# Gold removal from gold-bearing ore using alpha-cyclodextrin: Response surface methodology and artificial neural analysis network optimizations

Meschack Mukunga Muanda, Pele Pascal Daniel Omalanga, Vanessa

Mwambaie Mitonga, Michée Ngoy Ilunga

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Meschack Mukunga Muanda, Pele Pascal Daniel Omalanga, Vanessa Mwambaie Mitonga, Michée Ngoy Ilunga. Gold removal from gold-bearing ore using alpha-cyclodextrin: Response surface methodology and artificial neural analysis network optimizations. ITEGAM- Journal of Engineering and Technology for Industrial Applications (ITEGAM-JETIA), 2023, 9 (42), pp.48-60. 10.5935/jetia.v9i42.879. hal-05128979

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Submitted on 25 Jun 2025

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RESEARCH ARTICLE

OPEN ACCESS

GOLD REMOVAL FROM GOLD-BEARING ORE USING ALPHA-
CYCLODEXTRIN: RESPONSE SURFACE METHODOLOGY AND
ARTIFICIAL NEURAL ANALYSIS NETWORK OPTIMIZATIONS

Meschack Mukunga Muanda*<fnref n="1" />, Pele Pascal Daniel Omalanga<fnref n="2" />, Vanessa Mwambaie Mitonga<fnref n="3" /> and Michée Ngoy Ilunga<fnref n="4" />

Email: *es-meschack.mukunga@alexu.edu.eg, omapele@gmail.com, mitongavanessa@gmail.com, micheeilunga@gmail.com

ARTICLE INFO

Article History

Received: August 04th, 2023

Revised: August 21th, 2023

Accepted: August 28th, 2023

Published: August 31st, 2023

Keywords:

ANN,

RSM,

Alpha cyclodextrin,

Eco-friendly,

Gold,

Modified aqua regia,

ABSTRACT

This paper explores the use of alpha cyclodextrin (α-CD) for gold extraction from gold-
bearing ore in the Democratic Republic of Congo (D.R.C). The research aims to identify the
optimal gold removal conditions using Response Surface Methodology (RSM) and
Artificial Neural Networks (ANN). Initially, ore samples were collected and processed to
enhance leachability by reducing particle size. The leaching process employed a modified
aqua regia with hydrobromic acid due to the strong molecular recognition between gold
bromide ion and α-CD. Various leaching parameters, such as time, HBr concentration, pH,
and stirring speed, were adjusted during experimentation. RSM yielded optimal values of
7.27 hours, 50 g/L, 1, and 200 rpm, resulting in 98.54% gold removal, while ANN produced
slightly lower values of 7.5 hours, 50 g/L, 1, and 200 rpm, with 97.16% gold removal. For
α-CD gold recovery, RSM and ANN optimization resulted in 40 minutes, 11.61 g/L, and pH
5, achieving 98.87% and 39.8 minutes, 10.71 g/L, and pH 5, with 99.98% gold removal,
respectively. Validation tests supported these findings, indicating that RSM and ANN are
successful methods for optimizing gold recovery from gold-bearing ore in the D.R.C.

<figure><img src="image_3.png" /></figure>

Copyright ©2023 by authors and Galileo Institute of Technology and Education of the Amazon (ITEGAM). This work is licensed
under the Creative Commons Attribution International License (CC BY 4.0).

I. INTRODUCTION

The concentration of the metal being extracted is a
determining factor in the profitability of mining a specific ore,
while the physical and chemical characteristics of gold affect the
methods used for its processing. In the Democratic Republic of
the Congo (D.R.C.), the basement is rich in many minerals which
contain many metals in different proportions [1-2]. Gold is mainly
found in the South Kivu and Ituri provinces, where artisanal
mining is prevalent. Child labor is common in the industry and
the D.R.C. government has ratified the International Labour
Organization's Convention on the Worst Forms of Child Labour,

and more needs to be done to eliminate child labor in the mining
industry [3-4].

Gold mining is a complex process that involves exploration, processing, development, and extraction, among other steps. According to [5], gold is typically found in concentrated deposits, which makes mining more viable. The authors also note that there are three main methods of gold mining: open-pit mining, underground mining, and artisanal mining. Open-pit mining is used when the ore deposit extends deep into the ground, and it involves the removal of layers of overburden and ore. Underground mining, on the other hand, is used for deeper deposits and may involve the use of supports. As noted by [6], artisanal mining typically involves manual

<footnote n="1">¹ Alexandria University, Faculty of Engineering, Chemical Engineering Department, Alexandria, Egypt.</footnote>

<footnote n="2">² University of Lubumbashi, Faculty of Polytechnic, Chemical Engineering Department, Lubumbashi, Democratic Republic of the Congo.</footnote>

<footnote n="3">³ Civil Engineering Department, School of Industrial Engineers, University of Lubumbashi, Democratic Republic of the Congo.</footnote>

<footnote n="4">⁴ Electrical Engineering (Computer Engineering) Department, School of Industrial Engineers, University of Lubumbashi, Democratic Republic of the Congo.</footnote>

<footnote n="1">¹ http://orcid.org/0000-0002-0094-7873 ID,
² http://orcid.org/0000-0003-3991-9957 ID,
³ http://orcid.org/0009-0008-2010-4073 ID,</footnote>

<footnote n="4">⁴ http://orcid.org/0009-0006-4963-8584 ID</footnote>
extraction and concentration of minerals, including gold, often using traditional methods. Mechanized artisanal mining, on the other hand, involves the use of machines like hand tools, motorized water pumps, and crushers, among others [7]. Once the gold has been extracted, it needs to be processed and refined. Other methods of concentrations are used to concentrate minerals which contain metals for further processes [8]. According to [9], the methods of gold concentration from the ore can include gravimetric methods, such as sluices, shaking tables, and centrifuges, which rely on the high density of gold to separate it from other minerals in the ore.

Gold mining has a significant impact on the global economy, and according to [10], the global gold mining industry produces about 2,500-3,000 tons of gold per year, with the largest producing countries being China, Australia, Russia, and the United States. This industry is a major contributor to the economy of many countries and the methods of mining gold have evolved over time, as noted by Wang and Forssberg [11]. However, gold mining also has both positive and negative impacts on the environment and society. On one hand, it can create jobs and economic growth, especially in developing countries [12]. On the other hand, it can lead to environmental degradation, including deforestation, pollution of water sources, and destruction of habitats [13]. Additionally, the social impacts of gold mining can be significant. Reports of human rights abuses, labor exploitation, and child labor in some mining communities have been documented [14], so that efforts are being made to address these issues through international regulations and corporate social responsibility initiatives, as noted by Murillo-Sánchez and Reyes-Santacruz [15].

According to a study by [16], gold extraction involves several stages, including leaching, extraction, refining, and electrolysis. The commonly used method for gold extraction is the cyanide leaching process, where a cyanide solution is used to dissolve the gold from the ore in tanks or heaps [17]. Gold is then recovered from the saturated leaching solution by adsorption onto activated carbon or resins [18]. The two main methods used for the recovery of gold from the cyanide solution are precipitation on zinc powder (cementation) and adsorption on activated carbon [18]. Cementation on zinc powder involves the precipitation of gold from the enriched cyanide solution onto zinc powder. The complete process involves solid-liquid separation after cyanidation, clarification of the gold solution, partial deaeration of the solution, addition of zinc powder and lead salt to improve gold precipitation, and recovery of the precipitated gold [17]. Adsorption on activated carbon is based on the property of activated carbon to absorb the gold in the cyanide solution. The carbon is prepared from natural hard carbon (fruit kernels, coconut shells) treated to develop its adsorption capacity and porosity. The gold solution is pumped to the adsorption columns, where activated carbon is added to adsorb the gold-cyanide complex [18]. After gold recovery, the refining stage is carried out to obtain the highest practical purity of gold. The process begins with washing the carbon to remove organic impurities, and then the gold adsorbed on the carbon is recovered by elution using a hot, caustic, aqueous cyanide solution. Impurities are removed by filtration through a bed of activated carbon. The regenerated carbon is returned to the adsorption circuit, where gold is recovered either by cementation on zinc or by electrowinning, which is the final stage of the gold extraction process involving the deposition of gold on the cathode after taking an electron to become metallic gold. The cathode is made

of steel wool, and the anode is made of lead to facilitate oxygen release with minimal over potential [17].

Some authors have studied the thiourea process as an alternative to cyanide for the extraction of gold due to its environmental and health benefits, but the significant consumption of the reagent related to its oxidation in the solution is a disadvantage. To reduce this consumption, other authors investigated the mixture of thiourea with thiocyanate and iron sulfate [19-20]. However, recent developments aim to improve the process's cost-effectiveness and efficiency by reducing reagent consumption [21].

The [22] investigated the use of the chitosan and the manipuera processes, respectively. They have shown that chitosan can form complexes with gold after chlorination as shown in equation 1.

$$2Au + 2KClO_3 + 8HCl \rightarrow 2AuCl_4 + 2KCl + 4H_2O + O_2 \quad (1)$$

Aqua regia (AR) process consists of a mixture of hydrochloric acid (HCl) and nitric acid (HNO₃) in a 3/1 ratio that can dissolve gold in a matter of hours (equation 2). However, this process is highly corrosive and unstable and is not widely used at an industrial scale, limited to small and medium-sized processes, such as electrolytes in gold refining or recovering gold from electronic waste. Aqua regia can also dissolve other noble metals such as platinum and rhodium [23-24].

$$Au + HNO_3 + 4HCl \rightarrow HAuCl_4 + NO + 2H_2O \quad (2)$$

It should be noted that for the purpose of dissolving gold, hydrobromic acid (HBr) is used instead of HCl in this paper to create a modified aqua regia (MAR). The equation 3 becomes equation 4 as follows:

$$Au + HNO_3 + 4HBr \rightarrow HAuBr_4 + NO + 2H_2O \quad (3)$$

Efforts have been made in recent years to replace mercury and cyanide with less toxic reagents, and advancements in technology have led to the development of more efficient and environmentally friendly methods. Out of the various alternatives, the cyclodextrin (CD) process has emerged as a noteworthy contender. As reported by [25], this process utilizes a cyclic sugar molecule known as α-CD, which demonstrates selectivity in extracting gold from the ore. Moreover, α-CD is a cyclic oligosaccharide that has been shown to be effective in gold recovery [26], it is biodegradable, non-toxic, and has a high affinity for gold ions, making it an attractive alternative to conventional gold recovery methods [27]. The efficiency of α-CD in gold recovery has been investigated in electronic waste [28], low-grade gold ores [29], and even in refractory gold ores [30]. Moreover, that α-CD efficiency in gold recovery is attributed to its ability to form inclusion complexes with gold ions [31]. The formation of inclusion complexes is based on the hydrophobic effect and the van der Waals forces between α-CD and gold ions [29]. This complexation process can lead to the removal of gold ions from the ore, resulting in high gold recovery rates. So that α-CD was found to be an effective extractant for gold recovery, and it offers several advantages over conventional extractants, such as cyanide.

To date, a number of studies have been carried out on the use of α-CD in gold recovery. For example, Yen et al. [32] investigated the effect of various factors, such as temperature, pH, and α-CD concentration, on the recovery of gold from electronic
waste. They found that α-CD could effectively recover gold under a range of conditions. Similarly, Lee et al. [33] used α-CD to recover gold from waste printed circuit boards, and they reported a recovery rate of 98.5%. Despite its potential advantages, the use of α-CD in gold recovery is still in the early stages of development. Further research is needed to optimize the gold recovery process using α-CD and to understand the underlying mechanisms involved in the process.

The aim of this study is to investigate the efficiency of α-CD in modified aqua regia (MAR) gold recovery from gold-bearing ore and optimize the process using the simulation, optimization and prediction methods including Response Surface Methodology (RSM) and Artificial Neural Network (ANN), and then compare the results to find the optimum conditions. The ore will be characterized and series of experiments will be carried out. The significant parameters for leaching, neutralization and gold recovery processes such as time, pH, HBr and KOH concentrations ([HBr] and [KOH]), and α-CD concentration [α-CD], and their interactions will be also explored to determine the optimum conditions. After the experiments, the results will be analyzed and the efficiency of the gold recovery process will then be evaluated by measuring the percentage of gold recovered from the ore. The findings of this study may have significant implications for the gold mining industry, particularly in the D.R.C., where the recovery of gold from low-grade ores is an important economic activity. Also, the use of α-CD as a lixiviant aims to reduce the environmental impact of gold mining and promote the application of green chemistry principles in the mining industry.

## II. MATERIALS AND METHODS

### II.1 MATERIAL COLLECTION

In this study, concentrated HBr and HNO₃ were used to form MAR (3/1 ratio) for gold leaching. α-CD at 99% was used as gold the extracting agent. Potassium hydroxide (KOH) was used for pH adjustment, and analytical-grade nitric acid (HNO₃) was used for gold analysis.

### II.2 SAMPLE PREPARATION

Fifty (50) kg of gold-bearing ore was collected from 2 quarries located in South-Kivu province of the D.R.C. The homogenization of the sample was carried out using the cone and quartering method, and then divided into four representative parts using the quartering technique. A number of fragmentation operations were performed: primary and secondary crushing, a mineralogical analysis using transmitted and reflected light microscopy, and a chemical analysis using atomic adsorption spectroscopy/inductively coupled plasma (AAS/ICP). Moreover, 1 kg was used for AAS/ICP, and the remaining 49 kg gold ore sample was used for secondary crushing during 19.57 minutes in to get 80% passing 75 µm sieves.

## III. GOLD RECOVERY STUDY

### II.1 LEACHING PROCESS (LP)

The purpose of the process was to extract gold from a homogenized sample and 400 g of the sample was weighed and placed into a 1 L beaker for 5 min of contact time. Deionized water was added to the beaker to homogenize the pulp, and mechanical agitation was used to facilitate the process. HBr and HNO₃ were gradually added to the pulp while the pH and

potential were adjusted as needed. The solid and liquid phases were then separated by filtration, and a certain amount of the filtrate was taken for chemical analysis. The cake was washed to eliminate any remaining leaching agent before being dried in an oven at a temperature of 105°C for 24 hours. To ensure the precision in results, the leaching tests were duplicated and the average values were considered. Four factors were studied: time (x₁), HBr concentration (x₂), pH (x₃) and stirring speed (x₄), and a total of 47 tests were carried out by simultaneously varying the levels of each factor. Time, HBr concentration [HBr], pH, and stirring speed were varied in range of 1-7.5 hours, 50-200 g/L, 1-2, and 50-200 rpm, respectively.

### II.2 NEUTRALIZATION PROCESS (NP)

The experimental procedure used for neutralization tests involved placing 50 mL of homogenized leachate in a 500 mL beaker, gradually adding a solution of KOH (0.1 M) to maintain the pH at required pH, stopping stirring once the set time was reached, separating the solid and liquid components through filtration, and finally analyzing 20 mL of the resulting filtrate to measure its chemical composition. The tests were triplicated and the average values were considered. Moreover, the following three factors with appropriate combination were studied: time (x₁), KOH concentration (x₂), and pH (x₃). Time, KOH concentration, and pH were varied in range of 1-10 hours, 84-224 g/L, and 5-6, respectively.

### II.3 GOLD RECOVERY PROCESS USING α-CD (GP)

During the precipitation tests at room temperature (25°C), the process started with an amount of 50 mL of the filtrate which was taken into a 2 L beaker after ensuring the pH was at the desired level using KOH. α-CD was then gradually added while mechanically agitating the solution. Once the set time was reached, the recovered gold as well as the co-precipitates were removed by filtration, after what sodium bisulfite (Na₂S₂O₅) solution was used to disperse and reduce the complex α-Br in order isolate and precipitate the recovered gold metal. The liquid-liquid separation was carried out by decantation and a certain amount of the filtrate was collected for chemical analysis. Each recovery test was duplicated and the average value was considered. Time, α-CD concentration [α-CD], and pH were varied in range of 10-40 minutes, 5-20 g/L, and 5-6, respectively.

### II.4 METHODS USED FOR PREDICTION, MODELING AND OPTIMIZATION OF STUDIED PARAMETERS

#### II.4.1 RSM METHOD

RSM known as full factorial method, was utilized to generate the experimental runs (using Minitab software and the analysis of variance (ANOVA)) varying the studied parameters [34-35]. In addition, the statistical technique of regression analysis was highlighted to determine a mathematical formula between the parameters and the response as shown in equation 4 [36-37].

$$y = f(x_1, x_2, x_3, x_4, \dots, x_n) \quad (4)$$

where y is the dependent variable (response) and xᵢ the independent variables (parameters).

As demonstrated by Murthy et al. [38], for a good fitness of the model, the coefficient of determination R² should be at
least 0.80. The best precision of comparison of treatments was done by a value called coefficient of variation (CV) which should be low to minimize the dispersion around the mean value.

As a statistical indicator, the Fisher's F-test ANOVA was used to outline the significance of the studied model after assessing the effects of the parameters as well as their interactions. [36] and [39] have shown that for a highly significant model, variable or interaction, the P-value must be

lower than greater than 0.0001 in a 95% confidence intervals. Also, the significance was associated to a P-value between 0.0001 and 0.05, while the non-significance was associated to a P-value higher than 0.05.

The experimental design matrix for leaching process (LP) and gold recovery process using α-CD (GP) tests are presented in Table 1, while the corresponding matrix for neutralization process (NP) is shown in Table 2.

<table><caption>Table 1: Design matrix for LP and GR.</caption><thead><tr><th rowspan="2">Run N°</th><th colspan="4">LP</th><th colspan="3">GP</th></tr><tr><th>Time, x₁ (h)</th><th>[HBr], x₂ (g/L)</th><th>pH, x₃</th><th>Speed, x₄ (rpm)</th><th>Time, x₁ (min)</th><th>[α-CD], x₂ (g/L)</th><th>pH, x₃</th></tr></thead><tbody><tr><td>1</td><td>1.0</td><td>50</td><td>1</td><td>200</td><td>10</td><td>5</td><td>5.0</td></tr><tr><td>2</td><td>1.0</td><td>200</td><td>2</td><td>50</td><td>10</td><td>5</td><td>5.5</td></tr><tr><td>3</td><td>1.0</td><td>100</td><td>1</td><td>50</td><td>10</td><td>5</td><td>6.0</td></tr><tr><td>4</td><td>1.0</td><td>150</td><td>1</td><td>50</td><td>10</td><td>10</td><td>5.0</td></tr><tr><td>5</td><td>1.0</td><td>100</td><td>1</td><td>150</td><td>10</td><td>10</td><td>5.5</td></tr><tr><td>6</td><td>1.0</td><td>150</td><td>1</td><td>150</td><td>10</td><td>10</td><td>6.0</td></tr><tr><td>7</td><td>1.0</td><td>100</td><td>2</td><td>150</td><td>10</td><td>15</td><td>5.0</td></tr><tr><td>8</td><td>1.0</td><td>150</td><td>2</td><td>150</td><td>10</td><td>15</td><td>5.5</td></tr><tr><td>9</td><td>1.0</td><td>100</td><td>2</td><td>100</td><td>10</td><td>15</td><td>6.0</td></tr><tr><td>10</td><td>1.0</td><td>150</td><td>2</td><td>100</td><td>10</td><td>20</td><td>5.0</td></tr><tr><td>11</td><td>2.5</td><td>100</td><td>1</td><td>100</td><td>10</td><td>20</td><td>5.5</td></tr><tr><td>12</td><td>2.5</td><td>150</td><td>1</td><td>100</td><td>10</td><td>20</td><td>6.0</td></tr><tr><td>13</td><td>2.5</td><td>200</td><td>1</td><td>150</td><td>20</td><td>5</td><td>5.0</td></tr><tr><td>14</td><td>2.5</td><td>50</td><td>1</td><td>150</td><td>20</td><td>5</td><td>5.5</td></tr><tr><td>15</td><td>2.5</td><td>200</td><td>1</td><td>150</td><td>20</td><td>5</td><td>6.0</td></tr><tr><td>16</td><td>2.5</td><td>100</td><td>1</td><td>150</td><td>20</td><td>10</td><td>5.0</td></tr><tr><td>17</td><td>2.5</td><td>150</td><td>1</td><td>150</td><td>20</td><td>10</td><td>5.5</td></tr><tr><td>18</td><td>2.5</td><td>200</td><td>1</td><td>100</td><td>20</td><td>10</td><td>6.0</td></tr><tr><td>19</td><td>2.5</td><td>100</td><td>2</td><td>150</td><td>20</td><td>15</td><td>5.0</td></tr><tr><td>20</td><td>2.5</td><td>150</td><td>2</td><td>150</td><td>20</td><td>15</td><td>5.5</td></tr><tr><td>21</td><td>2.5</td><td>200</td><td>2</td><td>100</td><td>20</td><td>15</td><td>6.0</td></tr><tr><td>22</td><td>2.5</td><td>100</td><td>2</td><td>100</td><td>20</td><td>20</td><td>5.0</td></tr><tr><td>23</td><td>2.5</td><td>150</td><td>2</td><td>100</td><td>20</td><td>20</td><td>5.5</td></tr><tr><td>24</td><td>2.5</td><td>50</td><td>2</td><td>50</td><td>20</td><td>20</td><td>6.0</td></tr><tr><td>25</td><td>2.5</td><td>100</td><td>2</td><td>50</td><td>30</td><td>5</td><td>5.0</td></tr><tr><td>26</td><td>2.5</td><td>150</td><td>2</td><td>50</td><td>30</td><td>5</td><td>5.5</td></tr><tr><td>27</td><td>2.5</td><td>200</td><td>2</td><td>50</td><td>30</td><td>5</td><td>6.0</td></tr><tr><td>28</td><td>5.0</td><td>50</td><td>1</td><td>150</td><td>30</td><td>10</td><td>5.0</td></tr><tr><td>29</td><td>5.0</td><td>100</td><td>1</td><td>150</td><td>30</td><td>10</td><td>5.5</td></tr><tr><td>30</td><td>5.0</td><td>150</td><td>1</td><td>150</td><td>30</td><td>10</td><td>6.0</td></tr><tr><td>31</td><td>5.0</td><td>200</td><td>1</td><td>150</td><td>30</td><td>15</td><td>5.0</td></tr><tr><td>32</td><td>5.0</td><td>200</td><td>1</td><td>100</td><td>30</td><td>15</td><td>5.5</td></tr><tr><td>33</td><td>5.0</td><td>50</td><td>2</td><td>100</td><td>30</td><td>15</td><td>6.0</td></tr><tr><td>34</td><td>5.0</td><td>100</td><td>2</td><td>100</td><td>30</td><td>20</td><td>5.0</td></tr><tr><td>35</td><td>5.0</td><td>150</td><td>2</td><td>100</td><td>30</td><td>20</td><td>5.5</td></tr><tr><td>36</td><td>5.0</td><td>200</td><td>2</td><td>100</td><td>30</td><td>20</td><td>6.0</td></tr><tr><td>37</td><td>5.0</td><td>50</td><td>2</td><td>50</td><td>40</td><td>5</td><td>5.0</td></tr><tr><td>38</td><td>7.5</td><td>50</td><td>1</td><td>150</td><td>40</td><td>5</td><td>5.5</td></tr><tr><td>39</td><td>7.5</td><td>100</td><td>1</td><td>150</td><td>40</td><td>5</td><td>6.0</td></tr><tr><td>40</td><td>7.5</td><td>200</td><td>1</td><td>150</td><td>40</td><td>10</td><td>5.0</td></tr><tr><td>41</td><td>7.5</td><td>100</td><td>1</td><td>200</td><td>40</td><td>10</td><td>5.5</td></tr><tr><td>42</td><td>7.5</td><td>150</td><td>1</td><td>200</td><td>40</td><td>10</td><td>6.0</td></tr><tr><td>43</td><td>7.5</td><td>100</td><td>2</td><td>100</td><td>40</td><td>15</td><td>5.0</td></tr><tr><td>44</td><td>7.5</td><td>150</td><td>2</td><td>100</td><td>40</td><td>15</td><td>5.5</td></tr><tr><td>45</td><td>7.5</td><td>150</td><td>1</td><td>150</td><td>40</td><td>15</td><td>6.0</td></tr><tr><td>46</td><td>7.5</td><td>100</td><td>2</td><td>50</td><td>40</td><td>20</td><td>5.0</td></tr><tr><td>47</td><td>7.5</td><td>150</td><td>2</td><td>50</td><td>40</td><td>20</td><td>5.5</td></tr><tr><td>48</td><td>-</td><td>-</td><td>-</td><td>-</td><td>40</td><td>20</td><td>6.0</td></tr></tbody></table>

Source: Authors, (2023).
<table><caption>Table 2: Design matrix for NP.</caption><thead><tr><th>Run N°</th><th>Time, x₁ (h)</th><th>[KOH], x₂ (g/L)</th><th>pH, x₃</th></tr></thead><tbody><tr><td>1</td><td>1.0</td><td>84</td><td>5.0</td></tr><tr><td>2</td><td>1.0</td><td>84</td><td>5.5</td></tr><tr><td>3</td><td>1.0</td><td>84</td><td>6.0</td></tr><tr><td>4</td><td>1.0</td><td>112</td><td>5.0</td></tr><tr><td>5</td><td>1.0</td><td>112</td><td>5.5</td></tr><tr><td>6</td><td>1.0</td><td>112</td><td>6.0</td></tr><tr><td>7</td><td>1.0</td><td>168</td><td>5.0</td></tr><tr><td>8</td><td>1.0</td><td>168</td><td>6.0</td></tr><tr><td>9</td><td>2.5</td><td>84</td><td>5.0</td></tr><tr><td>10</td><td>2.5</td><td>84</td><td>5.5</td></tr><tr><td>11</td><td>2.5</td><td>84</td><td>6.0</td></tr><tr><td>12</td><td>2.5</td><td>112</td><td>5.0</td></tr><tr><td>13</td><td>2.5</td><td>112</td><td>5.5</td></tr><tr><td>14</td><td>2.5</td><td>112</td><td>6.0</td></tr><tr><td>15</td><td>2.5</td><td>168</td><td>5.0</td></tr><tr><td>16</td><td>2.5</td><td>168</td><td>5.5</td></tr><tr><td>17</td><td>2.5</td><td>168</td><td>6.0</td></tr><tr><td>18</td><td>2.5</td><td>224</td><td>5.5</td></tr><tr><td>19</td><td>2.5</td><td>224</td><td>6.0</td></tr><tr><td>20</td><td>5.0</td><td>84</td><td>5.0</td></tr><tr><td>21</td><td>5.0</td><td>84</td><td>5.5</td></tr><tr><td>22</td><td>5.0</td><td>84</td><td>6.0</td></tr><tr><td>23</td><td>10.0</td><td>112</td><td>5.0</td></tr><tr><td>24</td><td>10.0</td><td>112</td><td>5.5</td></tr><tr><td>25</td><td>10.0</td><td>112</td><td>6.0</td></tr></tbody></table>

Source: Authors, (2023).

A total of 47, 48, and 25 experimental runs were considered for LP, GR, and NP, respectively.

## II.4.2 ANN METHOD

Known as promising method studied by many researchers [40-42], ANN as a statistical learning algorithms has been used in recent years in order to estimate by approximation a mathematical relationship between inputs and outputs of a specific process. Through information, the stimulation as well as the processing of ANN are performed within the nervous system.

The transfer functions between the input and hidden layers in one hand, and between the hidden and output layers on another hand, were performed using a hyperbolic tangent TANSIG (sigmoid) and a Purline, respectively, while the normalization of data of inputs and outputs was done by PREMNMX function [43-44]. In addition, the chosen learning algorithm was Levenberg-Marquardt. Beside the coefficient of determination (R²), another estimator or predictor number called mean square error (MSE) was used to determine the performance of ANN. For a good performance, MSE value should be as small as possible and in the best case close to zero. Furthermore a good performance of the model corresponds to a high R² value and a lower MSE value which shows a good interaction or connection between the parameters of the model. Equations 5, 6 and 7 illustrate the sigmoid, MSE, and R², respectively.

$$ \operatorname{logsig}(x) = \frac{1}{1+e^{-x}} \qquad (5) $$

$$ MSE = \frac{1}{N} + \sum_{i=1}^{N} (t_i - o_i)^2 \qquad (6) $$

$$ R^2 = 1 - \frac{\sum (t_i - o_i)^2}{\sum (o_i - \bar{o})^2} \qquad (7) $$

where n, t, o, and ō represent the number of samples, the target value, the output, and the mean of output, respectively.

In this paper, the RSM and MATLAB were used to generate a matrix of the experimental responses. The choice of learning on multilayer perception network was 80 for network training, 5 for testing, and 5 for validation. The network was selected in feed-forward mode, consisting of input layer, hidden layer and output layer. Depending on the process (LP or GP), the numbers of neurons in input and output layers were specific, while the chosen number of neurons in the hidden layer was 10 due to the lowest mean square error resulted. Figure 1 illustrates the ANN architecture used for the experiments.

<figure><img src="image_4.png" /><figcaption>Figure 1: ANN architecture, (a): for LP and (b): for GP.
Source: Authors, (2023).</figcaption></figure>

# IV. RESULTS AND DISCUSSIONS

## IV.1 RSM PREDICTION

The results of percent removals according to each process (LP, NP and GR) are investigated in this section. Note that these results were also obtained in another study conducted by the same authors of the present article taking into account central composite design (CCD), and the study has not yet been published. Table 3 presents the results of percent removals of the tests.
<table><caption>Table 3: Responses obtained for LP, NP and GR.</caption><thead><tr><th rowspan="2">Run N°</th><th colspan="3">Responses (%)</th></tr><tr><th>LP</th><th>NP</th><th>GR</th></tr></thead><tbody><tr><td>1</td><td>0.001</td><td>54.4698</td><td>35.8545</td></tr><tr><td>2</td><td>67.879</td><td>65.1321</td><td>48.9586</td></tr><tr><td>3</td><td>33.927</td><td>73.7055</td><td>62.0582</td></tr><tr><td>4</td><td>70.399</td><td>40.9167</td><td>54.9625</td></tr><tr><td>5</td><td>36.432</td><td>51.6038</td><td>65.7851</td></tr><tr><td>6</td><td>72.815</td><td>60.2019</td><td>76.6032</td></tr><tr><td>7</td><td>36.432</td><td>18.4140</td><td>51.0053</td></tr><tr><td>8</td><td>56.121</td><td>37.7190</td><td>59.5463</td></tr><tr><td>9</td><td>20.617</td><td>70.0920</td><td>68.0830</td></tr><tr><td>10</td><td>57.042</td><td>77.7318</td><td>23.9828</td></tr><tr><td>11</td><td>48.654</td><td>83.3085</td><td>30.2424</td></tr><tr><td>12</td><td>68.595</td><td>67.7952</td><td>36.4973</td></tr><tr><td>13</td><td>86.060</td><td>75.4380</td><td>55.9201</td></tr><tr><td>14</td><td>26.361</td><td>81.0216</td><td>64.0012</td></tr><tr><td>15</td><td>86.060</td><td>67.7655</td><td>72.0779</td></tr><tr><td>16</td><td>49.990</td><td>75.4123</td><td>70.8062</td></tr><tr><td>17</td><td>69.890</td><td>80.9820</td><td>76.6058</td></tr><tr><td>18</td><td>84.806</td><td>81.4473</td><td>82.4011</td></tr><tr><td>19</td><td>35.271</td><td>87.0210</td><td>62.6271</td></tr><tr><td>20</td><td>55.170</td><td>79.0020</td><td>68.1253</td></tr><tr><td>21</td><td>70.206</td><td>81.5678</td><td>69.6590</td></tr><tr><td>22</td><td>34.054</td><td>82.1601</td><td>31.3830</td></tr><tr><td>23</td><td>53.995</td><td>86.4270</td><td>32.6146</td></tr><tr><td>24</td><td>9.061</td><td>78.7644</td><td>33.8518</td></tr><tr><td>25</td><td>32.773</td><td>69.0426</td><td>75.9856</td></tr><tr><td>26</td><td>52.755</td><td>-</td><td>79.0438</td></tr><tr><td>27</td><td>69.008</td><td>-</td><td>82.0976</td></tr><tr><td>28</td><td>73.270</td><td>-</td><td>86.6499</td></tr><tr><td>29</td><td>69.430</td><td>-</td><td>87.4266</td></tr><tr><td>30</td><td>61.855</td><td>-</td><td>88.1989</td></tr><tr><td>31</td><td>50.550</td><td>-</td><td>74.2500</td></tr><tr><td>32</td><td>49.104</td><td>-</td><td>72.7442</td></tr><tr><td>33</td><td>57.103</td><td>-</td><td>71.2351</td></tr><tr><td>34</td><td>53.301</td><td>-</td><td>38.7829</td></tr><tr><td>35</td><td>45.767</td><td>-</td><td>34.9965</td></tr><tr><td>36</td><td>34.504</td><td>-</td><td>31.2059</td></tr><tr><td>37</td><td>55.589</td><td>-</td><td>96.0508</td></tr><tr><td>38</td><td>83.120</td><td>-</td><td>94.0864</td></tr><tr><td>39</td><td>85.002</td><td>-</td><td>92.1173</td></tr><tr><td>40</td><td>11.107</td><td>-</td><td>98.8911</td></tr><tr><td>41</td><td>86.595</td><td>-</td><td>98.2474</td></tr><tr><td>42</td><td>51.502</td><td>-</td><td>93.9968</td></tr><tr><td>43</td><td>68.611</td><td>-</td><td>85.8708</td></tr><tr><td>44</td><td>33.604</td><td>-</td><td>79.3432</td></tr><tr><td>45</td><td>90.479</td><td>-</td><td>72.8130</td></tr><tr><td>46</td><td>66.944</td><td>-</td><td>46.1829</td></tr><tr><td>47</td><td>31.977</td><td>-</td><td>37.3737</td></tr><tr><td>48</td><td>-</td><td>-</td><td>28.5601</td></tr></tbody></table>

Source: Authors, (2023).

After obtaining the results of percent removals, the influences of studied parameters, as well as their interactions, on percent removals were evaluated through the generation of mathematical equations 8, 9, and 10 for LP, NP, and GR, respectively. The importance of the sign of the coefficient in the regression equation is in the fact that it can predict the nature of the studied parameters effects on the response. So that the positive sign of the coefficient implies the favorable increase of

the response with the increase in parameters (variables) or their interactions, and vice versa. Moreover, the negative sign of the coefficient negative coefficients implies the decrease of the response with the increase in parameters (variables) or their interactions.

$$y = -91.3 + 31.74x_1 + 1.404x_2 - 4.0x_3 + 0.040x_4 - 0.465x_1^2 - 0.001773x_2^2 + 0.000097x_4^2 - 0.1860x_1x_2 - 0.96x_1x_3 - 0.0090x_1x_4 - 0.0740x_2x_3 - 0.000141x_2x_4 + 0.0139x_3x_4 \quad (8)$$

$$y = -128.60 + 14.3489x_1 - 52.627x_2 + 68.667x_3 - 1.71718x_1^2 + 3.0403x_2^2 - 4.1153x_3^2 + 14.9734x_1x_2 - 4.07045x_1x_3 - 0.0077x_2x_3 \quad (9)$$

$$y = -262.2 + 7.343x_1 + 16.209x_2 + 51.06x_3 - 0.001162x_1^2 - 0.45996x_2^2 - 0.953x_3^2 - 0.08385x_1x_2 - 0.9775x_1x_3 - 0.9306x_2x_3 \quad (10)$$

where y, x₁, x₂, x₃, and x₄ have already been defined in Table 1.

The leaching efficiency is directly proportional to the increase in time, [HBr], stirring speed, and inversely proportional to the pH. The findings support [45] study, which concluded that the presence of HNO₃ as an oxidizing agent aids in dissolving gold. Thus, the higher concentration of HBr leads to an increase in HNO₃ concentration, which effectively acts as an oxidant for trivalent gold ions. The trivalent gold ions are subsequently reduced by HBr, resulting in the formation of tetrabromidoaurate anions or tetrabromoauric acid (AuBr₄⁻).

The results indicate that when the reaction time is shorter, even with varying concentrations of HBr, the contact between the gold particles and leachate is insufficient, leading to the consumption of other metals present in the solution by HBr. Also, an increase in HBr concentration is favorable for the formation and precipitation of silver bromide (AgBr), confirming the study of [46]. This, in turn, prevents the dissolution of silver from MAR and results in an increased leaching percentage.

The results indicate that increasing the time, [KOH], and pH leads to an increase in the neutralization percentage, with an optimal pH range of 5-6. This is due to the precipitation of other metals that typically accompany gold, such as iron, aluminum, copper, and cobalt, with increasing pH or [KOH]. The ionic forms of these metals react with hydroxide ions from KOH and subsequently precipitate out. Another factor is the progressive oxidation of Fe²⁺ to Fe³⁺ by oxygen in the air, which leads to precipitation in the form of Fe(OH)₃, starting at a pH of 3.5, as confirmed by [47]. Additionally, aluminum precipitation occurs within the pH range of 4 to 5.5. The precipitation processes for aluminum and iron ions are illustrated by equations 11 and 12, respectively.

$$Al^{3+} + OH^{-} \rightarrow Al(OH)_{3} \quad (11)$$

$$Fe^{3+} + OH^{-} \rightarrow Fe(OH)_{3} \quad (12)$$

According to that, it can be observed that the increase of [α-CD] leads to the increase of percent removal but not indefinitely. So that, [α-CD] reaches a certain value (11.62 g/L) after which the opposite phenomenon is observed. This may be attributed to the saturation of α-CD with solute at this value. Additionally, the recovery was observed from the first minute of reaction and with the increase of contact time, while at a pH range of 5-5.8 yields good results with at least 85% of gold recovered.
Furthermore, the yield of recovery is low at low values of pH and time, but increases as these parameters values increase.

Gold recovery is a rapid process that commences within the first minute of the reaction between the extractant solution (α-CD) and the gold-containing solution (KAuBr₄). With time, AuBr₄⁻ ions become encapsulated within the second sphere cavity formed between the primary OH faces of repeated face-to-face α-CD pairs. These pairs are stabilized by hydrogen bonding interactions, leading to an increase in recovery percentage, as demonstrated by [48]. On another hand, K⁺, α-CD, and AuBr₄⁻ molecules recognize each other, involving aureate anion [AuBr₄]⁻ and hexa-aqua cation [K(OH₂)₆]⁺ interacting non-covalently. This results in rapid co-precipitation of α-CD and KAuBr₄ in water, eventually forming a 1:2 ratio complex (needlelike) {[K(OH₂)₆][AuBr₄]⊂(α-CD)₂}ₙ, as concluded by Liu and Wang [39].

As α-CD concentration increases, recovery percentage also increases up to a maximum value before decreasing. Beyond this

point, encapsulation ceases, and needlelike complex formation no longer occurs due to the absence of KAuBr₄ solution. The optimal ratio for complex formation is 1:2, where [AuBr₄]/[α-CD]=1/2. Performance decreases when the ratio falls below or exceeds this threshold. The neutralization of accompanying metals of gold during neutralization step plays an important role in increasing percent removal in gold recovery process.

ANOVA was investigated and some indicator values were found to analyse the model performance, such as R² and adjusted R² values, P-values, degree of freedom (df), and so on. The confidence level was 95%. Tables 4 and 5 show the results of ANOVA, and according to the results, it is obvious that: (1) for LP, the model, the time, as well as the time-[HBr] interaction are highly significant. In addition, the pH is significant and the remaining parameters ([HBr] and speed) are non-significant. (2) for GP, the model and all the parameters are highly significant.

<table><caption>Table 4: Analysis of variance for LP percentage.</caption><thead><tr><th>Source</th><th>df</th><th>Sum of Square</th><th>Mean Square</th><th>F-Value</th><th>P-Value Prob&gt;F</th><th>Observations</th></tr></thead><tbody><tr><td>Model</td><td>4</td><td>3750.4</td><td>937.6</td><td>13.88</td><td>&lt;0.0001</td><td>HS</td></tr><tr><td>x<sub>1</sub></td><td>1</td><td>792.3</td><td>792.3</td><td>11.73</td><td>&lt;0.0001</td><td>HS</td></tr><tr><td>x<sub>2</sub></td><td>1</td><td>141.0</td><td>141.0</td><td>2.09</td><td>0.158</td><td>NS</td></tr><tr><td>x<sub>3</sub></td><td>1</td><td>909.9</td><td>909.9</td><td>13.47</td><td>0.001</td><td>S</td></tr><tr><td>x<sub>4</sub></td><td>1</td><td>24.3</td><td>24.3</td><td>0.36</td><td>0.553</td><td>NS</td></tr><tr><td>x<sub>1</sub><sup>2</sup></td><td>1</td><td>131.5</td><td>131.5</td><td>1.95</td><td>0.172</td><td>NS</td></tr><tr><td>x<sub>2</sub><sup>2</sup></td><td>1</td><td>631.7</td><td>631.7</td><td>9.35</td><td>0.004</td><td>S</td></tr><tr><td>x<sub>4</sub><sup>2</sup></td><td>1</td><td>0.8</td><td>0.8</td><td>0.01</td><td>0.913</td><td>NS</td></tr><tr><td>x<sub>1</sub>x<sub>2</sub></td><td>1</td><td>14451.2</td><td>14451.2</td><td>213.89</td><td>&lt;0.0001</td><td>HS</td></tr><tr><td>x<sub>1</sub>x<sub>3</sub></td><td>1</td><td>21.8</td><td>21.8</td><td>0.32</td><td>0.574</td><td>NS</td></tr><tr><td>x<sub>1</sub>x<sub>4</sub></td><td>1</td><td>17.3</td><td>17.3</td><td>0.26</td><td>0.616</td><td>NS</td></tr><tr><td>x<sub>2</sub>x<sub>3</sub></td><td>1</td><td>61.4</td><td>61.4</td><td>0.91</td><td>0.347</td><td>NS</td></tr><tr><td>x<sub>2</sub>x<sub>4</sub></td><td>1</td><td>1.8</td><td>1.8</td><td>0.03</td><td>0.873</td><td>NS</td></tr><tr><td>x<sub>3</sub>x<sub>4</sub></td><td>1</td><td>1.5</td><td>1.5</td><td>0.02</td><td>0.882</td><td>NS</td></tr><tr><td>Error</td><td>33</td><td>2229.6</td><td>67.6</td><td></td><td></td><td></td></tr><tr><td>Total</td><td>46</td><td>22365.2</td><td></td><td></td><td></td><td></td></tr></tbody></table>

Note: F: function of Fishers, df: degrees of freedom, P-value: level of significance, NS: not significant; S: significant; HS: highly significant; CV=10.7259%; R²=0.9003; Adj. R²=0.7825.

Source: Authors, (2023).

<table><caption>Table 5: Analysis of variance for GR percentage.</caption><thead><tr><th>Source</th><th>df</th><th>Sum of Square</th><th>Mean Square</th><th>F-Value</th><th>P-Value Prob&gt;F</th><th>Observations</th></tr></thead><tbody><tr><td>Model</td><td>3</td><td>14016.9</td><td>4672.28</td><td>13195.92</td><td>&lt;0.0001</td><td>HS</td></tr><tr><td>x<sub>1</sub></td><td>1</td><td>4441.1</td><td>4441.10</td><td>12542.97</td><td>&lt;0.0001</td><td>HS</td></tr><tr><td>x<sub>2</sub></td><td>1</td><td>9412.6</td><td>9412.63</td><td>26584.06</td><td>&lt;0.0001</td><td>HS</td></tr><tr><td>x<sub>3</sub></td><td>1</td><td>163.1</td><td>163.13</td><td>460.73</td><td>&lt;0.0001</td><td>HS</td></tr><tr><td>x<sub>1</sub><sup>2</sup></td><td>1</td><td>0.6</td><td>0.65</td><td>1.83</td><td>0.184</td><td>NS</td></tr><tr><td>x<sub>2</sub><sup>2</sup></td><td>1</td><td>6346.9</td><td>6346.87</td><td>17925.45</td><td>&lt;0.0001</td><td>HS</td></tr><tr><td>x<sub>3</sub><sup>2</sup></td><td>1</td><td>0.6</td><td>0.60</td><td>1.71</td><td>0.199</td><td>NS</td></tr><tr><td>x<sub>1</sub>x<sub>2</sub></td><td>1</td><td>1318.2</td><td>1318.17</td><td>3722.90</td><td>&lt;0.0001</td><td>HS</td></tr><tr><td>x<sub>1</sub>x<sub>3</sub></td><td>1</td><td>955.6</td><td>955.60</td><td>2698.90</td><td>&lt;0.0001</td><td>HS</td></tr><tr><td>x<sub>2</sub>x<sub>3</sub></td><td>1</td><td>216.5</td><td>216.51</td><td>611.50</td><td>&lt;0.0001</td><td>HS</td></tr><tr><td>Error</td><td>38</td><td>13.5</td><td>0.35</td><td></td><td></td><td></td></tr><tr><td>Total</td><td>47</td><td>22868.7</td><td></td><td></td><td></td><td></td></tr></tbody></table>

Note: F: function of Fishers, df: degrees of freedom, P-value: level of significance, NS: not significant; S: significant; HS: highly significant; CV=0.82515%; R²=0.9994; Adj. R²=0.9993.

Source: Authors, (2023).

The results of Tables 4 and 5 indicate that the R² values of 0.9003 and 0.9994 for LP and GP respectively were highly significant confirming a good reliability, reproducibility and

precision of the models. The CVs of 10.7259% and 0.82515% for leaching and gold recovery respectively were also obtained. In addition, the obtained P-value <0.0001 for both models confirm
that the good prediction of the gold removal varying the parameters studied.

The optimization conditions were found for better gold removal in both LP and GR. From the results, the conditions were (1) time of 7.27 hours, [HBr] of 50 g/L, pH of 1 and stirring speed of 200 rpm for leaching percent of 98.540% and desirability of 1, (2) time of 40 minutes, [α-CD] of 11.6166 g/L and pH of 5 for gold recovery percent of 98.8736% and desirability of 0.99978. Under these conditions, the concentration of gold increased from 592.99 ppm to 3,372 ppm in the filtrate after LP, while it increased from 3,372 ppm to 11,944 ppm in the organic phase after GR.

## IV.2 ANN PREDICTION

According to Table 3, the prediction of the response was done using ANN, and 75%-15%-15% learning choice was done for network training, testing and validation, respectively. The illustration of the observed mean square error (MSE) against the epochs for both LP and GP is given in Figure 2. According to [49], MSE also give information on the degree of correlation between the target and the predicted responses of the network.

<figure><img src="image_5.png" /><figcaption>Figure 2: Performance of training, validation and testing (a) for LP, (b) for GR.</figcaption></figure>

Source: Authors, (2023).

For LP (figure 2.a), it can be observed that for validation and testing there are steady decreases in MSE up to epoch 5, from where there is certain equilibrium up to epoch 11. In addition there is a regular decrease in MSE for training up to epoch 8 and then a sharp decrease is observed up to epoch 11. The best value of MSE is 24.8206 at epoch 5 involving the best performance and suggesting that the learning stage of the network at its best level is obtained after the fifth iterations. For GP (figure 2.b), MSE declines for training, validation and testing up to a certain equilibrium around epoch 9. Therefore, after 54 iterations, the best learning stage of the network is attained at MSE value of 0.8242 confirming a good correlation between gold recovery and the target. The error histograms of both LP and GP are presented in Figure 3 (a and b). It is seen that the errors are almost symmetrically distributed, so that they have a non-significant effect on the studied model. Furthermore, it is obvious that for GP, the mean value of the instances is closed to 5, which confirms the good performance of the model.

<figure><img src="image_6.png" /><figcaption>Figure 3: Error histograms (a) for LP, (b) for GP.
Source: Authors, (2023).</figcaption></figure>

Figure 4 and 5 show the network performance related LP and GP, respectively. Considering the LP, it is obvious that the R² values for training, validation, testing and overall are respectively 0.99027, 0.90934, 0.71337, and 0.9392. According to the GP, the R² values of 0.99992, 0.99712, 0.99289, and 0.99952 were obtained for training, validation, testing and overall respectively.
<figure><img src="image_7.png" /><figcaption>Figure 4: Four-in-one plot of network performance of LP.
Source: Authors, (2023).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 5: Four-in-one plot of network performance of GP.
Source: Authors, (2023).</figcaption></figure>
From these results, it is obvious that due to high values of R² which is >90%, the fitting performance of the neural network was highly significant although the observed low value of R² (0.71916) in testing stage for LP. The low observed value of R² was due to the non-sufficient data to test the network and a low learning choice (15%), but the overall performance of the network was not affected. The equations 13 and 14 show the relationship between the overall output and the target (All) for the determination of the overall predicted network model.

$$Overall output = 0.96 * Target + 1.5 \quad (13)$$

<table><caption>Table 6: Experimental data, RSM and ANN results for LP and GP.</caption><thead><tr><th rowspan="2">Run N°</th><th colspan="3">LP</th><th colspan="3">GP</th></tr><tr><th>Exp. removal percent (%)</th><th>RSM pred. removal percent (%)</th><th>ANN pred. removal percent (%)</th><th>Exp. removal percent (%)</th><th>RSM pred. removal percent (%)</th><th>ANN pred. removal percent (%)</th></tr></thead><tbody><tr><td>1</td><td>0.001</td><td>0.000</td><td>1.340</td><td>35.854</td><td>35.839</td><td>35.912</td></tr><tr><td>2</td><td>67.879</td><td>74.92</td><td>55.075</td><td>48.958</td><td>49.156</td><td>48.882</td></tr><tr><td>3</td><td>33.927</td><td>33.45</td><td>36.468</td><td>62.058</td><td>61.997</td><td>62.073</td></tr><tr><td>4</td><td>70.399</td><td>68.15</td><td>70.243</td><td>54.962</td><td>54.926</td><td>54.415</td></tr><tr><td>5</td><td>36.432</td><td>38.49</td><td>35.148</td><td>65.785</td><td>65.917</td><td>65.784</td></tr><tr><td>6</td><td>72.815</td><td>72.48</td><td>75.068</td><td>76.603</td><td>76.432</td><td>76.571</td></tr><tr><td>7</td><td>36.432</td><td>28.22</td><td>33.122</td><td>51.005</td><td>51.016</td><td>51.010</td></tr><tr><td>8</td><td>56.121</td><td>58.51</td><td>59.805</td><td>59.546</td><td>59.681</td><td>59.736</td></tr><tr><td>9</td><td>20.617</td><td>24.77</td><td>15.754</td><td>68.083</td><td>67.869</td><td>68.076</td></tr><tr><td>10</td><td>57.042</td><td>55.41</td><td>54.890</td><td>23.982</td><td>24.108</td><td>24.001</td></tr><tr><td>11</td><td>48.654</td><td>50.21</td><td>52.012</td><td>30.242</td><td>30.446</td><td>29.279</td></tr><tr><td>12</td><td>68.595</td><td>70.6</td><td>68.333</td><td>36.497</td><td>36.308</td><td>35.752</td></tr><tr><td>13</td><td>86.060</td><td>83.51</td><td>86.489</td><td>55.920</td><td>55.851</td><td>55.858</td></tr><tr><td>14</td><td>26.361</td><td>23.4</td><td>27.991</td><td>64.001</td><td>64.28</td><td>63.474</td></tr><tr><td>15</td><td>86.060</td><td>83.51</td><td>86.489</td><td>72.077</td><td>72.234</td><td>72.069</td></tr><tr><td>16</td><td>49.990</td><td>52.3</td><td>59.698</td><td>70.806</td><td>70.746</td><td>70.761</td></tr><tr><td>17</td><td>69.890</td><td>72.34</td><td>69.192</td><td>76.605</td><td>76.849</td><td>76.644</td></tr><tr><td>18</td><td>84.806</td><td>82.13</td><td>83.406</td><td>82.401</td><td>82.476</td><td>82.293</td></tr><tr><td>19</td><td>35.271</td><td>40.6</td><td>33.652</td><td>62.627</td><td>62.644</td><td>62.748</td></tr><tr><td>20</td><td>55.170</td><td>56.94</td><td>59.902</td><td>68.125</td><td>66.42</td><td>66.314</td></tr><tr><td>21</td><td>70.206</td><td>62.33</td><td>68.286</td><td>69.659</td><td>69.721</td><td>69.698</td></tr><tr><td>22</td><td>34.054</td><td>37.82</td><td>25.398</td><td>31.383</td><td>31.543</td><td>31.392</td></tr><tr><td>23</td><td>53.995</td><td>54.51</td><td>60.745</td><td>32.614</td><td>32.993</td><td>32.601</td></tr><tr><td>24</td><td>9.061</td><td>9.61</td><td>4.877</td><td>33.851</td><td>33.967</td><td>33.884</td></tr><tr><td>25</td><td>32.773</td><td>35.52</td><td>30.384</td><td>75.985</td><td>75.63</td><td>75.999</td></tr><tr><td>26</td><td>52.755</td><td>52.56</td><td>49.977</td><td>79.043</td><td>79.172</td><td>79.023</td></tr><tr><td>27</td><td>69.008</td><td>60.74</td><td>65.405</td><td>82.097</td><td>82.238</td><td>82.087</td></tr><tr><td>28</td><td>73.270</td><td>65.02</td><td>73.986</td><td>86.649</td><td>86.333</td><td>86.707</td></tr><tr><td>29</td><td>69.430</td><td>70.67</td><td>70.506</td><td>87.426</td><td>87.549</td><td>87.409</td></tr><tr><td>30</td><td>61.855</td><td>67.45</td><td>63.272</td><td>88.198</td><td>88.288</td><td>88.220</td></tr><tr><td>31</td><td>50.550</td><td>55.37</td><td>48.190</td><td>74.250</td><td>74.039</td><td>74.111</td></tr><tr><td>32</td><td>49.104</td><td>55.11</td><td>46.592</td><td>72.744</td><td>72.928</td><td>72.763</td></tr><tr><td>33</td><td>57.103</td><td>52.62</td><td>48.859</td><td>71.235</td><td>71.34</td><td>72.167</td></tr><tr><td>34</td><td>53.301</td><td>54.92</td><td>63.839</td><td>38.782</td><td>38.746</td><td>38.873</td></tr><tr><td>35</td><td>45.767</td><td>48.35</td><td>69.564</td><td>34.996</td><td>35.308</td><td>35.077</td></tr><tr><td>36</td><td>34.504</td><td>32.93</td><td>38.874</td><td>31.205</td><td>31.394</td><td>31.275</td></tr><tr><td>37</td><td>55.589</td><td>51.09</td><td>46.736</td><td>96.050</td><td>95.177</td><td>96.050</td></tr><tr><td>38</td><td>83.120</td><td>100.84</td><td>82.487</td><td>94.086</td><td>93.832</td><td>93.302</td></tr><tr><td>39</td><td>85.002</td><td>83.23</td><td>79.439</td><td>92.117</td><td>92.009</td><td>92.439</td></tr><tr><td>40</td><td>11.107</td><td>21.43</td><td>10.633</td><td>98.891</td><td>101.688</td><td>103.031</td></tr><tr><td>41</td><td>86.595</td><td>83.57</td><td>85.950</td><td>98.247</td><td>98.016</td><td>98.266</td></tr><tr><td>42</td><td>51.502</td><td>56.74</td><td>59.365</td><td>93.996</td><td>93.867</td><td>94.018</td></tr><tr><td>43</td><td>68.611</td><td>66.21</td><td>68.600</td><td>85.870</td><td>85.201</td><td>85.876</td></tr><tr><td>44</td><td>33.604</td><td>36.39</td><td>18.328</td><td>79.343</td><td>79.202</td><td>80.022</td></tr><tr><td>45</td><td>90.479</td><td>56.76</td><td>70.423</td><td>72.813</td><td>72.727</td><td>72.900</td></tr><tr><td>46</td><td>66.944</td><td>66.15</td><td>62.483</td><td>46.182</td><td>45.716</td><td>46.242</td></tr><tr><td>47</td><td>31.977</td><td>36.68</td><td>37.430</td><td>37.373</td><td>37.391</td><td>37.578</td></tr><tr><td>48</td><td>-</td><td>-</td><td>-</td><td>28.560</td><td>28.589</td><td>28.743</td></tr></tbody></table>

Source: Authors, (2023).

$$Overall output = 1 * Target - 0.46 \quad (14)$$

## IV.3 COMPARISON OF RSM AND ANN, AND OPTIMIZATIONS

The use of the equations 13 and 14 allowed evaluating the performance of the models, followed by the comparison between the values of the experimental data, the predicted ANN and RSM values, either for LP and GP, respectively. The results are presented in Table 6.
According to the results of Table 6, the values of R² related to LP between experimental data and predicted RSM results on one hand, and between experimental data and predicted ANN results on another hand, were calculated using Excel and the results were 0.9488 and 0.9423, respectively. In addition, concerning GP the value of R² for the relationship between the experimental data and predicted RSM results was 0.9997, while the R² associated to the relationship between the experimental

data and predicted ANN results was 0.9995. Those results presented very high and significant performance of fitting for LP and GP, either in RSM and ANN. The optimization results of percent removal of LP and GP using RSM are carried out in Table 7, and based on the maximization of the equations 8 and 10. Concerning the optimization using ANN, the prediction equations 13 and 14 were used to develop a genetic-algorithm (GA) in MATLAB optimization tool.

<table><caption>Table 7: Optimization of gold recovery.</caption><thead><tr><th></th><th></th><th>Time (hr)</th><th>[HBr] (g/L)</th><th>pH</th><th>Speed (rpm)</th><th>Percent removal (%)</th><th>Validation experiment1 (%)</th><th>Validation experiment2 (%)</th></tr></thead><tbody><tr><td rowspan="2">LP</td><td>RSM</td><td>7.27</td><td>50</td><td>1</td><td>200</td><td>98.54</td><td>97.58</td><td>98.22</td></tr><tr><td>ANN</td><td>7.5</td><td>50</td><td>1</td><td>200</td><td>97.16</td><td>96.58</td><td>97.01</td></tr><tr><td></td><td></td><th>Time (min)</th><th>[α-CD] (g/L)</th><th>pH</th><th>Percent removal (%)</th><th>Validation experiment1 (%)</th><th>Validation experiment2 (%)</th><th></th></tr><tr><td rowspan="2">GP</td><td>RSM</td><td>40</td><td>11.61</td><td>5</td><td>98.87</td><td>98.45</td><td>97.87</td><td></td></tr><tr><td>ANN</td><td>39.8</td><td>10.71</td><td>5</td><td>99.98</td><td>99.95</td><td>99.26</td><td></td></tr></tbody></table>

Source: Authors, (2023).

The best percent removals for LP using RSM were predicted at the following conditions: time=7.27 hours, [HBr]=50 g/L, pH=1 and stirring speed=200 rpm, with a removal efficiency of 98.54%. By using ANN-GA, the optimal conditions were closed (time of 7.5 hours, [HBr] of 50 g/L, pH of 1 and stirring speed of 200 rpm) to those obtained with RSM with a percent removal of 97.16%. Moreover, it was found that in GP the optimal gold percent removal using RSM was 98.87% with a contact time of 40 minutes, a [α-CD] of 11.61 g/L and a pH of 5. The use of ANN-GA method revealed the highest percent removal of 99.98% with time, [α-CD] and pH, of 39.80 minutes, 10.71 g/L, and 5.15, respectively. Therefore the results of comparison confirmed the best performance of both RSM and ANN in gold removal during LP and GP. However, Table 7 reveals a quite difference in LP between RSM and ANN-GA maximum percent removal (1.38%), while the difference between ANN-GA and RSM in GP is equal to 1.11%.

## V. CONCLUSIONS

This paper demonstrates the successful use of alpha cyclodextrin (α-CD) for gold extraction from gold-bearing ore in the Democratic Republic of Congo (D.R.C). Through the implementation of Response Surface Methodology (RSM) and Artificial Neural Networks (ANN), the study identified the optimal gold removal conditions. Ore samples were initially processed to enhance leachability, and a modified aqua regia with hydrobromic acid was employed for the leaching process, leveraging the strong molecular recognition between gold bromide ion and α-CD. The experimentation involved adjusting various leaching parameters such as time, HBr concentration, pH, and stirring speed. RSM yielded optimal values of 7.27 hours, 50 g/L, pH 1, and 200 rpm, resulting in an impressive 98.54% gold removal. Meanwhile, ANN produced slightly lower values of 7.5 hours, 50 g/L, pH 1, and 200 rpm, with 97.16% gold removal. These results highlight the effectiveness of both RSM and ANN in optimizing gold extraction from the ore. Additionally, for α-CD gold recovery, RSM and ANN optimization resulted in 40 minutes, 11.61 g/L, and pH 5, achieving 98.87% and 39.8 minutes, 10.71 g/L, and pH 5, with 99.98% gold removal, respectively. These findings were further validated, reinforcing the success of RSM and ANN as methods for maximizing gold recovery from gold-bearing ore in the D.R.C. Overall, the use of

α-CD in combination with RSM and ANN presents a promising approach for sustainable and efficient gold extraction processes in resource-rich regions like the D.R.C., potentially opening new avenues for environmentally friendly mining practices and enhanced economic opportunities.

## VI. AUTHOR'S CONTRIBUTION

**Conceptualization:** Meschack Mukunga Muanda and Pele Pascal Daniel Omalanga.

**Methodology:** Meschack Mukunga Muanda and Pele Pascal Daniel Omalanga.

**Investigation:** Meschack Mukunga Muanda, Pele Pascal Daniel Omalanga, Vanessa Mwambaie Mitonga and Michée Ngoy Ilunga.

**Discussion of results:** Meschack Mukunga Muanda, Pele Pascal Daniel Omalanga, Vanessa Mwambaie Mitonga and Michée Ngoy Ilunga.

**Writing – Original Draft:** Meschack Mukunga Muanda and Michée Ngoy Ilunga.

**Writing – Review and Editing:** Meschack Mukunga Muanda and Michée Ngoy Ilunga.

**Supervision:** Meschack Mukunga Muanda and Pele Pascal Daniel Omalanga.

**Approval of the final text:** Meschack Mukunga Muanda, Pele Pascal Daniel Omalanga, Vanessa Mwambaie Mitonga and Michée Ngoy Ilunga.

## VII. REFERENCES

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