The current practice for the production of wet-process phosphoric acid (H3PO4) involves leaching beneficiated phosphate rock in the presence of aqueous sulfuric acid (H2SO4). Typical processing involves mining the ore and beneficiating through sizing and flotation to produce a “phosphate rock” concentrate containing over 29 pct P2O5. This concentrate is ground to 90 pct minus 75 µm and leached to dissolve the phosphate.

Apatite, Ca5(PO4)3(F, Cl, ½CO3, OH), is the primary phosphate mineral in the phosphate rock. During leaching the apatite is solubilized as H3PO4 and the calcium content of the apatite is precipitated as calcium sulfate. In addition, any impurities in the ore are usually solubilized; the most common impurities are iron, aluminum, and magnesium. When iron or aluminum is present in a crude acid in sufficiently large quantities, concentration of the acid to obtain a 55 pct P2O5 product may result in the precipitation of insoluble compounds, such as Fe3KH14(PO4)8 or Al3KH14(PO4)8. These insoluble compounds limit the available phosphate and thereby render the product acid less suitable as a fertilizer precursor. Large amounts of magnesium may increase the viscosity of product acids to undesirable levels and also may form insoluble precipitates with phosphate during the preparation of final products. Therefore, the amount of solubilized metals must be kept at a minimum. The rule of thumb used by the industry is that the R2O3/P2O5 weight ratio, where R2O3 represents the sum of Fe2O3 and Al2O3, should be less than 0.1. Currently, no threshold limits for Mg content in product acids have been established by the industry. In general, the MgO/P2O5 weight ratio should be less than 0.03. With these requirements, many deposits containing high amounts of Fe, Al, and Mg are not useable, even though they contain significant amounts of phosphate.

The Bureau of Mines has investigated a leaching technique using a methanol-H2SO4 technique to reject metal impurities during the leaching process. Research using this technique has been conducted on a variety of phosphate ores and wastes from Florida and Idaho. Phosphate extractions varying from 65 to 88 pct have been obtained, but complete extraction of phosphate was not obtained even when using excess H2SO4 and long reaction times. Earlier research has shown that a calcium sulfate coating forms on the reacting phosphate particles which eventually forms a barrier that prevents further leaching. High extractions can be obtained by lowering the particle size of the phosphate rock, but grinding is very energy intensive and adds a significant cost to the operation. The reaction kinetics of phosphate leaching by the acid-alcohol process can be evaluated to determine the optimum particle size required for leaching, minimizing the amount of grinding necessary for high extraction of the phosphate.

Several kinetic models have been developed for systems in which small particles are leached and a product barrier layer forms on the particle surfaces. The Bureau has applied these models to develop a leaching model for acid-alcohol leaching of phosphate.

Description of Kinetics Model

Aqueous Sulfuric Acid Dissolution

The mechanism of phosphate leaching with aqueous sulfuric acid is fairly well understood. The reaction occurs in three steps: (1) Sulfuric acid dissociates forming H+ ions and SO4²- ions in the solution. (2) The H+ ions attack the apatite particles dissolving Ca²+, CaPO4-, and PO4³- ions into the solution. And (3), the two Ca-bearing ions encounter SO4²- ions and calcium sulfate precipitates out of the solution. The reaction rate is controlled by the rate of H+ ions attacking the surface of the apatite. Initially, H+ ions freely attack the particle surface, accompanied by the formation of a very fine precipitate of calcium sulfate. As more Ca²+ becomes available from the dissolution reaction, the fine crystals of gypsum or hemihydrate continue to grow. The apatite dissolution kinetics determines the rate of Ca²+ dissolution which allows the calcium sulfate crystals to grow in size. Some of these crystals attach to the apatite particle. As these crystals grow, eventually they will surround the apatite particle. At this point, the H+ ions must diffuse through space between these calcium sulfate crystals to reach the apatite surface. In addition, the dissolved Ca²+, CaPO4-, and protonated PO4³- ions must also diffuse between these crystals to reach the solution. Eventually the space between the calcium sulfate crystals will become small enough to effectively prevent the H+ ions from attacking the remaining apatite and also prevent the dissolved ions from leaving the apatite surface and entering the bulk solution.

In H3PO4 acid production all three reactions, dissociation of H2SO4, dissolution of Ca²+ and PO4³- ions, and precipitation of CaSO4, take place simultaneously in the reactor. Normally, the phosphate rock is ground to below 75 µm so that 95 pct dissolution is obtained in less than 5 min (1); however, the total retention time in the reaction vessels is generally 4 to 6 h. The gypsum recrystallization is the slowest controlled reaction (1). As the Ca²+ ion diffuses from the solid surface into the liquid, it is immediately surrounded by the available SO4²- ions in solution and on the surface of crystallized calcium sulfate. The crystal sites offer a more stable position for both the Ca²+ and SO4²- ions, but the attachment into the crystal lattice is the preferred process. Formation of large crystals is desired to ensure efficient filtration of the phosphoric acid solution from these waste solids. The sulfate level is controlled to encourage large crystal formation at the expense of slow rates.

Acid-Alcohol Dissolution

The acid-alcohol reaction is somewhat similar to the aforementioned aqueous sulfuric acid leaching reaction, but the solvent is methanol instead of water. The balanced reaction for apatite containing fluoride is:

The calcium sulfate crystallizes in the hemihydrate form. These calcium sulfate crystals form a barrier layer as the reaction proceeds that effectively prevents further dissolution of the apatite particle. This reaction can be modelled using the unreacted- core model. In this model the reactant particles are assumed to be spherical, as shown in figure 1. As the reaction proceeds, a reaction product is deposited at the surface of the reactant particle forming a porous layer surrounding the unreacted particle. The reaction proceeds until the unreacted particle is consumed leaving a porous reaction product of the same particle size. Applying this model to the acid-alcohol reaction, the kinetics would be determined by two phenomena: 1) the actual dissolution of the apatite particle by acid, and 2) the diffusion of H+ ions from the solution to the surface of the unreacted particle and the diffusion of the dissolved Ca²+, CaPO4-, H2PO4-, HPO4²-, and PO4³- ions from unreacted particle surface to the solution. Either of these could be rate- controlling at some point during the reaction.

Dissolution Reaction Kinetics

At the surface of the unreacted core, the quantity of phosphate reacting is proportional to the available surface of the unreacted core. Consequently, the rate of reaction for dissolution is

where phos is the moles of unreacted apatite still undissolved from the original apatite particle, rc is the radius of the unreacted core, Kp is the rate constant for the surface reaction of the apatite, and CH is the concentration of H+ ions at the surface. The amount of unreacted apatite can also be expressed in terms of the unreacted core size.

Levenspiel transformed the rate equation to provide phosphate extraction as a function of time.

where Xphos is the extraction of phosphate, Pp is the molar density of the apatite particle, and Ri is the initial radius of the apatite particle.

Diffusion Reaction Kinetics

At some point during the reaction, the calcium sulfate crystals on the surface of the unreacted particle create a barrier sufficient to slow down ion diffusion. Thus, the overall reaction rate becomes controlled by the rate of ion diffusion to and from the unreacted apatite surface. The rate of H+ ion diffusion at any point r between the initial particle surface and the unreacted particle surface becomes

where pc is the porosity of the calcium sulfate crystals surrounding the unreacted particle, De is the effective diffusion coefficient of the region between the calcium sulfate crystals, and d(-CH)/dr is the concentration gradient driving the diffusion of the H+ ions toward the surface of the apatite. The diffusion rate of H+ ions actually depends upon the diffusion of the product anions and molecules such as CaPO4-, H2PO4-, HPO4²-, HCaPO4, and H3PO4. As these relatively large anions and molecules diffuse towards the bulk solution, the calcium sulfate crystals slow down the diffusion. As the diffusion of these product anions and molecules away from the apatite surface becomes restricted, the concentration of these anions and molecules increases near the surface of the apatite. As the concentration of these ions increase at the apatite surface, the concentration of free H+ ions decreases because the H+ ion is tied up in the protonated anion species. The high ionic strength of this highly concentrated region near the apatite surface prevents additional H+ ions from diffusing into this region surrounding the apatite particle. The net effect is to lower the concentration of available H+ ions to zero, because nearly all of the H+ ions are tied up with the dissolved anions near the apatite surface. Therefore, the rate of H+ ions diffusing into this region is proportional to the rate of diffusion of all the product anions and molecules carrying the H+ complexes out of this region. Between the calcium sulfate crystals surrounding the apatite particle, the effective diffusion coefficient remains constant throughout the region; however, the porosity of the region between the calcium sulfate hemihydrate crystals depends upon the growth size of the crystals. As the crystals grow the porosity decreases until the crystals effectively seal up the unreacted apatite particle. The rate of calcium sulfate hemihydrate crystal growth is considered to be slow and steady throughout the reaction process.

During the reaction controlled portion of the dissolution process, the rate of calcium sulfate hemihydrate precipitation upon those crystals already attached to the apatite surface is only a fraction of the calcium sulfate hemihydrate being precipitated in the solution. Over the time frame of interest, the rate of calcium sulfate hemihydrate precipitation on the apatite surface can be approximated as a constant. Thus the porosity is linearly proportional to the reaction time.

where Kc is the rate of calcium sulfate hemihydrate crystal growth. According to Levenspiel (4), transforming equations 4 and 5 will give the degree of phosphate extraction for the diffusion controlled reaction.

Again the reaction time becomes a function of the degree of phosphate extraction and the initial apatite particle size.

Combined Reaction and Diffusion Kinetics Model

Both reaction and diffusion kinetics contribute to the overall reaction kinetics. Both steps of the process offer resistance to the overall reaction and these resistances act in series because the reaction is sequential. Combining the reaction resistance with the diffusion resistance, the overall kinetics equation becomes

Equation 7 must be integrated from rc = Ri and t = 0 to rc = rc and t = t to obtain time as a function of the unreacted radius. The integration can be approximated using the method of finite differences to solve for t in terms of rc. The calculation sequence proceeds as listed below:

Step

1. t = 0 and rc = Ri
2. A small finite value of Δrc is selected such as Δrc = 0.01 µm.
3. rc = rc – Δrc……………………………………….(8)
4. The Δt required to obtain the Δrc degree of leaching is obtained from equation 21.
   
5. The total reaction time becomes
   t = t + Δt……………………………………………………….(10)
6. The degree of phosphate extraction becomes
   
7. Steps 3 through 7 are repeated until the Xphos reaches the desired level.

Then t represents the total reaction time required to obtain that level of phosphate extraction. As long as Δrc remains very small, this technique will simulate the continuous integration of equation 7.

Preparation and Description of Sample

Since apatite is the dominant phosphate-containing mineral in the phosphate ores (1), a research-grade apatite was obtained from Ward’s National Science Establishment, Inc. The sample was crystalline apatite from a deposit in Ontario. The sample pieces ranging from ½ to ¾ in. in size were hand picked to obtain pure apatite. The apatite was ground in a rotary mill and wet screened at 150, 86, 75, 53, and 38 µm. The four narrow size fractions and the minus 38 µm apatite were used in this research. Each of the narrow size fractions of apatite were used to simulate the leaching of one uniform particle size. A chemical analysis of the apatite sample is shown in table 1.

XRD indicated that these pure apatite crystals were primarily fluorapatite. Based upon the chemical reaction, the stoichiometric sulfuric acid-to-apatite molar ratio for leaching is 5:1.

Equipment and Procedures

Leaching experiments were individually conducted on each size fraction of apatite, in a 3-neck, 500-mL, round-bottom flask, equipped with an overhead mixer and reflux condenser. A Metrohm 665 dosimat was used to add 56 mL of 93-pct H2SO4 to 200 mL of methanol over a 30-min period. An ice bath was used to absorb the heat of solvation generated as the H2SO4 was added to the methanol. The temperature of the solution was kept below room temperature to prevent H2SO4 ions from reacting with the methanol. Prior to the addition of the ore, the solution was raised to room temperature. The apatite charge was dumped into the solution all at once to begin the leaching test. Timed aliquots of slurry were removed from the flask at 1, 2, 4, 16, 32, 64, and 90 min. Each 5-mL aliquot sample was immediately centrifuged at 3,400 rpm to separate the solids from the leach solution. A sample of the clear leach solution was removed for chemical analysis and the reaction time for that sample was recorded to include the time in the centrifuge. After 90 min, the slurry remaining in the flask was vacuum-filtered on Whatman No. 3 filter paper using a laboratory aspirator. The filter cake was washed twice with 75-mL aliquots of methanol and re-filtered.

After washing, the filter cake was dried in an oven at 110° C. The liquor from each timed aliquot was analyzed for PO4³- and SO4²- ions using a Dionex 2002i ion chromatograph equipped with an AS4A column. Elemental analyses were obtained on the final tailings. Phosphate extractions were calculated using the final tailing phosphate analysis and the final PO4³- liquor concentration. The linear relationship between the PO4³- concentration in the solution and phosphate extraction was used to determine the phosphate extractions at each sample time. In addition, the depletion of SO4²- ions that formed the calcium sulfate precipitate was also monitored.

Results and Discussion

For each of the narrow size fractions of apatite, the plot of phosphate extraction versus time, shown in figure 2, shows faster extraction as the particle size decreases. The data was compared with the reaction kinetics model of equation 3. Figure 3 shows the reaction kinetics model and the results from each size fraction. The actual results lie fairly close to the model curves generated for each particle size fraction. After some time, the rate of extraction declines until the reaction appears to slow down significantly. According to equation 2, the depth of leaching is linearly proportional to the reaction time. Figure 4 shows how closely the initial reaction data fits this model concept. The slope of the plot is proportional to the reciprocal of the reaction rate constant (Kp). This rate constant is independent of the particle size. Figure 4 also shows that the reaction kinetics control the reaction speed until the reaction depth is around 5 µm. At this point, the barrier layer of calcium sulfate is thick enough to begin controlling the reaction kinetics. The rate of phosphate leaching slows down at this point, reflecting slower diffusion of ions through the calcium sulfate layer.

Similar regression analysis was performed on the data using the diffusion controlled system of equation 6. Figure 5 shows that the diffusion-controlled kinetics do not fit the initial reaction data, but may more closely fit the data at later reaction times.

Based upon equation 7, the reaction and diffusion kinetics both contribute to the dissolution rate during leaching, but to various degrees depending upon the stage of leaching. The finite differences approximation technique was used to solve this equation. This technique mathematically followed the equation from rc = Ri at time = 0 to any rc which corresponds to a calculated degree of phosphate extraction and the total reaction time. Regression analysis with this technique is virtually impossible. An alternative technique utilizing a “genetic algorithm” regression method was used to find the constants associated with the reaction, diffusion, and calcium sulfate crystallization constants. By this technique the best “least squares error” solution was obtained and figure 6 shows how closely the equation fits the data.

The reaction kinetics prevail in the early stages of the dissolution. However, as the calcium sulfate hemihydrate layer forms to a leaching depth greater than 5 µm, the diffusion kinetics begin to control the reaction. This causes the rate of phosphate extraction to slow down considerably as the barrier layer of calcium sulfate effectively prevents further dissolution of the apatite particle.

The reaction, diffusion, and calcium sulfate crystallization constants from this research can be used along with equation 7 to predict the extraction of an ore sample by the acid-methanol method. Using a size analysis of the ore, the kinetics of each size fraction can be individually calculated and mathematically combined to predict the overall extraction of the ore. For example, the minus 38-µm sample of ground apatite was also leached in this kinetic study. Figure 7 shows the results along with the predicted leaching response from equation 7. When only the mean particle size was used to predict the response, the data does not fit very closely. However, if the measured size distribution shown in table 2 is individually used in the kinetics equation, the predicted response is a better fit to the measured data.

Conclusions and Recommendations

The leaching mechanism for acid-alcohol dissolution of phosphate is somewhat similar to conventional aqueous acid dissolution of phosphate. Initially, the rate of phosphate dissolution is controlled by the reaction kinetics of phosphate dissolution. This reaction rate is a function of the exposed surface area of the particles. As the reaction proceeds, calcium sulfate hemihydrate is precipitated in the solution and on the surface of the apatite particle. When the depth of leaching from the original particle surface to the unreacted surface exceeds 5 µm, the rate of phosphate dissolution is dominated by the rate of diffusion of both the reacting H+ ions and the dissolved Ca²+, CaPO4-, H2PO4-, HPO4²-, and PO4³- ions that move through the precipitated calcium sulfate hemihydrate crystals. The calcium sulfate hemihydrate barrier layer continues to recrystallize into a dense mat of crystals that effectively slows down the rate of dissolution. The rate of diffusion is significantly slower than the rate of dissolution and effectively stops the dissolution of phosphate.

The reaction kinetics of the acid-alcohol phosphate dissolution are significantly slower than the conventional aqueous acid process. The dissolution rate of the aqueous acid process is believed to be completed after 10 min with a minus 75 µm ground phosphate rock; however, 4 to 6 h are required to obtain coarse gypsum crystals for effective filtration of the product acid. The reaction kinetics of the acid-alcohol phosphate dissolution requires about an hour to dissolve nearly all of the minus 38 µm ground apatite. These slower dissolution kinetics will require finer grinding of the rock to prevent the formation of a barrier layer before the dissolution reaction is complete. A barrier layer around 5 µm deep appears to have a significant effect upon the leaching kinetics. Therefore, particles above 10 µm diameter will not be completely leached before the kinetics begin to slow down. Furthermore, the formation of this barrier layer is directly proportional to the reaction time, indicating that virtually all of the dissolution must take place in the first hour of the reaction. At 1 h, the depth of leaching approaches 5 µm indicating the formation of a significant barrier layer. Therefore, phosphate rock grinding should be optimized to produce a ground product near 10 µm size, for complete dissolution of the apatite.