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

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.