Optimization of Flotation Conditions for Long-Flame Coal Mud by Response Surface Method

Abstract

With the application of modern coal mining technology and the fact that there are fewer and fewer high-quality coal seams, the quality enhancement and utilization of low-rank coal are gaining more and more attention. To solve the problems of high consumption of chemicals and low recovery of refined coal in the flotation separation process of low-rank coal, the long-flame coal from the Inner Mongolia Autonomous Region of China was selected as the research object, and the factors affecting the flotation process were analyzed and optimized by adopting the response surface method and establishing a regression model with high precision and reliability. The test results showed that the primary and secondary relationships of the factors on the fine coal yield were as follows: slurry concentration > frother dosage > collector dosage; and the primary and secondary relationships of the factors on the flotation refinement index were as follows: slurry concentration > collector dosage > frother dosage. The optimal conditions for flotation were 2453.09 g/t of collector, 795.84 g/t of frother, and 50.04 g/L of slurry concentration. Under these conditions, the fine coal yield was 51.51%, and the relative error of 53.71% was 4.27%. The flotation refinement index was 21.34%, and the relative error with the predicted value of 21.58% was 1.12%. The relative error of the experimental results was within a reasonable range, which indicated that the regression model obtained by the response surface method was highly reliable. The research results are of great significance to strengthen the comprehensive utilization of long-flame coal in full particle size and improve the economic benefits of coal enterprises.

1. Introduction

Coal is an important material for China’s national economy and social development. Considering this from the perspective of national energy strategy and security, the basic position of the coal industry in the national economy has been solid for a long time at present and will be solid for a long time into the future [1]. Low-rank coal is a type of young coal with a lower degree of coalization, including lignite, long-flame coal, non-sticky coal, weakly sticky coal, etc. It is mainly distributed in the western region of China [2]. The latest data on the third national coal field released by China’s General Administration of Coal Geology show that China’s predicted low-rank coal resources are 2.6 trillion tons, accounting for 57.38% of the country’s total predicted coal resources [3]. It can be seen that low-rank coal is an important part of China’s comprehensive utilization of coal resources and energy supply.

Due to the application of modern coal mining technology and fewer and fewer high-quality coal seams and other factors, the content of fine particles in coal is becoming higher and higher, so fine-grained coal slurry sorting and recycling technology is essential. Flotation is the most effective method to reduce the ash and improve the quality of fine-grained coal slurry at this stage. Low-rank coal has a low degree of coalization. It is prone to oxidation, generating many oxygen-containing functional groups or carbon–oxygen complexes, which cause changes in the physical and chemical properties of the coal slurry surface [4]. In the flotation process, certain polar oxygen-containing functional groups on the surface of low-rank coal can easily interact with water molecules to form a stable hydration film on the coal surface. The formed hydration film hinders the effective collision and adhesion between coal particles and air bubbles, which makes the surface hydrophilicity of coal slurry increase and the flotability decrease, and increases the difficulty of flotation [5].

In recent years, scholars have performed a lot of research work on the factors affecting the flotation conditions of coal slurry. Chen et al. [6] chose the orthogonal test method to study the flotation process of coal slurry and determined the optimal process of flotation. Xu et al. [7] found that the properties of coal samples with different particle sizes and different density levels are different, and their corresponding flotation chemicals have different properties through the coal sample sieving test and the flotation and sinking test. Cheng et al. [8] used the Box–Behnken response surface design method to explore the coal slurry flotation test. The results showed that there is an effect from interaction between the chemicals on the flotation effect. Aksoy et al. [9] used the central combination design method to establish a mathematical model of the flotation processes’ influencing factors on the response value and found out the magnitude of the influence of each factor on the experimental results. Vapur et al. [10] determined the parameters of the modified flotation by establishing the kinetic model. The results showed that combustible recovery of up to 94.83% was achieved by using the optimized flotation process parameters for the test. Naik et al. [11] used analytical factorial experimental design to establish a regression model to quantitatively analyze the role of each flotation agent and predict the flotation grade and recovery under the conditions of different agents. Azizi et al. [12] analyzed the optimization of flotation by using the Plackett–Burman design, and the results showed that the variation of response values can be determined visually by studying the relevant variables by this design method.

The response surface method is to fit the regression equation to obtain the functional relationship between the factors and the response value and adjust the optimization test plan to seek the optimal process parameters. The method is a mathematical statistical method for solving multivariate problems [13]. Studies have shown that the response surface method can be effectively applied to the modeling of the flotation process to improve the efficiency of flotation. Based on this, the author used the Box–Behnken experimental design of the response surface method to explore the interaction between factors in the flotation of long-flame coal slurry, to propose the optimal program for the experiment. The research results are of great significance to enhance the comprehensive utilization of long-flame coal at full-grain level and to improve the economic benefits of coal enterprises.

2. Materials and Methods

2.1. Test Material

The coal samples used in the experiment were long-flame coal from the Ordos area, Inner Mongolia Autonomous Region, China. The coal samples were placed in a ventilated place to dry naturally, then crushed, and finally −0.5 mm coal samples were prepared by sieving with a vibrating sieve machine, and the composition of the coal samples was analyzed.

2.1.1. Industrial and Elemental Analysis of Coal Samples

Coal samples were analyzed by a fully automatic industrial analyzer GYFX-611 (Hebi Huanor Electronic Technology Co., Ltd., Hebi City, China). M_ad represents the mass fraction of moisture in air-drying base coal samples, A_ad represents the mass fraction of ash in air-drying base coal samples, V_ad represents the mass fraction of volatile matter in air-drying base coal samples, and FC_ad represents the fixed carbon in air-drying base [14]. The results were shown in

Table 1. Industrial analysis of coal samples.

Industrial Analysis
Mad/%	Aad/%	Vad/%	FCad/%
2.65	20.84	20.29	58.16

. The elemental analyzer KZCH-8000 (Hebi Huanor Electronic Technology Co., Ltd., Hebi City, China) was used for the elemental analysis of the coal samples. The results were shown in

Table 2. Elemental analysis of coal samples.

Elemental Analysis
Cdaf/%	Hdaf/%	Odaf/%	Ndaf/%	Sdaf/%
61.30	3.88	13.79	1.04	0.63

.

From Table 1 and Table 2, it could be seen that the air-drying basis ash content of the coal sample was 20.84%, and the content of elemental oxygen was 14.84%. The C content of the coal sample was around 60%, and the O and H contents were relatively high, indicating that the oxidation degree of the coal sample was high.

2.1.2. The Sieving Analysis

The yield and quality of each particle size in the coal samples were determined by the sieving analysis as shown in

Table 3. Analysis of the results of the sieving analysis of coal samples.

Particle Size/mm	Fractional Distribution/%	Ash/%	Accumulated under Sieve
			Cumulative Passing/%	Ash/%
>0.5	1.24	15.98	100.00	20.87
0.5~0.25	4.79	17.50	98.76	20.93
0.25~0.125	12.12	18.36	93.97	21.11
0.125~0.075	43.87	20.19	81.84	21.51
0.075~0.045	23.83	20.85	37.97	23.05
<0.045	14.15	26.74	14.15	26.74
aggregate	100.00	20.87	—	—

. The sieving analysis test showed that the particle size of the experimental samples was mainly concentrated in the −0.25 mm, which indicated that the fine particle minerals in the samples accounted for in the main part of the coal samples were finer and more easily sludged, and it was difficult to achieve flotation.

2.1.3. XRF Analysis

Coal ash samples were analyzed using a ScopeX ASH 980A analyzer (LanScientific, Suzhou, China) to determine the type and percentage of elements contained in the ash. This test adopted the powder pressing method, when X-ray irradiation of coal samples, the valence electrons or inner electrons of the atoms or molecules in the coal samples will be excited and emitted, and by measuring the energy of the excited electrons, the elemental components on the surface of the coal samples can be analyzed qualitatively, quantitatively, or semi-quantitatively, as well as the valence state. The results are shown in

Table 4. XRF analysis of coal.

Test Items/%	Al	Si	Ca	S	Ti	Fe	Mg	K	P	Aggregate
quantity contained	11.84	9.96	2.36	0.96	0.79	0.53	0.45	0.58	0.05	27.52

.

From Table 4, it can be seen that the types of elements contained in the minerals in the coal ash are mainly aluminum, silicon, and calcium. Their contents are 11.84%, 9.96%, and 2.36%, respectively.

2.1.4. Fourier Transform Infrared Spectroscopy Test

The composition of oxygen-containing functional groups on the surface of coal samples is the most important factor in determining the flotation separation efficiency, and it also has a certain influence on the adsorption of chemicals in the flotation process, so it is necessary to understand the distribution characteristics of oxygen-containing functional groups in the microcosmic components of the coal samples.

FTIR spectroscopy is performed using a Shimadzu spectrometer (IRTracer-100) (Shimadzu Corporation, Kyoto, Japan), using a wavelength range of 4000–400 cm⁻¹, with a resolution of 4 cm⁻¹. The results of FTIR spectroscopy of the long-flame coal slurry used in the experiment are shown in Figure 1. The results showed that a variety of hydrophilic oxygen-containing functional groups existed on the surface of this coal sample, and the presence of these functional groups caused the surface of the coal particles to be covered by a hydration film, which affected the adsorption of flotation chemicals as well as the adhesion of air bubbles [15].

2.1.5. X-ray Diffraction Testing

XRD is performed on samples using an UltimalV diffractometer (Nippon Rigaku Corporation, Tokyo, Japan). The parameter is set to 40 kV, 150 mA, scanning range 5°–70°, scanning speed 5°/min, scanning span 0.01°. The XRD data are analyzed and processed by MDI Jade 9.6 software, and the characterization of the physical phase is based on the principle of three strong peaks.

Figure 2 showed the X-ray diffraction pattern (XRD) of the coal sample. It could be seen that the main mineral in the coal sample is kaolinite, followed by calcite and quartz, and small amounts of boehmite. The corresponding crystal types for each substance were Triclinic, Rhombohedral, Hexagonal, Orthorhombic, and the space group is C1(1), R$\overline{3\mathrm{c}}$(167), P3221(154), Amam(63), and the PDF cards are JCPDS No. 14-0164, JCPDS No. 47-1743, JCPDS No. 46-1045, JCPDS No. 21-1307. Kaolin is prone to produce dispersed fine mud, resulting in high resistance to the flotation process [16]. Calcite is a semi-soluble calcium-bearing mineral and is difficult to remove by flotation [17]. Quartz particles are hydrophilic and difficult to attach to air bubbles and are highly susceptible to discharge as tailings.

2.1.6. Coal Sample Contact Angle Testing

Wetting is a common natural phenomenon in the production process, i.e., the solid–liquid interface replaces the solid–gas interface. The contact angle is the angle between the solid–liquid interfacial force and the surface tension or the liquid–air interfacial force, and the direct manifestation of good or bad wettability is the size of the contact angle. The larger the angle, the higher the degree of repulsion between the water droplet and the surface of the object, indicating that the surface hydrophobicity of the water droplet is relatively high.

The DSA100 contact angle measuring instrument from Kruss (Hamburg, Germany) was used. Coal samples were pressed onto a boric acid surface at 30 MPa. The flake was placed on the DSA contact angle meter and the operating software controlled the volume of the droplets from the suspension needle. The contact between the flake and the droplet is recorded by a CCD camera connected to a computer system, and the image is analyzed by the system software to obtain the contact angle results, which are averaged over three measurements for each sample. Figure 3 shows the contact angle of the coal sample; through the measurement, it was determined that the contact angle is 42°, indicating that the coal sample belonged to the hydrophilic type.

2.2. Single-Factor Test

XFD-II1.5 L batch flotation cell was selected, and the rotational speed of the impeller was 1800 r/min. 0# Diesel oil is used as the collector, which belongs to non-polar hydrocarbon oil. In the flotation process, the collector is adsorbed on the surface of coal particles, forming an oil film, which makes the coal particles hydrophobic, thus realizing the separation from water. Sec-Octanol (C₈H₁₈O) was selected as the frother. Frother is responsible for generating stable foam during the flotation process, so that the coal particles attach to the foam and float up. After starting the stirring for 2 min, the trapping agent was added, and after 1 min, the foaming agent was added, waited for 10 s and then inflated, and ended the test after scraping the foam for 3 min.

Integrate the data and calculate the mineral’s fine coal yield and flotation refinement index respectively, to research and explore the slurry concentration, the collector dosage, and the frother dosage.

2.2.1. The Collector Dosage Exploration Test

In this single-factor test, the independent variable was the collector dosage, which was set as 600, 1200, 1800, 2400, and 3000 g/t. Considering the production practice, the frother dosage was 400 g/t, and the slurry concentration was 70 g/L. The results of the test were shown in Figure 4.

From Figure 4, it was known that after the increase in the collector dosage, the fine coal yield and flotation refinement index also increased, and the change was obvious. However, when the collector dosage was increased to 2400 g/t, the change in the refined coal yield was small. Therefore, the appropriate range of the collector dosage was determined as 1800~3000 g/t.

2.2.2. The Frother Dosage Exploration Test

During this single-factor test, the independent variable was the frother dosage, which was set at 200, 400, 600, 800, and 1000 g/t. Considering the production practice, the collector dosage was fixed at 1800 g/t, and the slurry concentration was fixed at 70 g/L. The results of the test were shown in Figure 5.

As illustrated in Figure 5. When the frother dosage increases, the fine coal yield and flotation refinement index were on the rise. When the frother dosage was 600 g/t, the fine coal yield was the largest, and the flotation refinement index was the highest when the frother dosage was 800 g/t. Therefore, the appropriate range of the frother dosage was 400~800 g/t.

2.2.3. The Slurry Concentration Exploration Test

In this single-factor test, the slurry concentration was set at 50, 70, and 90 g/L. Considering the production practice, the collector dosage was fixed at 1800 g/t, and the frother dosage was fixed at 400 g/t. The results of the test are shown in Figure 6.

From Figure 6, it can be seen that the fine coal yield and flotation refinement index increase firstly and then decrease with the increase in slurry concentration. The slurry concentration was selected in the range of 50~90 g/L, mainly because the particle size of this long-flame coal slurry was fine, and too high a slurry concentration would lead to agglomeration [18].

2.3. Response Surface Method

The response surface method is a statistical and mathematical method that can be used to model and analyze process problems. Its main objective is to optimize the response surface affected by different process parameters [19]. In this study, Design-Expert 13.0 software was used to design the experiment using Box–Behnken (BBD) statistical design of experiment principles. Based on the results of the above one-factor test, a three-factor, three-level response surface method experimental design was established. The three factors are collector dosage (A), frother dosage (B), and slurry concentration (C), and the response values are fine coal yield (E) and flotation refinement index (G). The lowest level is indicated by −1, 0 indicates the medium level, and 1 indicates the highest level. The test factors and levels were shown in

Table 5. Table of test factors and levels.

Level	Factor
	Collector Dosage (g/t)	Frother Dosage (g/t)	Slurry Concentration (g/L)
−1	1800	400	50
0	2400	600	70
1	3000	800	90

.

3. Analysis of Test Results

3.1. Box–Behnken Experimental Design

Combined with the table of test factors and levels in Table 3, BBD was used to design the test of the effect of different factor variations on the fine coal yield E and flotation refinement index G. The test was carried out by using Design-Expert13.0 software. The experimental design was carried out with Design-Expert 13.0 software, and 17 groups of tests were obtained, and the experimental conditions and results are shown in

Table 6. Design scheme and test results of BBD.

Coded Value	Variables			Response Value
	A	B	C	E	G
1	1800	400	70	30.09	12.69
2	3000	400	70	34.62	14.88
3	1800	800	70	36.76	13.56
4	3000	800	70	37.47	15.83
5	1800	600	50	44.12	18.05
6	3000	600	50	48.65	21.79
7	1800	600	90	29.34	12.18
8	3000	600	90	34.63	13.14
9	2400	400	50	44.13	19.45
10	2400	800	50	53.62	21.55
11	2400	400	90	35.53	13.09
12	2400	800	90	35.53	15.14
13	2400	600	70	36.04	14.85
14	2400	600	70	30.2	13.42
15	2400	600	70	34.41	14.17
16	2400	600	70	30.73	13.56
17	2400	600	70	34.85	14.34

. The results were analyzed to obtain the quadratic multinomial regression equations of the two response values on the three factors:

E = 33.25 + 1.88A + 2.38B − 6.94C − 0.955AB + 0.19AC − 2.37BC − 0.7643A² + 2.25B² + 6.7C²
G = 14.07 + 1.15A + 0.7463B − 3.14C + 0.02AB − 0.695AC − 0.0125BC − 0.4288A² + 0.5947B² + 2.64C²

From equation E, the absolute values of each factor coefficient can be seen, and they are as follows: a = 1.88, b = 2.38, c = 6.94. The fine coal yield influence on the primary and secondary relationship is as follows: slurry concentration > frother dosage > collector dosage. According to the absolute value of the coefficient of each factor of equation G, a = 1.15, b = 0.7463, c = 3.14, it could be seen that the importance of the influence of each factor on the flotation perfect index is as follows: slurry concentration > collector dosage > frother dosage.

3.2. Significance Test of the Model

Table 7. ANOVA results of the fine coal yield of response value E.

Source	Sum of Squares	Degrees of Freedom	Mean Square	F-Value	p-Value
Model	702.89	9	78.10	17.91	0.0005
A	28.35	1	28.35	6.50	0.0381
B	45.17	1	45.17	10.36	0.0147
C	384.89	1	384.89	88.27	<0.0001
AB	3.65	1	3.65	0.8367	0.3908
AC	0.1444	1	0.1444	0.0331	0.8608
BC	22.52	1	22.52	5.16	0.0573
A2	2.46	1	2.46	0.5640	0.4771
B2	21.38	1	21.38	4.90	0.0624
C2	189.19	1	189.19	43.39	0.0003
Residual	30.52	7	4.36	—	—
Lack of fit	3.18	3	1.06	0.1550	0.9212
pure error	27.34	4	6.84	—	—
Cor total	733.41	16	—	—	—
R2 = 0.9584			R2Pred = 0.8724
R2Adj = 0.9049			PAdeq = 15.2146

and

Table 8. ANOVA results of flotation refinement index G.

Source	Sum of Squares	Degrees of Freedom	Mean Square	F-Value	p-Value
Model	141.95	9	15.77	45.20	<0.0001
A	10.49	1	10.49	30.06	0.0009
B	4.46	1	4.46	12.77	0.0091
C	93.09	1	93.09	266.80	<0.0001
AB	0.0016	1	0.0016	0.0046	0.9479
AC	1.93	1	1.93	5.54	0.0509
BC	0.0006	1	0.0006	0.0018	0.9674
A2	0.7525	1	0.7525	2.16	0.1854
B2	1.49	1	1.49	4.27	0.0777
C2	29.45	1	29.45	84.41	<0.0001
Residual	2.44	7	0.3489	—	—
Lack of fit	1.07	3	0.3562	1.04	0.4664
pure error	1.37	4	0.3435	—	—
Cor total	144.39	16	—	—	—
R2 = 0.9831			R2Pred = 0.8667
R2Adj = 0.9613			PAdeq = 20.2462

show the results of ANOVA for the response value of the fine coal yield E and flotation refinement index G. p-value is the confidence level, the smaller the value indicates that the model is more significant. If the p-value is less than 0.05 and greater than 0.01, it indicates that the model is significant; if the p-value is less than 0.01, it indicates that the model is highly significant. F is the value obtained from the test, which indicates the impact of each factor on the response value, and the greater the value, the greater the impact degree is. When the F-value is larger and the p-value is smaller, it indicates that the model is more significant at this point [20].

As shown in Table 7, the p-value of model E was less than 0.01 and the F-value was 17.9, indicating that the model was significant. The coefficient of determination R² was 0.9584, indicating that the model correlation was good; the correction coefficient R²_Adj was 0.9049, indicating that less than 0.1% of the total variation could not be explained by the model; the prediction coefficient R²_Pred was 0.8724; the precision P_Adeq was equally as long as it was greater than 4, and the precision of the model was 15.2146. In summary, the model had high credibility and precision [21].

From Table 8, the p-value of model G was less than 0.01 and the F-value was 45.20, indicating that the model was highly significant. The coefficient of determination R² was 0.9831, which indicated that the test model was well-fitted. The calibration coefficient R²_Adj was 0.9613, which was very close to the coefficient of determination. The prediction coefficient R²_Pred was 0.8667; the precision P_Adeq was 20.2462. indicating that the model had sufficient accuracy and credibility.

Since the selection of the response surface factor ranges was based on the results of the single-factor test, the primary term p-values for each factor of both models should be less than 0.05. The primary term p-values for each factor of model E were 0.0381, 0.0147, and <0.0001, respectively. The primary term p-values for each factor of model G were 0.0009, 0.0091, and <0.0001, respectively. All of them were less than 0.05, so the significance of the model was further verified.

Although the prediction and correction coefficients of model E were not as good as those of model G, the precision of both models met the test requirements. Therefore, the established models can analyze and predict the effects of the factors on the response values in the test.

4. Results and Discussion

To analyze the influence of the interaction between factors on the response value by response surface method, surface and contour plots of the fine coal yield and flotation refinement index were plotted according to the established fitting model, as shown in Figure 7 and Figure 8.

The color and height of the response points in the surface plot indicate the size of the response value, i.e., the higher the height of the points on the response surface, and the closer the color of the points is to red, the larger the response value is. Contour lines are the projections of the surface map falling horizontally, the closer the shape of the contour line is to a circle, the weaker the interaction between the factors. On the contrary the closer the shape of the contour line is to an ellipse, the stronger the interaction between the factors [22].

4.1. Response Surface Analysis of Model E

From Figure 7A,B, it can be seen that the fine coal yield showed an increasing trend with the increase in the collector dosage; with the increase in the frother dosage, the fine coal yield first showed a slight decrease and then kept increasing. It showed that the increasing dosage of chemicals may not always be positive for the fine coal yield. Excessive collector dosage will lead to deformation or rupture of the bubbles, thus reducing the contact area between the ore particles and the bubbles. The adsorption between ore particles and bubbles was weakened, which will lead to a poor flotation effect. Excessive frother dosage will lead to too much foam and a decrease in the selectivity of the coal samples, making the coal samples flotation out together with impurities [23].

As can be seen from Figure 7C,D, with the increase in slurry concentration, the fine coal yield showed a trend of first a large decrease and then a small increase. The selection of the flotation slurry concentration level had an important relationship with the characteristics of the coal slurry itself [24], when the slurry concentration increased, the flotation space occupied by the coal particles increased, and the space between the gas–liquid two phases decreased. Then the homogeneity of the aeration will be reduced, which will affect the mineralization process of the bubbles.

From Figure 7E,F, it could be seen that the contour lines were sparsely distributed along the direction of the frother dosage and densely distributed along the direction of the slurry concentration, indicating that the fine coal yield was more significantly affected by the slurry concentration, which corresponds to the results of the ANOVA.

4.2. Response Surface Analysis of Model G

From Figure 8A,B, the contour shape was close to an ellipse, indicating that the performance of flotation concentration was synergistically affected by the dosage of the collector dosage and the frother dosage. When the frother dosage was increased, the polar group of the agent molecule could cover part of the hydrophilic surface of the coal particles, and the polar component of the frother dosage formed a long and short hydrocarbon chain synergistically adsorbed on the hydrophilic surface of the coal particles [25].

From Figure 8C,D, it could be seen that the flotation refinement index had been showing an upward trend when the frother dosage increased. When the slurry concentration increased, the flotation refinement index first decreased and then increased. In the flotation process, the size of the slurry concentration directly affected the volume concentration of the chemicals [26]. If the unit dosage of the agent is constant, the volume concentration of the agent changes with the change in the slurry concentration, and when the volume concentration of the agent is insufficient or excessive, it will affect the flotation index.

From Figure 8E,F, it could be seen that the contour shape was an ellipse with a large eccentricity, which indicates that the interaction of frother dosage and slurry concentration was very strong, and it corresponded to the results of ANOVA.

4.3. Validation of Optimal Flotation Conditions Optimization

The optimization analysis of the test was carried out by using the Numerical module in Design-Expert 13.0 software [27], and the optimal conditions for the flotation test were obtained as 2453.09 g/t of collector dosage, 795.835 g/t of frother dosage, and 50.041 g/L of slurry concentration, which predicted that the fine coal yield at this time would be 53.71%, and the flotation refinement index was 21.58%.

To verify the reliability of the model, we performed three replicates of the test under the optimal flotation conditions, and the average value was taken as the test result. The fine coal yield was 51.51%, and the relative error from the predicted value of 53.71% was 4.27%. The flotation refinement index was 21.34%, and the relative error with the predicted value of 21.58% was 1.12%. It could be seen that the relative error between the actual results and the predicted values was within a reasonable range, indicating that the regression model obtained by the response surface method was highly reliable.

From the test results, we could see that the effect of conventional hydrocarbon oil traps for low-rank coal flotation was really general. Under the optimal flotation conditions for low-rank coal, although the flotation effect has been significantly improved, it still needs to be improved. This is due to the low degree of metamorphism in low-rank coal, the particle surface contains a large number of hydrophilic oxygen-containing groups, which are easy to be covered by water molecules and form a thicker hydration film, resulting in the difficulty of conventional hydrocarbon oil trap to spread efficiently. When using hydrocarbon oil for low-rank coal slurry flotation quality improvement, there is often excessive drug consumption, high ash, and fine mud entrainment serious phenomena, hence, the flotation effect is poor.

5. Conclusions

(1)

In this study, the Box–Behnken design was used to optimize the flotation conditions, and the regression model of the fine coal yield and flotation refinement index was obtained. After testing, the model established by the test was reliable and had high precision. It could be used to analyze and predict the primary and secondary relationships of the influence of each factor on the response value.

(2)

The Numerical module in Design-Expert 13.0 software was used to optimize and analyze the test to obtain the best conditions for the flotation test. Through the flotation validation test, the results obtained were close to the predicted results, indicating that the response surface method was very reliable for optimizing the flotation conditions.

(3)

In this study, using the response surface methodology, we focused on the effect of the interaction between the main factors on flotation, as well as optimizing the flotation process and obtaining the optimal conditions. There have been many achievements in the current research aimed at developing efficient flotation chemicals. In future research work, the author believes that if the combination of developing efficient flotation chemicals and optimizing the flotation conditions by the response surface method is adopted, the flotation effect of low-rank coal can be improved even more.