Centrifugal separation experimentation and optimum predictive model development for copper recovery from waste copper smelter dust

This research has presented a three level-two factors full factorial experimental design that investigated the process parameterization of a centrifugal concentrator for the separation of a waste copper smelter dust (CSD). This was followed by a theoretical contribution involving the development of a scheme of predictive models premised on the concept of constrained interpolant models. These were used for the experimental trend, pattern investigation and furthermore to provide expressions that depicts optimal experimental conditions in this research. Based on the experimental outputs, it was observed that a maximum grade of about 35.02 wt% Cu was achieved at a Rotational Bowl Speed of 120G, Water Flow Rate of 3.0l/min and constant experimental flow rate of 1.48l/min with a Liquid to Solid Ratio of 0.5. Similarly, a minimum output of 14.58% SiO2 and 10.29% Al2O3 was achieved at same experimental conditions. This clearly depicts a trend geared towards optimum experimental conditions aimed at maximizing Cu output and Daniel Okanigbe ABOUT THE AUTHOR Mr. Daniel Okanigbe is a trained geoscientist with a bachelor’s degree from the department of applied geology and geophysics, Obafemi Awolowo University, Ile-ife, Osun State, Nigeria. He obtained a Master’s degree in metallurgy from University of Lagos, Akoka, Nigeria. He is about completing his doctoral study in the field of Engineering from the department of Chemical, Metallurgical and Materials Engineering, Faculty of Engineering and the Built Environment, Tshwane University of Technology, Pretoria, Republic of South Africa. His area of research interest stretches from igneous and metamorphic petrology, applied exploration and economic geology, structural geology, geological mapping, geochemistry, geochronology, hydrometallurgy, pyrometallurgy, mineral processing, nanotechnology, flowsheet design, with particular emphasis on waste management and treatment. At the moment, he is working on a project aimed at producing a novel process flowsheet for the recovery of copper from a waste CSD, a metallurgical waste material from primary copper ore processing. PUBLIC INTEREST STATEMENT The research was divided into two phases viz: the experimental and modeling phases. The experimentation which preceded the modeling phase was carried out via a three level-two factors experimental design. This investigated the process parameterization of a centrifugal concentrator for the separation of copper smelter dust (CSD). Following, was the development of a predictive model that aimed at recovering the experimental data pattern. The modeling is premised on developed constrained interpolation models. This was able to generate the optimal experimental conditions for this research and a trend capable of predicting future experimental output based on the set conditions. An additional experimental trend recovery was carried out using a tenth-order polynomial curve fitting in Matlab software. Both the constrained interpolation modeling and polynomial curve fitting produced a good output. However, the level of recovery accuracy was higher with the constrained interpolant modeling. Okanigbe et al., Cogent Engineering (2018), 5: 1551175 https://doi.org/10.1080/23311916.2018.1551175 © 2018 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. Received: 05 September 2018 Accepted: 19 November 2018 First Published: 22 November 2018 *Corresponding author: Okanigbe Daniel, Department of Chemical, Tshwane University of Technology, Pretoria 0183, South Africa E-mail: odanielifeoma@yahoo.com; odanielsade@gmail.com Reviewing editor: Julio Sánchez, Universidad de Santiago de Chile, Chile Additional information is available at the end of the article

Abstract: This research has presented a three level-two factors full factorial experimental design that investigated the process parameterization of a centrifugal concentrator for the separation of a waste copper smelter dust (CSD). This was followed by a theoretical contribution involving the development of a scheme of predictive models premised on the concept of constrained interpolant models. These were used for the experimental trend, pattern investigation and furthermore to provide expressions that depicts optimal experimental conditions in this research. Based on the experimental outputs, it was observed that a maximum grade of about 35.02 wt% Cu was achieved at a Rotational Bowl Speed of 120G, Water Flow Rate of 3.0l/min and constant experimental flow rate of 1.48l/min with a Liquid to Solid Ratio of 0.5. Similarly, a minimum output of 14.58% SiO 2 and 10.29% Al 2 O 3 was achieved at same experimental conditions. This clearly depicts a trend geared towards optimum experimental conditions aimed at maximizing Cu output and Daniel Okanigbe ABOUT THE AUTHOR Mr. Daniel Okanigbe is a trained geoscientist with a bachelor's degree from the department of applied geology and geophysics, Obafemi Awolowo University, Ile-ife, Osun State, Nigeria. He obtained a Master's degree in metallurgy from University of Lagos, Akoka, Nigeria. He is about completing his doctoral study in the field of Engineering from the department of Chemical, Metallurgical and Materials Engineering, Faculty of Engineering and the Built Environment, Tshwane University of Technology, Pretoria, Republic of South Africa. His area of research interest stretches from igneous and metamorphic petrology, applied exploration and economic geology, structural geology, geological mapping, geochemistry, geochronology, hydrometallurgy, pyrometallurgy, mineral processing, nanotechnology, flowsheet design, with particular emphasis on waste management and treatment. At the moment, he is working on a project aimed at producing a novel process flowsheet for the recovery of copper from a waste CSD, a metallurgical waste material from primary copper ore processing.

PUBLIC INTEREST STATEMENT
The research was divided into two phases viz: the experimental and modeling phases. The experimentation which preceded the modeling phase was carried out via a three level-two factors experimental design. This investigated the process parameterization of a centrifugal concentrator for the separation of copper smelter dust (CSD). Following, was the development of a predictive model that aimed at recovering the experimental data pattern. The modeling is premised on developed constrained interpolation models. This was able to generate the optimal experimental conditions for this research and a trend capable of predicting future experimental output based on the set conditions. An additional experimental trend recovery was carried out using a tenth-order polynomial curve fitting in Matlab software. Both the constrained interpolation modeling and polynomial curve fitting produced a good output. However, the level of recovery accuracy was higher with the constrained interpolant modeling.
minimizing SiO 2 and Al 2 O 3 impurities. The predicted outputs premised on the use of Matlab software are in good conformance with the experimental outputs with a high degree of accuracy and confidence level over 97% as shown in Table 1 and corresponding Figures.

Introduction
In the last few decades, the literature of extractive metallurgy has extended its research needs to proffering alternative and sustainable solutions for the readily availability of metallic resources. This measure has become very necessary for sustainability of the earth amongst other deteriorating environmental factors. One promising alternative measure for metallic extraction other than exploring the earth surface is the approach of scrap materials smelting. The smelting of abandoned scrap materials for the purpose of harnessing specific metals does not only aid in sustainability of the earth but controls and minimizes environmental pollution posed through non-biodegradable solid wastes in form of metallic solid wastes and powdery materials amongst others. This research is focused at providing both experimental and mathematical modeling solutions capable of exploring the effectiveness of a proposed experimental technique. A predictive modelling scheme premised on the use of constraint interpolants was used to model the percentage output proportion from the extraction and refinement of copper concentrates via smelting of scrap metallic copper concentrate also referred to as waste CSD.The process is not without its own challenges characterized usually with waste generation. The waste CSD contains a substantial amount of copper in close association with environmentally toxic compounds such as Arsenic, Bismuth, Lead, Antimony and Cadmium capable of affecting the purity of the refined copper. The generation of waste CSD is almost becoming a global menace requiring that stringent environmental regulations be put in place to inhibit its generation (Montenegro, Sano, & Fujisawa, 2008). However, the waste CSD if well harnessed and managed can be a sustainable secondary source of copper. Hence, the need for an appropriate technology becomes inevitable, principally from the stand point of mineral conservation, utilization of scanty copper resource and its sustainability. Mineral processing techniques can be employed as a pretreatment method to reduce the amount of contaminants in the waste CSD before subjecting the produced concentrate to hydrometallurgical treatments (Geldenhuis, 2002). Additionally, most of the heavy minerals are treated in gravity concentration at different stages of upgradation (Demi, Koci, & Boci, 2006;Meloy, Williams, Bevilacqua, & Ferrara, 1994). Furthermore, gravity concentration is considered advantageous because of its simplicity, low operating cost and ease of operation. However, the average size of this waste CSD falls within the size range of 5-50 µm; (Ha, Kwon, Park, & Mohapatra, 2015;Morales, Cruells, Roca, & Bergó, 2010;Okanigbe, Popoola, & Adeleke, 2017a, 2017b, a size range only the modern gravity techniques e.g. Knelson ( Figure 1) and Falcon concentrators have proven useful in separation of materials into different fractions (Wills & Finch, 2015). As expected in mineral processing a rigorous and costly experimental evaluation of laboratory and pilot-scale equipment trials are carried out to ascertain the performance of any unit operation. Consequently, designing a low cost, time saving tool (model), with the capacity to correctly predict the separation results of the unit operation would be advantageous.
The success of separation with centrifugal concentrator is a function of the selection of appropriate process variables at which the response attains its optimum. One of the approaches for achieving the optimum results is the Design of Experiments (DOE) using the full Factorial Methodology (FFM). Several experimental designs can be used for different objectives, just as the randomized block designs can be used for screening relevant factors (Aslan, 2008;Xiao & Vien, 2004).Some reports exist in literature of modeling methods been used in mineral and coal processing operations (Akar Sen, 2016). Optimization and modeling studies of hydrocyclone for treating Indian iron ore slime is an example (Mohanty & Das, 2010) as well as low-grade bentonite (Özgen, Yıldız, Çalışkan, & Sabah, 2009). Response surface methodology has also been used to assess the performance of the froth floatation on coal fines (Kalyani, Pallavika, Gouri Charan, & Chaudhuri, 2005). A Second order quadratic model was created by using the response surface methodology for separation of titanium bearing minerals from Indian beach sand minerals (Gunaraj & Murugan, 1999). In this investigation, the experiments were carried out as per the full factorial design, with an objective to develop the empirical models for predicting the maximum percentage grade in concentrate fraction of the centrifugal concentrator while treating waste CSD. The optimum conditions were obtained for achieving maximum grade and recovery of the concentrate fraction. The effects of different operating parameters Fluidized water flow rate (FWFR), Rotational bowl speed (RBS) on percentage grade of copper and its closely associated contaminants in concentrate fraction while treating waste CSD are presented.

Ore handling and sampling
Precisely 120 kg of waste CSD was received from Palabora Copper (PTY) Ltd, Limpopo, Republic of South Africa for the purpose of this study. The homogenization of the as-received waste CSD sample was carried out first by re-weighing it before subjecting it to coning and quartering method. The homogenized waste CSD was separate into two categories-undersized and oversized particles with a 300 micron sieve. The oversized particles were afterwards milled and sieved with the same 300 micron sieve and the produced undersized particles were mixed with the previously produced undersized waste CSD (segment diameter d 97 = 300 micron). After the milling and sieving exercise, the amount of particles with diameter less than 300 micron increased from 90.82% of total number of particles in the sample to 95.59%.This change is shown by the distribution curve before (Figure 2(a)) and after sample preparation (Figure 2(b)). After milling, the distribution curve ( Figure 2(b)) became skewed to the left making the distribution asymmetric.

Design of experiment (DOE) for centrifugal separation experiment
The DOE is based on principles of experimental design, mathematical equations or models and outcomes of the factors. In the present study, the FFM was used to determine the interaction

Modeling
2.2.2.1. Modeling procedure for output prediction. Software MATLAB 7.1 was used to perform data processing according to full factorial design procedure.
Step #1: Study trend of experimental samples Step #2: Set-up constraint models to categorize and group samples into sub-classes based on #1.
Step #3: Compute absolute difference between input and output samples in same class as grouped in #2.
Step #4: identify different experimental levels for selected classes.
Step #5: Apply interpolant model Step #6: End Table 4 is a generalized representation of the interpolant model variables. Herein, the assumed unknown output is for row one hence $ 1 is first computed. The Predicted output model O o 1 is trend driven and constraint based as presented in the following sub-section. Table 4 can however be adapted to compute $ 2 and $ 3 as the case may be. Given: Output = Output ¼ f ðspeed; flow rate; input; feed rate; liquid solid ratioÞ Let: serial number for inputs: s i ¼ 1; ::::; n À 1; n f g and serial number for outputs s o ¼ 1; ::::; n À 1; n f g for "n 2 R Where: ts ðiÞi;j ¼ Total available input samples ts ðoÞi;j ¼ Total available output samples exp ðiÞi;j ¼ Experimental inputs Where: j ¼ 1; :::; k À 1; k f g representing experimental levels Given the following absolute differences between I ij and O o j "Absolute difference" model with respect to Table 4 is given as: Expressions (4) to (14) represent the different constraint interpolant models proposed for this research. The constraint models are experiment specific with a corresponding positive or negative incremental difference between the input and output experimental proportion.
A complimentary curve fitting model of 10th order polynomial was also presented as shown in Equations (15)-(19).The 10th order polynomial curve fitting was adjudged the best fitment for this experiment amongst the different fitment option. While (15) represents a generalized form of the polynomial functions, (16)-(19) are specific functions with-respect-to the different concentrates in the mix.

Results and discussion
This section presents the simulation results of this research in two folds viz: experimentation and predictive outputs Firstly, considering the experimental procedure, it should be noted that the experiments were carried out using the KGC to separate the copper minerals from the closely associated impurities in the waste CSD. The experimental outputs of the beneficiation process alongside the respective operating conditions are presented in Table 4. The predictive outputs presented in Table 1 were obtained using an interpolant interval of 0.75units within the FWFR levels. At this interval, the entire experimental outputs as presented in Table 1 were adequately recovered for the different input feed concentrates viz: CuO, Fe 2 O 3 , SiO 2 , and Al 2 O 3 . The maximum error obtained between the predicted and experimental outputs is 1.86units. This is contained in

1-First Prediction
serial number 6 of Table 1 and under the CuO column. The experimental output herein is 23.74 wt % while the predicted is 25wt%. The predicted intervals without experimentations for varying levels of RBS and FWFR are with a high degree of accuracy ranging between 95 and 99% based on the extremely minimal discrepancy between the experimented and predicted outputs. In addition, Figures 3 through 6 present a graphical representation of specific predicted outputs and corresponding FWFR levels.
The graphical trend for CuO as contained in Figure 3 presents the lowest predictive value of 18.43 wt% when FWFR is 6.0 l/min with a RBS value of 60G. The highest predictive value of 35.02 wt% was obtained as RBS increased to 120G and for a corresponding lowest value of 3.0l/ min for FWFR. In Figure 4, results for Fe 2 O 3 are presented with an observed output trend similar to that of Figure 3. The least predictive value of 15.76 wt% was obtained for RBS of 60G and FWFR of 6.0 l/min. A higher value was obtained for CuO over Fe 2 O 3 as the RBS increased to a peak value of 120G perhaps due to a much higher concentration criterion (CC) between CuO  (specific gravity (S.G.) of 6.50) and the impurities-SiO 2 -(specific gravity of 2.13) and Al 2 O 3 -(specific gravity of 3.4) than for the CC between Fe 2 O 3 (specific gravity of 4.2) and the same impurities in the waste CSD amongst other factors. As mentioned earlier, the two major impurities present in the experimental waste CSD includes: SiO 2 and Al 2 O 3 . Unlike the behavioral pattern presented by outputs of CuO and Fe 2 O 3 compounds, Sio 2 and Al 2 O 3 compounds as respectively shown in Figures 5 and 6 both have peak predictive outputs of 31.37 wt% and 24.68 wt% at the least RBS of 60G and a corresponding FWFR value of 6.0 l/min. Similarly, the least predictive output values for Sio 2 and Al 2 O 3 were obtained while RBS was high at 120G at a corresponding low FWFR value of 3l/min. The accuracy of the experimentation process is reflected in the output data. Also, the impact of the predicted data in this research firstly, lies in the area of experimental cost savings by avoiding set-up costs, resource acquisition cost, cost of safety adherence and accidents amongst others. Furthermore is the facilitation of an efficient and effective long and short-term planning process prior to the conduct of an experiment. In addition, on comparing the predicted data (premised on the constrained interpolant  model) with the experimental data, a high level of statistical correlation was recorded. While CuO had a least square correlation coefficient of 0.992, Fe 2 O 3 , SiO 2 and Al 2 O 3 , respectively, had correlation coefficients of 1.000.

Conclusion
On a generalized note, this research has effectively demonstrated some competence by showing how the interactive effects of statistical attributes such as factorial design, optimum conditions etc., related to an experiment can be applied on experimental data for the accurate prediction of computational data. This can be linked to the work presented by Fagade, Tande, Cho, Seames, Sakodynskaya, Muggli, & Kozliak (2013) which stated that statistical studyspecific terms such as "effect," "factorial design," "interaction effect," "factors," "optimum condition" etc. are not common terminologies for general readers. Furthermore, this research has presented the experimental classification and mathematical prediction of Copper mineral in close association with contaminants in the waste CSD using the Knelson centrifugal gravity concentrator. The classification and predictive efforts in this research were achieved by setting up optimum combinations of the process parameters for the centrifugal concentrator. The four process parameters considered in this study include: FWFR, RBS, Flow rate of 1.48l/min and a Liquid to Solid Ratio of 0.5. The model proposed in this research was developed to maximize Cu output and minimize the output of SiO 2 and Al 2 O 3 impurities. The following deductions were reached in this research: • KGC separated the waste CSD's particles into light and heavy minerals with maximum CuO recovery and minimum SiO 2 and Al 2 O 3 recoveries in the resultant concentrates.
• Optimum separation conditions (giving highest CuO content and reduced amount of contaminants in concentrate) were: FWFR 3.0 l/min. and RBS 120G.
• The predicted values obtained using the models were in good agreement with the observed values with an error margin between 0.00 and 0.06%.
• Both variables considered i.e. FWFR and RBS had major influence on the experimentation process of the concentrates from the centrifugal concentrator.
• From the model, further outputs can be generated without any laboratory experimental effort.
• Future predictive work would present an automated algorithm capable of considering two or more experimental varying factors.