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Brazilian Journal of Chemical Engineering

Print version ISSN 0104-6632On-line version ISSN 1678-4383

Braz. J. Chem. Eng. vol. 14 no. 2 São Paulo June 1997 

Mechanism and Kinetics for the Dissolution of Apatitic Materials in Acid Solutions


C.E. Calmanovici1, B. Gilot2 and C. Laguérie2

1 RHODIA S.A. Research Center of Paulínia - 13140-000, Paulínia, Brazil.
2 Laboratoire de Génie Chimique, URA CNRS 192 - ENSIGC, Toulouse, France.


(Received: August 18, 1996; Accepted: February 3, 1997)


ABSTRACT - This work concerns the study of the digestion step in the production process of phosphoric acid. Some qualitative experiments indicate that the difference between the pH at the surface of the phosphate and that in the bulk of the solution is negligible and that the dissolution is controlled by diffusion of products away from the phosphate particle. In further experiments, to isolate the dissolution phenomenon from the formation of calcium sulfate, the sulfuric acid normally used industrially is replaced by hydrochloric acid. The phosphate material used in our experiments is a model apatitic material: synthetic hydroxyapatite (HAP). The dissolution of calcium hydroxyapatite was studied with increasing amounts of calcium and phosphate at different temperatures. A simple method was developed for this observation based on the time required for complete dissolution of the HAP powder. The results confirm that the dissolution is controlled by a diffusional process through an interface of calcium and phosphate ions released from the solid surface. A kinetic model for the dissolution of apatitic materials is proposed which assumes a shrinking particle behaviour controlled by diffusion of calcium ions. The experimental results are fitted to this model to determine the mass transfer constant for HAP dissolution in acid solutions. The activation energy of the reaction is about 14kJ/mol. This study was carried on in conditions similar to the industrial ones for the production of phosphoric acid by the dihydrate-process.
KEYWORDS: Kinetics, apatitic material, dissolution.



Heterogeneous non-catalytic reactions play a major role in the chemical industry. This kind of reaction is found in various fields such as mineral leaching or precipitation. According to Szekely et al. (1976), the overall reaction process between a solid and a liquid may involve the combination of specific resistances represented by the following steps:

1) diffusion of reactants: mass transfer of reactants from the bulk of the solution to the external surface of the solid particle;
2) diffusion of reactants through the pores of the solid matrix;
3) adsorption of reactants on the surface of the solid matrix;
4) chemical reaction at the surface of the solid matrix;
5) desorption of products from the surface of the solid matrix;
6) diffusion of products through the pores of the solid matrix;
7) diffusion of products: mass transfer of products from the external surface of the solid to the bulk of the solution.

These are consecutive steps and, therefore, the slowest one will be rate controlling for the overall reaction.

The dissolution of phosphate rocks (apatite forms) in acid solutions is essentially a solid-liquid surface reaction and therefore matches the above-mentioned category of heterogeneous non-catalytic reactions. Over the last two decades, the dissolution of synthetic or natural apatitic materials has been extensively studied (Thomann et al., 1991; Zhang and Nancollas, 1991). This is understandable when the important role of these minerals for agriculture and the biological sciences is considered. Phosphoric acid, the major component of many fertilizers, is mainly produced by digestion of phosphate ore by strong acids, in the so-called wet processes.

This paper concerns the study of the digestion step in the production process of phosphoric acid. Over 90% of the phosphoric acid produced worldwide is manufactured by digestion of phosphate rock by sulfuric acid; phosphoric acid is then separated from the resultant calcium sulfate slurry by filtration (Becker, 1989). This is the case of the dihydrate process in which calcium sulfate is separated mainly as gypsum. As there are sulfate ions in solution, a solid product, i.e., calcium sulfate, is formed simultaneously with the digestion of the phosphate. This solid formation (crystallization) creates a solid-solid-liquid system (phosphate-calcium sulfate-solution) which is much more complicated to deal with than the basic solid-liquid system. The complexity of the system is even more important since the calcium sulfate produced may form solid layers around the phosphate particles (coating phenomenon) and block, either partially or completely, the development of the reaction (Becker, 1989). Therefore, the industrial system must be simplified in order to be studied.



To isolate the dissolution phenomenon in order to study it separately from the calcium sulfate formation, we have replaced the sulfuric acid with hydrochloric acid. To avoid any influence of impurities, the phosphate material used in our experiments is synthetic pure hydroxyapatite (HAP), a model apatitic phosphate.


Hydroxyapatite Preparation

The HAP used in the experiments (supplied by Sociète Bioland, France) was prepared by a method based on the reaction, in aqueous solution, of ammonium phosphate [(NH4)2HPO4 or (NH4)H2PO4] with calcium nitrate Ca(NO3)2.4H2O, according to:

10 Ca(NO3)2.4H2O(s) + 20 NH3(aq) +
+ 6 H3PO4(aq) Ca10(PO4)6(OH)2(s) +
+ 20 NH4NO3(aq) + 38 H2O(l)

In the first step, an aqueous solution of tetrahydrated calcium nitrate is neutralized by a mixture of phosphoric acid and ammonia. Once the pH equals 9, the mixture is agitated for 5 to 6 hours. The precipitated HAP is then filtred, dried at 100 °C and calcined at 900 °C. The HAP obtained consists of fine agglomerates with a specific surface area of 27 m2/g. The shape of the agglomerates may be approximated by a sphere. The HAP obtained is 98 % pure. The powder particle size distribution was analysed by means of a Malvern analyser (laser diffraction). The mean size diameter was found to be 65 µm and the biggest particles have diameters of around 160 µm.


Determination of the Rate Controlling Step

Several publications concern the dissolution of apatitic minerals, although no agreement has been achieved about its mechanism. According to Van der Sluis et al. (1987), three different rate-controlling steps have been proposed: diffusion of calcium ions away from the particle, diffusion of hydrogen ions towards the particle, and chemical reaction of the acid with the ore.

Influence of the Hydrodynamics on the Dissolution of HAP
HAP crystals were placed with acid solutions in an agitated cell to verify the influence of the stirring rate on the dissolution kinetics.

- Description of the experiments:
The experimental apparatus is presented in figure 1. Agitation is supplied by a three-blade propellor stirrer. A weighted stoichiometric amount of HAP is introduced into the cell with a 5 % excess of hydrochloric acid. The conditions into the cell are quite dilute: 1.5 % of solids in mass. Two different amounts of phosphate in the liquid phase are considered by addition of phosphoric acid to the solution. The time for complete dissolution of the HAP powder, td, is measured by observation with the naked eye. All experiments are achieved at 75°C.

- Results and discussion
The results are summarized in figure 2 which shows the time for complete dissolution of HAP versus the agitation rate. The time for complete dissolution, td, is inversely proportional to the mean dissolution rate for one run, , according to the equation:


In both cases studied (with and without the addition of phosphoric acid), the time required for complete dissolution decreases as the stirring rate increases up to about 1500 rpm. From 1500 rpm upwards the influence of the agitation on the dissolution rate becomes negligible. This means that up to this agitation rate the reaction is controlled by the diffusion of ions towards or away from the HAP particle. The power consumption corresponding to the diffusion-controlled region, ranges from 0.2 to 2.5 W/kg. The phosphoric acid reactor is industrially operated within these conditions (around 1.0 W/kg).

Study of the pH at the Surface
The reaction of HAP in hydrochloric acid solutions was studied in the presence of acid-base indicators in order to verify the rate-controlling step.

When hydroxyapatite reacts with an acid, H+ ions are consumed at the solid surface. As a consequence, pH should increase locally. This increase in the pH value is even more significant if the diffusion of H+ ions is the rate-controlling step. We now describe a test that allows us to study the reaction on the HAP surface, by means of an acid-base indicator.

- Description of the experiments
Experiments were performed at ambient temperature (20 oC) as follows: a drop of acid solution containing the acid-base indicator was dropped on a big piece of compacted HAP of about 10 mm. The colour of the solution was then observed. The reaction was observed under a magnifying glass (magnification of 3 to 4 times). Two acid solutions were used:

a - solution containing 1.5 mass % of HCl;
b - solution containing 1.5 mass % of HCl and 38.6 mass % of H3PO4.

The experiments were carried out at ambient temperature (20 °C). The acid-base indicators are presented in table 1.



1 - jacketed thermostated cell (100 ml)
2 - agitator
3 - light spot
4 - support for light spot

Figure 1: Apparatus for dissolution experiments.


Figure 2: Complete dissolution time, td, as a function of the agitation rate, N, with 0 mass % of H3PO4 and with 38.6 mass % of H3PO4 at 75 oC.


Table 1: Acid-base indicators used in the experiments (Charlot, 1967)



End point



Thymol blue red yellow


Methylorange red yellow-orange


Bromocresol green yellow blue



- Results and discussion
The observation of the apatite/acid reaction shows that the solution keeps its acid colour for all situations studied. Dissolution of HAP actually occurs since the size of the solid decreases. The increase in the pH due to the reaction is not, however, sufficiently important to be detected by changes in the colour of the solution.

When the acid solution and the hydroxyapatite surface are in contact, the pH of the solution remains under 1.2-2.8. We may therefore conclude that the concentration of H+ ions at the surface of the apatite is quite important. If the reaction were controlled by H+ diffusion towards the surface of the apatite, the concentration of this ion should tend to zero at the solid surface. The very acid pH observed at the solid surface allows us to conclude that: H+ ions accumulate at the surface of the apatite, the difference between the pH at the solid-liquid interface and that of the bulk of the solution is negligible and the apatite/acid reaction is not controlled by diffusion of H+ towards the solid surface.

Partial conclusion
As observed above, the reaction between HAP and acid solutions is controlled, to some extent, by diffusion, in the industrial range of agitation. On the other hand, this reaction is not controlled by diffusion of H+ towards the solid surface. Therefore, the controlling step of the process should be the diffusion of products (calcium and/or phosphate) from the solid-liquid surface to the bulk of the solution.


Determination of HAP Dissolution Kinetics

In this part of the study, we varied the composition of the liquid phase in the reactor and the temperature of the system. Experiments were carried out in the same way as described in 2.2.1 but stirring rate was fixed at 600 rpm.

Increasing amounts of calcium were established by adding calcium chloride (CaCl2.2H2O) to the solution. Similarly, increasing amounts of phosphorous were considered by addition of phosphoric acid to the solution. Temperature was varied in the range of 50 to 75 °C.

- Results and discussion
The results presented in figure 3 show the evolution of the complete dissolution time, td, versus the initial total calcium content in liquid phase, [Ca]0, at 75 oC. The total calcium content, [Ca], is a convenient representation of concentration data since it considers all calcium-containing species, ion complexes included. As may be observed in figure 3, an increasing amounts of calcium slows down the dissolution rate since it increases the time for complete dissolution. The same trend is observed even in the presence of phosphoric acid. On the other hand, the presence of phosphoric acid shows an analogous effect on the dissolution kinetics.

A shrinking particle model (Levenspiel, 1972) may apply to the results presented above. Considering that the rate of the reaction is controlled by diffusion of calcium ions away from the solid surface, the calcium concentration at the surface of the HAP, [Ca]sat, should be constant during the reaction of the particle for a fixed temperature and corresponds to the solubility of HAP crystals. The dissolution of HAP crystals in acid solutions may be represented by the simplified chemical expression:

Ca10(PO4)6(OH)2 + 20 H+ 10Ca+2 +

+ 6H3PO4 +2H20 (i)

If the HAP particles are taken to be spherical, the following equation applies for the transport of calcium ions from the solid surface to the bulk of the solution:


where  [Ca] = [Ca]sat - [Ca]

Figure 3: Evolution of the complete dissolution time, td, as a function of the initial total calcium content in solution, [Ca]0, with 0 mass % of H3PO4 and with 38.6 mass % of H3PO4 at 75 oC and 600 rpm.



For one HAP particle, supposing constant density during dissolution, one can write:


By combining equations (2) and (3), we obtain the rate of the reaction, D, in terms of the shrinking radius of the particle:


It represents a numerical model for HAP crystals dissolution in acid solutions and may be integrated to determine the time for complete dissolution,td. But, since calcium concentration in the liquid phase varies during an experiment, we must first combine equation (4) with the calcium mass balance in the liquid phase which may be written as follows:


The mass transfer coefficient, kd, depends on the size of the dissolving particle and it has been correlated to fluid dynamics by various authors. Brian and Hales (1969) propose a correlation established for the dissolution of solids in agitated tanks. According to this correlation, the following equation applies:

kd = kc r-0.5213 (6)

where kc is an auxiliary coefficient independent of the size of the particles.

Let's suppose now that all particles in the system have the same size and that the number of particles remains constant throughout each dissolution experiment. In this case, by combining equations (4) to (6) with some additional mathematical operations, we obtain:


where r0 is the initial radius of the particles and is the initial mass of HAP introduced in the system.

Considering the initial calcium mass fraction in the liquid phase, [Ca]0, the mass balance from equation (5) may be integrated to give:


Substituting equation (8) in (7), we obtain the expression for the change in calcium concentration in the liquid phase with time.


This last equation may be integrated numerically and the results compared with those of the experiments in order to identify both unknown parameters kc and [Ca]sat.

The boundary conditions for the integration of equation (9) are:

The experimental results for the final calcium content in the liquid phase, [Ca]f, have been fitted to the numerical values obtained by integration of equation (9) and the two unknown parameters kc and [Ca]sat could be determined by the Gauss-Newton algorithm (least square method). Experimental and calculated values differ by no more than 1 %. This quite low deviation confirms the model adopted for dissolution process.

From equation (6) and with the calculated value of kc one may determine the mass transfer coefficient, kd, for the total dissolution experiments (td corresponds to the time of dissolution of the biggest particles since they are the last to disappear). In our case, the particle size is 160 µm.

In this way, kd values were determined for different temperatures in the range 50 to 75 °C. The results are presented in table 1 with 95 % confidence levels. These results are in good agreement with data concerning the dissolution rate of a commercial apatite in phosphoric acid solutions (Van der Sluis et al., 1987).

The results of the mass transfer coefficient are also shown in graphic form in figure 4 and it may be observed that the points fall around a straight line. Then, the Arrhenius equation (Denbigh, 1981) can be used to calculate the activation energy for the reaction between HAP and acid solutions. The value of the activation energy is found to be equal to 14 kJ/mol. This low value is consistent with the proposed diffusion-controlled mechanism.


Table 2: Mass transfer coefficient results (m/s) for different temperatures and phosphoric acid concentrations


without phosphoric acid
(x 10

with 38.6 mass % of H3PO4
(x 10+5)

50 °C

1,5 ± 0,4

1,6 ± 0,8

65 °C

1,9 ± 0,7


75 °C

2,2 ± 0,3

2,4 ± 0,6


ln (kd*10+5)

Figure 4: Variation of the logarithm of kd with the reciprocal of the absolute temperature.


Since the mass transfer coefficient is usually estimated by correlations involving dimensionless groups, it would be useful to express this value of kd in terms of the Sherwood number, . For this purpose, in our case we must estimate the diffusion coefficient of calcium ions in the acid solutions, Df. This was done by fitting the diffusion coefficient into Brian and Hales’ equation for known values of the mass transfer coefficient. For 75 oC and phosphoric acid solutions of 38.6 mass % of H3PO4, as in the production of phosphoric acid by the dihydrate process, we obtain:

Df = 8 x 10-10 m2/s

This diffusion coefficient value is reasonable for this kind of system and provides consistent results.



Experiments on the dissolution of calcium hydroxyapatite powder in hydrochloric acid solutions by increasing the agitation rate and observing the HAP’s dissolution rate point out that the controlling step of the reaction is the diffusion of products (calcium and/or phosphate) from the solid-liquid surface to the bulk of the solution.

The study of the dissolution of HAP powder in the presence of various concentrations of calcium and phosphate was achieved by the measurement of the time required for complete dissolution (100 % conversion) of HAP particles in hydrochloric acid solutions. The results allow us to establish a kinetic equation based on the shrinking particle model. The proposed kinetic equation fits the experimental results quite well.

The dissolution of HAP particles of 160 µm, at 75 °C and in hydrochloric acid solutions with 38.6 mass % of H3PO4 presents an estimated mass transfer coefficient of 1.5 x 10-5 m/s and a diffusion coefficient of 8 x 10-10 m2/s for the hydrodynamic conditions used in our experiments.

The time for complete dissolution is a simple experimental procedure which permits the study of heterogeneous non-catalytic reaction kinetics. Other phosphates are expected to show similar trends concerning the mechanism of dissolution in acid solutions, whereas the calcium concentrations at saturation (at the mineral surface), [Ca]sat, should differ from one to another. In fact, this value is related to the solid compound that predominates at the reaction surface and must be determined for each specific phosphate rock.



b Stoichiometric coefficient, dimension-less
D Linear dissolution rate, m/s
Df Diffusion coefficient of calcium ions in acid solutions, m2/s
[Ca] Mass fraction of calcium in the liquid phase at time t, dimensionless
kd Mass transfer coefficient, m/s
mp Mass of hydroxyapatite at time t, g
Mp Hydroxyapatite molecular weight, g/g-mol
m0p Initial mass of hydroxyapatite introduced in the reactor, g
MCa Calcium molecular weight, g/g-mol
Np Number of moles of hydroxyapatite, moles
r Mean radius of hydroxyapatite particles, m
r0 Mean initial radius of hydroxyapatite particles, m
Sh Sherwood number, dimensionless
T Temperature, K
td Time for complete dissolution, s
v Volume of one phosphate particle, m3
W Mass of the liquid phase in the system, g
r l Density of the liquid phase, kg/m3
r p Density of hydroxyapatite particles, kg/m3

sat Saturation value
0 Iinitial value
f Final value
l Liquid phase
P Hydroxyapatite



The first author would like to acknowledge financial support he received from the Brazilian Research Council - Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq).



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