on proper thermodynamic models for every phase, all available thermodynamic and phase equilibrium data for a system are evaluated simultaneously in order to acquire one set of model equations for the Gibbs energies of all phases as functions of temperature and composition. During optimization, all the data are condensed self-consistent, discrepancies in the data can often be resolved, and the data can be properly interpolated and extrapolated. For example, the properties of multicomponent solutions can normally be estimated with very good accuracy from the optimized model parameters of their binary and ternary sub-systems. The resulting databases of model parameters can be used for calculating phase equilibria and thermodynamic properties using the FactSage Gibbs energy minimization software [64].
The FactSage thermodynamic databases are developed as follow:
1.) A mathematical model for G (T, P, composition) is developed for each phase.
2.) The model parameters are optimized simultaneously by using all available thermodynamic and phase equilibria data from the literature.
3.) Use models and database to estimate properties of multicomponent systems.
4.) Through the minimization of Gibbs energy, thermodynamic properties and phase equilibria is calculated.
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In the Fact 53 database more than 4500 compounds are enlisted. It contains selected data for thousands of compounds taken from standard compilations as well as most of the data for those compounds which have been evaluated and optimized to be thermodynamically consistent. All individual thermodynamic extensive properties for elements and compounds can be extracted from the Fact 53 database. During evaluation of a multicomponent system, data from the gas phase is generally found from the Fact 53 database, while the solid and liquid data are found in other databases. The following databases are utilized to model these solid and liquid phase [64].
Slag phases
In a multicomponent system it is most likely that more than one phase will be present. For instance, during smelting a slag phase that contains elements in its oxide form will be formed and the FToxid databases that contain data for pure oxides and oxide solutions can be initiated. Some of the major compounds that are has been fully evaluated and optimized are Al2O3, CaO, FeO, Fe2O3, MgO and
SiO2 [64].
Matte phases
This database is particularly useful for matte/alloy/slag/gas equilibria in conjunction with Fact 53 and FT oxide databases. The principal phase in this group is the liquid matte [FTmisc-MATT]. It is designed for calculation of matte/slag/metal equilibria and is consistent with FToxid-SLAG, FTmisc- CuLQ, FeLQ and FTmisc-PbLQ [64].
Alloy phases
A molten metal phase is likely to occur during smelting of a concentrate with high iron content. The FeLQ from the FTmics database is suitable for diluted solutions (used in steel industry); however in the presence of other base metals, the FeLQ may give inaccurate results. The SGTE LIQUID phase will give more accurate results when the metal phase contains iron and other base metals.
In general, there are 78 elements included in this database and from these elements, there are some 350 completely assessed binary alloy systems, of which over 40 are newly assessed systems and many others have been reviewed or amended on the basis of newly published experimental information. The database also includes about 120 ternary and higher-order systems for which assessed parameters are available for phases of practical relevance. The systems now integrate approximately 180 different solution phases and 600 stoichiometric intermetallic compound phases [64].
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