Thermodynamic modelling of liquid slag-matte-metal equilibria applied to the simulation of the Peirce-Smith converter
Denis Shishin1, Taufiq Hidayat1, Sergei Decterov2, Evgueni Jak1
1PYROSEARCH, Pyrometallurgy Research Center, School of Chemical Engineering, The University of Queensland, Brisbane, Queensland, 4072, Australia.
2Centre for Research in Computational Thermochemistry (CRCT), École Polytechnique, Montréal, Québec, Canada
Keywords: copper production, slag, matte, liquid copper, thermodynamic modelling, Peirce- Smith converter, liquidus, distribution of elements
Abstract
Computer simulation plays an increasingly important role in improving the environmental and economic performance of pyrometallurgical extraction processes. The thermodynamic description of the chemical systems involved is at the core of such advanced simulation software.
A thermodynamic database has been developed to describe the phase relations and chemical reactions in the Al–Ca–Cu–Fe–Mg–O–S–Si chemical system with support from the leading copper producers. The database contains model parameters for gas, liquid slag, liquid matte and metal, spinel and numerous solid phases. Models based on the Modified Quasichemical Formalism were used for the slag, matte and liquid metal. The internal consistency of the database provides accurate and reliable predictions outside of the usual operating conditions. The development of the database was closely integrated with the experimental studies of this chemical system. The database works in the environment of FactSage software. The application of thermodynamic modelling is illustrated by the example of the Peirce-Smith converter.
Introduction
The overall economic efficiency and environmental performance of the copper plant depend on numerous factors. The examples of variable process parameters are temperature, oxygen enrichment of the blow, amount of fuel, internal recycle of slags and dusts, target slag composition (Fe/SiO2), final matte grade during smelting and converting and many others. The optimization of the process can be achieved by the implementation of the computer models of the process, which, in turn, require deep understanding of chemistry involved. The development of large thermodynamic databases is helps to collect and systematically evaluate the experimental information on the chemical systems, important for the industry. In copper industry, the core chemical system is Al–Ca–Cu–Fe–Mg–O–S–Si, plus major impurities Pb, Ni, plus minor elements As, Sb, Bi, Zn, Sn, Au, Ag. The most important phases are gas, liquid matte, metal and slag, spinel solid solution, and numerous solid silicates, oxides and sulfides. The recent experimental and modelling project aimed at addition of Cu and S to the core chemical system has been undertaken by Pyrosearch (The University of Queensland) in collaboration with CRCT (Ecole Polytechnique de Montreal). The introduction of Pb and minor elements to the copper database is currently in progress. The thermodynamic databases are developed within the environment of FactSage software [1].
In the thermodynamic modelling, all available thermodynamic and phase diagram data are evaluated simultaneously in order to obtain one set of model equations for the Gibbs energies of
Advances in Molten Slags, Fluxes, and Salts: Proceedings of The 10th International Conference on Molten Slags, Fluxes and Salts (MOLTEN16) Edited by: Ramana G. Reddy, Pinakin Chaubal, P. Chris Pistorius, and Uday Pal TMS (The Minerals, Metals & Materials Society), 2016
all phases as functions of temperature and composition. Recent advances in thermodynamic modeling of the subsystems of the core system are: Cu–O and Cu–O–S [2], Fe–O [3], Fe–O–S [4], Cu–Fe–O [5], Cu–Fe–O–S [6], Al–Fe–O [7], Ca–Fe–O [8], Fe–Si–O [9], Cu–Si–O, Cu–Ca–
O, Cu–Ca–O–Si [10], Ca–Fe–Si–O [11]. The results of project on the core chemical system are summarized in two PhD theses [12, 13].
In the present article the application of the database is demonstrated on the example of the simulation of Peirce-Smith converter.
1. Thermodynamic database
The following section contains brief descriptions of the thermodynamic models used for matte/metal, slag and spinel phases. More details on the model parameters are available elsewhere [12]. The gas phase is modeled as an ideal solution. The properties of the gaseous species were taken from the standard FactSage database [1].
1.1. Matte
Liquid matte and metal are modeled as one solution:
(
Cu , Cu , Fe , Fe , O, SI II II III)
(1) In this model, species are not charged and placed on one sublattice, so no condition of electroneutrality is imposed. This allows the model for the liquid phase to cover the whole compositional range inside the Cu–Fe–O–S system from metals to oxides (in absence of SiO2), to sulfides, to non-metals. This way, the deviation of Cu2S–FeS stoichiometry of mattes is taken into account. The very strong interaction between metals and nonmetals creates short range ordering (SRO) between first nearest neighbors (FNN), which affects the entropy of mixing. This effect is modeled using the Modified Quasichemical Formalism in pair approximation [14, 15].The meaning of numbers I, II and III is close to the concept of valence. They reflect the fact that in the MQM species have different coordination numbers. The ratio of coordination numbers determines the composition of maximum short range ordering (SRO) between a pair of species:
CuI:OII = 2:1, FeII:SII = 1:1, FeIII:OII = 2:3, etc. The absolute values of coordination numbers have minor effect, compared to their ratio. FeIII and CuII appear only at high oxygen partial pressure, in the order of 10-7 atm and 0.21 atm at 1200 °C, respectively. Under conditions of pyrometallurgical copper production, Cu and Fe in matte and in metal exist almost exclusively as CuI and FeII.
1.2. Slag
Compared to mattes, slags have more distinct ionic characteristics. With the introduction of silica into metal oxide melt, the structure of the liquid solution becomes more complicated. Metals surround themselves by oxygen, but at the same time there is a strong tendency to get Si4+
cations second next to basic cations (Fe2+, Ca2+ etc.):
FeSi/OO
(Fe -O-Fe)+(Si-O-Si)=2(Fe -O-Si), ∆g (2)
In other words, slags exhibit a significant second nearest neighbor (SNN) short-range ordering (SRO) between basic cations and acidic Si4+ cations. The existing thermodynamic models are not able to model simultaneously FNN and SNN SRO for species in one sublattice. However, in case of slags it is not necessary, because the range of nonstoichiometry towards metal and toward
nonmetal is usually very small. Sulfur is soluble in slags, but to a relatively small extend. Thus, slag is modeled using separate solution from matte, where cations and anions species are placed on separate sublattices:
(
Al , Ca , Cu , Fe , Fe , Mg , Si3+ 2+ 1+ 2+ 3+ 2+ 4+)(
O , S2− 2−)
(3) In this way, the magnitude of FNN SRO is represented by the Gibbs energies of the slag solution end-members: oxides CaO, FeO, SiO2 and sulfides CaS, Cu2S, FeS, etc. These Gibbs energies are the most important model parameters. To take into account the effect of SNN SRO on the thermodynamic properties of slag liquid, the Modified Quasichemical Formalism in quadruplet approximation was used [16].1.3. Spinel
The spinel solution, extended during the recent project, is represented by the formula
3 +2 +2 +3 +2 tetr 3 +2 +2 +2 +3 +2 oct -2
2 4
(Al ,Cu ,Fe ,Fe , Mg )+ [Al ,Ca ,Cu ,Fe ,Fe ,Mg ,Va] O+ (4) The model is developed within the Compound Energy Formalism (CEF) [17, 18]. According to CEF, 35 Gibbs energy expressions (Gij) are required for the pseudo components of this spinel.
They are related to those of real spinels, but they should not be confused. The procedure, developed by Decterov et al. [19] uses linear combinations of Gij to minimize the number adjustable of model parameters. The reader is referred to Shishin (2013) [12] for the detailed description of the spinel model.
2. Slag-matte equilibrium
The following section contains the description of the slag-matte equilibrium which is of primary importance for the copper smelting and converting. For the sake of simplicity, all calculations are performed within the Cu–Fe–O–S–Si system. The thermodynamic database can be used for the prediction of the effect of Al, Ca and Mg on the slag-matte equilibrium. In the Cu–Fe–O–S–Si system, 5 + 2 = 7 degrees of freedom must be fixed to set the equilibrium. The conventional selection of the degrees of freedom is 1) temperature 2) total pressure (usually 1 atm) 3) presence of slag phase 4) presence of matte phase 5) saturation with SiO2, or with spinel, or Fe/SiO2 in slag; first two are limiting cases 6) presence of metal phase (as in the direct-to-blister process) or fixed P(SO2) 7) final wt% Cu in matte, or wt%Fe in matte, or P(O2). The last degree of freedom serves as an X-axis in Figure 1, while other 6 are fixed. They demonstrate the model predictions of the slag-matte equilibrium at total pressure of 1 atm, 1200 °C, SiO2 or spinel saturation, P(SO2) = 0.16 atm as a function of matte grade. These conditions are close to those during the slag blow stage in the Peirce-Smith copper converter. The model calculations are in agreement with the available experimental data as shown in Shishin (2013) [12].
Copper industry is particularly interested in the equilibrium copper content of slag (Figure 1a), because it gives the lower limit of copper losses. In practice, copper content of slag is always higher than equilibrium value due to the physical entrainment of matte into the slag.
Nevertheless, the absence/existence of the maximum on the wt%Cu in slag vs wt% Cu in matte curve remains the object of debate among metallurgists. Previous FactSage model by Decterov and Pelton (1999) [20] and MPE model by Chen and Jahanshahi (2013) [21] give the monotonous rise of wt% Cu in slag vs matte grade. The group of Yazawa in Tohoku University
long believed in the existence of the maximum and explained it using the concept of sulfidic solubility of copper in slag [22]. This was supported by several authors [23, 24]. Some researchers did not observe the maximum [25].
In the updated database, sulfur in slag behaves as anion and forms quadruplets with Fe2+ and Cu+ cations and O2-. Thus, the sulfur content in slag and copper content in slag are correlated, and related to the Fe/SiO2 in slag. The quadruplet model makes it possible to describe the maximum, reported for equilibrium with liquid copper [26, 27]. The experimental work is currently under way in Pyrosearch to confirm the presence of the maximum at higher P(SO2).
3. Peirce-Smith process simulation
3.1. Simulation formulation
Peirce-Smith is the batch process [28], which mostly consists of reaction of between matte and oxygen aided by fluxing. The reactions may be represented as:
2 2 2 2
FeS (matte) + 3/2O + SiO =FeOx ⋅xSiO (in slag)+ SO ↑(slag blow) (5) And
2 2 2
Cu S (matte) + O = 2Cu (liquid) + SO ↑(copper blow) (6) The connection between thermodynamics and time is reached through division of the process into equilibrium steps. At each step, the portion of the blow participates in the reaction with condensed phases. The gas phase is removed from the reaction zone and condensed phases proceed to the next iteration. In this sense the procedure is similar to that of Pengfu (2007) [29].
Advanced thermodynamic database allows to take into account mass and energy balance at each iteration simultaneously using the Gibbs energy minimization software based on FactSage. Two external factors: the rate of heat loss to the environment and furnace heat capacity are treated as process parameters. To the first approximation, they are considered to be independent from temperature. The third process parameter is oxygen efficiency. Due to kinetic reasons, only a portion of oxygen participates in chemical reactions. At the same time, “inert” oxygen is assumed to participate in heat balance: some heat is required to raise its temperature. The last process parameter is matte entrainment in slag. It shows the mass of matte that should be tapped together with each 100 g of slag during the skimming. The level of entrainment depends on many factors, such as viscosity of slag, settling time and skimming procedure. In the present study it was assumed to be constant. The list of the process parameters is given in Table 1.
3.2. Results of the simulation
The process starts when a large amount of matte together with reverts is charged in the converter and blowing starts. The high copper slag from anode furnace or from over oxidized blister copper is often charged at some point during the slag blow. At this stage, it is acceptable to add reverts with significant iron content. The amount of input flux can be roughly calculated from the knowledge of starting matte grade, desirable final matte grade and mass of matte. The target Fe/SiO2 ratio in the slag is 1.5 – 2.0 depending on the final matte grade. Figure 2 shows slag liquidus in equilibrium with matte of different grades. It is evident from Figure 2 that higher matte grades require higher temperature in order to keep the slag liquid. The amounts of phases are plotted in Figure 3.
(a)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0 10 20 30 40 50 60 70 80
Weight%Cuinslag
Weight % Cu in matte Model, Spinel saturation Model, SiO saturation
(b)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
40 50 60 70 80
Weight%Sinslag
Weight % Cu in matte
(c)
1.0 1.5 2.0 2.5 3.0
40 50 60 70 80
Fe/SiO2inslag,wt/wt
Weight % Cu in matte
(d)
20 21 22 23 24 25 26
40 50 60 70 80
Weight%Sinmatte
Weight % Cu in matte
(e)
0 1 2 3 4 5
40 50 60 70 80
Weight%Oinmatte
Weight % Cu in matte
(f)
0 5 10 15 20 25 30 35
40 50 60 70 80
Weight%Feinmatte
Weight % Cu in matte
(g)
-4.0 -3.5 -3.0 -2.5 -2.0
40 50 60 70 80
Log10[P(S2),atm]
Weight % Cu in matte
(h)
-9.0 -8.8 -8.6 -8.4 -8.2 -8.0 -7.8 -7.6
40 50 60 70 80
Log10[P(O2),atm]
Weight % Cu in matte
2
Figure 1. Cu–Fe–O–S–Si system: Slag, matte, spinel or SiO2 equilibrium at P(SO2) = 0.16 atm and 1200 °C.
The starting temperature of the furnace is assumed to be 1100 °C, but the charge of high- temperature matte (see Table 2) from the smelting furnace causes the rise in temperature. Reverts and fluxes cool down the furnace (see Table 2). The cumulative effect is calculated by the model (Figure 4) with furnace heat capacity taken into the account.
When the blow starts, iron sulfide from matte reacts with oxygen to form spinel. Spinel is shown by purple patch in Figure 3. This exothermic reaction causes the rise of the temperature (Figure 4). The steepness of the rise is negatively correlated with the rate of heat loss to the environment and the heat capacity of the furnace. When temperature rises to the certain level, determined by solidus in Figure 2, spinel starts to react with silica flux to form liquid slag. Silica is show by light blue patch and liquid slag is shown by red patch in Figure 3.
After a significant amount of slag is accumulated, it is skimmed and replaced by the new portion of matte and flux (Table 2). The level of acceptable slag accumulation is determined by the geometry of the furnace. Large amounts of slag cause splashing. The ladle which collects the slag was assumed have 30 tons maximum capacity.
According to the model, the equilibrium concentration of chemically dissolved copper is always below 2%. (Figure 5). Due to the matte entrainment, it is substantially higher, 4.0-5.5% (see Table 2).
The procedure of accumulation and skimming of slag is repeated several times, while the overall matte grade increases (Figure 6). The goal is to remove iron from matte as much as possible during the slag blow, because during the copper blow all iron will convert to solid spinel causing problematic deposits. In the simulation, it is assumed that all the remaining slag is removed at Skim slag 4.
The oxygen partial pressure rises and sulfur partial pressure falls during the process (Figure 7).
Partial pressure of SO2 was calculated to be 0.15-0.20 atm for the chosen oxygen enrichment of the blow (25 vol% O2).
During the copper blow, it is not desirable to load any reverts containing iron. The temperature is kept lower than in the end of slag blow to prevent the excessive wear of refractory and tuyeres [28]. The cooling is achieved by the addition of high-copper reverts. The simulation shows that, once all iron is removed from matte and oxygen starts oxidize Cu2S, the reaction becomes much less exothermic. The converting continues until no matte is left. It is not desirable to further oxidize copper and form a high-copper slag due to its high corrosiveness and decrease in copper yield. Figure 10 shows the overblow and the disappearance of spinel and formation of high- copper slag after 424 minutes. This slag is to be collected and recycled.
Table 1. The list of process parameters used in the simulation of the Peirce-Smith copper converter.
Process parameters Slag blow 1-4 Copper blow
Blow rate, kNm3·hr-1 [28] 37 40
Oxygen enrichment, vol% O2 [28] 25 25
Matte entrainment, % 5 Not applicable
Oxygen efficiency, % 90 80
Rate of heat loss, MW 2.0 2.0
Furnace heat capacity, MJ·K-1 370 370
Table 2. The list of input and output of the Peirce-Smith copper converter. Output temperatures and compositions are the result of the simulation.
Time, min
Temperature,
°C Charge
Mass,
tonne wt%Cu wt%Fe wt%S wt%O wt%SiO2
0 25 Silica flux 9.0 0.0 1.0 0.0 0.4 94.6
0 1200 Anode slag 30.0 42.0 26.0 0.0 15.0 17.0
0 1200 Matte 200.0 62.0 12.9 24.8 0.2 0.1
0 25 High Fe reverts 15.0 50.0 20.0 15.0 5.0 10.0
0 25 Reverts 5.0 100.0 0.0 0.0 0.0 0.0
44 1171 Skim slag 1 -30.0 4.0 49.2 1.4 15.0 30.4
49 1210 Matte 30.0 62.0 14.0 23.8 0.1 0.1
49 25 Silica flux 5.0 1.0 0.5 0.0 0.4 94.6
84 1209 Skim slag 2 -30.0 4.3 48.5 1.3 14.8 31.1
87 1200 Matte 30.0 62.0 14.0 23.8 0.1 0.1
87 25 Silica flux 4.0 0.0 0.5 0.0 0.2 94.6
114 1232 Skim slag 3 -15.0 4.5 47.2 1.2 14.4 32.7
115 25 Silica flux 4.0 0.0 1.0 0.0 0.4 94.6
148 1263 Skim slag 4 -14.2 5.5 47.3 1.1 14.8 31.3
154 25 Solid blister 30.0 100.0 0.0 0.0 0.0 0.0
170 25 Anode scrap 10.0 100.0 0.0 0.0 0.0 0.0
178 25 White metal 10.0 78.0 1.0 19.5 0.5 1.0
220 25 Anode scrap 10.0 100.0 0.0 0.0 0.0 0.0
330 25 Solid blister 10.0 98.0 1.0 0.5 0.5 0.0
390 25 Solid blister 10.0 98.0 1.0 0.5 0.5 0.0
432 1191 Skim High-Cu slag -10.7 58.7 23.3 0.0 17.0 0.9
432 1191 Skim blister Cu -258.6 99.2 0.0 0.0 0.8 0.0
4. Conclusion and further development
The multicomponent thermodynamic database has been developed for applications in pyrometallurgy of copper. It covers the core chemical system that is necessary to predict phase equilibria, chemical reactions, energy balance and the distribution of elements in copper making processes. This is illustrated by the example of simulation of the Peirce-Smith converter.
Thermodynamic models used in the present study are flexible and can be used to extend the database further. In particular, lead and minor elements can be added to the database. These projects are currently under way in Pyrosearch.
1100 1150 1200 1250 1300 1350
P(SO2) = 0.15 atm, 55wt.%Cu in matte P(SO2) = 0.15 atm, 70wt.%Cu in matte P(SO2) = 0.15 atm, 78wt.%Cu in matte P(SO2) = 0.15 atm, 80wt.%Cu in matte
Wustite
Spinel Trid
ymite
Fe/SiO2, wt/wt
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Figure 2. Calculated liquidus of the slag in equilibrium with matte of different grades (55, 70, 78 and 80).
Symbols show the conditions at Slag blow 4 (115 – 148 min): squares are bulk composition of slag+solids, circles are compositions of liquid slag. The color of symbols correspond to matte grade.
Skim slag 1
Matte Silica flux Skim slag 2
Matte Silica flux Skim slag 3
Silica flux Skim slag 4
Solid blister Anode scrap
White metal
Anode scrap Solid blister Solid blister
0 50 100 150 200 250 300
0 20 40 58 78 96 116 134 154 172 192 212 232 252 272 292 312 332 352 372 392 412 432 Blister copper Matte Slag Spinel SiO2
Figure 3. The amounts of condensed phases in the Peirce-Smith copper converter as a function of time.
Results of the simulation.
Temperature°C Output gas, kNm3/hr
0 5 10 15 20 25 30 35 40 45
1120 1140 1160 1180 1200 1220 1240 1260 1280 1300
0 50 100 150 200 250 300 350 400
Rateoftheoffgas,kNm3/hr
Temperature,°C
Time, min
Figure 4. Temperature and flow rate of off gas in the Peirce-Smith copper converter as a function of time.
Results of the simulation.
wt% Cu Fe/SiO2
0 5 10 15 20 25
0 1 2 3 4 5
0 50 100 150 200 250 300 350 400
Fe/SiO2inslag,wt/wt
wt%Cuinliquidslag
Time, min
Figure 5. Composition of liquid slag in the Peirce-Smith copper converter as a function of time. Results of the simulation . Matte entrainment, solid SiO2 and spinel are not included.
wt% Cu
wt.%S
wt.%Fe
wt.%O
0 5 10 15 20 25
60 65 70 75 80 85
0 50 100 150 200 250 300 350 400
wt%Fe,wt%S,wt%Oinmatte
wt%Cuinmatte
Time, min
Figure 6. Composition of the matte phase in the Peirce-Smith copper converter as a function of time. Results of the simulation.
log10[P(O2),atm]
log10[P(S2), atm]
P(SO2), atm
0 0.1 0.2 0.3 0.4
-10 -9 -8 -7 -6 -5 -4 -3 -2
0 50 100 150 200 250 300 350 400
P(SO2),atm
log10[P(O2),atm],log10[P(S2),atm]
Time, min
Figure 7. Equilibrium partial pressures of O2, S2 and SO2 in the Peirce-Smith copper converter as a function of time. Results of the simulation. Please, note that the volume fraction of O2 in the offgas is much higher than equilibrium value when oxygen efficiency is less than 100%.
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