Low-grade fluorite sulfuric acid purification method for solving calcium sulfate wrapping problem
By combining segmented acid leaching, powerful mechanical stirring, and intermittent ultrasonic treatment, the problem of calcium sulfate coating was solved, achieving efficient purification of low-grade fluorite. The product purity and recovery rate were significantly improved, making it suitable for the mineral processing field.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HENAN FLUORINE BASED NEW MATERIAL TECH CO LTD
- Filing Date
- 2026-02-26
- Publication Date
- 2026-05-12
AI Technical Summary
Existing technologies cannot effectively solve the problem of calcium sulfate coating during the reaction of sulfuric acid with low-grade fluorite, resulting in low fluorite purification efficiency and difficulty in improving product purity.
A multi-layered debonding system is formed by combining segmented acid leaching, strong mechanical stirring, and intermittent ultrasonic waves. Segmented acid leaching avoids local oversaturation, while mechanical stirring provides fluid shear force and the cavitation effect of ultrasonic waves breaks down the encapsulation layer.
It significantly improves the grade and recovery rate of fluorite, with the CaF2 content in fluorite concentrate exceeding 91% and the SiO2 and CaCO3 contents reduced to below 0.5%. It is low-cost, environmentally friendly, and easy to industrialize.
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Abstract
Description
Technical Field
[0001] This invention belongs to the field of mineral processing technology, specifically relating to a method for purifying low-grade fluorite sulfuric acid to solve the problem of calcium sulfate encapsulation. Background Technology
[0002] Fluorite (CaF2) is an important strategic mineral resource. With the depletion of high-grade fluorite mines, the efficient utilization of low-grade fluorite has become a research hotspot. Low-grade fluorite typically contains gangue minerals such as calcite (CaCO3) and quartz (SiO2). Acid leaching is a commonly used purification method, among which dilute sulfuric acid has attracted much attention due to its low cost and wide availability.
[0003] However, a major technical obstacle in dilute sulfuric acid treatment lies in the low solubility of calcium sulfate (CaSO4•2H2O, gypsum) produced by the reaction of sulfuric acid with calcite in water (approximately 0.21 g / 100 mL at room temperature). During the reaction, gypsum rapidly crystallizes on the surface of fluorite particles, forming a dense coating that severely hinders the further diffusion of sulfuric acid into the particles and its reaction with residual calcite and other impurities. This leads to a rapid decline in impurity removal efficiency, making it difficult to further improve product purity (typically, the CaF2 grade struggles to consistently exceed 90%). Existing technologies either employ more expensive mixed acids (such as sulfuric acid-hydrochloric acid) or use highly irritating hydrofluoric acid, both of which present problems related to cost, environmental impact, and equipment corrosion.
[0004] To circumvent this problem, existing technologies often employ the following solutions: 1) Using acids with higher calcium salt solubility, such as hydrochloric acid and nitric acid, but this significantly increases costs (Patent Document CN105967190A); 2) Using strong fluorides such as hydrofluoric acid or fluorosilicic acid, which can simultaneously remove SiO2, but pose risks of high toxicity, strong corrosiveness, and environmental pollution (Patent Document CN108439452A); 3) Simply increasing the reaction temperature, extending the reaction time, or strengthening stirring, but these conventional optimization methods cannot fundamentally destroy the already formed dense coating layer, resulting in limited effectiveness and increased energy consumption (Patent Document CN101913641A).
[0005] Therefore, developing a new method that can effectively solve the problem of calcium sulfate encapsulation, fully leverage the cost advantages of dilute sulfuric acid, and significantly improve the purification efficiency of low-grade fluorite has important industrial application value. Summary of the Invention
[0006] Based on this, the purpose of the present invention is to provide a method for purifying low-grade fluorite with sulfuric acid by solving the problem of calcium sulfate encapsulation. This method can effectively break through the calcium sulfate encapsulation layer and significantly improve the grade and recovery rate of fluorite.
[0007] To achieve the above objectives, the present invention adopts the following technical solution: This invention provides a method for purifying low-grade fluorite sulfuric acid to solve the problem of calcium sulfate encapsulation, comprising the following steps: S1, Raw material pretreatment: First, the low-grade fluorite ore is crushed and ground, and then magnetic separation is performed to remove iron, so as to obtain pretreated fluorite powder. S2, Segmented acid leaching reaction: Dilute sulfuric acid with a mass concentration of 5~15wt% is added in segments to the pretreated fluorite powder described in S1, and a solid-liquid mixture is obtained after the segmented acid leaching reaction is completed; the total amount of dilute sulfuric acid used is in a mass ratio of 0.8~1.2:1 to the pretreated fluorite powder. S3, Post-processing: The solid-liquid mixture described in S2 is separated by gravity to obtain underflow; the underflow is then filtered, washed, and dried to obtain fluorite concentrate; preferably, the gravity separation process is as follows: the solid-liquid mixture is separated by a hydraulic separator, and the underflow is collected for later use.
[0008] Furthermore, the low-grade fluorite ore described in S1 contains 85-88 wt% CaF2, 0.8-0.9 wt% SiO2, 0.8-0.9 wt% CaCO3 and 1.4-1.5 wt% Fe2O3, with the balance being other impurities.
[0009] Furthermore, the low-grade fluorite ore described in S1 is crushed and ground to obtain fluorite powder with a particle size of less than 200 mesh.
[0010] Furthermore, the segmented acid leaching reaction described in S2 is divided into 2-3 stages, and the reaction conditions for each stage are: stirring at a stirring rate of 300-1000 rpm at 20-60°C for 10-50 minutes. The stirring is mechanical, using an anchor-type, turbine-type, or spiral-type impeller.
[0011] Furthermore, the staged acid leaching in S2 involves adding the total acid to the fluorite powder in batches. This avoids excessive local supersaturation caused by adding acid all at once, thus reducing the rapid crystallization of calcium sulfate and the thickness of the initial coating layer. Powerful mechanical stirring provides strong fluid shear force, which can macroscopically wash away, peel off, and break up larger blocky or sheet-like coating layers.
[0012] Furthermore, the reaction conditions for each stage of the acid leaching reaction may be the same or different. The reaction conditions include stirring at a stirring rate of 300-800 rpm at 20-60°C for 10-30 minutes, or stirring at a stirring rate of 400-1000 rpm at 20-60°C for 20-50 minutes.
[0013] Furthermore, when the segmented acid leaching reaction is divided into two stages, the amount of dilute sulfuric acid used in the first stage of the acid leaching reaction accounts for 40-60 wt% of the total amount of dilute sulfuric acid, and the remaining dilute sulfuric acid is used in the second stage of the acid leaching reaction; when the segmented acid leaching reaction is divided into three stages, the amount of dilute sulfuric acid used in the first stage of the acid leaching reaction accounts for 30-40 wt% of the total amount of dilute sulfuric acid, the amount of dilute sulfuric acid used in the second stage of the acid leaching reaction accounts for 30-40 wt% of the total amount of dilute sulfuric acid, and the remaining dilute sulfuric acid is used in the third stage of the acid leaching reaction; the concentration of dilute sulfuric acid used in each stage of the acid leaching reaction may be the same or different.
[0014] Furthermore, during at least one acid leaching reaction or between two adjacent acid leaching reactions, intermittent ultrasonic treatment is applied; utilizing the "cavitation effect" generated by ultrasound in the liquid, local high-temperature and high-pressure shock waves and microjets are formed, which can effectively break the dense calcium sulfate crystal structure at the microscale and release its "locked-in" state to the fluorite particles.
[0015] Furthermore, during at least one acid leaching reaction or between two adjacent acid leaching reactions, intermittent ultrasonic treatment is applied 2 to 3 times.
[0016] Furthermore, the frequency of the intermittent ultrasonic treatment is 20~40kHz, the power is 100~500W, and it adopts a mode of working for 1~5 minutes and intermittent for 5~15 minutes.
[0017] Furthermore, the washing liquid used in S3 includes water, and the washing is performed until the washing liquid is neutral; the drying temperature is 100~110℃.
[0018] The present invention further provides a fluorite concentrate obtained by the above-described method for purifying low-grade fluorite using sulfuric acid to solve the problem of calcium sulfate encapsulation.
[0019] Furthermore, the fluorite concentrate contains CaF2 content > 91 wt%, SiO2 content < 0.5 wt%, and CaCO3 content < 0.2 wt%.
[0020] The beneficial effects of this invention are: 1. The low-grade fluorite sulfuric acid purification method provided by this invention, which solves the problem of calcium sulfate encapsulation, creatively combines three methods—"segmented acid leaching," "powerful mechanical stirring," and "intermittent ultrasonication"—based on a synergistic encapsulation breaking mechanism, producing a significant synergistic effect. Specifically, the segmented acid leaching process avoids excessive local supersaturation caused by a single addition of acid, reducing the rapid crystallization of calcium sulfate and the initial thickness of the encapsulation layer. The powerful mechanical stirring process provides strong fluid shear force, macroscopically scouring, peeling, and breaking down large blocky or sheet-like encapsulation layers. The intermittent ultrasonication process utilizes the "cavitation effect" generated by ultrasound in liquids to form localized high-temperature, high-pressure shock waves and microjets, effectively breaking down the dense calcium sulfate crystal structure at the microscale and releasing it from its "locked-in" state to the fluorite particles. These three methods work synergistically to form a multi-level, three-dimensional encapsulation breaking system of "prevention-macroscopic breaking-microscopic cracking," fundamentally solving the problem of reaction kinetic hindrance.
[0021] 2. The method for purifying low-grade fluorite with sulfuric acid, which solves the problem of calcium sulfate encapsulation, provided by this invention, has excellent purification effect. This method can stably purify low-grade fluorite with a CaF2 content of 85-88% to over 91%, while also having an excellent removal effect on tightly coexisting SiO2 impurities, reducing their content to below 0.5%, far exceeding the purification limit of conventional dilute sulfuric acid methods.
[0022] 3. The low-grade fluorite sulfuric acid purification method provided by this invention, which solves the problem of calcium sulfate encapsulation, is economical and environmentally friendly. The entire process uses inexpensive dilute sulfuric acid as the main reagent, without introducing expensive or toxic chemical additives. The process is simple, the conditions are mild, it is easy to industrialize, and it has significant cost advantages and is environmentally friendly.
[0023] 4. The fluorite concentrate obtained by the low-grade fluorite sulfuric acid purification method provided by the present invention, which solves the problem of calcium sulfate encapsulation, has a CaF2 content >91 wt%, a SiO2 content <0.5 wt%, and a CaCO3 content <0.2 wt%. Detailed Implementation
[0024] The technical solutions in the embodiments of the present invention will be clearly and completely described below. All mentioned embodiments are implemented based on the technical solutions of the present invention, and detailed implementation processes are given. However, it should be stated that the scope of protection of the present invention is not limited to the following embodiments.
[0025] The following embodiments provide detailed implementation procedures for the technical solutions of the present invention. Unless otherwise specified, the experimental methods used in the following experimental examples are conventional methods; unless otherwise specified, the materials and reagents used are commercially available.
[0026] The chemical composition of the low-grade fluorite ore used in the following examples and comparative examples before pretreatment is shown in Table 1 below.
[0027]
[0028] Example 1
[0029] After crushing and grinding the raw fluorite ore, it was passed through a 200-mesh sieve to obtain the fluorite powder used in this series of experiments. 100g of pretreated fluorite powder was taken and mixed with 50g of 10% dilute sulfuric acid (first portion). The mixture was stirred at 500rpm at 40℃ for 20 minutes, with ultrasonic treatment (300W, 25kHz) twice (2 minutes of operation followed by a 10-minute interval) to complete the first stage of acid leaching. Then, another 50g of 10% dilute sulfuric acid (second portion) was added, and the mixture was stirred at 600rpm at 40℃ for another 40 minutes, with ultrasonic treatment twice during this period to complete the second stage of acid leaching. After the second stage of acid leaching, a solid-liquid mixture was obtained. This mixture was filtered to obtain a filter cake. The filter cake was washed with water until the washing solution was neutral. The washed filter cake was then dried at 110℃ to obtain fluorite concentrate.
[0030] Example 2
[0031] The difference between this embodiment and Embodiment 1 is as follows: First stage acid leaching reaction: Take 100g of pretreated fluorite powder, add 40g of 8% dilute sulfuric acid, and stir at 50℃ and 400rpm for 30 minutes without ultrasound. Second stage acid leaching reaction: Add another 60g of 12% dilute sulfuric acid, and stir at 50℃ and 800rpm for 30 minutes, during which time ultrasonic treatment (400W) is performed 3 times (2 minutes of operation followed by a 15-minute interval).
[0032] Example 3
[0033] The difference between this embodiment and Embodiment 1 is as follows: First stage acid leaching reaction: Take 100g of pretreated fluorite powder, add 60g of 12% dilute sulfuric acid, stir at room temperature (25℃) and 600rpm for 15 minutes, and then ultrasonically treat once (intermittent ultrasonic treatment frequency is 20kHz, power is 500W, working for 1 minute and then resting for 10 minutes). Second stage acid leaching reaction: Add another 40g of 12% dilute sulfuric acid, stir at room temperature and 600rpm for 45 minutes, and then ultrasonically treat twice (intermittent ultrasonic treatment frequency is 30kHz, power is 300W, working for 5 minutes and then resting for 5 minutes).
[0034] Example 4
[0035] The difference between this embodiment and Embodiment 1 is as follows: First stage acid leaching reaction: Take 100g of pretreated fluorite powder, add 35g of 10% dilute sulfuric acid, stir at 40℃ and 500rpm, and sonicate for 15 minutes (intermittent ultrasonic treatment frequency is 20kHz, power is 300W, working for 1 minute and then resting for 10 minutes). Second stage acid leaching reaction: Add another 35g of 10% dilute sulfuric acid, stir at 40℃ and 500rpm, and sonicate for 15 minutes (intermittent ultrasonic treatment frequency is 20kHz, power is 300W, working for 1 minute and then resting for 10 minutes). Third stage acid leaching reaction: Finally, add 30g of 10% dilute sulfuric acid, stir at 600rpm and sonicate for 30 minutes (intermittent ultrasonic treatment frequency is 20kHz, power is 300W, working for 1 minute and then resting for 10 minutes).
[0036] Example 5
[0037] The difference between this embodiment and Embodiment 1 is as follows: First stage acid leaching reaction: Take 100g of pretreated fluorite powder, add 50g of 10% dilute sulfuric acid, and react with a high-speed turbine at 40℃ and 800rpm for 25 minutes (without ultrasound). Second stage acid leaching reaction: Add 50g of 10% dilute sulfuric acid, and react with a turbine at 40℃ and 1000rpm for 35 minutes (without ultrasound).
[0038] The test results of concentrate yield and chemical composition of the obtained fluorite concentrate in Examples 1-5 are summarized in Table 2 below.
[0039]
[0040] As can be seen from the data in Table 2, the low-grade fluorite sulfuric acid purification method for solving the calcium sulfate encapsulation problem provided by this invention, used in Examples 1-5, achieves excellent purification results for low-grade fluorite ore. Specifically, the concentrate yield after purification is >94%, and the CaF2 content in the purified fluorite concentrate is >91 wt%, the SiO2 content is <0.5 wt%, and the CaCO3 content is <0.2 wt%. Compared with the raw fluorite ore, the CaF2 content in the purified fluorite is increased by >4.5%, and the SiO2 removal rate reaches over 50%. This is because under the simultaneous action of "segmented acid leaching," "powerful mechanical stirring," and "intermittent ultrasonic treatment," the silica particles embedded in the fluorite powder are stripped out. Due to their fine particle size (approximately 10 micrometers or less), a large amount of silica can be removed by a hydraulic classifier, resulting in high-purity fluorite with low SiO2 and CaCO3 content, far exceeding the purification limit of the conventional dilute sulfuric acid method.
[0041] Comparative Example 1 The difference between this comparative example and Example 1 is that the pretreated fluorite powder is purified using a traditional one-time acid leaching process. Specifically, 100g of pretreated fluorite powder is taken and 100g of 10% dilute sulfuric acid is added at once, and the mixture is stirred at 40°C and 500rpm for 60 minutes.
[0042] Comparative Example 2 The difference between this comparative example and Example 1 is as follows: First stage acid leaching reaction: Take 100g of pretreated fluorite powder, add 50g of 10% dilute sulfuric acid, and stir slowly at 40°C and 200rpm for 30 minutes. Second stage acid leaching reaction: Add another 50g of 10% dilute sulfuric acid, and stir slowly at 40°C and 200rpm for 30 minutes.
[0043] Comparative Example 3 The difference between this comparative example and Example 1 is that 100g of pretreated fluorite powder was added at once, along with 100g of 10% dilute sulfuric acid. The mixture was stirred vigorously at 40°C and 800rpm without ultrasound for 60 minutes.
[0044] Comparative Example 4 The difference between this comparative example and Example 1 is that 10% dilute sulfuric acid is replaced with 10% dilute hydrochloric acid.
[0045] Comparative Example 5 The difference between this comparative example and Example 1 is as follows: First stage acid leaching reaction: 100g of mineral powder was first mixed with 50g of 10% dilute sulfuric acid, and the mixture was gently stirred at 40°C and 150rpm, relying solely on ultrasonication for 30 minutes. Second stage acid leaching reaction: The remaining 50g of acid was then added, and the reaction was continued under the same conditions for 30 minutes.
[0046] The test results of concentrate yield and chemical composition of the obtained fluorite concentrate in Comparative Examples 1 to 5 are summarized in Table 3 below.
[0047]
[0048] Table 3 shows that the sulfuric acid purification methods used in Comparative Examples 1-5 for low-grade fluorite ore were ineffective. Specifically: Comparative Example 1 showed that the one-time acid addition resulted in extremely high local supersaturation of calcium sulfate, forming a dense coating layer that severely hindered subsequent reactions. CaF2 increase was limited (89.02%), and impurity removal was incomplete (SiO2 0.712%, CaCO3 0.580%). Comparative Example 2 showed that although segmented mixing reduced the initial coating, insufficient stirring intensity failed to effectively break down the formed coating layer, resulting in poor reaction interface renewal. The effect was better than Comparative Example 1 but far inferior to the examples. Comparative Example 3 showed that strong physical perturbation helped break the coating, but the initially formed coating layer was too dense, still limiting acid diffusion to some extent. The effect was better than Comparative Examples 1 and 2, proving the effectiveness of physical perturbation and the necessity of combining it with segmented mixing. Comparative Example 4 shows that, although using hydrochloric acid instead of sulfuric acid results in higher calcium hydrochloride solubility and no encapsulation issues, leading to more thorough removal of CaCO3, Cl... - This method causes severe corrosion to equipment, is costly, and has almost no effect on removing SiO2, making its overall performance inferior to the synergistic sulfuric acid method provided by this invention. The results of Comparative Example 5 show that while ultrasound is effective in microscopic local areas, the lack of macroscopic overall stirring prevents sufficient convective mixing of mineral particles and acid, leading to uneven treatment and poor results. This demonstrates the necessity of combining mechanical stirring with ultrasound.
[0049] A comprehensive comparison of the test results of Examples 1-5 and Comparative Examples 1-5 shows that the low-grade fluorite sulfuric acid purification method for solving the calcium sulfate encapsulation problem provided by this invention, based on a synergistic encapsulation breaking mechanism, creatively combines three methods—"segmented acid leaching," "powerful mechanical stirring," and "intermittent ultrasound"—to produce a significant synergistic effect. Specifically, the segmented acid leaching process avoids excessive local supersaturation caused by a single addition of acid, reducing the rapid crystallization of calcium sulfate and the thickness of the initial encapsulation layer. The powerful mechanical stirring process provides strong fluid shear force, macroscopically scouring, peeling, and breaking down the already formed large blocky or sheet-like encapsulation layers. The intermittent ultrasound process utilizes the "cavitation effect" generated by ultrasound in liquids to form local high-temperature, high-pressure shock waves and microjets, effectively breaking down the dense calcium sulfate crystal structure at the microscale and releasing its "locking" state on the fluorite particles. These three methods work synergistically to form a multi-level, three-dimensional encapsulation breaking system of "prevention-macroscopic breaking-microscopic cracking," fundamentally solving the problem of reaction kinetic hindrance.
[0050] Furthermore, the low-grade fluorite sulfuric acid purification method provided by this invention, which solves the problem of calcium sulfate encapsulation, is economical and environmentally friendly. The entire process uses inexpensive dilute sulfuric acid as the main reagent, without introducing expensive or toxic chemical additives. The process is simple, the conditions are mild, it is easy to industrialize, and it offers significant cost advantages while being environmentally friendly.
[0051] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for purifying low-grade fluorite sulfuric acid to solve the problem of calcium sulfate encapsulation, characterized in that, Includes the following steps: S1, Raw material pretreatment: First, the low-grade fluorite ore is crushed and ground, and then magnetic separation is performed to remove iron, so as to obtain pretreated fluorite powder. S2, Segmented acid leaching reaction: Dilute sulfuric acid with a mass concentration of 5~15wt% is added in segments to the pretreated fluorite powder described in S1, and a solid-liquid mixture is obtained after the segmented acid leaching reaction is completed; the total amount of dilute sulfuric acid used is in a mass ratio of 0.8~1.2:1 to the pretreated fluorite powder. S3, Post-processing: The solid-liquid mixture described in S2 is separated by gravity to obtain underflow; the underflow is then filtered, washed, and dried to obtain fluorite concentrate.
2. The method for purifying low-grade fluorite sulfuric acid to solve the problem of calcium sulfate encapsulation according to claim 1, characterized in that, The low-grade fluorite ore described in S1 contains 85-88 wt% CaF2, 0.8-0.9 wt% SiO2, 0.8-0.9 wt% CaCO3 and 1.4-1.5 wt% Fe2O3, with the balance being other impurities.
3. The method for purifying low-grade fluorite sulfuric acid to solve the problem of calcium sulfate encapsulation according to claim 1, characterized in that, The low-grade fluorite ore described in S1 is crushed and ground to obtain fluorite powder with a particle size of less than 200 mesh.
4. The method for purifying low-grade fluorite sulfuric acid to solve the problem of calcium sulfate encapsulation according to claim 1, characterized in that, The segmented acid leaching reaction described in S2 is divided into 2 to 3 stages. The reaction conditions for each stage of the acid leaching reaction are: stirring at a stirring rate of 300 to 1000 rpm at 20 to 60°C for 10 to 50 minutes.
5. The method for purifying low-grade fluorite sulfuric acid to solve the problem of calcium sulfate encapsulation according to claim 4, characterized in that, The reaction conditions for each stage of the acid leaching reaction may be the same or different. The reaction conditions include stirring at a stirring rate of 300-800 rpm at 20-60°C for 10-30 minutes, or stirring at a stirring rate of 400-1000 rpm at 20-60°C for 20-50 minutes.
6. The method for purifying low-grade fluorite sulfuric acid to solve the problem of calcium sulfate encapsulation according to claim 4, characterized in that, When the segmented acid leaching reaction is divided into two stages, the amount of dilute sulfuric acid used in the first stage of the acid leaching reaction accounts for 40-60 wt% of the total amount of dilute sulfuric acid, and the remaining dilute sulfuric acid is used in the second stage of the acid leaching reaction; when the segmented acid leaching reaction is divided into three stages, the amount of dilute sulfuric acid used in the first stage of the acid leaching reaction accounts for 30-40 wt% of the total amount of dilute sulfuric acid, the amount of dilute sulfuric acid used in the second stage of the acid leaching reaction accounts for 30-40 wt% of the total amount of dilute sulfuric acid, and the remaining dilute sulfuric acid is used in the third stage of the acid leaching reaction.
7. The method for purifying low-grade fluorite sulfuric acid to solve the problem of calcium sulfate encapsulation according to claim 4, characterized in that, Intermittent ultrasonic treatment is applied during at least one acid leaching reaction or between two adjacent acid leaching reactions.
8. The method for purifying low-grade fluorite sulfuric acid to solve the problem of calcium sulfate encapsulation according to claim 7, characterized in that, The intermittent ultrasonic treatment has a frequency of 20~40kHz and a power of 100~500W, and adopts a mode of working for 1~5 minutes and intermittent for 5~15 minutes.
9. The method for purifying low-grade fluorite sulfuric acid to solve the problem of calcium sulfate encapsulation according to claim 1, characterized in that, The washing liquid used in S3 includes water, and the washing is carried out until the washing liquid is neutral; the drying temperature is 100~110℃.
10. A fluorite concentrate obtained by purifying low-grade fluorite using the method for solving the calcium sulfate encapsulation problem as described in any one of claims 1 to 9.