Thermodynamic Modeling and Research for Processing Complex Concentrate Blends in Custom Copper Smelters for Maximum Revenue

Abstract

Custom copper smelters, which are dependent on purchased concentrates, are facing increasing economic pressures amid falling treatment and refining fees. With the declining availability of high-grade, low-impurity concentrates, copper demand is expected to surge to support the transition to renewable energy. This study, which is based on recent observations of Chinese custom smelters, examines their strategies to address the challenge of purchasing concentrates at record-low treatment and refining charges. By investing in slag flotation technology, smelters can enhance copper, gold, and silver recovery. By blending high-grade and low-grade concentrates, they can capitalize on the gap between the recoverable and payable metals, which are often referred to as “free metals”, while also benefiting from byproducts, mainly sulfuric acid. While this approach offers economic opportunities, it introduces operational complexities. To mitigate these, laboratory testing, combined with advanced digital predictive tools based on thermodynamics, is crucial. This study demonstrates the use of thermodynamic models supported by experimental work for analyzing furnace operations. FactSage^® software and a custom database are employed to define the operating window of two common flowsheets: (1) flash smelting + flash converting and (2) bottom-blown smelting + bottom-blowing converting.

1. Introduction

Custom smelters purchase concentrates from miners, paying for the contained copper, gold, and silver while charging penalties for impurities (As, F, Bi, Pb, Zn, Hg, Ni, Co, and Cd). Additionally, smelters impose treatment charges and refining charges (TC/RC) on miners, which are fees paid for converting copper concentrate into copper cathode, representing a key revenue source for smelters. The sale and purchase of copper concentrates on the international market are driven by the benchmark TC/RCs, which are negotiated annually between the major miner and smelter. Historically, the benchmark was set by Escondida or Freeport Indonesia with the Japanese smelters. During the last 20 years, as the dynamic of the market has shifted toward China, the benchmark has been dominated by Freeport and Antofagasta Minerals with the major Chinese smelters. Due to the low supply of copper concentrates, the spot TC/RCs have been declining, as illustrated in Figure 1, reaching zero values. A meaningful increase in future TC/RCs is unlikely due to a shortage of new mining projects to match recent smelter expansions in China [1]. Furthermore, countries producing concentrates may also restrict their export to secure access to copper as a critical metal for energy transition. China operates over 44 custom copper smelters, primarily processing concentrates from Chile, Peru, Kazakhstan, Mongolia, Mexico, and Panama. According to the World Integrated Trade Solution (WITS) website, China imported over 27 million tonnes of copper ores and concentrates in 2023, accounting for a substantial 69% share among countries importing these materials. As ore grades of deposits across the world have been decreasing, the resulting concentrates have also been exhibiting lower grades with higher impurity levels (As, Bi, Sb, Pb, Zn, etc.). China has access to significant quantities of low-grade concentrates, but their processing is economically challenging without blending them with a higher-grade material.

Thus, a trend has emerged in which Chinese custom smelters purchase concentrates from 10 to 20 different sources to create an optimal feed blend for processing. They increasingly rely on other revenue streams, including “free metal”, which arises from the difference between the recovered metal and the metal paid for in the concentrate and is calculated as follows:

$$\mathrm{Free} \mathrm{Metal}=\mathrm{Recovered} \mathrm{Metal}-\mathrm{Paid} \mathrm{Metal}$$

(1)

Recent observations of Chinese smelters indicate that those operating flash furnaces target a feed blend close to 25 wt.% Cu [2], while those working with bath-type furnaces (bottom-blown, side-blown, or TSL) tend to target lower grades, around 21 wt.% Cu. For flash smelting, the stability and temperature of the flame largely depend on the concentrate grade [3]. This study provides the economic justification for custom smelters to incorporate more low-grade materials into their flowsheets, along with a technical analysis of process conditions.

In the future, more smelters are expected to adopt a market-driven, value-added blending strategy to maximize revenue from metal production. This approach requires flexible operating strategies supported by feed-forward control and adjustable process conditions. In such a dynamic environment, advanced computational tools are crucial for maintaining operational stability. Two primary philosophies are emerging to address this need. The first involves leveraging vast amounts of plant-generated data to train computer models, potentially enhanced by artificial intelligence. Alternatively, a more traditional approach combines laboratory-controlled experiments with fundamental thermodynamic principles to create predictive tools capable of operating outside normal conditions. While the second approach is not entirely new, recent advancements in large thermodynamic databases and software like FactSage 8.3^® [4] have made it more practical. To capitalize on this, a collaborative research program was initiated in 2014 between the Pyrometallurgy Innovation Laboratory and a consortium of copper producers, including Rio Tinto. This program has yielded significant results, enabling predictions for up to 20 elements, as demonstrated in this study.

Two typical smelter types, bottom-blown and flash, are analyzed, considering their kinetic differences. Thermodynamic predictions are validated through a multicomponent chemical system experimental study, mainly focusing on the solubility of copper in slag, the Fe/SiO₂ ratio for sub-liquidus slags, and the distribution coefficients of gold and silver.

2. Materials and Methods

2.1. Concentrate Evaluation

For custom smelters, the price of concentrate is the sum of the values of the payable metals (Cu, Au, and Ag) minus the sum of the deductions, such as TC/RCs and penalties. Custom smelters have four major revenue streams: TC/RCs, the premium for metals, “free metals”, and sulfuric acid. Treatment charges are calculated per tonne of dry concentrate, while refining charges are calculated based on the payable amount of copper. Figure 2 shows a typical payable curve (in %) as a function of concentrate grade (in wt. %) [5]. The curve is non-linear; from the maximum of 96.75% payable, it decreases only slightly to 96.65% at 30 wt.% Cu, below which the drop rate increases. The recovery curve is also shown in Figure 2 and is based on a smelter survey and calculations of the present study, which will be demonstrated further. The difference between recovery and payables creates the “free metal” source of revenue.

The mineralogical composition of lower-grade concentrates is dominated by chalcopyrite (CuFeS₂) and pyrite (FeS₂), while the higher-grade concentrates contain bornite (Cu₅FeS₄), chalcocite (Cu₂S), and covellite (CuS). As a result, higher-grade concentrates often have a higher ratio of Cu/S compared to lower-grade concentrates. In the context of flash smelting, the Cu/S ratio is a crucial parameter influencing flame temperature [3]. However, exceptions arise when low-grade concentrates, despite their high Cu/S ratios, contain substantial amounts of gangue materials, like SiO₂, Al₂O₃, CaO, and MgO. For custom smelters, the primary economic value lies in processing challenging low-grade concentrates rich in impurities and valuable metals, such as Ag, Au, Pt, and Pd. This area is currently the focus of significant research efforts.

To demonstrate the economic value of treating lower-grade concentrates, the following two process flowsheets of copper making were considered:

Case 1: flash smelting + flash converting (double flash);

Case 2: bottom-blowing smelting + bottom-blowing converting.

Flash smelting furnaces are most valued for their high throughput, but they are more sensitive to the quality of the concentrate, such as moisture, sulfur content, particle size distribution, etc. We will consider a smelter with a capacity for 230 t/h of dry concentrate and up to 290 t/h of combined solid feed. Case 2 is the process consisting of a bottom-blown smelter and a bottom-blown converter, representing bath-type smelter operations. These furnaces do not reach such high throughputs but are tolerant to moisture and deviations in composition. The smelter from Case 2 has a design capacity of 150 t/h of dry concentrate and up to 190 t/h of combined solid feed. To simplify the analysis, let us assume that no investment has been allocated to the dust leaching for the removal of harmful elements, such As, Bi, and Sb, from the flue dust. All the generated dust is recycled back to the furnace, and the dust collection is 100% efficient. At the same time, both are invested in the facility of slow slag cooling, crushing, and flotation, which significantly increases the recovery of Cu, Au, and Ag. Slag concentrate containing recovered Cu, Ag, and Au is sent back to the smelting, while the rest is discarded. These facilities are assumed to operate with the same efficiency in both cases. Thus, in both cases, there are only three outputs: off-gas free from flue dust, discard slag, and anode copper. Valuable and harmful metals partition amount the latter two streams.

To further simplify the analysis, let us assume that four concentrates are available on the market. Their compositions are shown in

Table 1. Compositions of concentrates used in the present study and parameters to estimate their market price.

Dry Composition	Cu, wt%	Ag ppm	Au ppm	Fe, wt%	O, wt%	S, wt%	SiO2, wt%	Al2O3, wt%	CaO, wt%	MgO, wt%	+H2O, wt%
Concentrate 1 (blend for Case 1)	25	40	4	28.0	0.1	34	8	2.5	0.5	1.0	8.0
Concentrate 2	18	70	80	30.0	0.3	24	18	4.5	2.0	2.0	8.0
Concentrate 3	20	3300	3	20.0	0.1	31	7	0.5	1.0	0.5	8.0
Concentrate 4	18	30	3	34.5	0.1	38	7	1.5	0.5	0.3	8.0
Blend for Case 2	21	144	26.5	29.9	0.2	32	10.7	2.8	1.0	1.1	8.0
	USD/t	USD/g	USD/g
Price	+9800	+0.8	+75
Dry Composition (continued)	Pb, wt%	Zn, wt%	Ni, wt%	As, wt%	Sb, wt%	Bi, wt%	Cd, wt%	F, wt%	Hg, wt%	Se, wt%	Price USD/t
Concentrate 1 (blend for Case 1)	0.08	0.5	0.01	0.30	0.02	0.03	0.001	0.01	0.0003	0.005	2650
Concentrate 2	0.30	0.5	0.2	0.05	0.02	0.02	0.003	0.05	0.0003	0.008	7551
Concentrate 3	6.50	8.5	0.01	2.40	1.50	0.30	0.003	0.01	0.0024	0.008	3940
Concentrate 4	0.01	0.1	0.03	0.02	0.00	0.01	0.001	0.01	0.0004	0.017	1873
Blend for Case 2	0.32	0.6	0.07	0.22	0.06	0.03	0.002	0.02	0.0004	0.009	3972
Penalty, USD/0.1 wt. %	−0.3	−0.3	−1.0	−2/−5	−15	−25	−30	−15	−3000	−15
Penalty limit, wt. %	1	3	0.5	0.2/1.0	0.05	0.05	0.03	0.03	0.0005	0.03

. Concentrate 1 represents average-quality concentrate. Concentrate 2 has a very high content of gold in ppm, but a low content of copper. It approximately represents the concentrates available in Western Australia. Concentrate 3 has a high content of silver but also high concentrations of impurities, such as Pb, Zn, As, Sb, and Bi. These types are available in Peru. The last concentrate, Concentrate 4, is neither rich in copper nor in gold or silver, but it is very clean of the same impurities and based on some compositions reported in Pakistan.

The procurement team is given the task of maximizing the profit that can be generated per year from processing these concentrates. First, it is necessary to estimate the price of the concentrates. Copper, gold, and silver contribute positively to the price. For instance, copper from Concentrate 1 contributes 1 tonne × 25 wt. % × 9800 USD/tonne × 96%Payable = 2352 USD/tonne. A very important parameter is %Payable, which is established through negotiations on the market. Examples of payable functions for copper and gold are shown in Figure 2 [5,6]. For silver, the common practice is to use only 90%Payable on concentrations over 30 ppm [5,6]. Many other metals have negative contributions to the price of the concentrate, in recognition of the fact that resources are necessary for their safe utilization. These often kick off starting from a certain concentration and then increase for every 0.1 wt. % in the concentrate, as shown in the last two rows of Table 1 [7]. For instance, the contribution of As to the price of Concentrate 3 is 1 tonne × 2.4/0.1 wt. %/wt. % × (−5) USD/tonne = − 120 USD/tonne. Prices calculated using this procedure are given in the last column of Table 1.

2.2. Thermodynamic Calculations

Equilibrium calculations are performed using FactSage 8.3^® software [4] and complemented by non-thermodynamic factors that represent the main potential deviations of furnaces from the equilibrium conditions. The thermodynamic database developed by the authors is used [8,9]. It combines experimental phase equilibria studies, calorimetric measurements, activity data, and distribution among phases for all elements in Table 1, except Cd, F, Hg, and Se. Predictions of copper solubility in slag were modeled previously by the authors [10,11]. The models for the distribution of gold and silver among slag and matte were developed, as well [12]. The database is gradually improved by the iterative process of targeted experiments and reassessments of model parameters. A thermodynamic model for the liquid slag has been developed using modified quasichemical formalism in quadruplet approximation using two sublattices, as follows [13]:

Slag: (Cu⁺¹, Fe⁺², Fe⁺³, Si⁺⁴, Al⁺³, Ca⁺², Mg⁺², Pb⁺², Zn⁺², Ni⁺², Sb⁺³, As⁺³, Bi⁺³, Ag⁺¹, Au⁺¹)(O⁻², S⁻²)

(2)

Liquid solution covering matte and metallic phases was developed using the combination of modified quasichemical formalism in pair approximation [14] and ideal mixing Bragg–Williams models.

Liquid matte/metal: (Cu^I, Cu^II, Fe^II, Fe^III, Pb^II, Zn^II, Ni^II, Sb^III, As^III, Bi^III, Ag^I, Au^I, O^II, S^II)

(3)

Spinel solid solution was developed within the framework of compound energy formalism with two sublattices, as follows:

Spinel: [Cu⁺², Fe⁺², Fe⁺³, Ni²⁺, Al⁺³, Mg⁺², Zn⁺²]^tetrahedral
[Cu⁺², Fe⁺², Fe⁺³, Ni²⁺, Al⁺³, Ca⁺², Mg⁺², Zn⁺², Vacancy⁰]₂^octohedralO₄, CEF

(4)

The approach to modeling process units deviating from equilibrium conditions has been described and tested in recent publications [15,16]. Process units are divided into equilibrium zones connected with streams of materials. Each stream contains information about the mass flow of elements and the enthalpy value. Enthalpy values are calculated by FactSage 8.3^® for all streams, including concentrates, fluxes, and other materials whose mineral (phase) compositions are predicted based on elemental composition. The energy balance in each zone is calculated simply as a difference between the output and input streams. User interface and operations with streams (dividing, combining, and transferring from one unit to another) are performed in Excel. A macro language built into Excel initiates FactSage^® calculations through the application programming interface of EquiSage.exe (Figure 3).

Non-thermodynamic factors are necessary to account for the fact that a portion of a stream may bypass the equilibrium zone without reacting. Unreactive portions are assumed to participate in energy balance but not in chemical equilibrium.

Process parameters used in the present study are collected in

Table 2. Summary of process parameters, targets,, and non-thermodynamic factors used for flowsheet modeling in this study.

Process Parameters	Case 1 Smelting	Case 1 Converting	Case 2 Smelting	Case 2 Converting
Furnace type	Flash	Flash	Bottom-Blown	Bottom-blown
Slag type	Fayalite	Cu2O-Calcium ferrite	Fayalite	Cu2O-Fayalite-based
Dry concentrate rate, t/h	230 [2]		130 [17]
Moisture in feed, t/h (%)	0.5 (0.2%) [18]	0.0	13 (8%) [19]	0.0
Feed temperature, °C	150	25	25	1200 [20]
Temperature in Reactor zone, °C	1300 [20]	1260 [20,21]	1250	1250 [20]
Temperature in Settler zone, °C	1250 [20]	1250 [20,21]	1200 [19]	1250 [20]
Oxygen enrichment in the blast, vol. %	85 [2]	85 [20]	68 [19]	25 [20]
Phase equilibria target	Fe/SiO2 in slag = 1.4 (~50 °C above liquidus) [22]	Fe/CaO in slag = 3.0 (~10 °C above liquidus) [22]	Fe/SiO2 in slag + solids = 1.55 (8% solids in slag) [19]	Fe/SiO2 in slag = 1.0 (10 °C above liquidus) [20]
Chemical target	70 wt% Cu in matte [20]	22 wt% Cu in slag [23]	74 wt% Cu in matte [24]	23 wt% Cu in slag [25]
Energy balance (−1 × Heat loss), MW	−30	−7	−15	−4
Non-thermodynamic factors
Oxygen efficiency, %	99	99	90	99
Volatile coal, %	10	10	10	10
Mechanical dust carryover, %	6 [16]	5 [20]	2 [17]	1
Non-equilibrium As evaporation, %	60 [16]	1 [26]	60	1
Entrainment, grams in 100 of slag + solids (estimated from industrial samples)	1.5 [27]	0.5	2.5 [24]	0.5

.

2.3. Experimental Study

The purpose of this experimental study is to verify the predictive power of thermodynamic models for the chemical solubility of Cu, Ag, and Au in slag, as well as recommend the Fe/SiO₂ ratio for the smelting step. The latter is an important factor influencing the amount of slag through flux addition, as well as the energy balance due to the need to heat flux materials. The experimental methodology involves high-temperature equilibration, quenching, and the direct measurement of the compositions of phases using electron probe X-ray microanalysis (EPMA) or laser ablation ICP-MS. This technique has been described in many articles by the authors [28], but in this study, it was pushed to the limit by studying many more components than were previously evaluated.

Conditions for equilibration experiments were selected close to the corresponding smelting conditions. The targeted equilibrium was among gas, slag, matte, and spinel (Fe₃O₄). Powdered mixtures in proportions estimated using FactSage 8.3^® were made from analytical grade reagents (e.g., SiO₂, Fe₂O₃, Fe, Cu, CaCO₃, Al₂O₃, MgO, Ni, Co, As, Sb, Bi, PbO, ZnO, Ag, Au), and pre-melted master slags (e.g., PbO-SiO₂, CaO-SiO₂, CaO-Fe₂O₃). Master slags improve the kinetics during equilibration and mitigate the initial evaporation of volatile elements. Pelletized samples were placed onto the substrate of spinel (Fe₃O₄). It was made in the shape of an open basket obtained from the oxidation of Fe foil in a controlled CO/CO₂ atmosphere. For experiments with high concentrations of MgO in slag, magnesia crucibles were used. The furnace setup and sample location are shown in Figure 4. The experimental samples were suspended in a 30 mm ID recrystallized alumina reaction tube and positioned in the calibrated uniform hot zone of a vertical, electrically heated furnace. An alumina-shielded Pt-Rh 6%/Pt-Rh 30% B type thermocouple placed immediately next to the sample controlled its temperature within ±5 K. P(SO₂) and P(O₂) were fixed by a 500 mL/min gas flow of Ar, SO₂, CO and CO₂ in pre-calculated proportions during the equilibration. Gases were supplied by Coregas (NSW, Australia). Flow rates were controlled using U-tube pressure differential-type gas flowmeters. The accuracy of the targeted oxygen partial pressure was verified using a DS-type oxygen probe made from a Y₂O₃-stabilized ZrO₂ solid electrolyte cell, which was supplied by Australian Oxycontrol Systems (Bendigo, VIC, Australia).

After equilibration, samples were quickly dropped into CaCl₂ or MgCl₂ brine solutions at −20 °C, ensuring quenching from >1250 °C to 500 °C within 2–3 s. After cooling to room temperature, phases present during the equilibration retained their compositions. Samples were dried, placed in epoxy resin, polished, and coated with a thin layer of carbon to improve the current discharge during EPMA. The typical microstructures are shown in Figure 5.

Concentrations of elements in phases were measured using a JEOL JXA 8200L electron probe X-ray microanalyzer (EPMA) by Japan Electron Optics Ltd., Tokyo. It was supplied with five wavelength dispersive detectors (WDD). Electrons emitted by tungsten filament were sped up by a 15 kV electrical field. X-rays were generated under the bombardment of electrons with a quantity per second equivalent to a 20 nano Ampere (nA) current. X-ray counts detected using WDD were recalculated to concentrations by using the Duncumb–Philibert ZAF correction procedure included in the probe software. The procedure also requires standards measured in the same session as samples. In this study, we used compounds with well-known stoichiometry as standards: CaSiO₃ (wollastonite) for Si and Ca, Al₂O₃ (corundum) for Al, MgO (periclase) for Mg, Fe₂O₃ (hematite) for Fe, InAs for As, CuFeS₂ for S, ZnO for Zn, and pure metal standards (Cu, Au, Ag) for Cu and minor elements. Standards were purchased from Charles M. Taylor Co., Stanford, CA, USA. The PbO-SiO₂ K456 glass from NIST was used for Pb. To increase the X-ray generation volume and compensate for the scattering of results caused by micro inhomogeneity introduced during quenching, probe diameters of 20–50 microns (μm) were used. This also reduced the evaporation of volatile species from the surface of slags and mattes caused by localized overheating by electrons. Concentrations of silver and gold (Ag, Au) in the slag were too low for accurate measurement by EPMA. For Ag and Au, a different analytical method was used, which is called laser ablation inductively coupled plasma mass spectrometry (LA-ICPMS). The NWR193 Laser Ablation System was provided by Electro Scientific Industries Inc, Portland, OR, USA. The connected ICP-MS Agilent 8800 machine was supplied by Agilent Technologies, Santa Clara, CA, USA. This method also requires standards with well-known concentrations of elements. The synthetic glasses, NIST610 and NIST612, were used as standards. Additional samples with higher-than-typical concentrations of certain elements in slag, measured with EPMA (>1 wt. %), were used as references for other samples in which these elements could only be detected via LA-ICPMS.

Compared to previous studies [28] using similar methodologies, this work has significantly expanded the number of elements participating in chemical and phase equilibrium experiments. While traditional methods using equilibration, physical separation, and wet-chemical analysis [30] are limited in their ability to analyze multiphase samples, our approach employs rapid quenching and electron probe microanalysis (EPMA) to directly measure the chemical composition of individual phases, i.e., slags with suspended spinel crystals. A current limitation of EPMA is its inability to accurately determine the Fe³⁺/(Fe²⁺ + Fe³⁺) ratio in slag. However, ongoing improvements in sample preparation and EPMA techniques are addressing this issue. The use of FactSage calculations for experimental design and data analysis has significantly reduced the number of unsuccessful or less-informative experiments.

3. Results

3.1. Revenue Calculations

To calculate revenue for Cases 1 and 2, the same prices listed in Table 1 were used for Cu, Ag, and Au. Price premiums were assumed to be zero. Recoveries for modern smelters exceed payables. Recoveries for copper and gold vary based on factors like chemistry, physics, and management. When optimized, these recoveries primarily depend on slag generation per unit of copper. More slag means higher losses, even with slag-cleaning equipment. Lower copper concentrate grades increase slag-forming impurities (Fe, SiO₂, Al₂O₃), leading to the downward trend shown in Figure 2. Gold and silver recoveries also inversely correlate with the slag amount, and hence with the copper concentrate grade in the feed, but they are largely independent of their own concentrations (Figure 2). The difference between payable and recovery, which is referred to as “free metal” in this study, becomes one of the main revenue sources under conditions of low TC/RCs and premiums.

For Case 1, using a flash furnace, the procurement team selected Concentrate 1 due to its 25% Cu content, which is a typical target for flash smelters. With recoveries of 98.5% for Cu, 98.9% for Ag, and 99.2% for Au, the “free metal” value is (2743.6 − 2650.0) = 93.6 USD/tonne. The byproduct revenue from sulfuric acid, assuming 95% recovery and a 70 USD /tonne price, is 69.2 USD/tonne of dry concentrate. Operating at 230 t/h 24/7, this yields USD 328 million in annual revenue under unfavorable conditions of zero TC/RCs and premiums.

For Case 2, using bottom-blown smelting, the team optimized for maximum “free metal” by blending concentrates. While targeting 21% Cu, they imposed impurity limits of <0.25% As, <0.1% Sb, <0.035% Bi, <0.03% Cd, F, Se, and <0.0005% Hg. This blending approach, similar to Wang et al. [31], uses industry standards to set limits (the Nonferrous Metals Industry Standard YS/T 318-200X). The resulting blend (Table 1) is 43% Concentrate 1, 30% Concentrate 2, 3% Concentrate 3, and 24% Concentrate 4. With recoveries of 97.5% for Cu, 97.8% for Ag, and 98.2% for Au, the “free metal” value is 108.6 USD/tonne, which is higher than that of Case 1. The H₂SO₄ revenue is 64.9 USD/tonne. At 150 t/h, the annual revenue is USD 228 million under unfavorable conditions of zero TC/RCs and premiums. Although higher “free metal” values are possible, throughput, which is linked to furnace capacity, remains a dominant economic factor. Bottom-blown furnace capacities have steadily increased since 2000 but remain lower compared to the largest flash smelters [20]. The same calculation, at 150 t/h with only Concentrate 1, i.e., without blending, would provide only USD 214 million in revenue. Thus, the benefit of blending for Case 2 is USD 228 – USD 214 = USD 14 million in annual revenue.

While this study does not delve into capital costs (higher for Case 1), oxygen enrichment and concentrate drying costs (higher for Case 1 [32]), campaign life, refractory replacement, or furnace availability, these factors will significantly impact annual revenue. A common criticism of bath-type smelters is higher operating costs due to tuyeres blockage, but this may be solved in the future using a jetting regime of injection [33].

For a custom smelter, the strategy of concentrate purchase requires the following key engineering parameters: recovery functions for Cu, Au, and Ag and maximum acceptable impurity concentrations in the blended concentrate. The next section will outline a potential procedure for obtaining these values.

3.2. Results of Thermodynamic Calculations

Mass and energy balances estimated for concentrate blends from Table 1 and process conditions in Table 2 are presented in Figure 6 (Case 1) and Figure 7 (Case 2), and in Table 3.

A flowsheet’s recirculation ratio for an element in Table 3 is defined as the mass flow in all recycling streams at steady-state conditions (i.e., smelter dust, converter slag, converted dust, slag concentrate, anode slag, and anode furnace dust) divided by the total input of that element. Recirculation generally reduces throughput and can lead to element accumulation in the process.

Case 2’s lower recoveries are attributed to the use of a concentrate blend with lower copper content, resulting in higher slag production per unit of copper. This does not indicate technological inefficiency; as demonstrated in Section 3.1, the gap between recovery and payables allows for extracting more value from “free metal”. Recoveries for Ag and Au into anode copper are higher compared to that of Cu. This analysis does not include losses of copper electrorefining and anode slime treatment, but the additional losses at those stages are typically considered small [34]. The same 70% recovery efficiency was assumed for Cu, Au, and Ag in the slag cooling, crushing, and flotation process for both Case 1 and Case 2. This value for copper was achieved using xanthates [35], but reliable information for Au and Ag was not found. More environmentally friendly frothers are currently being developed [36], but they have not yet reached the recovery of 70% for copper. Higher concentrations of these metals in discard slag are due to the initially higher entrainment of matte droplets in slags with suspended solids, as observed in Case 2. This is evident in micrographs of quenched flash furnace and bottom-blown furnace slags [19,27]. In practice, the efficiency of slag cooling, crushing, and flotation may vary between Case 1 and Case 2, but comprehensive research on this topic is lacking. Alternative methods of slag cleaning are proposed, as well, for instance, using aluminothermic reactions from recycled LIBs [37] or sulfidation treatment [38] so the recoveries may further increase in the near future.

Table 3. Calculated compositions of important streams in copper smelting flowsheets: Case 1 (Figure 6) and Case 2 (Figure 7). Flows of Cd, F, Hg, and Se were not modeled.

Compositions	Cu, wt%	Ag ppm	Au ppm	Fe, wt%	O, wt%	S, wt%	SiO2, wt%	Al2O3, wt%	CaO, wt%	MgO, wt%
Discard slag Case 1	0.6	0.7	0.1	43.9	14.4	0.4	31.2	4.1	2.5	1.6
Discard slag Case 2	0.8	4.7	0.7	45.0	15.5	0.4	29.0	4.0	1.8	1.7
Anode copper Case 1	99.5	161.0	15.8	<0.001	1490 ppm	20 ppm	<0.001	<0.001	<0.001	<0.001
Anode copper Case 2	99.0	679.3	124.4	<0.001	1460 ppm	8 ppm	<0.001	<0.001	<0.001	<0.001
Smelter dust Case 1	11.2	19	2	12.8	40.0	17.5	3.9	1.2	0.3	0.5
Smelter dust Case 2	8.2	68	10	11.6	37.8	15.4	4.3	1.1	0.4	0.4
Flowsheet recirculation Case 1, %	20	15	15	20	16	10	10	13	65	10
Flowsheet recirculation Case 2, %	14	10	7	11	6	4	12	7	9	7
Compositions (continued)	Pb, wt%	Zn, wt%	Ni, wt%	As, wt%	Sb, wt%	Bi, wt%	Mol As/(Bi +Sb)	Cu recov., %	Ag recov., %	Au recov., %
Discard slag Case 1	0.1	0.8	<0.01	0.4	0.03	0.01
Discard slag Case 2	0.5	1.0	0.05	0.2	0.07	0.01
Anode copper Case 1	830 ppm	9 ppm	410 ppm	930 ppm	140 ppm	840 ppm	2	98.5	98.9	99.2
Anode copper Case 2	480 ppm	9 ppm	2170 ppm	2780 ppm	705 ppm	1010 ppm	3	97.5	97.8	98.2
Tolerable levels, ppm [39,40]	4000	100	3000	500–1500	350	300	>2
Smelter dust Case 1	0.3	0.4	<0.001	9.6	0.02	2.2
Smelter dust Case 2	2.1	0.7	0.03	12.6	0.06	5.2
Flowsheet recirculation Case 1, %	290	40	80	570	30	1100
Flowsheet recirculation Case 2, %	200	25	50	400	15	1030

Table 3. Calculated compositions of important streams in copper smelting flowsheets: Case 1 (Figure 6) and Case 2 (Figure 7). Flows of Cd, F, Hg, and Se were not modeled.

Compositions	Cu, wt%	Ag ppm	Au ppm	Fe, wt%	O, wt%	S, wt%	SiO2, wt%	Al2O3, wt%	CaO, wt%	MgO, wt%
Discard slag Case 1	0.6	0.7	0.1	43.9	14.4	0.4	31.2	4.1	2.5	1.6
Discard slag Case 2	0.8	4.7	0.7	45.0	15.5	0.4	29.0	4.0	1.8	1.7
Anode copper Case 1	99.5	161.0	15.8	<0.001	1490 ppm	20 ppm	<0.001	<0.001	<0.001	<0.001
Anode copper Case 2	99.0	679.3	124.4	<0.001	1460 ppm	8 ppm	<0.001	<0.001	<0.001	<0.001
Smelter dust Case 1	11.2	19	2	12.8	40.0	17.5	3.9	1.2	0.3	0.5
Smelter dust Case 2	8.2	68	10	11.6	37.8	15.4	4.3	1.1	0.4	0.4
Flowsheet recirculation Case 1, %	20	15	15	20	16	10	10	13	65	10
Flowsheet recirculation Case 2, %	14	10	7	11	6	4	12	7	9	7
Compositions (continued)	Pb, wt%	Zn, wt%	Ni, wt%	As, wt%	Sb, wt%	Bi, wt%	Mol As/(Bi +Sb)	Cu recov., %	Ag recov., %	Au recov., %
Discard slag Case 1	0.1	0.8	<0.01	0.4	0.03	0.01
Discard slag Case 2	0.5	1.0	0.05	0.2	0.07	0.01
Anode copper Case 1	830 ppm	9 ppm	410 ppm	930 ppm	140 ppm	840 ppm	2	98.5	98.9	99.2
Anode copper Case 2	480 ppm	9 ppm	2170 ppm	2780 ppm	705 ppm	1010 ppm	3	97.5	97.8	98.2
Tolerable levels, ppm [39,40]	4000	100	3000	500–1500	350	300	>2
Smelter dust Case 1	0.3	0.4	<0.001	9.6	0.02	2.2
Smelter dust Case 2	2.1	0.7	0.03	12.6	0.06	5.2
Flowsheet recirculation Case 1, %	290	40	80	570	30	1100
Flowsheet recirculation Case 2, %	200	25	50	400	15	1030

3.3. Analysis of Accuracy of Thermodynamic Predictions

The estimation of entrainment coefficients for matte in slag is often based on the difference between measured and calculated Cu concentrations. The optimal Fe/SiO₂ ratio in slag depends on the matte grade, the P(SO₂) in the system, and the concentrations of Al₂O₃, CaO, and MgO. The losses of Au and Ag are commonly attributed to matte entrainment, which is a claim that needs testing. Overall, 25 multicomponent (17 elements) gas–slag–matte–spinel experiments have been performed in the temperature range of 1250–1300 °C with matte grades from 50 to 75 wt.% Cu. All results are provided in the Supplementary Materials.

Due to the large number of elements and phases present in the experiments, it is impractical to compare model predictions with experimental data using binary or ternary phase diagrams. A methodology for comparison has been developed and discussed in a recent publication [29]. The composition of each phase can be considered as coordinates in multicomponent space. As an example, experimentally measured compositions for experiment #23 are provided in

Table 4. Example of experimental results and thermodynamic calculations for Sample #23 equilibrated at 1250 °C at P(SO₂) = 0.8 atm on an Al₂O₃ substrate. Compositions are in wt. %; the last column is an approximate proportion of phases used to calculate bulk composition for FactSage^® input.

Wt%	Cu	Fe	S	[O]	Al2O3	SiO2	Ni	Co	As	Bi	Pb	Zn	Au	Ag	Sb	Mass
Slag (exp)	1.1	39.6	0.2	11.3	12.2	32.1	0.10	0.25	0.036	4.1 × 10−6	0.170	0.476	5.4 × 10−5	0.005	0.55	0.90
Matte (exp)	72.4	2.7	20.4	0.6	0.0	0.0	0.84	0.06	0.004	3.3 × 10−5	0.100	0.090	0.3920	0.478	0.11	1.00
Spinel (exp)	0.0	48.9	0.0	14.0	31.7	0.3	0.37	0.46	0.011	<1 × 10−6	0.017	1.440	<1 × 10−6	0.000	0.01	0.10
FactSage Input	73.4	43.3	20.5	11.9	14.1	28.9	0.96	0.33	0.038	3.7 × 10−5	0.254	0.662	0.3921	0.483	0.61
Slag (calc)	0.9	37.7	0.2	11.9	12.2	35.4	0.06	0.24	0.040	1.1 × 10−5	0.143	0.594	6.4 × 10−5	0.004	0.63	0.82
Matte (calc)	72.8	3.8	21.2	0.2	0.0	0.0	0.84	0.08	0.005	2.8 × 10−5	0.137	0.078	0.3924	0.480	0.09	1.00
Spinel (calc)	0.0	53.5	0.0	19.6	25.4	0.0	0.46	0.33	0.000	<1 × 10−6	0.000	0.606	0.0000	0.000	0.00	0.16

. For each experiment, a FactSage^® calculation was performed at the bulk composition within the shape formed by the phases in equilibrium. This is marked as the “FactSage Input” row in Table 4. The theory behind FactSage^® calculations is that the atoms under equilibrium conditions arrange themselves to form physically distinct phases with uniform compositions. The proportions and compositions of phases correspond to the minimum of the Gibbs free energy of the system. In the case of a three-phase equilibrium, the composition of phases forms a triangle in the multicomponent space. To provide the input for FactSage in terms of moles of atoms, a composition within the triangle is selected by assigning proportions to the experimentally observed phases, as shown in the last column of Table 4. These proportions may be close to those in the experiment but do not have to be exact values. Since the procedure respects the Gibbs phase rule, the calculated compositions of the phases do not change with varying proportions. However, temperature, total pressure, and P(SO₂) must be fixed to match the experimental conditions. The latter was adjusted by adding an excess SO₂/N₂ mixture to the FactSage^® input table, forming a gas phase with the target P(SO₂). The amount of oxygen was not measured by EPMA, so it was also adjusted to represent the target oxidation/reduction conditions in the system. In this work, the selected target was the matte grade, which is the wt.% Cu in the matte. A summary of the conditions is provided in Figure 8. After the calculation, the accuracy of the predictions was compared by examining the difference in composition between the phases measured in the experiment and those predicted by FactSage^®. The results for the Fe/SiO₂ ratio, the wt.% Cu, and the ppms of Au and Ag in the slag are provided in Figure 9. The experiments demonstrate good predictive power of thermodynamics models under large variations in matte grade and wt. % Al₂O₃, CaO, and MgO. Model predictions can be performed far from the normal operational range of smelting furnaces so that the introduction of low-grade concentrates can be tested in advance.

A deeper analysis of the accuracy of thermodynamic models is provided in Figure 10. The predicted chemical solubility of Cu in the slag is within 0.2 wt. % of the experimental uncertainty (Figure 10). These values correlate with the wt.% S in the slag. However, a small but systematic deviation has been observed for the predicted Fe/SiO₂ ratio (Figure 10). This indicates that when planning operations using FactSage^®, corrections should be made. For slags with >5 wt% Al₂O₃, the predicted Fe/SiO₂ in equilibrium with spinel must be corrected by +0.15. For a given Fe/SiO₂, the current model overestimates the proportion of spinel, as illustrated in the last row and last column of Table 4. For slags with >2 wt.% MgO, the predicted Fe/SiO₂ in equilibrium with spinel must be corrected by −0.10. For Ag and Au, the predictions were confirmed to be accurate within the uncertainty of the experimental tests. A detailed analysis of the distribution of other elements is beyond the scope of this study, but the results are reasonable and provided in the Supplementary Materials.

These results will be used to inform further fundamental experimental and modeling activities within the consortium program to improve predictions.

4. Discussion

Let us analyze the thermodynamic calculations presented in Table 3. According to the predictions for the concentrate blends selected in Section 2.1, higher recirculation rates are observed in Case 1 compared to Case 2 for all elements. This is primarily due to two factors: higher mechanical dust carryover from the flash smelting furnace in Case 1 and a lower matte grade selected for smelting in Case 1 (70 vs. 74 wt.% Cu). The impact of the second factor is that lower matte grades result in the transfer of more iron to the converting stage, where it is turned into slag and must be recycled back to the smelter. Historically, high matte grades have been avoided due to difficulties in maintaining a fully liquid slag under more oxidizing conditions and to prevent copper losses through chemical solubility and the entrainment of matte droplets. However, advancements in bath smelting technologies, such as the tolerance to solid spinel and the implementation of slag crushing and flotation, have allowed for higher matte grades, thereby reducing the load on the converting stage. The higher recirculation rate in Case 1 may contribute to the selection of higher-grade concentrate blends for treatment in flash furnaces. Dust and high-copper converter slag do not add calorific value to the process, making it challenging to maintain the energy balance.

Regarding the energy balance, the value of −15 MW obtained for Case 2 smelting is slightly less exothermic than expected based on a simple scaling of Case 1’s value using throughput data: −30 MW/(230 t/h) × (150 + 13 t/h) = −21 MW. This is reasonable since a bottom-blown smelter operates at a lower temperature, thereby reducing radiation heat loss. Flash smelter shafts also have active water-cooling systems, which bath smelters usually do not use. There are several factors that should make the Case 2 smelting process relatively more exothermic, such as a higher operating matte grade, lower amounts of recirculated dust and converter slag, and a higher Fe/SiO₂ ratio, requiring less silica flux to melt. Factors that contribute to Case 2 being less exothermic are high moisture content and lower oxygen enrichment. To achieve the −15 MW value in Case 2, it was necessary to introduce a lower oxygen efficiency of 90%, compared to 99% in Case 1. This may not be the final conclusion, and other factors, such as the addition of cool-reverted or recycled materials, could be influencing the energy balance.

Importantly, the copper recovery values for Cu, Ag, and Au obtained in Table 3 align well with those used for revenue calculations, as shown in Figure 2.

For the selected concentrate blend in Case 2, the resulting concentrations of As, Sb, and Bi in the anode copper exceed tolerable levels (Table 3). The concentration of Bi is also too high in Case 1. This indicates that the generated dust needs to be periodically leached [41]. Utilizing calcium ferrite slags at the converting stage can revert more As and Sb back to the smelting process, reducing their concentration in anode copper. However, this also means that arsenic will accumulate in discarded slag tailings. Arsenic in vitreous slag matrices can be quite stable under environmental conditions, but using it as a destination for arsenic is a complex issue, with ongoing discussions among researchers, policymakers, and businesses. Recent research has demonstrated the application of calcium ferrite in the ISACONVERT^® process for bath smelting [42,43]. However, there is limited research available on the use of this slag chemistry in bottom-blown converters.

5. Conclusions

This study presents the operating dynamics of custom copper smelters. As the number of high-quality deposits of copper is decreasing, custom smelters are adopting an advanced level of operational excellence to improve the economy of copper production. At the core of a successful custom smelter lies a sophisticated value-added blending model for optimum performance in copper-making. The model maximizes the revenue streams while maintaining the operating limits of the plant. By leveraging an understanding of recovery curves and the maximum tolerable levels of impurity elements, the authors have demonstrated the potential for increasing the “free metal” value. Specifically, our findings highlight the benefits of blending low-grade copper concentrates (<20 wt% Cu) with higher-grade concentrates (25 wt% Cu) to maximize overall revenue, with the potential for up to USD 14 million for a 150 t/h throughput.

To further enhance the process, future research should focus on advanced modeling techniques. Refining computational tools based on advanced thermodynamics such as FactSage^® should rely both on laboratory-controlled experiments and the calibration of kinetic factors using real-time process data. The maximum tolerable impurity levels of As and Sb can be increased either by investments in dust-leaching equipment or by exploring calcium ferrite slag chemistries at the converting stage.