Introduction

Phosphate ore is an important and indispensable strategic resource that is widely used in cutting-edge technologies, chemical and metallurgical industries (especially the P chemical industry), national food production security, and other fields [1, 2]. After decades of development, China has developed globally dominant phosphate ore, phosphate fertilizer, and phosphate chemical industries. Although the storage capacity of phosphate ore resources in China accounts for 19.36 billion tons, which is approximately 30% of the world's total phosphate ore resource storage, the average grade of its rich and poor ore resources is only 17%. China has one of the lowest average grade phosphate ores in the world, in which its low-grade phosphate ore resources (P2O5 < 30%), which cannot be directly utilized, account for more than 90% of the resources [3]. In recent years, the development and utilization of phosphate ore resources have centered around sources rich in minerals, but some high-quality phosphate ore resources have not been protected from exploitation, or scientific and rational utilization, resulting in a loss of high-quality phosphate ore resources. Therefore, it is important to determine how to utilize low-grade phosphate ore and improve its comprehensive utilization ratio and economic benefit.

Currently, the primary production methods of phosphoric acid from phosphate rock include three types [4, 5]: wet phosphoric acid, thermal phosphoric acid, and kiln phosphoric acid. The wet-process phosphoric acid method has low equipment requirements, but high requirements for the grade of phosphate rock (P2O5 > 30%); further, the prepared phosphoric acid has many impurities and low concentrations. Meanwhile, the product prepared by the thermal phosphoric acid method has a high concentration and good quality, though its production cost is high and its energy consumption is large [6]. Physical methods are unsuitable because of the high content of gangue in low-grade phosphate ore resources, close symbiosis of gangue and P minerals, and fine grain size of minerals embedded in such rocks. Thus, a fire method was suggested for widespread use [7, 8]. Based on the carbothermal reduction mechanism [9, 10], some researchers proposed directly using low-grade phosphate ore to produce industrial phosphoric acid via the tunnel method. The gordian technique implemented in the method is efficient in that it realizes reduction and oxidation separately [11]. Meanwhile, some scholars have focused on the utilization of low-grade ore and the process of mechanism. In particular, Wu et al. [12, 13] studied the technological conditions and kinetics of low-grade phosphate ore melting reduction. The results showed that the reduction ratio of P2O5 increased with increasing reaction temperature. Cao et al. [14] and Liu et al. [15] studied the thermodynamic behavior and reduction kinetics of Ca5(PO4)3F, finding that Ca5(PO4)3F first reacted with SiO2 to form Ca3(PO4)2 in a vacuum, after which Ca3(PO4)2 was reduced by carbon to form CaO and combined with SiO2 to form calcium silicate, and F was discharged in the form of SiF4 (g). Liu et al. [16, 17] studied the influences of SiO2 on vacuum carbothermal reduction of calcium fluorophosphate and found that the addition of SiO2 could improve the reduction rate, and the reduction rate increased rapidly at 1350 °C. This occurred because the calcium fluorophosphate was directly returned by the carbon, after which the product CaO combined with SiO2 to form silicon with a low melting point. Huang et al. [18,19,20] studied the influences of carbon content, temperature, and pressure on the vacuum carbothermal reduction of low-grade phosphate ore. Their results showed that the optimal carbon content was approximately 14%, and the optimal reduction temperature ranged from 1250 to 1300 °C when the pressure was 10 Pa. Thus, the reduction mechanism of low-grade phosphate ore resources has been widely investigated. However, various scholars have obtained different reaction mechanisms and contradictory results because they employed different systems or experimental methods. Nevertheless, the entire reduction mechanism of phosphate ore based on vacuum metallurgy can be revealed using isotherm kinetics, providing a theoretical foundation for the research and development of the vacuum carbothermic reduction treatment of low-grade phosphate ore resources.

Experiment

Raw Materials and Equipment

In this study, phosphate ore was acquired from an enterprise in Yunnan, and coke was used as the reductant. Table 1 and Fig. 1 show the chemical composition analysis and XRD patterns of the phosphate ore and coke powder. Overall, the main phase was Ca5(PO4)3F and SiO2, the content of P2O5 was 29%, and there were small amounts of Fe2O3, MgO, and Al2O3 in the raw material. The particle size of the phosphate ore and coke powder was less than 75 μm. The equipment used in the test included a desktop electric pressing machine (DY-20), a temperature control system, heating system, and vacuum pumping system, as shown in Fig. 2.

Table 1 Chemical composition of raw materials (wt%)
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Fig. 1
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XRD diagram of raw ore and carbon-containing pellet

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Fig. 2
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Schematic diagram of vacuum carbon tube furnace

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Experimental Method

A previous study [19] showed that in the process of carbothermic reduction of low-grade phosphate ore in a vacuum, with constant temperature and pressure, the reduction efficiency was the best at a carbon dosage of 14%. In the vacuum reduction experiment, phosphate ore and coke were crushed in a ball mill, filtered through a 200 mesh standard, sieve, and dried for more than 10 h. Then 20 g of phosphate rock, coke (14%), and adhesive (4‰) were mixed and pressed into a ball block with a diameter of 30 mm and a height of 13 mm at a pressure of approximately 15 MPa. After the sample was dried at 110 °C for 180 min, it was weighed and placed into a graphite crucible. This crucible was placed on the graphite gasket in the furnace body. The upper part of the graphite crucible was connected to a condensation tube in the upper insulation layer and extended to the condensation collecting device. Note that the experiment was conducted in a vacuum carbon tube furnace equipped with a graphite heater at a heating rate of 6 °C/min. The dried samples were weighed and then heated to 1200 °C, 1250 °C, 1300 °C, and 1350 °C, before heating preservation 0 min, 10 min, 20 min, 30 min, 60 min, and 90 min in the vacuum carbon short-circuiting furnace. Finally, the cooled samples were weighed to determine the weight loss ratio (Eq. (1)) and prepared for chemical analysis of P content (Quinoline phosphomolybdate gravimetric method was used to determine the P content of reduced samples, and the detailed operation method refer to references [21, 22].) for calculation of volatilization ratio of P by Eq. (2), XRD analysis, SEM appearance, and EDS. Table 2 summarizes the experimental test equipment parameters.

Table 2 Main technical parameters of equipment
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$$\alpha =\frac{{m}_{0}-{m}_{1}-{m}_{2}+{m}_{3}}{{m}_{0}-{m}_{2}}\times 100\%.$$
(1)

Generally speaking, the weight loss ratio can characterize the degree of reduction without metal volatilization for the carbothermal reduction of solid–solid reaction. However, in this study, the reduced phosphorus volatilized in gaseous form, so the volatile phosphorus was taken into account when calculating the reduction ratio.

$$\eta =\frac{{m}_{0}{w}_{0}-{m}_{1}{w}_{1}}{{m}_{0}{w}_{0}}\times 100\%,$$
(2)

where α is the overall weight loss ratio of the sample, η is the volatilization ratio of phosphorus, m0 is the mass of the sample before reduction, m1 is the mass of the reduced sample, m2 is the mass of adding binder, and m3 is the mass of phosphorus volatilization, w0 is the content of phosphorus in the sample before reduction, and w1 is the content of phosphorus in the reduced sample.

Results and Discussion

Weight Loss Ratio of Reduced Samples

Figure 3 shows the influences of holding time and reduction temperature on the weight loss ratio of the reduced samples. Overall, the weight loss ratio of the reduced samples increased with increasing holding time and temperature, and the influence of temperature on the weight loss ratio was even more significant. Further, the change trends of the weight loss ratio at 1200 °C and 1250 °C, and 1300 °C and 1350 °C, were different, indicating that a reaction started at 1300 °C. Specifically, the weight loss ratio of the samples slowly increased with increasing duration when the reduction temperature was less than 1250 °C. Conversely, at temperatures greater than 1300 °C, the weight loss ratio of the samples rapidly increased before 30 min, and the increasing trend of weight loss rate decreases with decreased. The increasing trend of volatilization ratio decreased with increasing holding time.

Fig. 3
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Effect of reduction temperature and holding time on weight loss rate of the reduced sample

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The Volatilization Ratio of Phosphorus

Figure 4 shows the influences of holding time and reduction temperature on the volatilization ratio of P. The volatilization ratio of phosphorus increased with the increase in holding time and temperature, and the influence of temperature on the volatilization ratio was more significant. Moreover, the volatilization ratio of P slowly increased with increasing duration when the reduction temperature was less than 1250 °C. Conversely, when the reduction temperature was 1300 °C, the volatilization ratio of phosphorus increased rapidly before holding for 30 min. The increasing trend of volatilization ratio decreased after 30 min.

Fig. 4
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Effect of heat preservation time and reduction temperature on the volatilization ratio of phosphorus element in the reduced sample

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Phase Transformation

Figure 5 shows the X-ray diffraction analysis of the sample at different temperatures and 60 min holding time, and the main phases are listed in Table 3. The low-grade phosphate ore samples were mainly composed of calcium fluorophosphate and SiO2 phases. When the temperature increased from 1200° C to 1250 °C, the peak of the phase characteristic of SiO2 reduced, the main phase of the reduction product was composed of Ca5(PO4)3F, Ca3(PO4)2, and CaSiO3, and the peak intensity of Ca5(PO4)3F decreased. At 1300 °C, the CaO diffraction peak appeared, and the main phase of the reduction product was composed of Ca5(PO4)3F, Ca3(PO4)2, CaO, CaSiO3, and CaF2. At 1350 °C, no new phase production was observed, but the CaO and CaF2 diffraction peaks gradually increased, and the Ca5(PO4)3F diffraction peak gradually decreased. This was mainly because of the accelerated carbothermal reduction reaction ratio. In addition, most of the Ca5(PO4)3F was reduced by coke. Thus, the intensity of the Ca5(PO4)3F diffraction peak weakened, which is similar to the results of Cao et al. [23].

Fig. 5
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XRD spectra of the sample at different reduction temperatures and duration 60 min

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Table 3 Main phases of reduced product at different temperatures
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Microstructure Analysis

The BSE and surface scanning of reduced samples at 60 min under different temperatures are shown in Fig. 6. The analysis of the same contrast in Fig. 5 was conducted. Overall, the number of dots was more than six, and the average percentage of elemental atoms was obtained. As shown in Fig. 6, the contrast region a was mainly silicate, the contrast region b was P iron alloy, iron-carbon alloy, and partial iron oxide, and the contrast region c was mainly unreacted Ca5(PO4)3F, partial calcium salt, and coke black contrast. The contrast regions a and b depended on the contrast region c and coke edge aggregation and growth. This contrast was disordered, and the coke was distributed in bright blocks when the temperature was 1200 °C. However, the contrast became smooth when the temperature increased to 1250 °C. The ferroalloy phase accumulated and grew with increasing temperature, and the coke was evenly distributed around the contrast region c. At 1300 °C, P content in the ferroalloy phase and the contrast region c increased and decreased, respectively, and the composition of the three contrast elements in regions b and c remained constant.

Fig. 6
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BSE and surface scan of reduced samples held for 60 min at different temperatures

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Analysis of the Reduction Process

Figure 7 shows the liquid-phase projection of the ternary system of SiO2–CaO–P2O5. Figure 7 shows that A, B, and C were the slag composition points after the carbothermal reduction reaction of phosphate ore at 1200 °C, 1250 °C, and 1300 °C, respectively, at a holding time of 60 min. As shown in Fig. 7, at different temperatures holding for 60 min, with increasing temperature, the slag composition points in the phase diagram gradually shifted to the primary crystal zone of CaO, indicating that an increase in temperature effectively promotes the reaction, which was confirmed with the aforementioned conclusions. When the reaction temperature increased, the farther the slag composition point was from the primary crystal zone of P2O5, the greater was the reaction degree. Below 1250 °C, the slag composition point was in the primary crystal zone of dicalcium silicate in the phase diagram. Meanwhile, when the temperature was higher than 1300 °C, the slag composition point shifted to the primary crystal zone of CaO, indicating that the reaction of SiO2 in the slag was relatively complete, and some CaO was not involved in the reaction. This indicates that the CaO diffraction peak could appear in the XRD pattern, which is consistent with these findings.

Fig.7
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Projection diagram of liquidus of the ternary system of SiO2–CaO–P2O5

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The results showed that Ca5(PO4)3F was more likely to react with SiO2 than with C. The reaction of Ca5(PO4)3F with SiO2 was calculated using the reaction module of the Factsage 7.2 software. The reduction process of low-grade phosphate ore was shown in Fig. 8. The initial temperature of the reaction was 1080 °C, at which, Ca5(PO4)3F reacted with a small amount of SiO2 in the ore sample to form Ca3(PO4)2, CaSiO3, and SiF4 (escaped in the form of gas), and Ca3(PO4)2 was reduced by C. When the temperature reached 1300 °C, a large number of Ca5(PO4)3F in phosphate ore began to react with C to form CaO, P2 (g), CO (g), and CaF2. The main reactions are as follows:

$$ {\text{4Ca}}_{{5}} \left( {{\text{PO}}_{{4}} } \right)_{{3}} {\text{F }} + {\text{ 3SiO}}_{{2}} = {\text{ 6Ca}}_{{3}} \left( {{\text{PO}}_{{4}} } \right)_{{2}} + {\text{ 2CaSiO}}_{{3}} + {\text{ SiF}}_{{4}} \left( {\text{g}} \right), $$
(3)
$$ {\text{Ca}}_{{3}} \left( {{\text{PO}}_{{4}} } \right)_{{2}} + {\text{ 5C }} = {\text{ 3CaO }} + {\text{ P}}_{{2}} \left( {\text{g}} \right) + {\text{ 5CO}}\left( {\text{g}} \right), $$
(4)
$$ {\text{2Ca}}_{{5}} \left( {{\text{PO}}_{{4}} } \right)_{{3}} {\text{F }} + {\text{ 15C }} = {\text{ 9CaO }} + {\text{ 3P}}_{{2}} \left( {\text{g}} \right) + {\text{ 15CO}}\left( {\text{g}} \right) + {\text{ CaF}}_{{2}}. $$
(5)
Fig. 8
figure 8

The reduction process of low-grade phosphate ore at different temperatures

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Kinetic Analysis

Methods of Isothermal Kinetics

At present, there are mainly two kinds of kinetics research: isothermal method and non-isothermal method. The isothermal method is relatively simple, according to its kinetic equation [24, 25]:

$$G\left(\alpha \right)={\int }_{0}^{t}A{\text{exp}}\left(-\frac{E}{RT}\right){\text{d}}t=kt,$$
(6)

where \(G\left(\alpha \right)\) is the integral form of mechanism function, A is the pre-exponential factor, E is the activation energy, R is the gas constant, T is the temperature, and t is the time.

In general, the method of matching experimental data with the kinetics model is adopted—"Mode fit method"[26]. The rate constant \(k(T)\) is a constant for a simple reaction in the isothermal method, so it can be separated from \(f(\alpha )\), or \(G(\alpha )\), and then the three factors of kinetics can be obtained by two steps:

  1. (1)

    In an isothermal α-t curve, select a set of α, t value into \(G(\alpha )\), the \(G(\alpha )\)-t graph is a straight line, with slope k. The \(G(\alpha )\) which can make the line linear best is selected as the appropriate mechanism function.

  2. (2)

    The same method is used to obtain a set of k values on a set of isothermal \(G(\alpha )\)–t curves measured at different temperatures, using the general form of Arrhenius empirical equations:

    $$k =Aexp(-E/RT).$$
    (7)

Take the log of both sides:

$$-lnk=-1nA+E/RT$$
(8)

A straight line can be fitted by plotting \(-\mathrm{ln}\left(k\right)\) with 1/T, and the values of apparent activation energy E and pre-exponential factor A can be obtained by its slope and intercept, respectively.

Kinetic Model Functions

Table 4 Integral expressions of common reaction mechanism functions [27,28,29,30]
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Kinetic Analysis of Integral Reduction Samples

The reduction ratio is considered to be the reduction degree of the sample. The linear fitting of the integral expressions listed in Table 4 were determined using Eqs. (6), (7), and (8), respectively. As shown in Fig. 9, the integral expression with the highest fitting precision was selected. Subsequently, the kinetic parameters were obtained, as listed in Table 5. The results show that, overall, in the process of the carbothermic reduction of low-grade phosphate ore in vacuum, during the 0–30 min stage, the fitting effect of internal diffusion, \(1-2\alpha /3-{(1-\alpha )}^{2/3}=kt\), was best when the temperature was lower than 1350 °C, indicating that the reduction reaction was controlled by internal diffusion. Then, during the 30–90 min stage, the fitting effect of the interface chemical reaction \(1-{(1-\alpha )}^{1/3}=kt\) was the best when the temperature was lower than 1300 °C. According to the integral method, the activation energies of the reduction reaction were 265.90 kJ/mol and 124.67 kJ/mol, respectively. Hu et al. [31] and Guo et al. [32] applied the electric furnace method with the temperature conditions between 1300 and 1450 °C to study the activation energy of the phosphate ore reduction reaction, obtaining values of 184.644 kJ/mol and 217.360 kJ/mol, respectively. With activation energies greater than 124.67 kJ/mol, the amount of CaSiO3, CaO, and other products attached between the reactant and coke increased with time, limiting reaction progress.

Fig. 9
figure 9

Relationship between link and 1/T

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Table 5 Control models and dynamic parameters
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Kinetic Analysis of the Volatilization of Phosphorus

The volatilization ratio of P in the reduction process was considered to be the reduction degree of P. The linear fitting of the integral expressions listed in Table 4 were performed Eqs. (6), (7), and (8), respectively. As shown in Fig. 10, the integral expression with the highest fitting precision was selected. Based on these results, the kinetic parameters were obtained, as listed in Table 6. At the 0–30 min stage, the fitting effect of the interface chemical reaction, \(1-{(1-\alpha )}^{1/3}=kt,\) was best when the temperature was lower than 1300 °C. During this stage, the activation energy of P volatilization was 339.49 kJ/mol, and the volatilization ratio of P was controlled by the interface chemical reaction when the holding time was less than 30 min. At the 30–90 min stage, the fitting effect of internal diffusion,\(1-2\alpha /3-{(1-\alpha )}^{2/3}=kt,\) was the best when the temperature was lower than 1250 °C, at which the activation energy of P volatilization was 604.77 kJ/mol. Note that, the volatilization ratio of P in the reduction process was controlled by internal diffusion when the holding time was more than 30 min.

Fig. 10
figure 10

Relationship between link and 1/T

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Table 6 Control models and dynamic parameters
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The Analysis of the Reaction Mechanism

The reduction mechanism of phosphate ore during the vacuum carbothermal reduction is shown in Fig. 11. When the reaction conditions were reached, Ca5(PO4)3F first defluorinated with SiO2 to from Ca3(PO4)2, and then the reduction reaction began at the two-phase interface of Ca3(PO4)2 and C. As SiO2 depleted, Ca5(PO4)3F in the phosphorite directly reacted with C. The reduction reaction was a typical gas–solid reaction, which gradually advanced inward. As the reaction proceeded, the solid-state products, including CaSiO3 and CaO, increased and attached to the reactant surface. In addition, a shrinking core consisting of unreacted reactants existed in the reduced ore until the end of the reaction. The existence of this solid-state product layer reduced the contact area between Ca5(PO4)3F, Ca3(PO4)2, and C, limiting the reaction. Gaseous yellow P continuously diffused from the surface of the reactants to the surface of the sample and escaped with CO. The diffusion of yellow P denotes the restrictive section of its volatilization process. In summary, the middle-low-grade phosphate ore was more easily reduced by C or reacted with silica during vacuum conditions. This is mainly because the system's low pressure under vacuum contributed to the low temperature of the reaction, indicating that, it could be reduced or reacted with silica at a lower temperature.

Fig. 11
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Vacuum carbothermal reduction mechanism of low-grade phosphate ore

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Conclusions

The isothermal kinetics and reduction process of carbothermic reduction of low-grade phosphate ore was investigated in vacuum by XRD, SEM, EDS, chemical analysis, and FactSage 7.2. The conclusions were summarized as follows:

  1. (1)

    The reduction ratio of the sample and the volatilization ratio of P increased with increasing temperature and holding time. This tendency accelerated significantly above 1250 °C and the reaction proceeded in large quantities. After 30 min, the rate of reaction began to slow.

  2. (2)

    Ca5(PO4)3F first reacted with a small amount of SiO2 in the ore sample at 1080 °C to form Ca3(PO4)2, CaSiO3, and SiF4 (escaped in the form of gas), after which Ca3(PO4)2 was reduced by C. When the reaction temperature reached approximately 1300 °C, a large amount of Ca5(PO4)3F in the ore sample began to react with C to produce CaO, P2 (g), CO (g), and CaF2.

  3. (3)

    Through the mutual verification of the trial-and-error method, it was concluded that the unitary reduction process was under the control of the shrinking core model and diffusion, and the activation energies of the unitary reduction were 124.67 kJ/mol and 265.9 kJ/mol. Meanwhile, the volatilization of P was under the control of the diffusion and shrinking core model, for which the activation energies were 604.77 kJ/mol and 339.49 kJ/mol.