Extraction of Vanadium from High Phosphorus Vanadium Containing Waste Residue via Carbonation: Optimization Using Response Surface Methodology

Abstract

Vanadium (V) was successfully extracted from a high phosphorus vanadium residue (HPVR) through a carbonation process. Vanadium within HPVR substitutes for Fe in the mineral structure of Ca₉(Fe,V)(PO₄)₇ at elevated temperatures, Na₂CO₃ reacts with V to form sodium metavanadate (NaVO₃), concurrently generating calcium carbonate (CaCO₃) through its interaction with Ca₉(Fe,V)(PO₄)₇. Subsequently, V is liberated and leached by water, dissolving in the aqueous phase as metavanadate ions (VO³⁻). Crucial factors influencing V leaching efficiency include roasting time, roasting temperature, and the amount of Na₂CO₃ utilized. Response Surface Methodology (RSM) was employed. The optimized parameters determined were as follows: a roasting temperature of 850 °C, a roasting duration of 120 min, a Na₂CO₃ dosage of 8.01%, a liquid-to-solid ratio (L/S) of 3, and a leaching time of 60 min. Under these conditions, a remarkable V leaching efficiency of 83.82% was achieved. This study underscores the viability of a simplified approach for treating solid waste containing metal slag, which not only mitigates environmental pollution but also yields valuable metals.

1. Introduction

Rusakovite ((Fe³⁺,Al)₅(V₄,PO₄)₂(OH)₉·3H₂O) is a pivotal raw material of the phosphorus (P) chemical industry. The extraction of P from this mineral typically involves a process of sodium (Na) roasting, followed by water-leaching, ultimately yielding sodium phosphate (Na₃PO₃) and sodium vanadate (NaVO₃). However, this process also generates a by-product known as high phosphorus vanadium residue (HPVR).

In addition to the P element, HPVR also contains valuable metal element V (0.5–3wt%), compared with 0.13w to 1.2wt% for stone coal which is an important source of V. V is an essential strategic metal and is widely used in the iron and steel, chemical engineering, aerospace and energy industries, so the comprehensive recovery of V from HPVR is imperative. Currently, there are various techniques for extracting V from vanadium residue (VR) including roasting leaching [1,2], polymetallic extraction, low-temperature, and cost-effective extraction, etc [2,3,4,5]. Nevertheless, some of these processes face challenges, such as operational difficulties, short maintenance intervals, complexity that hinders industrialization, and high acid/base consumption, which imposes additional environmental burdens [2,3,6,7,8]. Notably, although the calcium (Ca) content in VR is generally low during V extraction, the generation of HPVR necessitates the use of calcium salts for purification and impurity removal, resulting in higher Ca content in HPVR. Consequently, the extraction process of V from HPVR differs from that of VR due to the presence of P and Ca.

This paper focuses on the extraction of V from HPVR using three methods: Na₂CO₃ roasting followed by water-leaching, direct acid-leaching, and blank roasting with subsequent acid-leaching, aiming to mitigate environmental impacts [4,9,10]. After rigorous testing and comparisons, Na₂CO₃ roasting followed by water-leaching emerged as the most viable option. Given the intricate composition of the raw material and the intricate interplay among various factors influencing V extraction, Response Surface Methodology (RSM) was employed to optimize conditions for maximum leaching efficiency.

2. Experimental Methods

2.1. Materials

The HPVR used in this paper was obtained from a phosphorus chemical company. The test samples were obtained after being crushed and ground to a state in which the size of minus 0.074 mm accounted for more than 80% of the sample by a vibrating grinding machine (XAM-100, kechuang, WuHan, China). The inductively coupled plasma atomic emission spectroscopy (ICP-AES; IRIS Advantage Radial, Waltham, MA, USA) results and the X-ray diffraction (XRD; Bruke D8 Advance, PANalytical B.V., Almelo, NL, USA) pattern of the raw sample are given in

Table 1. Composition analysis results of the HPVR.

Composition	Si	Fe	Ca	Mg	Na	P	V	Cr	Ti	Mn	Ni
Content (wt%)	2.58	18.70	11.10	0.70	10.40	12.20	0.80	2.20	0.50	0.05	0.48

and Figure 1. It was found that V accounted for 0.80% of the total mass. The major minerals in the HPVR are ferric oxide, calcium silicate, and several kinds of whitlockites, which contain different metallic elements. The morphology of the HPVR was observed by using a scanning electron microscope (SEM; JSM-5610, Jeol, Tokyo, Japan) and is shown in Figure 2. It can be seen above that V existed locally in the HPVR, and the element correlation was consistent with XRD results.

As can be seen from Table 1, Ca and P contents in raw materials are relatively high, which accords with the elemental characteristics of vanadium slag after impurity removal.

2.2. Experimental Design and Statistical Analysis

2.2.1. Direct Acid-Leaching and Blank Roasting Acid-Leaching

A beaker was utilized to blend sulfuric acid (H₂SO₄) solution ranging from 1/9 to 4/1 (V_H2SO4/V_H2O) with HPVR for conducting direct acid-leaching experiments (2 h, L/S = 1.5). Initially, the HPVR was placed in a corundum crucible, subjected to roasting in a muffle furnace (850 °C, 2 h), and then cooled down to room temperature via natural convection. Subsequently, the blank roasting clinker underwent leaching with H₂SO₄ (1/9 to 4/1, 2 h, L/S = 1.5).

2.2.2. Na₂CO₃ Roasting Water-Leaching

A separate procedure involved mixing ground HPVR with Na₂CO₃ and positioning the mixture in a corundum crucible. The mixture was then roasted in a muffle furnace, cooled down to ambient temperature, and finally, the alkali roasting clinker was leached with water. The V leaching efficiency was calculated using the following formula [11]:

X% = M × v/(C₀ × m₀) × 100%

(1)

where X% is the V leaching efficiency; M is the V concentration in the leaching solution (g/L); v is the solution volume in the volumetric flask (L); C₀ is the mass fraction of V in the high HPVR (%); m₀ is the total mass of the HPVR sample (g).

Under atmospheric conditions and room temperature, a comprehensive study was conducted to assess the influence of various factors on V leaching efficiency, including roasting temperature, roasting time, leaching time, dosage of Na₂CO₃, liquid-to-solid ratio (L/S), and leaching duration.

2.2.3. Response Surface Optimization (BBD) Experiment

Building upon the findings from single-factor experiments, the Box-Behnken Design (BBD) response surface methodology was applied to refine and optimize three critical factors that significantly affect V leaching efficiency [12]: roasting time, roasting temperature, and dosage of Na₂CO₃.

Table 2. Levels of process variables in actual and coded values.

Factors	Low	High	Value of Code
A Roasting temperature (°C)	650	850	−1 = 650; 0 = 750; 1 = 850
B Roasting time (min)	10	120	−1 = 10; 0 = 65; 1 = 120
C Dosage of Na2CO3 (wt%)	2	10	−1 = 2; 0 = 6; 1 = 10

details the experimental parameters and levels employed in this optimization process.

3. Result and Discussion

3.1. Selection of Vanadium Extraction Method

In this paper, three distinct extraction methods were employed: direct acid-leaching, blank roasting acid-leaching, and sodium carbonate (Na₂CO₃) roasting water-leaching. Our observations indicated that both direct acid-leaching and blank roasting acid-leaching struggled to attain satisfactory results. The V extraction efficiencies of these methods are presented in Figure 3, highlighting that their performance fell short of expectations, with efficiencies below 10% for both techniques. In contrast, the application of Na₂CO₃ roasting water-leaching yielded significantly higher V leaching efficiency. This finding underscores the advantage of adopting Na₂CO₃ roasting water-leaching for enhancing V recovery.

3.2. Na₂CO₃ Roasting Water-Leaching Experiments

It is evident that the V leaching efficiency is influenced by multiple factors, including roasting temperature, roasting time, Na₂CO₃ dosage, leaching time, and the liquid/solid ratio (L/S) during water-leaching (Figure 4). As the roasting time elongates, and with the rise in both roasting temperature and Na₂CO₃ dosage, the V leaching efficiency initially surges before tapering off. Notably, there exists a strong interdependence among roasting temperature, time, and Na₂CO₃ dosage. Regarding leaching time, an initial steep increase in V leaching efficiency is observed, which plateaus after 60 min. Similarly, the V leaching efficiency initially escalates swiftly with increasing L/S ratio, but this trend saturates when the L/S ratio reaches 3.

During roasting, a reaction occurs as described in Equation (2), wherein V in Ca₉(Fe,V)(PO₄)₇ interacts with Na₂CO₃ to form NaVO₃, subsequently transforming Ca₉(Fe,V)(PO₄)₇ into Na₁₈Ca₁₃Mg₅(PO₄)₁₈ upon losing V. As seen in Figure 5, V within HPVR is intermixed in compound phosphate, and NaVO₃ is generated through roasting. Post-roasting, water-leaching dissolves NaVO₃, leading to its absence in the filter slag’s spectrum. Additionally, Ca₉(Fe,V)(PO₄)₇ located in HPVR transforms into CaCO₃ upon roasting, evident from the emergence of calcium carbonate (CaCO₃) peaks in the roasted HPVR’s XRD pattern.

$${\mathrm{Ca}}_9{\mathrm{V}(\mathrm{PO}}_4{)}_7+{\mathrm{Na}}_2{\mathrm{CO}}_3\to {\mathrm{Ca}}_3{{(\mathrm{PO}}_4)}_2+{\mathrm{NaVO}}_3+\mathrm{Ca}{\mathrm{CO}}_2$$

(2)

The TG analysis of HPVR’s reaction with Na₂CO₃, depicted in Figure 6, mirrors that of CaCO₃, indicating CaCO₃ formation and decomposition during roasting. It is postulated that Equation (2) proceeds sequentially, with Na₂CO₃ binding to Ca in Ca₉Fe(PO₄)₇ to yield CaCO₃, while V dissociates to form soluble NaVO₃.

Due to the complex composition of HPVR and the complex reaction process, it is impossible to determine the process of calcium carbonate generation, but various decompositions of calcium carbonate have been observed, indirectly proving that calcium carbonate is generated during the roasting process and V is free.

3.3. Optimization of Roasting Experiment by Using RSM (BBD)

A pronounced correlation exists among three critical factors: roasting temperature, roasting time, and dosage of Na₂CO₃. Consequently, Response Surface Methodology (RSM) with Box-Behnken Design (BBD) was employed to ascertain optimal experimental conditions.

Table 3. BBD response surface test design and results of roasting immersion factors.

		Factor 1	Factor 2	Factor 3	Response 1
St d	Run	A	B	C	V Leaching efficiency
		°C	min	m%	%
14	1	750.00 (0)	65.00 (0)	6.00 (0)	66.92
17	2	750.00 (0)	65.00 (0)	6.00 (0)	68.52
2	3	850.00 (1)	10.00 (−1)	6.00 (0)	64.92
3	4	650.00 (−1)	120.00 (1)	6.00 (0)	51.08
15	5	750.00 (0)	65.00 (0)	6.00 (0)	67.19
1	6	650.00 (−1)	10.00 (−1)	6.00 (0)	40.75
13	7	750.00 (0)	65.00 (0)	6.00 (0)	66.47
16	8	750.00 (0)	65.00 (0)	6.00 (0)	68.05
8	9	850.00 (1)	65.00 (0)	10.00 (1)	72.49
6	10	850.00 (1)	65.00 (0)	2.00 (−1)	56.36
4	11	850.00 (1)	120.00 (1)	6.00 (0)	81.36
7	12	650.00 (−1)	65.00 (0)	10.00 (1)	39.25
9	13	750.00 (0)	10.00 (−1)	2.00 (−1)	47.08
11	14	750.00 (0)	10.00 (−1)	10.00 (1)	44.77
12	15	750.00 (0)	120.00 (1)	10.00 (1)	66.39
10	16	750.00 (0)	120.00 (1)	2.00 (−1)	53.67
5	17	650.00 (−1)	65.00 (0)	2.00 (−1)	39.28

showcases the BBD response surface test design for Na₂CO₃ roasting water-leaching of HPVR, utilizing Design-Expert 8.0 software, alongside corresponding test results (with a fixed leaching time of 60 min and liquid/solid ratio (L/S) of 3).

Table 4. Suitability test of V leaching efficiency approximation model.

Source	Sum of Squares	df	Mean Square	F Value	Prob > F
Mean	58,156.02	1	58,156.02
Linear	1834.82	3	611.61	9.44	0.0014
2FI	131.84	3	43.95	0.62	0.6187
Quadratic	701.61	3	233.87	183.32	<0.0001	Suggested
Cubic	6.12	3	2.04	2.90	0.1650	Aliased
Residual	2.81	4	0.70
Total	60,833.23	17	3578.43

evaluates the suitability of various models for approximating V leaching efficiency. Models are typically assessed based on the significance of their Prob > F (p-value); a value significantly less than 0.05 indicates a good fit [13,14,15]. Notably, the cubic model proved intricate and was thus discouraged by the system. Conversely, the quadratic model exhibited a p-value less than 0.0001, establishing it as the preferred choice for modeling the relationship between V leaching efficiency and the influential factors [7,16,17].

Based on the test data and fitting analysis of the results, Equation (3) represents a quadratic multinomial regression model that describes the relationship between V leaching efficiency and three main influencing factors: roasting time, roasting temperature, and sodium carbonate content:

Y = −262.9139 + 0.7334A − 0.0467B + 0.4214C + 2.8664E − 00AB + 0.0101AC + 0.0171BC − 4.5475E − 004A² − 1.1289E − 003B² − 0.6898C²

(3)

3.4. Model Validation

Table 5. The regression model for predicting V leaching efficiency and conducting variance analysis of various influencing factors.

Source	Sum of Squares	df	Mean Square	F Value	Prob > F
Model	2668.28	9	296.48	232.39	< 0.0001	significant
A	1356.82	1	1356.82	1070.59	< 0.0001
B	381.16	1	381.16	298.77	< 0.0001
C	87.85	1	87.85	68.86	<0.0001
AB	10.08	1	10.08	7.90	0.0261
AC	65.29	1	65.28	51.17	0.0002
BC	56.48	1	56.48	44.27	0.0003
A2	87.07	1	87.07	68.25	<0.0001
B2	49.10	1	48.10	38.49	0.0004
C2	512.95	1	512.95	402.08	<0.0001
Residual	8.93	7	1.28
Lack of Fit	6.12	3	2.04	2.90	0.1650	not significant
Pure Error	2.81	4	0.7
Cor Total	2677.21	16
R2 = 0.9967 R2adj = 0.9924

presents the outcomes of variance analysis for the model equations and associated factors. Notably, the Prob > F value of model Equation (3) falls below 0.0001, confirming its high statistical significance. Additionally, the p-value of “Lack of Fit” equals 0.0508, indicating insignificance and suggesting a robust fit between the quadratic regression equation and the test results. The model’s regression determination coefficient R² of 0.9967 and adjusted determination coefficient R²adj of 0.9924 further emphasize its high degree of fit. The marginal difference between these coefficients underscores the model’s accuracy in predicting actual values [18].

Figure 7 showcases the diagnostic verification results, including plots of residual normal probability distribution, residuals versus predicted values, residuals versus predicted values order, and predicted versus actual values. The closer the normal probability distribution of residuals is to the straight line, the more the residuals conform to the normal distribution. The closer the combination of predicted and actual values indicates, the higher reliability and accuracy of the model prediction. When the predicted residuals are discrete and regularly distributed, the variance between residuals is better. The nearly straight line in Figure 7a attests to the residuals’ conformity with a normal distribution. While Figure 7c,d exhibit fluctuations, they signify good equal variance among residuals. In Figure 7b, the close alignment of predicted and actual values supports the model’s reliability and precision in predictions [19].

To evaluate the key factors affecting V leaching efficiency in Na₂CO₃ roasting water-leaching of HPVR and their interactions, 3D response surface maps and contour maps were generated (Figure 8, Figure 9 and Figure 10). The interpretation of response surface analysis is straightforward: on contour maps, a steeper contour line, indicative of a broader numerical range, along a factor’s axis underscores its more profound impact on the index. Conversely, a flatter contour line implies minimal influence. Furthermore, the proximity of contours to an elliptical shape points to a robust interaction between two factors and their combined effect on the index [16].

The contour map in Figure 8 exhibits an almost elliptical contour, signifying a significant interplay between roasting temperature and time in influencing V leaching efficiency. The notably wider contour range for temperature compared to time underscores its greater influence. Similarly, Figure 9 and Figure 10 reveal that roasting time exerts a more pronounced effect on V leaching efficiency than the dosage of Na₂CO₃.

In summary, the order of significance for the individual factors in enhancing V leaching efficiency, as determined by response surface analysis, is as follows: roasting temperature, roasting time, and dosage of Na₂CO₃. Additionally, notable interactions were observed between roasting temperature and time, as well as between Na₂CO₃ dosage and both roasting temperature and time (

Table 6. Result of optimization experiment on V leaching efficiency.

Number	Roasting Temperature	Roasting Time	Na2CO3%	V Leaching Efficiency
	°C	min	wt%	%
1	850	120	8.01	83.82
2	850	120	8.05	83.81
3	850	119.99	7.98	83.81
4	850	120	7.94	83.81
5	850	120	7.85	83.80
6	850	120	8.18	83.80
7	850	119.48	8.00	83.78
8	848.92	120	8.02	83.73
9	850	118.57	7.12	83.71
10	850	115.68	7.82	83.52

).

The maximum V leaching efficiency was optimized based on the previously established approximate model. Under the specified conditions—HPVR particle size less than 0.074 mm exceeding 80%, water-leaching time of 60 min, and L/S ratio of 3—the roasting temperature, roasting time, and dosage of Na₂CO₃ were adjusted to maximize efficiency. Ten feasible optimization schemes were identified, with the optimal range for roasting temperature and duration found to be between 848.92 °C and 850 °C and 115.68 to 120 min, respectively. The sodium carbonate dosage ranged from 7.12% to 8.18%, predicting a vanadium leaching efficiency of 83.52% to 83.82%.

The deviation between the predicted maximum V leaching efficiency and the actual outcome is minimal, at approximately 0.3%. Thus, in selecting the optimal prediction scheme, comprehensive consideration of energy consumption and production efficiency is crucial. Consequently, a revised scheme was chosen: roasting temperature of 850 °C, roasting time of 120 min, and Na₂CO₃ dosage of 8.01%, resulting in a predictive value of 83.82%, closely mirrored by the actual test result of 83.54%.

4. Conclusions

Vanadium (V) in HPVR exists in the complex salt Ca₉(Fe,V)(PO₄)₇, necessitating a specialized extraction approach. Direct acid-leaching and blank roasting acid-leaching are ineffective due to the chemical structure; hence, Na₂CO₃-activated roasting water-leaching is adopted. This method leverages Na₂CO_3′s reaction with Ca, freeing V to form soluble vanadate (VO₃^-). Employing single-factor experiments and Box-Behnken Design (BBD) response surface methodology (RSM), we optimized roasting temperature, time, and Na₂CO₃ dosage to enhance V extraction efficiency. The roasting temperature, the most critical factor, was determined in conjunction with energy consumption considerations. The optimal conditions were identified as 850 °C roasting temperature, 120 min roasting time, 8.01% Na₂CO₃ dosage, and 60 min leaching time with an L/S ratio of 3, achieving an experimental V leaching efficiency of 83.82%. These conditions not only mitigate HPVR’s environmental impact but also improve the utilization rate of the strategic metal V.