Steady-state simulation of pyrometallurgical processes

R.T. Jones (Chief Engineer, Pyrometallurgy Division),

Mintek, Private Bag X3015, Randburg, 2125, South Africa

Synopsis: Pyrosim is a general-purpose computer program for the steady-state simulation of pyrometallurgical processes. The program uses a variety of models to predict the flowrates and analyses of product streams, as well as the distribution of elements between phases. One of the primary strengths of the program is its built-in capability to calculate multi-component multi-phase equilibria, along with the automatic performance of energy-balance calculations. This predictive ability allows the program to simulate novel processes rather accurately. Pyrosim provides a convenient framework for the calculation of material and energy balances, as well as a simple basis for cost comparisons between process options.


Pyrometallurgical operations are essentially concerned with the high-temperature processing of materials. These processes can be extremely complex, involving reactions between gas, solids, liquid slag, and liquid metal (and sometimes other phases as well).

Pyrometallurgical processes must be evaluated at many stages during their development and design, and when operating changes are introduced. Because experimental work in pyrometallurgy is expensive, a system should be characterised as thoroughly as possible before experimental work is undertaken. Computer simulation allows the requirements of a particular process to be determined quickly and reliably.

The essential problem of process simulation involves the development of a technique that will allow the prediction of the outcome of a particular process under specified operating conditions. To this end, a computer program, Pyrosim, was developed by the author to calculate predictive steady-state mass and energy balances for a wide variety of processes. Since many different raw materials must be taken into account, the program is very flexible in this regard.

Pyrosim was originally developed as a program to simulate processes used in the production of raw stainless steel. The initial development work started in 1985 on an Apple II computer equipped with 64 kb of memory. Fortunately, the program's structure was kept very general to allow other processes to be simulated.

The program was first presented in public (outside of Mintek) at the APCOM 87 conference [1] (The 20th International Symposium on the Application of Computers and Mathematics in the Mineral Industries) in October 1987. The first version of the program to be used in industry (v1.0 for IBM-compatible personal computers) was released at the end of 1988. A dissertation [2] based on Pyrosim was submitted for an MSc(Eng) degree at the University of the Witwatersrand during 1989.

Pyrosim software runs on personal computers using the MS-DOS operating system. There are no special hardware requirements needed to run the program, although 640 kb of memory and a math coprocessor are recommended. Obviously, from the point of view of speed, an i386 or higher processor will be most suitable for intensive calculational work.

A typical simulation using the present version of the program (v1.2) may take just over three seconds on a 33 MHz i486 computer, whereas the same simulation would have taken over an hour on an Apple II. This represents a speeding up by a factor of 1200.

The program has been successfully applied to the processing of ferroalloys, metal carbides, base metals, and refractory metals. The program has also been used for the study of various pyrometallurgical pretreatment options, such as preheating and prereduction, as well as processes involving combustion. Pyrosim has also recently been used successfully to model the plasma-arc treatment of electric-arc furnace dust, a process inherently complex because of the number of chemical elements involved.


The simulator is based on the description of the process units and streams involved in a flowsheet. The state of any stream is completely specified by the vector of flowrates of each chemical species together with the temperature and pressure. A complete specification of the the section of plant being simulated can be obtained by including the operating conditions of each process unit. These conditions include the operating temperature, pressure, and the energy losses from the unit. (Additionally, the differences between the temperatures of individual product streams and the nominal process temperature may also be specified.) It is also necessary to specify whether the process is temperature-controlled or energy-controlled.

Any process unit has a number of feed streams, each at its own particular temperature. From the chemical analysis of the feed streams, the number of moles of each chemical species is calculated. It is often necessary to treat minerals as ideal mixtures of chemical compounds, since thermodynamic data is not readily available for minerals as such.

The appropriate thermodynamic constants (the standard enthalpy and entropy of formation, and CP coefficients) are then assigned (from the built-in database) to each of the chemical species so that the partial molal enthalpy of each component can be calculated at the stream temperature. In general, the partial molal enthalpy is a function of temperature, pressure, and composition. The effect of composition on the enthalpies of individual components is small in most cases; there is also very little data available on the variation in enthalpy with composition. The effects of composition on enthalpy are therefore ignored, which is equivalent to the treatment of the process streams as ideal solutions (for the purposes of the energy balance). Except for gases at high pressure, the dependence of enthalpy on pressure is small. (If deemed important, the effect could be allowed for by the use of equations of state or reduced property correlations, outside of the program.) In this field of interest, the enthalpy is assumed to depend solely on temperature. The enthalpy of each pure species is calculated relative to the elements in their standard state at 25°C and 1 atm. The total enthalpy of a stream is taken to be equal to the sum of the enthalpies of all the species in the stream.

The total number of moles of each of the chemical species entering a particular unit is then placed in a vector of feed species. In this way, an indefinite number of feed streams (limited, of course, by available memory) containing material of any composition and at any temperature can be accommodated. The unit model is then applied to the feed vector. The model is essentially a mapping of the elements in the chemical species of the feed vector onto vectors of the species in the resulting product streams (e.g. gas, solids, slag, and metal). The total enthalpy of these resulting streams is then calculated as described above.

The energy requirement of a process is calculated as the difference between the enthalpy of the products and that of the feed streams. The specified losses of energy from the process unit are then added to this amount to give the energy requirement of the process unit. In this way, the enthalpy calculation can be performed independently of any specific reaction path.

Some or all of the products (e.g. gas, solids, slag, and metal) from the first unit may then become part of the feed to the next unit. The fraction of each of the product streams entering the next unit can be independently specified.

The present version of Pyrosim supports the saving of analyses of product streams, to simplify the solution of recycle loops. For most pyrometallurgical flowsheets, one of the streams within a recycle loop can usually be estimated. In this way, the loop is 'torn' open, and the calculations can be continued as explained previously. Some form of iteration (direct substitution is usually adequate) is then applied to the calculation of the 'tear' stream until convergence is attained. The topology of most pyrometallurgical flowsheets is fairly simple, and this approach is therefore usually adequate.

The Pyrosim program achieves its generality by obtaining all the required information from a number of data files. These files cover the names of the process units, the thermodynamic data and stoichiometry of the chemical species under consideration, the chemical analyses of the feed materials, the unit costs of raw materials and electrical energy, and the specifications of the chemical species present in each phase at equilibrium. All these files are managed by the program, and data can be added, deleted, edited, or listed. Thus, the program is kept independent of any particular process route.

A sample printout from the program is presented in the Appendix. This shows all of the sections of the printed report, namely the Flowsheet, Flowrates, Operation, Energy, Analyses (in mass %, with gas analyses shown in mol % as well), Elemental Analyses, Distribution of Elements, and Material and Energy Costs sections, each of which may be printed individually if desired.


Because the program relies heavily on thermodynamic data for its predictions and for the energy calculations, it is imperative to use the best available data. For all chemical species of interest, therefore, data has been obtained from the F*A*C*T [3] thermodynamic database in Canada, as well as from other sources where necessary. A small sample of the data used by the program is shown in Table 1.

Table 1: A sample of the thermodynamic data used by Pyrosim


Cp (J/K/MOL) = C1 + 1E-3*C2*T(K) + 1E5*C3*T(K)^-2 + 1E-6*C4*T(K)^2

H0 (J/MOL) = Standard Enthalpy of Formation at 298K, 1 atm

S0 (J/K/MOL) = Standard Entropy of Formation at 298K, 1 atm

COMPOUND MW PHASE TEMP (K) H0(J) S0(J/K) C1 C2 C3 C4 Cr2O3 151.99 S1 298 - 1800 -1129680 81.170 119.370 9.205 -15.648 0.000 FeO 71.85 S1 298 - 1650 -272044 60.752 50.802 8.615 -3.310 0.000 L2 1650 - 3687 -261069 55.413 68.199 0.000 0.000 0.000 Cr 52.00 S1 298 - 1000 0 23.640 17.715 22.966 -0.377 -9.033 S2 1000 - 2130 4051 32.681 18.067 15.531 -16.698 0.000 L3 2130 - 2945 11758 18.065 39.330 0.000 0.000 0.000 G4 2945 - 3100 378631 154.528 30.786 0.000 0.000 0.000 Fe 55.85 S1 298 - 800 0 27.280 28.175 -7.318 -2.895 25.041 S2 800 - 1000 -52991 -111.337 -263.454 255.810 619.232 0.000 S3 1000 - 1042 157699 354.770 -641.905 696.339 0.000 0.000 S4 1042 - 1060 -529453 -1036.133 1946.255 -1787.497 0.000 0.000 S5 1060 - 1184 -418215 -979.395 -561.932 334.143 2912.114 0.000 S6 1184 - 1665 8260 35.959 23.991 8.360 0.000 0.000 S7 1665 - 1809 6144 33.243 24.635 9.904 0.000 0.000 L8 1809 - 3135 3401 17.276 46.024 0.000 0.000 0.000 G9 3135 - 3600 406766 173.396 27.062 0.000 0.000 0.000 STOICHIOMETRY

Cr2O3 : Cr 2 O 3 FeO : Fe 1 O 1 Cr : Cr 1 Fe : Fe 1

Pyrosim determines which of the phase regions to use to obtain the coefficients in the calculations, according to the temperature range in which the system temperature falls. If the temperature is beyond the highest temperature for which data is available, the values are extrapolated using the functional form of the closest set of data. If it is necessary to override the automatic selection of the appropriate phase region, the temperature ranges can be 'adjusted' so as to force the desired phase region to be selected. However, a better method is to create a separate entry for each phase region using the data pertaining to that region only. For example, instead of using the species Al2O3, one could create two separate entries for Al2O3(s) and Al2O3(l) using only the relevant set of data in each case.


The models of individual process units that are to be included in the program all have a standard form, since the output from a unit must be calculated from the input to that unit and the specified operating conditions. The following features need to be borne in mind when a model for a process is set up.

It is assumed that the amount, composition, and temperature of the feed materials entering the unit are known. The operating pressure and the energy losses are also known. The temperature is specified for process units where an external energy source is present. Otherwise, the process is said to be energy-controlled and the temperature is determined by the model. The temperature is rapidly calculated, by trial and error, to be such that the difference between the enthalpy of the products and that of the feed is equal to the loss of energy from the unit. (Note that an adiabatic process is the special case of an energy-controlled process where the energy loss is equal to zero.) Energy-controlled calculations can be performed for all process models within Pyrosim.

The model must simulate real operation as closely as possible. The user is required to specify only what he is free to specify in practice. For example, one can specify the ratio of the materials in the feed but not the composition of the metal. The amounts and compositions of the product streams are calculated from the feed materials and the operating conditions. Any additional parameters of interest can also be calculated at this stage. For example, it is useful to report the calculated liquidus temperature of the slag for an electric-arc furnace model.

No process model should be regarded as being absolutely definitive. Through a process of interaction with the users of the program, there will hopefully be a steady evolution of improved process models.

Models may be empirical, specific, general, kinetic, or based on equilibrium. Of course, the ideal for every simulation is to be able to predict the outcome of any process. For this reason, much effort was expended to provide a technique for the prediction of the distribution of the elements between the various chemical species in the product streams. The models that are most generally applicable are those based on a fundamentally sound description of the process being simulated. A technique has been made available that will provide a model based on the description of the chemical equilibrium of a multi-phase system.

Non-Equilibrium Models

Pyrosim contains a simple Heater/Drier model which simply separates the feed streams into a gas stream and a solids stream. The two product streams are normally at a higher temperature than the feed materials, and the model calculates the energy required to raise the temperature of the materials (and perhaps to vaporise any moisture that may be present). The criterion for deciding whether a particular species goes to the gas stream or the solids stream is whether or not the stable phase of that species is gaseous at the process temperature. The degree of moisture removal and devolatilisation may also be specified by the user of the program.

An example of an empirical model, described fully elsewhere [2], is one developed for a rotary kiln, where a number of empirical factors are specified, as shown in Figure 1, and the remaining variables calculated from these.


Figure 1: Specification of parameters for the empirical Rotary Kiln model

Equilibrium Models

Pyrometallurgical processes take place at high temperatures. For this reason, the attainment of equilibrium in many processes is not prevented by kinetic limitations. However, a general method for the prediction of the composition of an isothermal multi-phase system at equilibrium is required.

Problems relating to the chemical equilibrium of a system involving several chemical species are notoriously intractable, requiring the solution of many simultaneous non-linear equations. However, such problems can be reduced to the minimization of the Gibbs free energy of the system, which is the fundamental description of chemical equilibrium. In general, there is an infinite number of ways in which non-negative mole numbers can be assigned to the possible product species such that the chemical reactions involving the specified reactants will be balanced. At a specified temperature and pressure, the most stable products (the desired solution to the problem) are those associated with the lowest free energy.

This minimization problem has the free energy of the system as the objective function, and the number of moles of each of the chemical species in each phase as the variables. The constraints that apply are those of mass conservation for each element present in the system, as well as those of non-negativity of the number of moles of each species present. The equality constraints can be taken care of by the use of the technique of undetermined Lagrange multipliers. Eriksson [4] has devised a method for free-energy minimization which uses a truncated Taylor series expansion of the non-linear equations around successive estimates of the solution to provide a system of linear equations to be solved within each iteration. Pyrosim provides a starting estimate (which can be arbitrary) of the number of moles of each of the chemical species present in each phase. The number of equations to be solved is equal to the number of elements plus the number of phases. A number of possible compounds may therefore be included in the description of the equilibrium system, since the program will be able to show which species will not form to any appreciable extent.

The linear equations that must be solved in each iteration are often somewhat ill-conditioned, i.e. they form a matrix with a very small determinant. These systems can still be solved accurately using only single-precision arithmetic, if the matrix is first scaled before being solved by Gaussian elimination with partial pivoting.

A number of corrections are applied to the calculations to ensure that all the solutions will be positive and to eliminate species that are present only in negligible quantities, since their inclusion would unduly slow down convergence of the system of equations.

Figure 2 shows a typical intermediate display during an equilibrium calculation. Note that the current estimate of the number of moles of each species in each phase (gas, slag, and metal, in this case) is displayed on the screen, along with some other information.


Figure 2: Pyrosim screen display during an equilibrium calculation

Convergence of the equilibrium calculations is monitored by means of 'convergence factors' for each phase, which are calculated after each iteration. For each phase, the factor is the ratio of (the total number of moles in the phase in the present iteration) divided by (the total number of moles in the phase in the previous iteration) minus one. These factors approach zero as the system converges. The convergence criterion is set so that all convergence factors must have an absolute value of less than 10^-5. These factors are sometimes useful indicators of possible reasons for non-convergence, in that if a particular factor remains large it usually means that the corresponding phase is probably unstable. The way to correct this problem is to redo the equilibrium specification, leaving out the unstable phase.

Also shown on the screen, is the number omega!, which is explained in detail elsewhere [2]. While omega! is less than one, the uncorrected estimated number of moles of at least one of the species is negative. omega! is the fraction by which the estimated number of moles of each of the species has to be corrected in order for all estimates to be made positive. Note that omega! must be equal to one before convergence can occur. (If a pure condensed phase is specified as being present at equilibrium, but in fact proves to be unstable, the estimated number of moles for that species will be zero and so will omega!. In this case, the equilibrium specification should be redone, leaving out the unstable pure phase. In a later version of the program, this will hopefully be taken care of automatically.)

The usual reasons for non-convergence are: 1) disappearance of one of the phases. 2) inclusion of an extremely unstable species in one of the mixed phases. (This shows up by the estimated number of moles of the species rapidly disappearing to zero within the first few iterations.) 3) violation of the phase rule, by including too many pure condensed phases.

However, most problems converge to a solution rather easily. A typical problem might require about a dozen iterations to solve the system of equations to an accuracy of more than five decimal places.

The technique has been applied to a wide variety of systems and has been found to be extremely reliable and stable over a wide range of conditions.

Probably the most severe limitation of a simple equilibrium model is the fact that real process units are not actually isothermal. For example, conditions vary within furnaces; the temperature is lower further from the arc, and the pressure is higher the deeper the position within the liquid layer. The most useful application of this technique has been to the simulation of electric-arc furnaces where, as a fairly good approximation, it can be said that the temperature (and pressure) of the tapped products are approximately uniform. Here the assumption of isothermal equilibrium is reasonably accurate.

Specification of Equilibria

The specification of the chemical species present at equilibrium is very simple. A list of all species of interest is displayed by the program, and the user then indicates which species might be expected to be present in each phase at equilibrium. Once the list of species has been specified, the matrix of equations is automatically set up by the program. Large systems (e.g. 100 feed materials, 100 species in the system, 60 species per equilibrium phase, 30 elements) are handled routinely by Pyrosim. The limits on the number of feed materials, species in the system, species per equilibrium phase, and number of elements in any given equilibrium calculation can now be tailored to any particular requirements, simply by editing a simple configuration file.

Table 2 shows a sample printout of an equilibrium specification for the ferrochromium smelting system. This system contains 3 phases, 36 species, and 16 elements.

Table 2: Species possibly present at equilibrium in the ferrochromium system

Gas:  CO  CO2  H2  H2O  N2  Ar  Mg  SiO
Slag:  Cr2O3  FeO  SiO2  CaO  MgO  Al2O3  MgCr2O4  MgAl2O4  FeCr2O4  MnO  TiO2  NiO  CaS  Ca3P2O8
Metal:  Cr  Cr3C2  Cr7C3  CrSi  Fe  Fe3C  Fe3Si  Si  SiC  C  Mn  Ni  P  FeS

ELEMENTS:  C   O   H   N   Ar  Mg  Si  Cr  Fe  Ca  Al  Mn  Ti  Ni  S   P

The reactions taking place in such a system are extremely complex, and the solution of the resultant equilibria is virtually impossible without the use of a computer program using the technique of free-energy minimization.

Activity Calculations

In equilibrium calculations, it is assumed that the activity of each species in the specified system can be calculated from the chemical composition of each phase. The activity of a component in a solution is defined as the ratio of its fugacity to its standard-state fugacity. The activity function can, at least in theory, be calculated from the equation of state of the solution. However, because of the low accuracy of liquid-phase equations of state in general, other techniques are required for the calculation of activities in slag and metal solutions. Unfortunately, accurate activity data for components in slags and metals is limited. For example, data is often available for simple slag systems, but not for the more complex slags encountered in actual practice.

The ideal-solution model, in which the activity of each component equals its mole fraction, is the simplest model of activities in a solution. This model takes into account only the effect of dilution on activities, and ignores the chemical and physical effects of mixing. Although very few metal solutions and even fewer oxide systems display 'ideal' behaviour, this is chosen as the reference for solution behaviour.

It is usually expedient to assume that the gas phase behaves ideally, as this is a reasonably accurate assumption under the conditions most frequently encountered (namely low pressure and high temperature).

Slags are relatively concentrated solutions of oxides, and usually contain oxides such as SiO2, CaO, MgO, and Al2O3, together with the oxides of the metals involved in the process. They are complex solutions in which each component influences the activity of the others, and hence their behaviour is not easily described. Some authors have derived solution models for slags based on the ideal or regular constitutional models, using various species as components. Others have adopted a structural approach, modelling the slag properties in terms of some hypothetical structure. It is now generally accepted that slags are essentially ionic systems, although they have on occasion been viewed as having a molecular structure, with the molecules envisaged as combining to form more complex (and unreactive) molecular structures, for example, 2CaO.SiO2, which exist in dissociated equilibrium with the corresponding components.

Metallic systems comprising dilute solutions can often be modelled using activity coefficients at infinite dilution, and interaction coefficients. However, a solution model that can satisfactorily deal with non-dilute metallic solutions is required.

Ideal Mixing of Complex Components

A major improvement on the ideal-mixing model is the use of the Ideal Mixing of Complex Components [5] approach, as proposed by Hastie and Bonnell [6,7,8]. This generally allows good estimates for the equilibrium products to be generated, by including a list of possible intermediate compounds in the equilibrium specification, to model some of the chemical interactions between species. This model attributes deviations from ideal-solution behaviour to the formation of complex component liquids and solid phases. Although this solution model may be fictitious, it is useful for the derivation of expressions for the dependence of thermodynamic quantities on composition. The derived expressions are helpful in the extrapolation of data to other composition ranges, and in the estimation of the thermodynamic properties of related systems.

The terminology used in this section requires definition. The term 'components' refers to the usual reference-state oxides, such as SiO2, CaO, MgO, and Al2O3 in slag systems, and to the elements, such as Fe and Si, in metallic solutions. 'Complex components' refers to compounds (liquid or solid) of the simple components, such as 2MgO.SiO2 in a slag, or Fe3Si in a metal.

The model is based on the identification of complex components (such as alkali silicates) in solution. These complex components account for the non-ideal solution interactions. These complex components, together with the non-complexed constituent components, are explicitly included in a multi-component equilibrium calculation to determine the equilibrium distribution of each component in any phase, with the calculations being constrained to obey the Gibbs-Duhem activity and Gibbs phase-rule relationships. The activities are taken to be equal to the equilibrium mole fractions of the uncomplexed components.

The key assumption of the present model is that complex solution phases can be approximated as mixtures of known, or hypothetical, liquids based on melts of established complex solids. The liquid components are not independent molecular or ionic species, but are essentially sub-phases that serve as models for the local associative order. Therefore, the complex thermodynamic interactions that occur between components are essentially contained in the Gibbs free energies for the complex components. A typical multi-component oxide system can then be represented as an ideal mixture (or any other physical model) of many such component liquids and solids.

The use of molecular formulae in this model does not imply the actual presence of molecular species. The model deals only with liquids or solids as components of the mixture, and not with molecular or ionic species as is often the case with other solution models. For the most part, the component liquids are established neutral, stable, thermodynamic compounds, appearing in phase diagrams in equilibrium with congruently melting solids, and also in reference tables of thermodynamic functions. The free energies of formation are either known or can be estimated for these complex component liquids (and solids).

In the IMCC model, it is implicit that the physical interactions (i.e. those not attributed to chemical bonding) among the complex components are considered negligible compared to the strong chemical interactions leading to their formation. It is noteworthy that this is the case for many metal-oxygen and metal-sulphur systems, as well as oxide ceramic mixtures and certain alloy systems, that are influenced primarily by the chemical interaction caused by the formation of associated species and secondarily by the physical interactions among all the species.

One of the prime benefits of this predictive model is that it is equally capable of handling systems containing few or many components. The fact that this model can therefore be applied to systems where essentially no phase-stability information is available, represents a significant improvement in the prediction of activity relations for complex systems.

The IMCC approach has been used previously [5] to model simple industrial slags. Calculated activities in the CaO-MgO-SiO2 ternary system were compared with the experimentally-determined data of Rein and Chipman [9]. For the calculations, all possible species and phases for which thermodynamic data is available were considered as possible candidates for formation at equilibrium. The species considered were CaO, MgO, SiO2, CaO.MgO, CaO.SiO2, 2CaO.SiO2, 3CaO.SiO2, 3CaO.2SiO2, MgO.SiO2, 2MgO.SiO2, CaO.MgO.SiO2, CaO.MgO.2SiO2, 2CaO.MgO.2SiO2, and 3CaO.MgO.2SiO2.

Figure 3 shows the activity -- mole-fraction relationship for MgO in the CaO-MgO-SiO2 ternary system at a constant level of 30 mole % CaO. So that a comparison can be made with the experimental data, the figure pertains to that portion of the phase diagram where only a liquid is present, although the model is able to deal with the presence of solids as well. The composition boundaries are indicated on the diagram. From the figure, a comparison can be made between the calculated activities, the experimentally determined activities, and the ideal activities.

Figure 3: Activity - mole fraction curve for MgO in the system CaO-MgO-SiO2 (at 30% CaO) at 1600°C

There is excellent agreement between the calculated and experimentally determined activities of CaO and MgO, and reasonably good agreement between the activity curves for SiO2. It is also important to note the large discrepancies that would result if the assumption of an ideal solution was made.

The Ideal Mixing of Complex Components (IMCC) solution model has been shown to be applicable to the prediction of activities in complex solutions where chemical interactions are dominant over physical interactions. Such systems are often encountered in pyrometallurgical systems. This solution model works well and is easy to use in equilibrium calculations.

Work is currently in progress to provide more support for a variety of methods for the calculation of activity coefficients in specific systems. There is some good data available on the slag system SiO2-CaO-MgO-Al2O3-FeO-Fe2O3-MnO, for example.


As Pyrosim had its beginnings in the attempt to model processes leading up to the production of raw stainless steel, models have been developed for a number of process units and process steps in the 'Stainless Steel' (`SS') system. The models include a drier, gas drier, fluidized bed, electrothermal fluidized bed, rotary kiln, two-zone kiln, electric-arc furnace, coal-oxygen injection furnace, and an empirical furnace model. The details of these models are published elsewhere [2]. Some of these models also provide a significant quantity of derived information, such as the liquidus temperature, viscosity, and basicity of slags, as well as gas ratios and degrees of reduction.

The 'SS' system is supplied as a full working simulation system which shows the flexibility of the program in incorporating both empirical and predictive process models. The 'SS' system includes pre-defined equilibrium specifications (for those process models which make use of equilibrium calculations) and the analyses of a number of raw materials. Note that the models used in this system are specific to the 'SS' set of data files (for the Fe-Cr-Ni system), and can not be applied directly to other systems.


Pyrosim contains a number of built-in models that are generally applicable to any system. These models describe simple heating (or drying), multi-reaction multi-phase equilibrium (for example, gas-solid or gas-slag-metal), and multi-stage equilibria with continuous removal of the gas phase. A simple-to-use utility program called Pyromake is supplied with Pyrosim, to allow the user to construct a simulation system containing only the chemical species of interest. By means of a simple selection from a list of species on the screen, a database containing all the relevant thermodynamic data is automatically constructed.

The Pyromake utility automatically copies the Pyrosim program to the disk (or directory) where the data files for a particular system are created, thus providing a self-contained simulation disk (or directory) for the system under consideration. The built-in models can then be used on the selected system. Energy balance calculations are also performed automatically.

The Pyromake utility program has now been rendered obsolete by the data export feature in Thermo software, which is usually used in conjuction with Pyrosim.


Simulations must be simple to perform and directly applicable if they are to be used successfully. Experience has shown that simulation programs will be used only if they are able to produce results that are easy to interpret and that can be obtained from a limited quantity of readily available data. Furthermore, the program must be easy and logical to use. It is essential for the program to be accessible to as many people as possible, since this is the best way to ensure a steady evolution of improved process models.

The Pyrosim program can simulate the production of a number of materials by a variety of different process routes. Similar processes can then be compared on the basis of the costs of raw materials and the consumption of electrical energy.

The availability of a computer program for the simulation of pyrometallurgical processes should be of value to everyone concerned with the comparison of process routes. A great deal of time and effort can be saved by the use of such a program.


This paper is published by permission of Mintek.

Paper presented at the SAIMM School: Pyrometallurgy in the 90's. Mintek, Randburg, 7-9 October 1992.


1. Jones R.T. Computer simulation of pyrometallurgical processes, APCOM 87, Proceedings of the Twentieth International Symposium on the Application of Mathematics and Computers in the Minerals Industries, Volume 2: Metallurgy, Johannesburg, SAIMM, October 1987, pp. 265-279.

2. Jones R.T. Computer simulation of process routes for producing crude stainless steel, MSc(Eng) Dissertation, University of the Witwatersrand, Johannesburg, 3 October 1989.

3. Thompson W.T., Bale C.W., & Pelton A.D. Interactive computer tabulation of thermodynamic properties with the F*A*C*T system, Journal of Metals, December 1980, pp. 18-22.

4. Eriksson, G. Thermodynamic studies of high temperature equilibria. XII. SOLGASMIX, a computer program for calculation of equilibrium compositions in multi-phase systems. Chem. Scr., Vol. 8, 1975, pp. 100-103.

5. Jones R.T. & Botes B.D. Description of non-ideal slag and metal systems by the intermediate-compound method, Proceedings of Colloquium on Ferrous Pyrometallurgy, SAIMM, Vanderbijlpark, 18 April 1989.

6. Hastie J.W. & Bonnell D.W. A predictive phase equilibrium model for multicomponent oxide mixtures: Part II. Oxides of Na-K-Ca-Mg-Al-Si. High Temp. Sci., vol.19. 1985. pp. 275-306.

7. Hastie J.W., Horton W.S., Plante E.R., & Bonnell D.W. Thermodynamic models of alkali-metal vapor transport in silicate systems. High Temp. High Press., vol. 14. 1982. pp. 669-679.

8. Hastie J.W. & Bonnell D.W. Thermodynamic activity predictions for molten slags and salts. Abstract, Third International Conference on Molten Slags and Glasses, University of Strathclyde, Glasgow, 27-29 June 1988. The Institute of Metals.

9. Rein R.H., & Chipman J. Activities in the liquid solution SiO2-CaO-MgO-Al2O3. Trans. Metall. Soc. AIME, vol.233. Feb. 1965. pp. 415-425.



Production of ferrochromium

쿑eed                       Feed                          
    旼컴컴컴컴컴컴컴컴컴     旼컴컴컴컴컴컴컴컴컴    
 읕>                     읕>                       
       Heater / Drier   쳐컴컴>   Furnace (SS)        
     1                  쳐    2                  쳐  
     읕컴컴컴컴컴컴컴컴컴     읕컴컴컴컴컴컴컴컴컴   
                           V                          V  
                      Products                   Products

                 FLOWRATE (kg/h)      TEMPERATURE (°C)
FEED  1 
Chromite             100.00                   25
Gas                    2.43                  800
Solids                97.60                  800
FEED  2 
Coal                  30.00                   25
Quartzite             20.00                   25
Limestone             10.00                   25
Gas                   47.83                 1700
Slag                  60.61                 1650
Metal                 49.19                 1600


Heater/Drier model is based on a simple rise in temperature
Operating temperature = 800°C
Operating pressure = 1.00 atm
Degree of moisture removal =100.000%

Furnace model based on multi-phase multi-reaction equilibrium
Operating temperature = 1650°C
Operating pressure =  1.0000 atm

Slag basicity [Molar ratio of (CaO + MgO) / SiO2] = 1.1
Slag basicity [Mass ratio of (CaO + MgO) / SiO2]  = .8
Slag liquidus temperature (four components SiO2, CaO, MgO, Al2O3) = 1569°C
Slag viscosity =  8.34 poise
Partition ratios (slag/metal):   S = 101  P = 299
Slag analysis (four component)  SiO2 = 40.3  CaO = 10.0  MgO = 21.8  Al2O3 = 28.0
Effective Slag   Cr2O3 =  9.3  FeO =  0.4  SiO2 = 36.3  CaO =  9.0  MgO = 19.6  Al2O3 = 25.2  Cr/Fe = 20.94
Effective Metal   Cr = 56.7  Fe = 37.3  Si = 0.94  C =  5.08  S = 0.003  P = 0.000  Cr/Fe =  1.52
Cr recovery (Cr in metal / Cr in feed) = 87.9%
Fe recovery (Fe in metal / Fe in feed) = 99.0%

Slag : Metal ratio =  1.23


UNIT 1 requires  21.5 kWh ( 77.3 MJ) per hour of operation, including a rate of energy loss of 0 kW

UNIT 2 requires  135 kWh ( 487 MJ) per hour of operation, including a rate of energy loss of 0 kW
  This is 2.74 MWh per ton of Metal produced in this unit

(MASS %)
                  Cr2O3    CrO     FeO    Fe2O3   Fe3O4    SiO2    CaO    CaCO3    MgO    MgCO3   Al2O3  
Chromite         46.300   .....  20.000   4.000   .....   1.100   0.200   .....  11.500   .....  14.500
Gas(vol %)        .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Gas               .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Solids           47.439   .....  20.492   4.098   .....   1.127   0.205   .....  11.783   .....  14.857
Coal              0.311   .....   0.420   .....   .....   6.086   0.303   .....   0.236   .....   2.440
Quartzite         .....   .....   0.500   .....   .....  99.500   .....   .....   .....   .....   .....
Limestone         .....   .....   .....   .....   .....   4.200   .....  92.070   3.280   .....   0.450
Gas(vol %)        .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Gas               .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Slag              0.617   .....   0.389   .....   .....  36.287   8.390   .....  10.338   .....   7.581
Metal             .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....

                 MgCr2O4 MgAl2O4 FeCr2O4   MnO    Mn2O3   Mn3O4    TiO2    NiO      Cr    Cr3C2   Cr7C3  
Chromite          .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Gas(vol %)        .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Gas               .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Solids            .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Coal              .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Quartzite         .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Limestone         .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Gas(vol %)        .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Gas               .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Slag             10.963  24.591   0.003   .....   .....   .....   .....   .....   .....   .....   .....
Metal             .....   .....   .....   .....   .....   .....   .....   .....  19.366  16.362  25.139

                   CrSi     Fe     Fe3C   Fe3Si     Si     SiC      C       Mn      Ni      S       P    
Chromite          .....   .....   .....   .....   .....   .....   .....   .....   .....   0.010   0.017
Gas(vol %)        .....   .....   .....   .....   .....   .....   .....   .....   .....   0.233   0.409
Gas               .....   .....   .....   .....   .....   .....   .....   .....   .....   0.412   0.700
Solids            .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Coal              .....   .....   .....   .....   .....   .....  57.000   .....   .....   0.560   0.090
Quartzite         .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Limestone         .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Gas(vol %)        .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Gas               .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Slag              .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Metal             0.438  31.039   1.870   5.237   0.017   0.019   0.505   .....   .....   .....   0.000

                   FeS     CaS   Ca3P2O8    CO     CO2      H2     H2O      O2      N2      Ar      Mg   
Chromite          .....   .....   .....   .....   .....   .....   2.400   .....   .....   .....   .....
Gas(vol %)        .....   .....   .....   .....   .....   .....  99.358   .....   .....   .....   .....
Gas               .....   .....   .....   .....   .....   .....  98.888   .....   .....   .....   .....
Solids            .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Coal              .....   .....   .....   .....   .....   .....   2.900   .....   .....   .....   .....
Quartzite         .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Limestone         .....   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....
Gas(vol %)        .....   .....   .....  86.251   0.076  11.076   0.046   .....   2.292   .....   0.024
Gas               .....   .....   .....  95.961   0.134   0.889   0.033   .....   2.550   .....   0.023
Slag              .....   0.618   0.222   .....   .....   .....   .....   .....   .....   .....   .....
Metal             0.009   .....   .....   .....   .....   .....   .....   .....   .....   .....   .....

                   SiO     C3H8   C4H10    VOL.    CaF2    K2O     Na2O   Na2CO3 
Chromite          .....   .....   .....   .....   .....   .....   .....   .....
Gas(vol %)        .....   .....   .....   .....   .....   .....   .....   .....
Gas               .....   .....   .....   .....   .....   .....   .....   .....
Solids            .....   .....   .....   .....   .....   .....   .....   .....
Coal              .....   .....   .....  29.744   .....   .....   .....   .....
Quartzite         .....   .....   .....   .....   .....   .....   .....   .....
Limestone         .....   .....   .....   .....   .....   .....   .....   .....
Gas(vol %)        0.234   .....   .....   .....   .....   .....   .....   .....
Gas               0.411   .....   .....   .....   .....   .....   .....   .....
Slag              .....   .....   .....   .....   .....   .....   .....   .....
Metal             .....   .....   .....   .....   .....   .....   .....   .....

(MASS %)
                    Al      Ar      C       Ca      Cr      F       Fe      H       K       Mg      Mn   
Total feed        7.672   .....   .....   0.143  31.670   .....  18.338   0.268   .....   6.934   .....
Gas               .....   .....   .....   .....   .....   .....   .....  11.065   .....   .....   .....
Total feed        0.685   .....  36.982   6.250   0.106   .....   0.293   0.710   .....   0.401   .....
Gas               .....   .....  41.186   .....   .....   .....   .....   0.891   .....   0.023   .....
Slag             13.340   .....   .....   6.426   6.353   .....   0.303   .....   .....  11.822   .....
Metal             .....   .....   5.083   .....  56.703   .....  37.274   .....   .....   .....   .....

                    N       Na      Ni      O       P       S       Si      Ti   
Total feed        .....   .....   .....  34.433   0.017   0.010   0.514   .....
Gas               .....   .....   .....  87.822   0.701   0.412   .....   .....
Total feed        2.032   .....   .....  34.973   0.045   0.280  17.244   .....
Gas               2.550   .....   .....  55.089   .....   .....   0.262   .....
Slag              .....   .....   .....  44.476   0.044   0.274  16.961   .....
Metal             .....   .....   .....   .....   0.000   0.003   0.935   .....


PRODUCTS 1       Gas      Dust     Solids     Slag     Metal     Matte    
    Al:        .....     .....  100.000%     .....     .....     .....
    Ca:        .....     .....  100.000%     .....     .....     .....
    Cr:        .....     .....  100.000%     .....     .....     .....
    Fe:        .....     .....  100.000%     .....     .....     .....
    H :     100.000%     .....     .....     .....     .....     .....
    Mg:        .....     .....  100.000%     .....     .....     .....
    O :       6.187%     .....   93.813%     .....     .....     .....
    P :     100.000%     .....     .....     .....     .....     .....
    S :     100.000%     .....     .....     .....     .....     .....
    Si:        .....     .....  100.000%     .....     .....     .....

PRODUCTS 2       Gas      Dust     Solids     Slag     Metal     Matte    
    Al:        .....     .....     .....  100.000%     .....     .....
    C :      88.735%     .....     .....     .....   11.265%     .....
    Ca:        .....     .....     .....  100.000%     .....     .....
    Cr:        .....     .....     .....   12.130%   87.870%     .....
    Fe:        .....     .....     .....    0.993%   99.007%     .....
    H :     100.000%     .....     .....     .....     .....     .....
    Mg:       0.153%     .....     .....   99.847%     .....     .....
    N :     100.000%     .....     .....     .....     .....     .....
    O :      49.428%     .....     .....   50.572%     .....     .....
    P :        .....     .....     .....   99.667%    0.333%     .....
    S :        .....     .....     .....   99.015%    0.985%     .....
    Si:       1.151%     .....     .....   94.615%    4.234%     .....

(Per hour of operation)

Coal                  0.0300 t     @ R    70.00 / t   =   R      2.10
Chromite              0.1000 t     @ R   100.00 / t   =   R     10.00
Quartzite             0.0200 t     @ R    50.00 / t   =   R      1.00
Limestone             0.0100 t     @ R    50.00 / t   =   R      0.50
Electricity            0.157 MWh   @ R    90.00 / MWh =   R     14.12

TOTAL:                                                    R     27.72

PYROSIM  v1.20         Copyright 1988-92  Rodney Jones, Mintek            01-SEP-92

Pyrosim User's Manual
Copyright © 1996-97 Rodney Jones,
19 June 2001

Pyrometallurgy Division, Mintek,
200 Hans Strijdom Drive, Randburg, 2125, South Africa
Private Bag X3015, Randburg, 2125, South Africa.

Phone: +27 (11) 709-4602
Fax: +27 (11) 793-6241