Optimization of Low-Rank Coal Flotation Using Jatropha curcas Biodiesel via Response Surface Methodology

Abstract

In this study, the focus is on investigating the performance of Jatropha curcas biodiesel as a potentially eco-friendly and non-edible collector for use in the flotation of low-rank coal. Due to its high cost and limited efficiency, using diesel as a collector for treating low-rank coal flotation presents several challenges. To achieve this aim, a systematic approach was adopted, employing a statistical design methodology to develop comprehensive mathematical models for combustible recovery and ash content. These models considered various parameters, including the dosage of the collector and frother, the solid percentage, and the depressant. The test results indicated that both models were statistically significant (p < 0.05). Furthermore, the findings showed that when the collector, frother, solid percent, and depressant were set at 0.5 kg/t and 2.13 kg/t, 0.26 kg/t and 0.214 kg/t, 15.00% and 14.40%, and 0.50 kg/t and 0.51, respectively, the ash content and recovery efficiency were 11.2% and 80.08%, respectively. The results also indicated that the doses of the frother and collector had a greater impact on the response variables than the other factors. In addition, verification experiments were conducted under the ideal conditions specified by the models to assess their validity and sufficiency. The SEM-EDS results confirmed that the concentration of carbon in coal cleaned with Jatropha biodiesel was higher than that cleaned with diesel oil. Furthermore, an FT-IR investigation showed that Jatropha biodiesel was more effective than diesel oil in reducing hydrophilic groups and enhancing hydrophobic groups. The hydrogen bonding between the oxygen-containing groups in Jatropha biodiesel and the surface of low-rank coal was responsible for the improvement in floatability and flotation recovery, which means Jatropha biodiesel, could be utilized as a substitute collector in the flotation of low-rank coal.

1. Introduction

Coal is a crucial fossil fuel and energy resource, accounting for 42% of the world’s electricity generation and approximately 30% of primary energy consumption [1]. Most global coal reserves consist of low-rank coal, primarily due to the depletion of high-quality sources by industrial activities. Low-rank coal offers several advantages, including low mining costs, high reactivity, and affordability, making it attractive for various industrial and energy applications. Their utilization presents opportunities for sustainable energy practices and improved operational efficiency. Additionally, the versatility of low-rank coals helps meet the growing energy demands of modern society, contributing to global energy security and stability [2,3,4,5,6]. The use of low-rank coal leads to solid waste accumulation in the form of ash and the emission of harmful pollutants. Consequently, scientists recommend cleaning low-rank coal before its use in industrial applications. This proactive approach aims to enhance environmental standards and optimize resource utilization in industrial production [7,8]. That is why surface modification and highly efficient flotation reagents are being used around the world to increase the efficiency of clean usage [9,10].

In the flotation system, hydrophobic coal particles cling to bubbles to form particle-air aggregates, and the coal particles are separated from the pulp by the bubbles floating on top of the coal particles [11]. Therefore, the natural surface hydrophobicity of particles is generally low; as a result, most particles have a low natural surface hydrophobicity, making it impossible for them to float [12]. This means the low-rank coal’s hydrophilic surface is not favorable to flotation [13]. Collectors are typically introduced during the flotation process to enhance the hydrophobicity of coal particles [9]. However, the surface of low-rank coal contains abundant oxygen-containing functional groups, making it difficult for conventional hydrocarbon-based oil collectors to achieve efficient flotation recovery [14]. In contrast, bio-based collectors such as those derived from Jatropha biodiesel offer a promising alternative. Their unique chemical composition can more effectively interact with the polar surfaces of low-rank coal, thereby improving flotation performance. Additionally, Jatropha-based collectors contribute to environmental sustainability by reducing reliance on fossil-derived reagents, minimizing associated pollutants, enhancing beneficiation, and potentially increasing combustion efficiency.

Building on the growing interest in alternatives to conventional hydrocarbon-based reagents, numerous studies over the past few decades have explored the use of bio-based and renewable collectors in coal flotation. These investigations have addressed key flotation parameters such as hydrogen bonding, reagent dosage, slurry concentration, stirring speed, and temperature that influence flotation efficiency [15,16,17,18,19,20,21]. For example, Ao et al. [17], they employed Central Composite Design (CCD) to address challenges such as high chemical consumption and low recovery in low-rank coal flotation. Their study-optimized variables including slurry concentration, frother, and collector dosage using Response Surface Methodology (RSM), resulting in a regression model with enhanced predictive accuracy. Similarly, Hamza et al. [18] Optimized flotation parameters using CCD-RSM, highlighting the importance of leaching variables in influencing recovery efficiency. Mohammadnejad et al. (2024) [19], also applied CCD to evaluate the effects of operational factors such as feed flow rate, aeration, collector, and frother dosage on flotation performance using diesel oil and methyl isobutyl carbonyl (MIBC). Their findings underscored the aeration rate as the most influential factor in ash removal. These studies collectively demonstrate the effectiveness of CCD-RSM in optimizing flotation conditions and further support the exploration of alternative, sustainable collectors. In this context, bio-based collectors have gained attention due to their environmental benefits and chemical compatibility with the polar surfaces of low-rank coal. For example, Hu et al. (2024) found that vegetable oils rich in polar components enhanced coal hydrophobicity by spreading more uniformly on the coal surface [20]. Zhu et al. (2020) demonstrated that non-edible waste cooking oil improved the cleanliness of fine coal flotation, with oxygen-containing functional groups (e.g., C=O, C–O) facilitating strong adsorption and improved hydrophobicity [21]. Likewise, Zhang et al. (2021) used octanoic acid as a polar collector and reported enhanced flotation performance through the formation of stable hydrogen bonds and electrostatic interactions that created a durable adsorption layer on the coal surface [22]. These findings reinforce the potential of renewable, bio-based collectors such as those derived from Jatropha biodiesel as viable and effective alternatives to fossil-based reagents in enhancing low-rank coal flotation performance while promoting sustainability. This study, therefore, has employed Response Surface Methodology (RSM) to model and optimize the flotation performance of Jatropha biodiesel as a bio-based collector, and its role in modifying the surface properties of low-rank coal. Jatropha biodiesel contains polar components, notably oleic acid, which possesses a long hydrophobic tail and a polar head group. This molecular structure enables strong interactions with the oxygen-containing functional groups on low-rank coal surfaces. Through these interactions, Jatropha biodiesel enhances coal hydrophobicity and promotes better attachment between coal particles and air bubbles thereby improving flotation recovery.

Coal flotation of low-rank coal incurs higher costs and restricts efficiency improvements. This study aims to provide novel insights into the use of Jatropha biodiesel as a renewable flotation collector, owing to its higher content of unsaturated fatty acids, which can form strong hydrogen bonds between the oxygen-containing groups in Jatropha biodiesel and low-rank coal. This interaction facilitates the attachment of air bubbles to coal particles, thereby improving floatability and optimizing its application through Response Surface Methodology (RSM). The findings are expected to have significant implications for the coal industry, particularly in enhancing the beneficiation of low-rank coal, improving energy efficiency, and promoting cleaner, more sustainable energy production. By addressing both performance and environmental considerations, this research supports the broader goal of resource optimization and sustainable energy development

2. Materials and Methods

2.1. Preparation of Raw Coal

This study utilized a representative coal sample from the Kiwira mine in Tanzania, which were crushed to a particle size of less than 0.25 mm and then sieved to determine its properties, as detailed in

Table 1. Characterization of the feed sample.

Proximate Analysis					Ultimate Analysis
F.C	Ash	F.M	V.M	C.V	Carbon	Hydrogen	Nitrogen	Oxygen
%	%	%	%	MJ/kg	%	%	%	%
48.05	29.71	3.43	21.78	5.73	58.12	3.28	1.76	20.38

Jatropha seeds were collected from around Arusha, and oil was extracted from them. Jatropha biodiesel was prepared using the Trans-esterification process. Nebrix Limited the local distributor of Sigma Aldrich chemical Reagent, Mwanza, Tanzania supplied the chemical reagents, including 99% methanol, sodium hydroxide (NaOH), and methyl isobutyl carbonyl (MIBC). Distilled water was used in all experiments for solution preparation.

2.2. Collector Preparation (Trans-Esterification Process)

The trans esterification is a chemical reaction that transforms triglycerides (fats and oils) present in the crude oil into fatty acid alkyl esters (biodiesel) and glycerol. This process involves reacting the crude oil with an alcohol, typically methanol or ethanol, in the presence of a catalyst [23]. Biodiesel, a renewable, non-toxic fuel, is a biodegradable, renewable fuel. It contains unsaturated fatty acids, polar and nonpolar functional groups, and oxygenated groups. The polar groups in biodiesel, such as carboxyl groups, can interact with the oxygenated functional groups on the coal surface through hydrogen bonding [24].

The experiments with the Jatropha collector were conducted in batch mode using a glass beaker (Nebrix Limited, Mwanza, Tanzania) on a bench apparatus. Initially, extraction of oil from seeds (c), the catalysts were pre-activated by stirring and mixing them with methanol for 30 min at room temperature Figure 1. Following this, heating was initiated, and Jatropha biodiesel was added to the reactor. The operating conditions included a molar ratio of 9:1 for methanol to Jatropha biodiesel and one weight percent of catalyst relative to the Jatropha biodiesel (e). Alcohol was employed to facilitate the separation of the biodiesel and glycerol phases, thereby shifting the reaction equilibrium towards the products (f), as illustrated in Figure 1.

2.3. Experimental Test

An XFD 3L flotation machine manufactured by Jiangxi Jinshibao Mining Machinery Manufacturing Co, Ltd., Jiangxi, China. Flotation cell with a 2.50-L capacity, operating at 1800 rpm, was employed for the experiments. Each test utilized a 250 g coal sample, prepared with fresh water at a pH of 7.50. Wetting and conditioning times were set at 5 min and 90 s, respectively. Various dosages of MIBC frother and Jatropha biodiesel collectors were tested based on preliminary results to determine optimal conditions. Subsequently, optimization tests were conducted using the selected compounds, with sodium silicate employed as the depressant.

To evaluate flotation efficiency, the ash content of dry coal samples was analyzed. After each flotation experiment, the ash content of the products was measured, leading to the derivation of the ash content (Ash) and combustible recovery (CR) formula from Equations (1) and (2).

$$Ash\left(\%\right)={\displaystyle \frac{m_3-m_1}{m_2-m_1}}\times 100\%$$

(1)

$$C_R\%={\displaystyle \frac{\%Wtconcetrate\ast 100-Ashconcentrate}{100\ast (100-Ashcontetfeed)}}\times 100$$

(2)

2.4. Characterization of Raw Coal, Collectors, and Clean Coal

The morphologies and chemical compositions of the low-rank coal powders were analyzed using scanning electron microscopy coupled with energy-dispersive X-ray spectroscopy (SEM-EDS) both before and after treatment. An X-ray diffract meter (XRD) was employed to investigate the primary mineral phase of the raw coal and to assess the stability of inorganic minerals in various solutions, given that coal contains both biological and inorganic components. To explore the differences in functional groups between the coal and the adsorption mechanism of Jatropha biodiesel molecules, Fourier-transform infrared spectroscopy (FTIR) was utilized to identify the functional groups present in Jatropha biodiesel collectors, raw coal, and clean coal. The FTIR operated with a wavenumber range set between 400 and 4000 cm⁻¹. Lastly, the contact angle was measured to evaluate the hydrophobicity and floatability of the mineral surface, using an optical contact angle measurement device.

2.5. Experimental Design for Coal Flotation Process Modeling and Optimization

The interaction effects of variables such as pulp concentration, collector dosage, froth dosage, and airflow on coal flotation efficiency were examined using the central composite design of the response surface methodology. The central composite design has been the most effective multivariate statistical technique for optimizing low-rank coal flotation processes in recent years [16,20,25]. The central composite design greatly aids in reducing operating costs and time. Along with the reduction in experimental runs, it is also claimed that the outcomes obtained using the central composite design are statistically acceptable [25]. In addition, to determine parabolic effects, RSM requires each parameter to have at least three levels. Following variance analysis, a second-order regression equation of the response variable (y) is typically obtained in the form of dependent variables ($X_{ij}$) and their coefficients (${\beta }_{ij}$), as given in Equation (3). RSM is the culmination of statistical and mathematical methods that enable more data collection with fewer experiments. The model equations derived from RSM in conjunction with the desired functions created by Derringer and Suich, can be used to estimate the optimal conditions. Additionally, it is possible to do simultaneous optimization for different response variables [26]. The ash content and combustible recovery of clean coal in coal flotation were the two response variables that were simultaneously optimized in this study using the CCD approach.

2.6. Experimental Design by Central Composite Design

Central composite design is an experimental design technique that is frequently used in process optimization to generate a second-order response surface model [27]. Unlike a complete factorial design, this approach permits the collection of more data with fewer trials. Also, CCD is not like axial points, where each parameter needs two experiments [28]. To estimate and optimize the coal flotation efficiency of Jatropha biodiesel collectors on low-rank coal surface adsorptive conditions, the four most important factors and their values were chosen from the one-factor-at-a-time batch tests as summarized in

Table 2. Independent factors and their levels.

Factors	Level
	−α	−1	0	+1	+α
A: Collector (kg/t)	−0.75	0.50	1.75	3.00	4.25
B: Frother (kg/t)	0.05	0.20	275	0.50	0.65
C: Solid percent (wt%)	7.50	10.00	12.50	15.00	17.50
D: Depressant (kg/t)	0.25	0.50	1.25	2.00	2.75

. In this study, Design Expert 13.0 software was used to design the experiment using a central composite design (CCD). Statistical design of experiment principles were used to optimize responses, ash content, and combustible recovery of treated coal in the coal flotation process using Jatropha biodiesel (biodiesel) and pine oil as frothers. Using different concentrations supplied by the central composite design of the response surface methodology, as shown in Table 2, the batch coal flotation experiments were conducted by applying the proper dosage of the pine oil and Jatropha biodiesel collector, solid percent, and airflow into the XFD flotation cell (3L) for the best recovery.

3. Results and Discussion

3.1. Characterization of Feed Coal and Jatropha Biodiesel

Coal samples from the Kiwira mine in the Mbeya region of Tanzania were crushed and ground to particle diameters of 0.1 and 0.2 mm. Proximate and ultimate analyses of the coal sample are displayed in Table 1. The analyses reveal an ash content of 29.71%, a volatile matter content of 21.72%, and a fixed carbon content of 48.05%. The coal samples contain 58.12% carbon and 20.38% oxygen. Based on these results, the coal samples are classified as typical low-rank coal [29].

Figure 2 presents the FT-IR spectra of both diesel oil and the renewable Jatropha-based collector, revealing key differences in their functional group compositions. The Jatropha biodiesel collector exhibits more pronounced absorption peaks across several functional regions, indicating a richer presence of oxygen-containing and polar functional groups compared to fossil diesel. Notably, the C–H stretching vibration observed between 720 and 921 cm⁻¹ is more intense in Jatropha biodiesel, highlighting its higher fatty hydrocarbon content [30]. The C–O stretching vibration at 1170 cm⁻¹, associated with esters and ethers, is also stronger in the Jatropha sample, signifying a higher concentration of oxygenated compounds. Peaks corresponding to carboxyl groups (C=O stretching in the 1602–1742 cm⁻¹ range), methyl/methylene groups (CH₃/CH₂ at 1400–1436 cm⁻¹), and aromatic structures also show greater intensity in Jatropha biodiesel. Furthermore, the C=C stretching vibration in the 3000–3300 cm⁻¹ range is more prominent, reflecting the unsaturated fatty acid components of the oil [31]. Additional peaks observed at 2925 cm⁻¹ and 2854 cm⁻¹ correspond to the CH₂ and CH₃ symmetric and asymmetric stretching vibrations typical of fatty hydrocarbons, while 1460 cm⁻¹ is attributed to CH₂/CH₃ bending. The C=O peak at 1745 cm⁻¹ and the C–O peak around 1100 cm⁻¹ (linked to phenols, alcohols, esters, and ethers) further confirm the high presence of oxygen functional groups. These functional groups especially C=O, –CH₂, –CH₃, and C–O– are commonly found in conventional flotation reagents [15]. Their presence in Jatropha biodiesel facilitates multiple interaction mechanisms on the coal surface. The nonpolar hydrocarbon chains (C–C, C–H) interact with the hydrophobic regions of coal via van der Waals forces and π–π interactions, while the polar oxygen-containing groups (C=O, C–O) form hydrogen bonds with the oxygenated sites on low-rank coal surfaces [12]. This dual interaction mechanism significantly enhances coal particle hydrophobicity, which is critical for efficient flotation. The FT-IR peaks at 1740 cm⁻¹ (C=O) and 1655 cm⁻¹ (C–O) further support the higher concentration of reactive oxygen-containing groups in Jatropha biodiesel compared to diesel [31,32]. These groups can adsorb onto the polar regions of the coal surface, forming a stable collector layer that promotes bubble attachment and particle recovery. Consequently, the use of Jatropha biodiesel enhances the hydrophobicity of low-rank coal surfaces and improves flotation efficiency. These findings are consistent with previous studies, which report improved flotation response when polar functional groups on collectors interact with oxygen-containing groups on the coal surface [30,33].

3.2. Characteristics of Clean Coal

3.2.1. XRD Analysis

X-ray diffraction was employed to examine the microstructure and crystallization of raw coal and coal treated with Jatropha biodiesel collectors. The results of the XRD analysis, presented in Figure 3, reveal that kaolinite, quartz, and calcite are the primary mineral components of the cleaned coal samples. The presence of hydrophilic components in the raw coal is indicated by sharper diffraction peaks of contaminants in the raw samples compared to those treated with diesel and Jatropha biodiesel. Furthermore, the high diffraction peak intensities of quartz and kaolinite in the profiles suggest a significant background intensity in the raw coal samples, highlighting the presence of disordered components in the form of amorphous carbon [32]. The high amount of clay minerals like kaolinite and their capacity to coat coal particle surfaces leads to increased water absorption in coal slurries, making water removal more challenging. Additionally, the amorphous nature of low-rank coal, along with its hydrophilic components such as oxygen-containing functional groups resulting from a low degree of coalification, hinders particle aggregation. This situation decreases the filtration rate, raises moisture content, and ultimately compromises flotation performance [34]. Highlighted at distinct (002) peak at 26° indicates the presence of crystalline carbon structures resembling graphite. This unique asymmetric (002) peak is attributed to saturated structures, such as aliphatic side chains, associated with the edges of the coal. The alteration in the microcrystalline structure of the coal is a result of surface modification induced by the jatropha collector. The reduction of oxygen-functional groups such clay mineral kaoline, quartz increased hydrophobicity of coal indicate an effective removal of impurities, this implies a decrease in amorphous components and an increase in crystalline minerals, reflecting modifications in the coal’s hydrophobicity structure following the flotation treatment, of crystalline minerals while minimizing hydrophilic content and enhanced flotation performance [35]. The enhanced hydrophobicity and flotation performance can be attributed to hydrogen bonds and van der Waals interactions between the collector and the coal surface [36]. Furthermore, post-treatment jatropha biodiesel showed an reduction in kaolinite and quartz peaks, indicating a reduction in amorphous components and an enhancement of crystalline materials observed at 15 °C, 26 °C, and 31 °C. This phenomenon can be explained by a higher aliphatic content resulting from the flotation process, leading to a reduction in amorphous chains and an increase in hydrophobicity [37,38]. This change contributes to a more uniform particle size distribution, the elimination of cracks, reduced porosity, enhanced hydrophobicity and performance.

3.2.2. Functional Group Analysis of Coal Before and After Treatment

Fourier transform infrared spectroscopy was used to study the functional groups of coal, before and after treatment as indicated in Figure 4. The functional groups that correlate to the relevant peaks in the coal samples are as follows: intermolecular hydroxyl (–OH), carbonyl (C=O), or carboxyl (COOH), and the stretching vibration of carbonyl are represented by the absorption peaks at 3500 cm⁻¹, 1600 cm⁻¹, and 1200 cm⁻¹. This occurs as a result of poor flotation of low-rank coal in the presence of hydrophilic functional groups [38]. It is evident from Figure 4 that the treatment with the collector Jatropha weakens the peaks for the hydrophilic groups in coal. It suggests that Jatropha biodiesel collectors can improve the floatability of low-rank coal are represented by the adsorption peaks at 3600 cm⁻¹ ad 1600 cm⁻¹. Thus, it seems that the polar group of the Jatropha interacts with the oxygenated functional group on the coal surface through a hydrogen bond, which is the mechanism of contact between the Jatropha (polar and nonpolar) collector and the coal surface [39]. This can be attributed to the reduction in clay minerals, such as kaolinite and quartz, in the coal after treatment. This situation is reflected in the distinct (002) peak at 26°, which signifies the presence of enhanced hydrophobicity and carbon structures resembling graphite. This peak is associated with saturated structures, including aliphatic side chains, located at the edges of the coal, as shown in the XRD results in Figure 3. By forming hydrogen bonds that encourage alkyl adsorption at these sites, polar hydroxyl and carboxyl cover the hydrophilic sites while non-polar alkyl covers the hydrophobic sites [40]. In other words, the synergistic interaction between the two types of alkyls led to an enhancement in flotation performance [41].

3.2.3. Surface Hydrophobicity for the Feed Coal

Surface hydrophobicity is a critical parameter in evaluating the flotation behavior of feed coal, as it directly influences the coal particles’ ability to attach to air bubbles during the flotation process. Low-rank coals typically exhibit poor flotation performance due to the abundance of oxygen-containing functional groups (e.g., hydroxyl, carbonyl, and carboxyl), which increase surface polarity and reduce hydrophobicity. Therefore, analyzing the surface hydrophobicity of the feed coal is essential to assess its floatability and determine the necessity for surface modification or collector addition. Figure 5 illustrates the contact angle measurements of the feed coal before and after treatment with the Jatropha biodiesel collector. The results indicate a significant increase in surface hydrophobicity after treatment, with the contact angle rising from 52.35° for the untreated feed coal to 90.86° following flotation with Jatropha biodiesel. This notable increase demonstrates the effectiveness of Jatropha biodiesel in modifying the coal surface from hydrophilic to hydrophobic.

As a bio-based collector, Jatropha biodiesel contains both long-chain hydrocarbon groups and polar functional groups, such as esters and carboxylic acids [17]. The polar groups facilitate adsorption onto the oxygen-rich, polar surface of low-rank coal through hydrogen bonding and electrostatic interactions, while the nonpolar hydrocarbon tails orient outward, creating a hydrophobic surface. This orientation enhances the attachment of coal particles to air bubbles during flotation, thereby improving separation efficiency.

The increase in contact angle confirms that Jatropha biodiesel effectively renders the coal surface more hydrophobic, highlighting its potential as a sustainable and efficient alternative to conventional fossil-derived flotation collectors [29].

3.2.4. SEM-EDS Analysis

Scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS) measurements were used to analyze the surface morphology and elemental composition of raw coal (RC) before and after treatment.

Table 3. Proportional elements analyses estimated from SEM-EDS for feed coal and clean coal with diesel oil and Jatropha biodiesel.

Element (%)	Products Concentrate
	Feed Coal	With Diesel Oil	With Jatropha Biodiesel
	S1	S2	S3
C	60.80	69.70	73.70
O	32.77	24.30	21.06
Al	2.15	1.40	1.70
Si	0.21	4.40	2.70
Ca	0.15		0.10
Ti	0.32		0.10

provides a summary of the SEM-EDS analysis results for the images that were taken, which are displayed in Figure 6 and Figure 7. The main aim of this investigation was to identify how the low-rank coal’s physical makeup differed before and after beneficiation trials. The image shows a significant decrease in hydrophilic content in the coal concentrates. The SEM images in Figure 6a reveal an uneven distribution of particle sizes, with many tiny particles, primarily fine mud, adhering to the coal surface. This fine mud, influenced by hydrophilic components like clay, contributes to the high ash content and contains numerous pores and cracks. Figure 6b illustrates that after treatment with Jatropha biodiesel, the hydrophilic components in the raw coal have decreased. This change results from a more consistent particle size distribution, the removal of cracks, reduced porosity, and enhanced hydrophobicity. Figure 7, display the EDS analysis, indicating that the carbon composition increased from 60% before to 69.7% after treatment using diesel oil, and 73.7% after treatment using jatropha biodiesel collectors. Oxygen decreased from 32.77% to 24.3% after treatment using diesel oil and 21.1% using jatropha. This suggests that the Jatropha collector effectively modified the coal surface. These observations conform with the findings by [8].

3.3. Experimental Design and Modeling

Using the central composite design, 20 batch tests with various combinations of the components were carried out to ascertain the interactive effects, model, and optimize the independent parameters for ash content and combustible recovery from the flotation system.

3.3.1. Response Prediction

To examine the interactive behavior among the chosen independent parameters as a function of (1)-ash content and (2)-combustible recoveries, as shown in

Table 4. Statistics on model fitness to experimental data of Ash content (%).

Source	Std. Dev.	R2	Adjusted R2	Predicted R2	Ad. Precis	Remark
Linear	0.0058	0.7722	0.7357	0.6661		Suggested
2FI	0.0066	0.7764	0.6588	0.6086
Quadratic	0.0052	0.8915	0.7901	0.6730	11.4800	Suggested
Cubic	0.0000	1.0000	1.0000			Aliased

and

Table 5. Statistics on model fitness to experimental data of Combustible recovery (%).

Scheme	Std. Dev.	R2	Adjusted R2	Predicted R2	Ade. Precis	Remark
Linear	5.28	0.8929	0.8758	0.8498
2FI	6.05	0.8934	0.8374	0.8094
Quadratic	3.01	0.9791	0.9596	0.8928	21.4900	Suggested
Cubic	0.0000	1.0000	1.0000			Aliased

, respectively, the central composite design of response surface methodology in Design Expert software was used and the quadratic models were selected. As seen in Table 4 and Table 5, respectively, it was observed that, the cubic model was aliased and could not be used for any further modeling of experimental data.

The quadratic model chosen for the (1)-Ash content, as indicated in Table 4, has a 3.1 standard deviation and strong correlation coefficients for R², adjusted R², and projected R², respectively, of 0.8915, 0.7901, and 0.6730. The chosen quadratic model for the (2)-Combustible recovery has good R², adjusted R², and anticipated R² of 0.9791, 0.9596, and 0.8928, respectively. It was observed that there was less than a 0.20 difference between the adjusted and predicted correlation coefficients of the quadratic models that were developed for the responses (1) Ash content and (2) Combustible recovery attained for the modified surface of low-rank coal concentrate from the flotation system. Accordingly, the constructed quadratic models were sufficient and accurate, and they could be applied to response prediction. Furthermore, as indicated in Table 4 and Table 5, respectively, the adequate precision, which establishes the signal-to-noise ratio derived from the quadratic models created for each response, was higher than 4.0. This implies further that the quadratic models chosen are appropriate and acceptable.

The regression model equations were developed using all of the dependent factors, such as (1) ash content and (2) combustible recovery. The responses as a function of the independent components were optimized using these quadratic model equations, which have the form of Equation (3)

$$y=\beta o+{\sum }_{j-1}^k{\beta }_j{X}_j+{\sum }_{j-1}^k{\beta }_{jj}{{\beta }_j}^2+\sum {\sum }_{1<j-2}^k{\beta }_{ij}{X}_{ij}{X}_j+\epsilon$$

(3)

where y represents the expected response, ${\beta }_i$ is the linear regression coefficient, ${\beta }_{ij}$ is the regression coefficient for two-factor interaction effects, and ${\beta }_0$ is the constant of the coefficient. $X_i$ and $X_j$ are the factor levels, while ${\beta }_{ij}$ is the regression coefficient for quadratic main effects.

The coded quadratic model regression equations produced for the (1) combustible recovery and (2) ash content in the current investigation are provided in Equations (4) and (5), respectively. The relative importance of the various independent factors can be determined using these coded regression model equations by comparing the factor coefficients. In regression model Equations (4) and (5), the positive sign appears before the model terms.

$$y1=+0.0937+0.0099A+0.0056B-0.0005A{A}^2-0.0032B{B}^2+0.0012C{C}^2+0.0012D{D}^2$$

(4)

$$y2=+8.58+0.9400A-0.726-0.2918A^2-0.2014B^2+{0.0198C}^2+{0.0198D}^2$$

(5)

3.3.2. ANOVA for a Quadratic Model of the Responses

The analysis of variance (ANOVA) was used to examine the model significance as well, the interaction and quadratic impacts of the independent factors on the responses ($y1$) Ash content and ($y2$)-combustible recovery. A model’s acceptability, suitability, and significance are determined by looking at its F-value, p-value, precision level, and the difference between the adjusted and projected R-squared.

A factor is considered significant at a 95% confidence level if its p-value is less than 0.05, as shown by the ANOVA v.13 findings for the quadratic models in Table 5 and

Table 6. ANOVA for response surface quadratic model for ash content.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value	Remark
Model	0.0033	14	0.0002	8.80	<0.0001	significant
A-Collector dosage	0.0020	1	0.0020	74.84	<0.0001
B-frother dosage	0.0008	1	0.0008	28.33	<0.0001
C-Solid percent	0.0000	1	0.0000	0.0000	1.0000
D-Depressant	0.0000	1	0.0000	0.0000	1.0000
AB	0.0000	1	0.0000	0.5902	0.4543
AC	0.0000	1	0.0000	0.0000	1.0000
AD	0.0000	1	0.0000	0.0000	1.0000
BC	4.337 × 10−19	1	4.337 × 10−19	1.609 × 10−14	1.0000
BD	0.0000	1	0.0000	0.0000	1.0000
CD	0.0000	1	0.0000	0.0000	1.0000
A2	4.149 × 10−6	1	4.149 × 10−6	0.1539	0.7003
B2	0.0003	1	0.0003	10.78	0.0050
C2	0.0000	1	0.0000	1.51	0.2388
D2	0.0000	1	0.0000	1.51	0.2388
Residual	0.0004	15	0.0000
Lack of Fit	0.0004	10	0.0000
Pure Error	0.0000	5	0.0000
Cor Total	0.0037	29

, respectively. p-values less than 0.05 (p < 0.001) indicate that the quadratic models fitted to the responses are significant, as shown in Table 6 and

Table 7. A NOVA for response surface quadratic model for combustible recovery.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value	Remark
Model	2321.32	14	165.81	102.29	<0.0001	Significant
A-Collector	2035.76	1	2035.76	1255.85	<0.0001
B-Frother	66.67	1	66.67	41.13	<0.0001
C-Solid percent	54.00	1	54.00	33.31	<0.0001
D-Depressant	4.17	1	4.17	2.57	0.1297
AB	16.00	1	16.00	9.87	0.0067
AC	2.25	1	2.25	1.39	0.2571
AD	0.2500	1	0.2500	0.1542	0.7001
BC	0.2500	1	0.2500	0.1542	0.7001
BD	0.2500	1	0.2500	0.1542	0.7000
CD	8.777 × 10−11	1	8.777 × 10−11	5.414 × 10−11	1.0000
A2	138.72	1	138.72	85.58	<0.0001
B2	1.16	1	1.16	0.7144	0.4113
C2	9.24	1	9.24	5.70	0.0305
D2	1.16	1	1.16	0.7144	0.4113
Residual	24.32	15	1.62
Lack of Fit	20.98	10	2.10	3.15	0.1088	not significant
Pure Error	3.33	5	0.6667
Cor Total	2345.64	29

. When flotation from a low-rank coal system occurs, the F-value determines the degree of importance and how the flotation components interact. The most significant model term and a lower p-value are indicated by a greater F-value. The created quadratic models are highly significant and could be utilized to reliably predict the responses, as indicated by the model terms with p-values less than 0.05. Additionally, Table 5 illustrates the fit statistics of the quadratic model developed for a biodiesel collector in ash content reduction efficiency from the waste coal flotation process. The correlation coefficients such as R-squared (R²), adjusted R², and predicted R² values of 0.8915, 0.7901, and 0.6730, respectively, were observed to be close to unity. A closer correlation coefficient (R²) to 1.0 indicated a greater fitness and better prediction of the response by the quadratic model [25,26,27,28,29,30,31,32,34,35,36,37,38,39,40,41,42,43,44]. Consequently, Table 5 and Table 6 demonstrate that, with p-values less than 0.05, every model term for ash content and combustible recovery including A, B, C, AB, AC, BC, A², B², and C², D²—is significant. Additionally, it was discovered that, the replies’ p-values for the Lack of Fit test were greater than 0.05, indicating that the models’ lack of fit is not significant. As a result, the responses needed to optimize coal flotation system could be predicted using the quadratic models. Therefore, Table 6 illustrates the fit statistics of the quadratic model developed for a biodiesel collector in ash content reduction efficiency from the waste coal flotation process. The correlation coefficients such as R-squared (R²), adjusted R², and predicted R² values of 0.9791, 0.9596, and 0.8928, respectively, were observed to be close to unity. A closer correlation coefficient (R²) to 1.0 indicated a greater fitness and better prediction of the response by the quadratic model [19,22].

Table 6 shows that the model is significant, according to the model’s F-value of 8.80 An F-value this is small and could only be the result of small noise in 0.01% of cases. Model terms are significant if the p-value is less than 0.0500. In this instance, important model terms are A, B, C, and AC. The model terms are not significant if their values exceed 0.1000. Model reduction could help your model if it has many unnecessary terms (aside from those needed to maintain hierarchy). Given the pure error, the F-value for lack of fit, o, suggests that the lack of fit is not substantial. A significant F-value for Lack of Fit could be the result of noise, with the probability that it is insignificant.

In Table 7, the significance of the model is indicated by its F-value of 102.29. An F-value this enormous could only be the result of noise in 0.01% of cases. Model terms are significant if the p-value is less than 0.0500. Significant model terms in this instance are A, B, C, AB, and A². The model terms are deemed not significant if their values exceed 0.1000. Model reduction could help your model if it has many unnecessary terms (aside from those needed to maintain hierarchy). Given the pure error, the F-value for lack of fit, which is insignificant, suggests that the lack of fit is not substantial. A significant F-value for Lack of Fit could be the result of noise with a 10.88% probability.

Furthermore, there is a discrepancy of less than 0.2 between the adjusted R² of 0.8915, 09791 and the predicted R² of 0.7901, 09596 for ash content and combustible recovery, respectively, which is indicative of good conformity of the model to the experimental data [20,45]. Similarly, the lack of fit p-value of 1.84 demonstrated that the quadratic model’s lack of fit is not significant, proving that the developed model is accurate and suitable for fitting the experimental data [45,46,47].

3.3.3. Interactive Effect of Collectors and Frother Dosage on Ash Content and Combustible Recovery of the Concentrate

The experimental findings regarding the effects of various variables are illustrated in Figure 8, which includes A (collector), B (frother), C (solids percent), and D (depressant). The findings demonstrate that the jatropha biodiesel collectors are appropriate for carrying out flotation studies, as seen in Figure 8. An increase in collectors, frother dosage results on increase of coal recovery and decrease of ash content. As the dosage of the collector decrease, the ash content also rises, as shown in Figure 8a. Conversely, the dosage of the collector does not much affect the ash content. At a dosage of 1 kg/t, the ash content decreased to 11.2%, while at 3 kg/t, it increased to 14.2%. Additionally, coal recovery has significantly improved, with approximately 3 kg/t of collectors resulting in the highest recovery rate of 80.08%. This is because Jatropha biodiesel demonstrates a greater affinity and selectivity for coal compared to diesel oil, attributed to its longer chain length and higher content of unsaturated fatty acids. This characteristic enhances bubble-droplet formation, resulting in increased yield and the removal of additional mineral particles from the coal cell [8]. Figure 8b it is shows that the ash content increase when the amount of frother (MIBC) increase. Figure 8c presents the results, which aims to determine the optimal solids percentage for flotation tests by analyzing the relationships between solids percentage, coal recovery, and ash content. The graphical analysis indicates that a solids recovery rate of approximately 14% produced significantly better results compared to other conditions, although it may have slightly increased the ash content. By prioritizing both coal recovery and ash content, we can identify the ideal solids percentage for optimization.

The effect of sodium silicate depressant is illustrated in Figurer 8d. The results indicate that the grade and recovery of coal are not significantly affected by sodium silicate. At sodium silicate doses ranging from 0.5 to 2.5 kg/t, the ash concentration varies between 12.4% and 14%, while coal recovery ranges from 53% to 69%, although not necessarily in that order. The findings suggest that a dose of 1.5 kg/t Sodium silicate can achieve a flotation concentrate with 12% ash from coal with an initial ash content of 30%, resulting in a recovery of 53% of the coal concentrate.

Coal recovery, ash content, and the interactions among these factors were examined, revealing their effects on one another. Software was utilized to analyze the experimental findings, enabling the identification of these effects. This approach facilitates the selection of a significant model and accurately portrays the impact of various variables in Figure 9 and Figure 10. The analysis demonstrated that increases in solid content, collector dosage, and frother enhanced coal recovery and decrease the ash content. Figure 9 indicates that at high levels of both collector dosage and solid percentage, the ash content of the clean coal ranges from 9% to 15%. In contrast, the ash concentration drops to approximately 10% when the depressant is applied at a rate of 2 kg/t. At lower levels of collector dosage and solid percentage, the minimum ash concentration for the clean coal is determined to be 10%. Thus, the influence of depressants on ash content seems to be contingent upon the levels of solid percentage and collector dosage. High values indicated that these variables had a substantial impact on coal recovery, with interactions among them being preserved. Although there were no noticeable changes in ash content, the study found that increasing the dosage of depressants led to higher ash content. A three-dimensional graph enhanced the understanding of the relationships among these factors in the flotation process. Additionally, when increasing frother dosage in coal flotation can reduce ash content by enhancing bubble surface area which is observe at 0.32–0.5 kg/t, promoting selective flotation, and improving the recovery of combustible material, but only up to an optimal level [48]. Below 0.32 kg/t this point, frother cannot affect much on ash content. This can be attributed to, the ability of sodium silicate to depress specific gangue minerals may be hampered if biodiesel has a higher affinity for them [49]. Additionally, as shown in Figure 10, the interactions between these variables and their effects on coal recovery were maintained, leading to notable outcomes. The findings indicated that, the coal recovery increased with increased dosages of jaropha biodiezelcollector and frother up to the optimum level, higher dosages can negatively affecting coal recovery. These results revealed a significant improvement in coal recovery as solid content, collector dose, and depressant dosage increased. Coal recovery observed between 48, 48% to 86, 83% the maximum coal recovery was observed at higher jatropha biodiesel collectors dosage and solid percent. Additionally, variations in the dosage of the depressant did not significantly affect the ash content. Furthermore, interactions among the variables were maintained, it was observed that there was a notable interaction between solid content, collector dosage, and depressant dosage at intermediate values of these variables. Based on the results of the variance analysis, it can be concluded that the triple interaction of collector dosage, solid percentage, and frother dosage is the most significant factor. Consequently, the effect of the depressant on ash content appears to vary depending on the levels of collector dosage and solid percentage.

3.3.4. Optimization of Coal Flotation Factors

Determining the optimal operating conditions for the component system in coal flotation represents the final phase of the Central Composite Design (CCD) under Response Surface Methodology (RSM). In this study, the desirability function within the CCD-RSM framework was applied to identify the experimental conditions that yield the highest ash removal and combustible recovery in the concentrate. This optimization was conducted to evaluate the efficiency of Jatropha-based collectors synthesized via trans-esterification for use in the coal flotation process. For optimal performance of the coal flotation system, the maximum operating conditions were identified as follows: a collector dosage of 0.5 kg/t, a frother dose of 0.26 kg/t, 15% solids, and a depressant dosage of 0.5 kg/t for ash content. For coal recovery, the optimal conditions included a collector dosage of 2.13 kg/t, a frother dose of 0.21 kg/t, 14.4% solids, and a depressant dosage of 0.54 kg/t. Following the search for 20 optimization solutions at a desirability value of 1.0, the optimal ash content and combustible recovery under the ideal experimental conditions were found to be 9.97% and 83.22%, respectively, as illustrated in Figure 11.

3.3.5. Validation of Quadratic Models and Confirmation of Optimization Results

The quadratic models created for the dependent factors (responses) as a function of the independent components need to be validated. Confirmatory tests were conducted under ideal working conditions. The data mean of five confirmatory experimental runs employing the optimal operating conditions in coal flotation for the alteration of low-rank coal surface using Jatropha biodiesel collectors is displayed in

Table 8. Confirmation of optimum response obtained for ash content and combustible recovery of the concentrate from the flotation system.

Solution 1 of 100 Response	Predicted Mean	Predicted Median	Observed	Std. Dev.	n	SE Pred	95% PI Low	Data Mean	95% PI High
Ash	9.97	9.97	11.20	0.51	1	N/A	8.83	10.32	11.31
C.R	83.22	83.22	80.08	3.01	1	3.37	75.43	80.64	87.81

at a two-sided 95% confidence level. The optimal ash concentration of the concentrate at this setting is 11.2%, according to the confirmatory experimental data, and the combustible recovery is 80.08%. It falls within the forecasted periods. There is a strong correlation between the expected and confirmatory experimental data in comparison, with low residual and standard deviations, suggesting that created quadratic models have been validated and could be used in predicting future cases. To validate the quadratic model developed for the adsorption ability of biodiesel from the Jatropha biodiesel into the low-rank coal surface, laboratory confirmatory experiments were conducted. Table 8 shows the average data of the five confirmatory experimental runs performed at a two-sided 95% confidence level using the best operating conditions achieved during the efficient recovery of waste coal. The confirmatory experimental results showed that at the optimal conditions, the optimum recovery efficiency of 80.08% was attained. The obtained optimum recovery efficiency from the predicted is found to be between the 95% prediction interval of 83.08%, which is within the prediction interval [50]. Therefore, there exists a good conformity between the confirmatory experimental and the predicted results with a standard error prediction (SE Pred) of 3.37, indicating that the developed quadratic model is valid and could be used in predicting future cases [51]. Additionally, the proposed quadratic model’s minimal standard deviation indicators have been validated and may be utilized to forecast future cases [52].

In this study, the optimum combustible recovery from the coal flotation system using the non-edible oil (Jatropha biodiesel) collectors derived from the plants is compared with previous studies using different oils. Comparatively, the combustible recovery of the concentrate from the separation of hydrophilic components in coal flotation by these collectors was found to be higher than most of the collectors prepared using fossil oil for low-rank coal flotation. This indicates that the collectors prepared from the Jatropha seeds are very efficient in the flotation performance and other hydrophilic components from low-rank coal.

Table 9. Comparison of combustible recovery in the coal flotation process using different collectors.

Collectors	Combustible Recovery	Efficiency
Compound (Methyl oleate + DDAB)	76.73%	[29]
Compound (Kerosene + SCG (sodium cocoyl glycinate))	45.00%	[53]
Compound (Diesel + Oxygen)	65.00%	[21]
Compound (Glycerol + Mono oleate)	88.00%	[54]
Manhua oil	79.00%	[8]
Waste colza oil	65.68%	[55]
Octanoic acid	65.00%	[22]
Fossil oil + oleic acid	77.00%	[56]
Waste fried cooking oil	80.00%	[57]
Jatropha biodiesel (biodiesel)	80.08%	Current study

shows the comparison of combustible recovery from the flotation with the non-edible oil obtained from the Jatropha biodiesel with other collectors. As shown in Table 9, conventional fossil collectors containing oxygen groups improved recovery, reaching above 80%. However, the use of fossil collectors raises environmental concerns. A non-edible jatropha biodiesel proved to be a suitable substitute for edible oil, achieving a recovery of 80%. These results demonstrate that Jatropha biodiesel can be an alternative sustainable collector to low-rank coal to overcome the environmental and food issues challenge of fossil compounds and edible collectors.

4. Conclusions

This study aimed to evaluate the effectiveness of Jatropha biodiesel as a collector in the flotation of low-rank coal, employing a statistical modeling approach to optimize and validate performance in terms of ash content and combustible recovery. Response Surface Methodology was employed to develop predictive models and identify optimal conditions. The predicted values obtained from the model equations closely aligned with the observed values, yielding an R² value of 0.9791 for combustible recovery and an R² value of 0.8915 for ash content. The results of the optimization indicated that, for minimizing ash content, the model predicted a value of 9.97% under specific conditions: a collector dosage of 0.5 kg/t, a frother dosage of 0.26 kg/t, a solid percentage of 15.00%, and a depressant dosage of 0.5 kg/t. A verification test under these settings yielded an ash content of 11.20%, with a deviation of just 2.03%, confirming the model’s accuracy. To maximize combustible recovery, the model projected a value of 83.22% with a collector dosage of 2.13 kg/t, a frother dosage of 0.2 kg/t, a solid percentage of 15.00%, and a depressant dosage of 0.504 kg/t. The corresponding test resulted in a recovery of 80.08%, deviating by only 2.8%. A desirability function was utilized to find the optimal trade-off between low ash content and high combustible recovery. This resulted in 11.20% ash content and 80.08% coal recovery at optimized conditions: 1 kg/t of collector dosage, 0.26 kg/t of frother dosage, solid percentage of 15.00%, and depressant dosage of 0.5 kg/t for ash content, and 3 kg/t collector dosage, 0.214 kg/t frother, solid percentage of 14.40%, and 0.50 kg/t depressant for combustible recovery. Experimental results matched predictions, further validating the model. Additional EDS and FT-IR analyses confirmed that Jatropha biodiesel enhanced the coal’s hydrophobicity more effectively than diesel oil, as indicated by higher carbon content and improved surface chemistry, thereby supporting its potential as a superior flotation collector.