# Quantitative Methods to Support Data Acquisition Modernization within Copper Smelters

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}offgas. This instrument spectrometrically measures trace amounts of lead and copper sulfides and oxides in the offgas and signals when the level of sulfides starts to decrease, signaling the end of the batch [6]. The precise endpoint control saves significantly in processing time at Rönnskär in the subsequent anode furnace, thus lowering operating costs and allowing higher throughput.

## 2. Radiometric Sensors for Extractive Pyrometallurgy of Copper

#### 2.1. Reactive Systems

_{3}O

_{4}), and copper oxides (CuO/Cu

_{2}O) as indicators of the concentrate smelting/oxidation/combustion process [7,8,9]. This information is of special interest to track the physicochemical dynamics of the process in real-time and establish operating criteria for a smelting reactor. Examples of such criteria could include adjustments to concentration/oxygen ratios, oxygen enrichment for the incoming blast, and the quantity of cold charge that will be required to maintain the heat balance.

#### 2.2. Nonreactive Systems

## 3. Unifying Framework for Copper and Nickel–Copper Smelter Dynamics

#### 3.1. Overview of Copper and Nickel–Copper Smelter Operations

_{2}offgas, eventually resulting in molten copper [13,14]. This pyrometallurgical technique accounts for approximately 75% of the primary copper production worldwide [15,16], the majority of which is carried out using the conventional approach depicted in Figure 3. In some cases, the incoming concentrates are subject to roasting reactions prior to being fed into the smelting operation; these roasted concentrates are known as calcines.

_{2}and SO

_{2}are exhausted through a hood mounted on the vessel (Figure 4). The offgas is captured in order to convert SO

_{2}into sulfuric acid; meanwhile, N

_{2}acts as a coolant in the process [14]. Copper and nickel–copper smelters both apply the first stage of PS converting, which is called the slag-blow, producing an iron-rich slag that forms atop the denser matte (Figure 4a). This stage may require intermittent pauses in order to skim away slag accumulation and replenish the vessel with fresh matte and cold charge. Once all of the slag is removed (<1% Fe in matte), copper smelters continue blowing the remaining matte; this final stage of converting is known as the copper-blow, as it results in the formation of blister copper that sinks to the bottom of the vessel (Figure 4b). The copper-blow does not produce any more slag and, therefore, does not require intermittent skimming. Nickel–copper smelters, however, only apply the slag-blow (Figure 4a), not the copper-blow. In either context, the cycle is complete when all of the matte is converted to the correct endpoint and discharged (Figure 3).

#### 3.2. Detailing of Smelter Dynamics Within Discrete Event Simulation

_{x}represents a mixture of wustite FeO and magnetite Fe

_{3}O

_{4}, such that x = 1 and x = 1.25 corresponds to pure wustite and magnetite, respectively. For simplicity, x can be fixed to 1, although typical values can range between 1.0 and 1.1, depending on the nature and quantity of the flux and the monitoring and control of the process itself; in particular, a low level of magnetite in slag is desirable, which is associated with low slag viscosity. In practice, the flux is predominantly silica SiO

_{2}, but certain smelters include varying quantities of CaO and other stable oxides; CaO is especially common in continuous converting [21], which is an alternative to the conventional PS converting [16]. The SO

_{2}is captured for sulfuric acid production, and the blister copper is subject to fire refining prior to being cast into anodes that undergo electrolytic refining. A similar reaction can describe nickel–copper smelters:

_{S}and x

_{C}, characterize the slag of the smelting furnace. A similar decomposition of the global x could be applied to Equation (1b) in the case of nickel–copper smelters.

_{S}characterizes the slag of the smelting furnace, and, depending on the level of detail, x

_{Ci}can characterize the types of converter cycles or can characterize the individual types of slag-blow segments, for i = 1 to n. For example, Figure 5a shows an action graph that occurs within a smelter that practices two kinds of converter cycles, long and short; hence, n = 2. Figure 5b shows a more detailed representation, which considers 13 kinds of blow segments. (The slag-blow segments are punctuated with charging and skimming actions, although these are not explicitly shown in Figure 5b). For a conventional copper smelter, actions 1–9 describe slag-blow segments (Figure 4a); hence, n = 9, and the remaining actions 10–13 represent copper-blow segments (Figure 4b) that complete the cycle as a batch of blister copper is discharged. In the case of a nickel–copper smelter, all of the arcs represent slag-blow segments; hence, n = 13, noting that the discharge is the so-called Bessemer matte (Ni, Cu, Co and S) that is described in Figure 3 and Equation (1b).

_{2}effluent. If the smelter is running in its normal operational mode when the unfavorable meteorological conditions emerge, there is a so-called “environmental incident”. The model of Navarra et al. [25] computes the trade-off between production and environmental risk. Moreover, this model quantifies the improved trade-off that can result from a more accurate array of meteorological sensors.

^{Previous}. Thus, each feed k would require two discretely dynamic variables (${m}_{k}^{\mathrm{Previous}}$ and ${\dot{m}}_{k}^{\mathrm{Previous}}$), in addition to the t

^{Previous}variable that remembers the time of the previous event. Equation (4) can used in simulations that consider alternating modes of operation that control feed blends in response to imbalances in incoming concentrates [29].

#### 3.3. Slag Iron Speciation and Other Thermochemical Considerations

_{3}O

_{4}, can be quantified as the oxygen-to-iron ratio x presented in Equations (1)–(3). Indeed, x represents a degree of freedom that must be resolved in order to complete the mass balance. This degree of freedom can also be expressed as the ratio of ferric to ferrous ions within the slag, α = Fe

^{3+}/Fe

^{2+}, often called the degree of oxidation. The homeomorphic relationship between x and α is given by

_{3}O

_{4}. Equation (6) can be further detailed in a similar manner as Equations (2) and (3) by assigning appropriate subscripts to α, as in [20].

_{2}, CaO, etc.). For instance, the role of SiO

_{2}flux is made more evident by expressing the wustite as a component within a fayalite matrix FeO·2SiO

_{2}; hence, the balance of FeO versus Fe

_{3}O

_{4}is considered as FeO·2SiO

_{2}and Fe

_{3}O

_{4}. In practice, SiO

_{2}is added into the slag in proportions that surpass the stoichiometry of fayalite and may be accompanied by other stable oxides. Under matte-processing conditions, the stable molecules SiO

_{2}, CaO, etc. can be regarded as if they were indivisible atoms. Most notably, the strongly bonded oxygen is not explicitly represented in Equations (1)–(3) and is not taken into account in x; these equations only explicitly consider the blast oxygen. The degree of oxidation α considers only the iron species isolated from any mention of the blast and flux oxygen.

_{2}S; in the case of nickel–copper smelters, the matte will also contain nickel and cobalt sulfides [18], but Equation (7) is still correct. The incoming blast includes N

_{2}, as well as O

_{2}(see Figure 4). As the N

_{2}passes through the bath and is exhausted into the offgas, along with the SO

_{2}, it carries away sensible heat and is a critical consideration in controlling the bath temperature.

_{0}= 622,549 J/mol and ΔS

_{0}= 342.64 J/mol K, respectively, which can be obtained from HSC Chemistry

^{TM}. The corresponding Gibbs free energy balance is

_{ij}is the activity of species i within phase j. The activity of SO

_{2}in the offgas is taken to be the partial pressure p

_{SO2,Offgas}.

_{FeS,Matte}, a

_{FeO,Slag}, and a

_{Fe3O4,Slag}) can be re-expressed in terms of α, T, and the operational parameters. The usual parameters include the oxygen enrichment of the blast φ and the silica–iron mass ratio r = (m

_{SiO2,Slag}/m

_{Fe,Slag}), which are considered in Section 4. Empirical measurements relate the activities a

_{ij}to their respective mole fractions X

_{ij}. In particular, the classic model of Goto [30,31] is validated for smelting and converting, in both the copper and nickel–copper contexts [32], and is the subject of Appendix A.

^{(k)}, α

^{(k)}) denote the results of the kth Newton iteration. The righthand sides of Equations (10) and (11) include proxy functions, f

_{G}and f

_{H}, and their derivatives, which are all evaluated at the preceding values (T

^{(k−1)}, α

^{(k−1)}), considering (T

^{(0)}, α

^{(0)}) = (1473 K, 0.15) as typical starting values. The proxy function f

_{G}must be formulated so that f

_{G}= 0 when the Gibbs free energy balance of Equation (9) is satisfied, i.e., when ΔG = 0. Appendix A presents a formulation of f

_{G}that is based on the classic Goto model [30,31]. Likewise, f

_{H}is formulated such that f

_{H}= 0 when the heat balance is satisfied [19].

_{3}O

_{4}can depend on various parameters, including flux quality, refractory wear, and amount of charge (hence, affecting mixing), and so, an empirical approach to speciation may be more effective.

#### 3.4. Estimation of Threshold Crossing Times Using Time-Adaptive Finite Differences

## 4. Sample Computations and Context

- has been successful for decades in processing reasonably clean feeds;
- is confronted with increasingly challenging feeds that carry excess quantities of arsenic, bismuth, and antimony; and
- is aware of an approach to draw a critical portion of the undesirable elements into the converting slag, which is only effective as the iron in matte approaches zero

^{TM}software and replicated the general aspects of conventional smelters while incorporating smelter-specific data. Table 1, Table 2 and Table 3 contain sample data that are loosely based on published values from [2,5,6,13,39,40]. As stated in Section 3.1, conventional smelters have smelting capacities that normally exceed the downstream converting capacity; indeed, the smelting furnace should not usually produce matte at full capacity, nor should it function in fits and starts. The definition of so-called short and long converter cycles (Figure 6) provides the operational flexibility to set a fixed smelting rate. Moreover, some smelters may have several cycle types under consideration to respond to build-ups of cold charges or compositional imbalances in the feeds that are received from the supplying mines. For simplicity, the current computations consider only two types of cycles.

_{2}S, an elemental mass balance determines that a 60% Cu grade corresponds to roughly 24% S and 16% Fe.

^{3}/min of oxygen into a bath in order to decrease the iron content from 39% to 16% as it burns the FeS. The smelting blast also includes 550 Nm

^{3}/min of nitrogen, which carries away a portion of the heat. The control of the temperature at 1275 °C depends on this nitrogen flow. Given the stable temperature T = 1275 °C = 1548 K, oxygen enrichment φ = 0.5, and silica-iron ratio r = 0.7, the Newton iterations of Equation (10) are used to obtain the degree of oxidation α = 0.166, with a corresponding throughput of 36.928 t/h of matte or equivalently 1.231 ladles/h. At a matte grade of 60% Cu, this corresponds to 22.157 t Cu/h.

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Proxy Function for Gibbs Free Energy Balance Based on Goto’s Model

_{G}considers that each mole of wustite FeO contains one mole of ferrous, that each mole of magnetite FeO·Fe

_{2}O

_{3}contains one ferrous and two ferric, and that all other iron-bearing slag compounds are negligible. It follows that α = Fe

^{3+}/Fe

^{2+}can be taken as

_{ij}generally denotes the number of moles of i within phase j.

_{FeS,Matte}, a

_{FeO,Slag}, and a

_{Fe3O4,Slag}), a series of algebraic manipulations were performed by Navarra et al. [18,19] to obtain the following form that explicitly features T and α:

_{l}, B

_{l}, C

_{l}, and D

_{l}) are given in Table A1, from which a viable proxy function is obtained:

_{G}= 0. Moreover, the partial derivates of f

_{G}can be obtained with respect to α and T, so to complete the Newton iterations described by Equations (10) and (11). To obtain the expression for $\frac{\partial {f}_{G}}{\partial T}$, it is helpful to notice that D

_{l}is zero for all factors except for the third and ninth.

_{SO2,offgas}. Additionally, the mole fraction of FeS within the matte is taken to be

_{NiS,Matte}and n

_{CoS,Matte}are set to zero. Moreover, Table A1 has several instances of the silica-to-iron mole ratio (n

_{SiO2,Slag}/n

_{Fe,Slag}), which can be related to the silica-to-iron mass ratio r within the slag:

_{SiO2}and M

_{Fe}are the molar masses of silica and iron, respectively; r is a common operational parameter used to control the flux additions.

**Table A1.**Coefficients for Equation (A2) (adapted from [19]).

l | A_{l} | B_{l} | C_{l} | D_{l} |
---|---|---|---|---|

1 | 1 | 1 | 1 | 0 |

2 | 2 | −1 | 10 | 0 |

3 | $\left(2.44-0.4\left(\frac{{n}_{\mathrm{SiO}2,\mathrm{Slag}}}{{n}_{\mathrm{Fe},\mathrm{Slag}}}\right)\right)$ | $-\left(1.42-0.4\left(\frac{{n}_{\mathrm{SiO}2,\mathrm{Slag}}}{{n}_{\mathrm{Fe},\mathrm{Slag}}}\right)\right)$ | 0 | 15,430 |

4 | ${X}_{\mathrm{FeS},\mathrm{Matte}}{e}^{\frac{\mathsf{\Delta}{S}_{0}}{R}}$ | 0 | 1 | 0 |

5 | 0 | 1 | 3 | 0 |

6 | $\left(\frac{3-\varphi}{2\varphi}\right)$ | $\left(\frac{7-3\varphi}{4\varphi}\right)$ | 1 | 0 |

7 | $\left(1.38+12.28\left(\frac{{n}_{\mathrm{SiO}2,\mathrm{Slag}}}{{n}_{\mathrm{Fe},\mathrm{Slag}}}\right)\right)$ | $\left(56.8+12.28\left(\frac{{n}_{\mathrm{SiO}2,\mathrm{Slag}}}{{n}_{\mathrm{Fe},\mathrm{Slag}}}\right)\right)$ | 3 | 0 |

8 | $2\left(1+\left(\frac{{n}_{\mathrm{SiO}2,\mathrm{Slag}}}{{n}_{\mathrm{Fe},\mathrm{Slag}}}\right)\right)$ | 2$\left(\frac{{n}_{\mathrm{SiO}2,\mathrm{Slag}}}{{n}_{\mathrm{Fe},\mathrm{Slag}}}\right)$ | 4 | 0 |

* 9 | $2\left(1+\left(\frac{{n}_{\mathrm{SiO}2,\mathrm{Slag}}}{{n}_{\mathrm{Fe},\mathrm{Slag}}}\right)\right)K$ | 2$\left(\frac{{n}_{\mathrm{SiO}2,\mathrm{Slag}}}{{n}_{\mathrm{Fe},\mathrm{Slag}}}\right)K$ | 0 | 15,430 |

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**Figure 1.**Representation of “Industry 4.0”—the 4th industrial revolution. Adapted from [1]. ICT: information and communication technology.

**Figure 2.**Radiometric measurement scheme and associated radiative processes: (

**a**) single-heated particle radiative emission with its surroundings, in which the intensity I of the emitted radiation is a function of wavelength λ, particle temperature T

_{p}and particle emissivity ε

_{p}and (

**b**) sensing scheme depicting the different particle states as they fall through the reaction zone (adapted from [8]).

**Figure 3.**Schematic of conventional copper or nickel–copper sulfide smelter operations. The smelting furnace and converting aisle eliminate iron and sulfur, producing blister copper in the case of copper smelters and Bessemer matte in the case of nickel–copper smelters.

**Figure 5.**Examples of action graphs that represent Peirce-Smith converting cycles, which consider two types of cycles: long and short. (

**a**) The low-detail representation shows the long and short cycles as single actions that are characterized by broad distributions of cycle times, whereas (

**b**) a more detailed representation considers individual blow segments, from 1 to 13; each of the segments can be characterized by comparatively narrow time durations (which were omitted from the figure).

**Figure 6.**Relationship between smelter kinetics, internal and external smelter logistics, and broader system dynamics.

**Figure 7.**Fundamental components of a discrete event simulation (DES) framework, including (

**a**) a virtual timeline that is subject to discrete steps and (

**b**) a future event list.

**Figure 8.**Threshold-crossing event in relation to another event e. Time-adaptive finite differences determine if the threshold is crossed (

**a**) before e or (

**b**) after e.

Element | Weight% |
---|---|

Copper | 20 |

Iron | 39 |

Sulfur | 40 |

Arsenic | 0.4–1.0 |

Bismuth | 0.02–0.20 |

Antimony | 0.02–0.10 |

Parameter | Value |
---|---|

Matte holding capacity | 900 t |

Bath temperature | 1275 °C |

Blast rate | 1100 Nm^{3}/min |

Oxygen enrichment | 50 vol%O_{2} |

SiO_{2}/Fe in slag | 0.7 |

Matte grade | 60 wt% Cu |

Short Cycle | Long Cycle | |||
---|---|---|---|---|

Duration (h) | * Ladles Added | Duration (h) | * Ladles Added | |

First slag-blow segment | 2.0 | 3 | 3.0 | 4 |

Second slag-blow segment | 0.5 ± 0.2 | 1 | 1.0 | 2 |

Third slag-blow segment | - | - | 0.5 ± 0.2 | 1 |

Copper-blow | 4.5 ± 0.7 | - | 5.0 ± 1.2 | - |

Regular Short C. | Extended Short C. | Regular Long C. | Extended Long C. | |||||
---|---|---|---|---|---|---|---|---|

Duration (h) | * Ladles Added | Duration (h) | * Ladles Added | Duration (h) | * Ladles Added | Duration (h) | * Ladles Added | |

First SB segment | 2.2 ± 0.2 | 3 | 2.2 ± 0.2 | 3 | 3.4 ± 0.2 | 4 | 3.4 ± 0.3 | 4 |

Second SB segment | 0.3 ± 0.1 | 1 | 0.3 ± 0.1 | 1 | 0.7 ± 0.2 | 2 | 1.2 ± 0.2 | 3 |

Third SB segment | - | - | 0.4 ± 0.1 | 1 | 0.4 ± 0.1 | 1 | 0.3 ± 0.1 | 1 |

Fourth SB segment | - | - | - | - | - | - | 0.4 ± 0.1 | 1 |

Copper-blow | 4.5 ± 0.7 | - | 5.6 ± 0.8 | - | 5.0 ± 1.2 | - | 7.0 ± 1.7 | - |

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**MDPI and ACS Style**

Navarra, A.; Wilson, R.; Parra, R.; Toro, N.; Ross, A.; Nave, J.-C.; Mackey, P.J.
Quantitative Methods to Support Data Acquisition Modernization within Copper Smelters. *Processes* **2020**, *8*, 1478.
https://doi.org/10.3390/pr8111478

**AMA Style**

Navarra A, Wilson R, Parra R, Toro N, Ross A, Nave J-C, Mackey PJ.
Quantitative Methods to Support Data Acquisition Modernization within Copper Smelters. *Processes*. 2020; 8(11):1478.
https://doi.org/10.3390/pr8111478

**Chicago/Turabian Style**

Navarra, Alessandro, Ryan Wilson, Roberto Parra, Norman Toro, Andrés Ross, Jean-Christophe Nave, and Phillip J. Mackey.
2020. "Quantitative Methods to Support Data Acquisition Modernization within Copper Smelters" *Processes* 8, no. 11: 1478.
https://doi.org/10.3390/pr8111478