Optimization of medium–low-grade phosphorus rock carbothermal reduction process by response surface methodology

Abstract Phosphorus extraction from phosphorus rock was conducted by carbothermal reduction with silica and coke. The effects of reaction temperature, reaction time, coke excess coefficient, molar ratio of silicon–calcium, and phosphorus rock particle size on the phosphorus reduction rate were investigated by the response surface methodology (RSM). The central composite design (CCD) with five factors and five levels was used to explore the effects of variables’ interactions on the phosphorus reduction rate. The results showed that there are significant interactions between reaction time and temperature; reaction temperature and molar ratio of silicon–calcium; reaction temperature and phosphorus rock particle size; coke excess coefficient and molar ratio of silicon–calcium; and coke excess coefficient and phosphorus rock particle size. The optimum conditions in the experimental range are reaction time 92 min, reaction temperature 1340°C, coke excess coefficient 1.27, molar ratio of silicon–calcium 1.28, and phosphorus rock particle size 75–106 µm, which were derived from the quadratic statistic model. Under these conditions, the phosphorus reduction rate can reach 96.88%, which is close to the model prediction value 99.40%. The optimized carbothermal reduction conditions of phosphorus rock by the RSM are helpful to reduce the energy cost of thermal phosphoric acid process.


Introduction
Yellow phosphorus is mainly obtained from phosphate ore, coke, and silica by carbothermal reduction method in the electric furnace, and the main components of the three raw materials are Ca 5 (PO 4 ) 3 F, C, and SiO 2 , respectively. In this process, coke is mainly used as a reducing agent and conductor, whereas silica is mainly used as a flux to form stable silicate and promote the reduction reaction of phosphate [1][2][3]. The main reaction equation is shown in Eq. 1: (1) The phosphorus obtained by carbothermal reduction process is an irreplaceable raw material to produce phosphates and their derivatives. It is an important raw material for producing food-grade, electronic-grade, and medical-grade phosphoric acid, as well as the basic raw material for agricultural chemical products [4,5]. However, in order to facilitate slag discharge, the operating temperature of yellow phosphorus production by the electric furnace process should be about 150°C higher than the melting point of the residue, and the power consumption is 13,000-15,000 kWh per ton, which makes it a typical huge energy consumption industry [6,7]. Therefore, the development of an energy-saving technology is vital to promote the sustainable development of yellow phosphorus industry.
In China, medium-and low-grade phosphate ores are the majority of phosphorus resources. The utilization percentage of medium-and low-grade phosphorus resources is lower than expected. Effective utilization of medium-and low-grade phosphate ores is necessary to realize the sustainable development of phosphorus chemical industry [8]. Phosphoric acid prepared by wet process of medium-and low-grade phosphate requires ore dressing, and the purity of the prepared phosphoric acid is not high enough, which leads to the subsequent complicated separation process [9]. Kiln phosphoric acid process is still in the research stage due to its immature technology [10]. Medium-and low-grade phosphate ores can be directly used in the thermal process of phosphoric acid to obtain high-purity phosphoric acid. The huge energy consumption is its main disadvantage [4,11]. Therefore, reducing energy consumption is an important issue in thermal phosphoric acid process.
Many studies on thermal phosphoric acid technology have been carried out. Jiang et al. [12] studied the kinetics of fluorapatite carbothermal reduction reaction. After reaction at 1,250°C for 60 min, the reduction rate of fluorapatite reached about 48%. The reaction at 1,300°C for 60 min resulted in a reduction rate of 76%. Li et al. [13] found that a reduction rate of 98.9% with medium-and low-grade phosphate ores was approached at 1,550°C for 60 min and the reaction temperature is the most important factor that influences the reduction rate of phosphate ore. Cao et al. [14] added a certain amount of alkali metals to enhance the activity of carbon and the reduction rate of phosphorus rock. By adding 1.5% K 2 CO 3 and reacting at 1,300°C for 60 min, the reduction rate of phosphorus rock was increased to 67%. When the reaction time was prolonged to 4 h, the reduction rate of phosphorus rock could reach 91.32%. Yang et al. [15] revealed that the carbothermal reduction reaction of fluorapatite promoted by Al 2 O 3 mainly occurred in the low-temperature zone and at the initial stage of the reaction. The reaction was conducted at 1,250°C for 50 min, and the reduction rate of phosphorus rock can be increased from 65% to 75% by adding Al 2 O 3 . Li et al. [16] used medium-and low-grade phosphorus rocks with high content of calcium to react at 1,300°C for 210 min, and the reduction rate of phosphorus rock could reach more than 94%. They proposed that the reduction rate of phosphate ore decreases with the increase in the molar ratio of silicon-calcium, and the decrease in the reduction rate is more significant when the molar ratio of silicon-calcium >2. Li et al. [17] studied the growth behavior and size characterization of metallic iron particles in coal-based reduction of oolitic hematite-coal composite briquettes and manifested that reduction temperature, time, and ore size fraction strongly influenced the reduction. Li et al. [18] studied the feasibility of potassium feldspar as a flux to reduce phosphate rock, and they found that when the coke excess coefficient increased from 1.0 to 1.05, the reduction rate of phosphate rock increased from 95% to 99.61%. In order to reduce the temperature (time) of the carbothermal reduction reaction and save energy, orthogonal experiments are mainly used by the current researchers to optimize the process conditions. When the reaction temperature is mainly in the range of 1,250-1,350°C and the reaction time is 60-120 min, the reduction rate of phosphate ore could usually reach 40-95%. From the above description, one can see that in addition to reaction temperature and time, coke excess coefficient, molar ratio of silicon-calcium, and phosphorus rock particle size are other pivotal factors to determine the reduction rate of phosphorus ore. In this paper, these five factors are chosen to study their effects on the phosphorus reduction rate.
The response surface methodology (RSM) is a relatively scientific and efficient parameter optimization method, which is widely used in chemical, agricultural, pharmaceutical, environmental, and mechanical engineering fields. This method is simple and efficient, especially for studying the interaction between several experimental factors. Compared with single-factor optimization, the response surface methodology has the advantages of fewer experiments, accurate prediction, and the ability to study the interaction between several factors at the same time [19], which makes this method better than the traditional orthogonal methodologies. In this paper, based on single-factor experiment and literature research, the response surface methodology is used to optimize the process variables (reaction temperature, reaction time, coke excess coefficient, molar ratio of silicon-calcium, and phosphorus rock particle size) of carbothermal reduction reaction of phosphorus rock to improve the energy efficiency of thermal phosphoric acid process.

Materials and methods
The phosphorus rock used in the experiments was from Yichang, Hubei Province. PANalytical Axios wavelengthdispersive X-ray fluorescence spectrometer was used to determine the composition of the phosphorus rock. The main chemical components are shown in Table 1. The industrial analysis of the reducing agent coke is shown in Table 2. Silica (analytical purity) was supplied by Sinopharm Chemical Reagent Co. Ltd.
The phosphorus rock powder was mixed with coke and silica powders, which passed 200-mesh sieve evenly according to the designed ratio, pressed into several φ 15 × 3 mm flakes under 5 MPa, and then dried for further use. 5-6 g of dried sample was placed in a graphite crucible and heated in the LFT-1600 tube furnace, with the rate of flow of nitrogen of 80 mL min −1 for 30 min. Under the protection of nitrogen, the temperature was elevated at a rate of 5°C min −1 to a specified temperature. After the reaction ended, the slag was removed from the graphite crucible after cooling to room temperature. After ground through 200-mesh sieves, the residue was used for the analysis of the content of P 2 O 5 and further characterization. The phosphorus rock particle size was determined using sieves with different meshes.
The content of P 2 O 5 in the residue was analyzed by gravimetric method with quinoline phosphomolybdate as agent. The phosphorus rock reduction rate (Y) was calculated according to Eq. 2: where M 0 and M 1 are the mass of samples before and after the reaction and w 0 and w 1 are the mass fraction of P 2 O 5 before and after the reaction, respectively. The reaction time (A), reaction temperature (B), coke excess coefficient (C), molar ratio of silicon-calcium (D), and phosphorus rock particle size (E) were the factors and the phosphorus reduction rate (Y) was the response value in this paper.

Single-factor investigation
The results of the single-factor investigation are displayed in Figure 1. The results in Figure 1a show that the reduction rate increases with the reaction time. When the reaction time continues to extend, the reduction rate will tend to close to 100% as the most phosphates had reacted out. Considering the reduction rate and economic cost, the reaction time in the RSM experiments is in the range of 30-120 min.
As shown in Figure 1b, the reduction rate increases gradually with the reaction temperature. When the temperature is above 1,300°C, the reduction rate increases slowly and becomes stable. From the point of view of thermodynamics, the increase in the temperature provided a favorable thermodynamics condition and promoted phosphorus rock reduction. Considering the reduction rate and application feasibility, the RSM experiments were conducted at 1,200-1,400°C.
Considering the effects of the amount of reduction agent coke on the reduction rate, the relation between different coke excess coefficients and the reduction rate is demonstrated in Figure 1c, which shows that the reduction rate increases with CEC. In order to study the effects of coke excess coefficient on the reduction rate comprehensively, the coke excess coefficient (CEC) was set in the range of 0.80-1.60 in the RSM experiments.
The effects of molar ratio of silicon-calcium (Si/Ca) on the reduction rate and the results are shown in Figure 1d. One can see that the reduction rate increases first and then decreases with the increase in the molar ratio of silicon-calcium (Si/Ca). In the process of phosphorus production, silica is used as a flux to reduce the reaction temperature. The melting point of slag usually depends on the value of silicon-calcium ratio. The amount of silica should not be too high to prevent side reactions from occurring. The molar ratio of silicon-calcium (Si/Ca) was set in the range of 0.80-1.60 in the RSM experiments.
The phosphorus rock particle size influences the heat and mass conduction and thereby the reduction rate. Figure  1e shows that the reduction rate increases first and then decreases with the decrease in the phosphorus rock particle size. When the phosphorus rock particle size is in the range of 75-106 µm, the reduction rate is the highest in the singlefactor investigation experiments. Therefore, five different particle sizes of 0-48 µm, 48-75 µm, 75-106 µm, 106-150 µm, and 150-270 µm were chosen in the RSM experiments.

Optimization of reaction conditions by RSM
Based on the literature investigation and previous singlefactor experiments, reaction time (A, 30-120 min), reaction    Table 3. The optimum conditions for phosphorus rock carbothermal reduction were obtained by the response surface methodology. Through CCD procedure, the detailed fifty experiments with five different factors and levels were generated and are shown in Table 4. The phosphate reduction rates of 50 runs of the experiments are also displayed in Table 4, and the reduction rate was obtained in the range of 61.18% to 97.90%.

Quadratic regression fitting and the result of variance analysis
The experimental results were fitted to various models (linear, interactive (2FI), quadratic, and cubic) to get regression equation. Three different tests, namely the sequential model sum of squares, lack-of-fit tests, and model summary statistics, were conducted in this paper to determine the adequacy of various models to represent the maximum reduction rate of phosphorus rock, and the results are listed in Table 5. The fit summary output indicated that the quadratic polynomial model was significant for the present system as shown in Table 5, while the interaction of two factors (2FI) and the linear model were suggested to be insignificant. As   shown in Table 5, linear and interactive (2FI) models exhibit lower R 2 , adjusted R 2 , predicted R 2 , and also high p-values as compared to quadratic model. Cubic model was found to be aliased. Therefore, the quadratic model including linear, interactive, and quadratic terms was chosen to describe the effects of process variables on the reduction rate of phosphorus rock. Furthermore, the analysis of variance (ANOVA) was used to evaluate the adequacy of the model equation. ANOVA evaluations of the model, including its variables and their interactions, are given in Table 6. As can be seen from Table 6, the effects of the reaction time (A), reaction temperature (B), coke excess coefficient (C), molar ratio of silicon to calcium (D), and phosphorus rock particle size (E) on the reduction rate of phosphorus rock (Y) are all significant because their prob >F-values for phosphorus rock reduction rate (Y) are all lower than 0.05 (p value < 0.05), indicating that these factors are significant [20][21][22]. In addition, the interactions A-B, B-D, B-E, C-D, and C-E are also significant because their prob >F-values are also below 0.05. In the analysis of variance, the larger the F-value of the variable(s) and their interaction item is, the greater influence of those item(s) on the response value is [23]. Therefore, the sequence of the effect of various factors on the phosphorus rock reduction rate (Y) is as follows: B > A > D > C > E. The effect order of the interaction items on the reduction rate (Y) is CE > AB > CD > BD > BE.
The data shown in Table 4 were regressed by Design-Expert 8.0.6, and the derived quadratic polynomial model equation includes the reaction time (A), reaction temperature (B), coke excess coefficient (C), molar ratio of silicon to calcium (D), phosphorus rock particle size €, and the reduction rate of phosphorus rock (Y). Combined with ANOVA results in Table 6 and removing insignificant items from the model, the obtained quadratic polynomial model equation is as follows: (3) Figure 2 shows the relationship between the predicted and actual reduction rates of phosphorus rock. As can be seen from the diagram, most of the actual values are close to the predicted values, and a few of the actual values fall on both sides of the predicted values symmetrically, indicating that the model fits the actual responses well. Table 5 gives the R 2 = 0.988, which means the model can explain 98.8% of the variation of response values. A good fit between the predicted and the actual values proves that the good fitting model can be used to analyze and predict the optimum reduction conditions of phosphorus rock. In order to show how any two factors affect the response, the 3D response surface plots and the contour plots are demonstrated in Figures 3 and 4, respectively.
It is important to focus on the effects of the significant terms. Therefore, the 3D response surface plots of the interactions AC, AD, AE, BC, and DE are not shown.
The 3D response surface plot in Figure 3a, which gives the reduction rate as a function of the reaction time and reaction temperature, indicates that a higher reduction rate could be achieved with reaction time and temperature. Combining that with Figure 4a, the reaction temperature is more influential than the reaction time as to the reduction rate. Figure 3b shows the 3D response surface plot at varying reaction temperatures and molar ratios of silicon to calcium. It can be inferred that the reduction rate increases with the reaction temperature and the molar ratio of silicon to calcium. Figure 4b demonstrates that the effect of reaction temperature on the reduction rate is stronger than that of molar ratio of siliconcalcium.
In Figure 3c, the 3D response surface plot is developed for the reduction rate with varying reaction temperatures and phosphorus rock particle sizes. The figure indicates that the reduction rate increases with the reaction temperature, while it increases to a certain extent and then decreases with the decrease in the phosphorus rock particle size. Figure 4c  reflects that the reaction temperature affects the reduction rate stronger than the phosphorus rock particle size. The 3D response surface plot based on the independent variables coke excess coefficient and molar ratio of silicon to calcium is shown in Figure 3d, indicating that the reduction rate increases with increasing coke excess coefficient and molar ratio of silicon-calcium. The molar ratio of silicon to calcium is obviously a stronger factor of the reduction rate  than the coke excess coefficient, which can be found in Figure 4d. Figure 3e gives the 3D response surface plot at varying phosphorus rock particle sizes and coke excess coefficients. It shows that the reduction rate increases with increasing coke excess coefficient. However, the reduction rate increased to a certain level and then decreased with decreasing phosphorus rock particle size. It can be seen from Figure 4e that the influence of coke excess coefficient on the reduction rate is slightly stronger than that of phosphorus rock particle size.

Response surface optimization validation test results
Under the prediction result of the CCD model, the theoretical optimum reduction conditions and the result are as follows: reaction time 92 min, reaction temperature 1,340°C, coke excess coefficient 1.27, molar ratio of silicon-calcium 1.28, phosphorus rock particle size 75-106 µm, and the maximum reduction rate 99.40%. In order to test the accuracy of the model, the reduction rate of phosphorus rock is 96.88% under the optimum reduction conditions. The deviation from the predicted value is only 2.52%, which implies the model can predict the experimental results well. Based on the investigation of the related literature, the reduction rate is close to or higher than most of the reported values in the literature. In order to illustrate the innovation and the significant improvement of this study, similar reports about phosphorus rock carbothermal reduction were searched. Their reaction conditions and results are listed in Table 7. It can be seen that our optimized conditions of phosphorus rock carbothermal reduction are relatively mild and the reduction rate is fairly good as compared to the other published results.

Conclusions
The process conditions of carbothermal reduction of medium-and low-grade phosphorus rocks were optimized by the response surface methodology. The effects of reaction time, reaction temperature, coke excess coefficient, molar ratio of silicon to calcium, and phosphorus rock particle size on the reduction rate of phosphorus rock were investigated. The optimum conditions are as follows: reaction time 92 min, reaction temperature 1,340°C, coke excess coefficient 1.27, molar ratio of silicon-calcium 1.28, and phosphorus rock particle size 75-106 µm. Under these conditions, the reduction rate of phosphorus rock (96.88%) is close to the predicted value (99.40%). The reduction rate of phosphorus rock in this paper is close to or higher than most of the reported results in the literature, which provides the experimental basis for energy saving and consumption reduction in thermal phosphoric acid process.