New Model to Predict Nickel Extraction from Lateritic Ores During the Roasting–Reduction of the Caron Process

Abstract

Determining nickel extraction during the roasting–reduction stage of the Caron process is an essential tool for controlling the metallurgical efficiency of the technology. This study evaluated the performance of a new semi-empirical kinetic model for predicting nickel extraction during the reduction of lateritic ores predominantly composed of iron oxides and oxyhydroxides in multiple-hearth furnaces. To achieve this, the lateritic ore was characterised by scanning electron microscopy (SEM) before and after the reduction process. The temperature in hearth six was varied between 495 and 780 °C by adjusting the post-combustion air supply. The proposed model demonstrated high predictive accuracy for nickel extraction, with absolute and residual errors below 1.70% and 1.15%, respectively. The findings emphasise the importance of controlling metallurgical efficiency through mathematical models that incorporate key technological variables and the kinetic behaviour of the process.

1. Introduction

Nickel (Ni) mining is currently regarded as an important, strategic and critical economic activity that makes a direct contribution to the promotion of sustainable development [1,2,3,4]. In 2024, 90% of nickel utilisation was directed towards the production of stainless steel (65%), batteries (17%) and alloys (8%) [5].

In recent years, owing to the depletion of high-grade nickel sulphide ores, lateritic ores have come to be regarded as the principal source of raw material [6,7]. The most recent estimates indicate that, of the 350 million tonnes of nickel identified worldwide, 54% is contained in lateritic deposits [8]. In general, the extraction of nickel involves the use of hydrometallurgical or pyrometallurgical processes, or a combination of both [9,10].

The hybrid pyro–hydrometallurgical technology known as the Caron process is one of the principal alternatives currently employed for nickel extraction, particularly in the processing of the limonite and transition zones of lateritic profiles [11,12,13]. Although considered by some to be uneconomical [14], it can be profitable during the processing of minerals with Ni and Iron (Fe) contents greater than 0.9% and 25% respectively [15,16,17].

In the Caron process, the roasting–reduction stage is a key step that ensures the chemical and mineralogical transformation of the lateritic ore [18,19]. On a commercial scale, multiple-hearth furnaces are used to carry out the roasting–reduction process. The key variables to be controlled are the particle size distribution of the ground ore, the thermal profile, and whether the reducing atmosphere is enriched with additives [15,20,21,22,23].

Specifically in Cuba, Ni extraction has traditionally been determined by Equation (1) [12,13,15,20,23]. Although its determination by the traditional method [18] is highly practical, the associated mathematical model has the limitation of not accounting for temperature variations in key hearths (such as hearth six) or for the furnace residence time. It considers only the Ni or cobalt (Co) and Fe contents before reduction (feed contents) and after the reduction and leaching of the ore (residual contents).

$$C_{Ext\text{-}Ni}=\left[1-{\displaystyle \frac{C_{Ni\text{-}leached ore}{C}_{Fe\text{-}fed}}{C_{Ni\text{-}fed}{C}_{Fe\text{-}leached ore}}}\right]100$$

(1)

where

C_Ext-Ni is the extracted content of the Ni or Co under analysis, %,

C_{Ni-leached ore} is the content of the Ni or Co in the ore after leaching, %,

C_Ni-fed is the content of Ni or Co in the ore fed to the reduction furnace,

C_Fe-fed is the content of iron in the ore fed to the reduction furnace, %,

C_{Fe-leached ore} is the content of iron in the ore after leaching, %.

Various studies (see

Table 1. Proposed polynomial models to determine Ni extraction in the roasting/reduction stage of the Caron process.

Authors (Year)	Equations	Equation Nº	Parameters (R2)
Chang, Arce and Toirac (2005) [24]	$C_{Ext\text{-}Ni}=-0.2428{\left({\displaystyle \frac{L}{S}}\right)}^2+3.8591\left({\displaystyle \frac{L}{S}}\right)+70.795$	(2)	L/S: Limonite/serpentine ratio in the ore fed to the furnace (0.4101)
Chang, Arce and Toirac (2005) [24]	$C_{Ext\text{-}Ni}=-0.0893{\left(M\right)}^2+1.7552\left(M\right)+77.039$	(3)	$\mathrm{M}: \mathrm{Ratio} \mathrm{of} \mathrm{the} \mathrm{mass} \mathrm{percentages} {\displaystyle \frac{Ni·Fe}{Mg·Si}}$ of the lateritic ore fed to the furnace (0.4080)
Angulo et al. (2021) [25]	$C_{Ext\text{-}Ni}=-0.000044{\left(T_{H\text{-}6}\right)}^2+0.041136\left(T_{H\text{-}6}\right)+80.28$	(4)	$T_{H\text{-}6}$: temperature of the hearth six of the furnace, °C Reducing additive: 2.5% fuel oil (0.9637)
Angulo et al. (2025) [26]	$C_{Ext\text{-}Ni}=-0.000037{\left(T_{H\text{-}6}\right)}^2+0.017714\left(T_{H\text{-}6}\right)+90.72$	(5)	$T_{H\text{-}6}$: temperature of the hearth six of the furnace, °C Reducing additive: Mixture of 2% bituminous coal and 1.25% fuel oil (0.9892)

) have proposed alternative polynomial mathematical models for determining nickel extraction at industrial and pilot scales; however, these have not fully addressed the limitations inherent in the traditional model.

Therefore, building on the findings of Angulo et al. [26] regarding the determination of the reaction rate constant as a function of the temperature in hearth six of the furnace (see Equation (6)), this study proposes to evaluate the accuracy of a new mathematical model for determining nickel extraction during the roasting–reduction stage of the Caron process. In addition, the study includes the mineralogical characterisation of the lateritic ore before and after the roasting–reduction process.

$$k=-0.000000002{\left(T_{H\text{-}6}\right)}^2-0.000033805\left(T_{H\text{-}6}\right)+0.056859445$$

(6)

where

k is reaction rate constant, min⁻¹,

T_H-6 is temperature of the hearth six of the furnace, K.

2. Materials and Methods

2.1. Experimental Data

For this study, a roasting/reduction process was carried out on a lateritic ore (previously dried and ground) with a high degree of homogenization at three temperature profile levels (described by [26]) for five days of continuous operation each. The pilot multi-hearth furnace used in this study closely mirrored the design reported by Angulo et al. [12,15]. This configuration ensured that the lateritic ore, fed from the top, was in direct counter current contact with the reducing gases generated in the combustion chamber—which contained considerable concentrations of CO (see Figure 1). The main operating parameters and the values of the reaction rate constant (as a function of the post-combustion air level supplied to the furnace), are presented in

Table 2. Relevant data on operating conditions and kinetics from Figure 1.

Main Operating Variables
Laterite ore feeding, kg/h	750
Amount of hearth (H)	17
Amount of chamber	2
Temperature in H-0, °C *	205–285
Temperature in H-4, °C *	350–460
Temperature in H-6, °C *	495–780
Temperature in H-9, °C	675
Temperature in H-11, °C	718
Temperature in H-13, °C	742
Temperature in H-15, °C	780
Temperature in chamber, °C	1380–1400
Fuel fed by the chamber	Fuel oil
Reducing additive	Mixture of 2% bituminous coal and 1.25% fuel oil
Residence time, min	80
Days of continuous operation	15
Reaction rate constant values
No post-combustion H-6 (TH-6 = 495 °C, min−1)	0.0298
Low post-combustion H-6 (TH-6 = 660 °C, min−1)	0.0240
High post-combustion H-6 (TH-6 = 780 °C, min−1)	0.0190

* The temperature value depends on the level of post-combustion air supply.

.

2.2. Analytical Techniques

The chemical characteristics of the lateritic ore and the reduced/leached mineral (see values reported in

Table 3. Relevant data on lateritic ore.

Characteristics of Lateritic Ore
Limonite/serpentine ratio	3/1
Mass content of Ni and Fe, % (σ)	1.17 and 39.32 (<0.42)
Mass content of MgO, SiO2 and Al2O3, % (σ)	2.83, 7.79 and 8.08 (<0.52)
Moisture content, % (σ)	3.66 (<0.23)
Degree of homogenization, %	≥90
Particle size < 75 μm, %	84–88

σ is standard deviation.

and Appendix A respectively) were determined by atomic absorption spectrometry (AAS, model SOLAR 929, Solar System ATI, Unicam Analytical Technology Inc., Cambridge, UK).

Scanning electron microscopy (SEM) was used for the phase characterisation of the lateritic ore before and after the roasting–reduction process. Initial observations were carried out using binocular optical microscopy with a MEIJI EMZ-5TR microscope (Meiji Techno Co., Ltd., Miyoshi-machi, Iruma-gun, Saitama, Japan), operating at magnifications ranging from 7× to 45×. The analyses were performed under incident light. In addition, images and spectra were obtained using a Tescan MIRA 3 microscope (Tescan, Brno, Czech Republic) equipped with an Oxford Instruments INCA Energy X-ray analyser (Brno, Czech Republic). The main operating conditions are presented in

Table 4. Working conditions during SEM analysis.

Electron Microscope
Detectors	Secondary and backscattered electrons
Acceleration voltage	20 kV
Working distance	15 mm
Beam current	At position 10
Stage inclination	0 degrees
X-ray microanalysis
Processor	PT 5
Acquisition time	30 s (live time)
Swept area	Rectangular, inscribed

.

Additionally, powder XRD analyses were performed on the lateritic ore (before feeding and after reduction/leaching) to obtain a more detailed understanding of the crystalline structure, using a PANalytical X’PERT3 diffractometer (Malvern Panalytical, Malvern, Worcestershire, UK).

Table 5. Working conditions during XRD analysis.

XRD
Sweep; Angular registration	Gonio type
Angular registration	[°2θ] from 4.0042° to 79.9962°
Step distance	0.0080°
Radiation	Cu
Filter	Ni
Potential difference and current	40 kV and 30 mA
Calibration checked	External silicon standard scanning

presents the main working conditions of the team. Phase identification was performed using HighScore Plus v3.0.2 software and the Crystallography Open Database (COD, 2014), applying a routine analysis based on the major chemical constituents of each sample.

2.3. Methodology for the Evaluation of the New Mathematical Model

To validate the modified mathematical model, independent experimental data were used, specifically those reserved for determining Ni extraction during the 15 days of continuous operation (4 daily values during the five days of evaluation of the thermal profiles without afterburner and with low and high afterburner, respectively). In general, the following steps were performed:

(a)

Substitute the unconverted fraction of nickel in Equation (1) by incorporating the kinetic model based on T_H-6, based on the experiences obtained by Angulo et al. [26]; see Equations (7) and (8).

$$C_{Ext\text{-}Ni}=\left[1-\left({\displaystyle \frac{C_{Ni\text{-}leached ore}}{C_{Ni\text{-}fed}}}\right)\left({\displaystyle \frac{C_{Fe\text{-}fed}}{C_{Fe\text{-}leached ore}}}\right)\right]100$$

(7)

$$C_{Ext\text{-}Ni}=\left[1-{e_{Ni}}^{-kt}\left({\displaystyle \frac{C_{Fe\text{-}fed}}{C_{Fe\text{-}leached ore}}}\right)\right]100$$

(8)

where:

t is residence time, min.

(b)

Substitute Equation (6) in Equation (8) and evaluate the new and conventional model based on experimental results obtained at pilot scale.

(c)

Determine the percentage of error of the new model, with respect to the conventional one, with Equation (9).

$$\epsilon =\left({\displaystyle \frac{C_{Ext\text{-}N{i}_{New}}-C_{Ext\text{-}N{i}_{Conventional}}}{C_{Ext\text{-}N{i}_{Conventional}}}}\right)100$$

(9)

(d)

Analysis and interpretation of the results obtained.

3. Results and Discussion

3.1. Mineralogical Characteristics of Lateritic Ore Before and After the Roasting/Reduction Process

Figure 2 and Figure 3 show the mineralogical phases and the distribution of the main chemical elements present in the lateritic ore.

It is observed that Fe and oxygen (O) predominate in the lateritic ore fed, mainly associated with the mineralogical phases goethite [FeOOH; Ref. Code: 00-029-0713], maghemite [Fe_21.16O_31.92; Ref. Code: 01-089-5892] and hematite [Fe₂O₃; Ref. Code: 01-079-0007]. Ni is uniformly distributed throughout the sample and shows a high degree of association with the iron within the crystalline structure of FeOOH. A small proportion of silicon (Si) combines with oxygen to form quartz [SiO₂; Ref. Code: 01-083-0539]. However, it is important to note that the combination of magnesium (Mg), silicon and oxygen forming lizardite [Mg₃Si₂O₅(OH)₄; Ref. Code: 01-073-1336] represents the most predominant serpentine phase present in the sample. Finally, aluminium (Al) is associated with oxygen in the form of gibbsite [Al(OH)₃; Ref. Code: 01-076-1782] within the ore.

In the case of the reduced ore (see Figure 4, Figure 5 and Figure 6), Fe and O are observed as the predominant elements, mainly in the form of the magnetite [Fe₃O₄; Ref. Code: 01-088-0866] and the maghemite produced [Fe₂O₃; Ref. Code: 00-004-0755]. These elements also combine with Mg–Cr–Al or Mg–Si to form the magnesiochromite and ferroan phases [(Mg,Fe)(Cr,Al)₂O₄; Ref. Code: 00-009-0353] as well as fayalite [Mg_2.6Fe_1.74(SiO₄); Ref. Code: 01-079-1207], respectively.

These results confirm that the roasting/reduction stage of the lateritic ore is adequate, highlighting the dehydroxylation of FeOOH and the formation of Fe₃O₄ and Mg_2.6Fe_1.74(SiO₄) as the principal transformations. Furthermore, Ni is uniformly distributed throughout the sample, irrespective of the level of post-combustion air fed into furnace hearth six and is associated with the leachable taenite phase (Fe–Ni alloy), while some remains trapped within the structure of the spinels formed. Overall, both the feed and the reduced ore exhibit characteristics similar to those of samples used in previous studies [12,15,19,26,27,28].

Finally, it is important to highlight that the shapes of the peaks and the raised background in Figure 2 and Figure 4 suggest amorphous phases in the samples fed into the furnace and reduced/leached. However, these phases did not have a significant impact on Ni extraction, which exceeded 80% in each experiment (see

Table A1. Results of the validation of the new model for the determination of Ni extraction without post-combustion (TH-6 range: 490–500 °C).

Days of Operation	N°	Reduced/Leached Mineral, %		Ni Extraction by Equation (1), %	TH-6, °C	k Equation (6), min−1	Ni Extraction by Equation (8), %	Error, %
		Ni	Fe
1	1	0.123	48.16	91.39	498	0.0296	92.35	1.05
	2	0.128	46.79	90.78	495	0.0297	92.20	1.56
	3	0.122	45.53	90.97	493	0.0298	92.03	1.16
	4	0.125	46.83	91.01	492	0.0298	92.27	1.39
2	5	0.126	47.33	91.03	496	0.0297	92.26	1.36
	6	0.120	47.03	91.40	491	0.0299	92.33	1.01
	7	0.121	47.45	91.41	494	0.0298	92.33	1.01
	8	0.125	48.15	91.25	499	0.0296	92.33	1.18
3	9	0.115	48.62	92.03	500	0.0295	92.38	0.38
	10	0.120	48.16	91.60	490	0.0299	92.53	1.01
	11	0.120	47.28	91.45	492	0.0298	92.35	0.98
	12	0.117	48.38	91.85	498	0.0296	92.39	0.58
4	13	0.131	46.83	90.57	499	0.0296	92.11	1.70
	14	0.125	46.07	90.86	499	0.0296	91.98	1.24
	15	0.127	46.24	90.75	500	0.0295	91.99	1.37
	16	0.129	45.82	90.51	500	0.0295	91.91	1.55
5	17	0.121	46.30	91.19	498	0.0296	92.05	0.93
	18	0.119	46.17	91.32	494	0.0297	92.12	0.88
	19	0.117	44.29	91.10	490	0.0299	91.88	0.86
	20	0.123	44.11	90.60	492	0.0298	91.80	1.32
	Average	0.123	46.77	91.15	496	0.0297	92.18	1.13

,

Table A2. Results of the validation of the new model for determining Ni extraction with low post-combustion (TH-6 range: 655–665 °C).

Days of Operation	N°	Reduced/Leached Mineral, %		Ni Extraction by Equation (1), %	TH-6, °C	k Equation (6), min−1	Ni Extraction by Equation (8), %	Error, %
		Ni	Fe
1	1	0.195	47.05	86.03	665	0.0234	87.13	1.27
	2	0.189	46.77	86.38	662	0.0235	87.17	0.91
	3	0.189	46.65	86.35	660	0.0236	87.21	1.00
	4	0.182	47.81	87.17	664	0.0234	87.37	0.23
2	5	0.192	47.36	86.34	655	0.0238	87.59	1.45
	6	0.200	47.73	85.88	665	0.0234	87.31	1.67
	7	0.194	48.38	86.49	656	0.0237	87.82	1.54
	8	0.199	48.42	86.15	665	0.0234	87.49	1.56
3	9	0.194	47.99	86.38	660	0.0236	87.57	1.38
	10	0.195	46.75	85.95	662	0.0235	87.16	1.42
	11	0.189	47.02	86.46	665	0.0234	87.12	0.77
	12	0.194	47.52	86.24	655	0.0238	87.63	1.61
4	13	0.190	45.85	86.04	657	0.0237	87.11	1.24
	14	0.183	48.43	87.27	655	0.0238	87.87	0.69
	15	0.189	46.42	86.28	660	0.0236	87.15	1.01
	16	0.194	47.08	85.97	661	0.0235	87.29	1.53
5	17	0.193	48.28	86.53	658	0.0236	87.72	1.37
	18	0.194	47.73	86.30	660	0.0236	87.50	1.38
	19	0.197	46.63	85.76	662	0.0235	87.13	1.59
	20	0.195	47.57	86.19	661	0.0235	87.42	1.43
	Average	0.192	47.37	86.29	660	0.0237	87.40	1.25

and

Table A3. Results of the validation of the new model for determining Ni extraction with high post-combustion (TH-6 range: 775–785 °C).

Days of Operation	N°	Reduced/Leached Mineral, %		Ni Extraction by Equation (1), %	TH-6, °C	k Equation (6), Min−1	Ni Extraction by Equation (8), %	Error, %
		Ni	Fe
1	1	0.241	48.72	83.76	779	0.0191	82.46	1.56
	2	0.233	48.33	83.42	781	0.0190	82.21	1.45
	3	0.237	48.58	83.50	778	0.0191	82.46	1.25
	4	0.235	47.94	83.55	775	0.0192	82.39	1.40
2	5	0.229	47.72	83.87	775	0.0192	82.31	1.87
	6	0.239	49.19	83.71	777	0.0192	82.73	1.17
	7	0.234	48.84	83.77	779	0.0191	82.50	1.51
	8	0.253	48.53	82.36	783	0.0190	82.17	0.23
3	9	0.271	49.43	81.11	785	0.0188	82.39	1.58
	10	0.276	48.27	81.08	780	0.0190	82.24	1.43
	11	0.268	48.78	81.15	782	0.0190	82.32	1.43
	12	0.270	48.01	80.84	779	0.0191	82.20	1.68
4	13	0.273	48.45	80.98	783	0.0189	82.14	1.44
	14	0.271	48.16	80.90	785	0.0188	81.93	1.26
	15	0.263	47.96	81.01	781	0.0190	82.07	1.31
	16	0.265	47.39	80.83	781	0.0190	81.85	1.27
5	17	0.259	47.84	82.04	779	0.0191	82.13	0.12
	18	0.246	48.14	82.77	777	0.0192	82.35	0.50
	19	0.261	49.05	82.21	774	0.0193	82.84	0.75
	20	0.255	48.09	82.23	777	0.0192	82.33	0.12
	Average	0.254	48.37	82.26	780	0.0191	82.30	1.17

in Appendix A).

3.2. Evaluating the Effectiveness of the New Model

Figure 7 and Figure 8 (see Appendix A) present the results of the evaluation of the new semi-empirical kinetic model developed to determine Ni extraction during the roasting/reduction stage of the Caron process.

Comparison with the conventional model demonstrates that the new model ensures high effectiveness in determining Ni extraction, irrespective of operating conditions, with a coefficient of determination greater than 0.97 and mean absolute and residual errors of less than 1.70% and 1.15%, respectively. The residuals obtained from the difference between the results of both models do not exceed 1.40%, highlighting the high precision of the proposed model, as the differences in extraction are within ±1.50% (the error estimation range of the conventional model according to [25]).

4. Conclusions

The effectiveness of a new semi-empirical kinetic model was evaluated for determining Ni extraction during the roasting/reduction of lateritic ores (with a limonite/serpentine ratio of 3:1 and a predominance of Fe oxides and hydroxides) in a multi-hearth pilot furnace operating under the Caron process. Overall, the integrated analysis of the results indicates that the proposed model predicts Ni extraction with high accuracy, with residuals below 1.40% and the coefficients of determination exceeding 0.97. In the future, owing to the depletion of the limonitic zone in lateritic deposits, it will be necessary to develop mathematical models capable of predicting nickel extraction in the Caron process when treating lateritic blends containing a higher mass percentage of saprolite, as well as mixtures with varying proportions of overburden and saprolite. Furthermore, it will be of interest to model the combined effect of post-combustion air injection in furnace hearths four and six during the introduction of lateritic mixtures into the pyrometallurgical process.