The PG samples used in this work came from Fertiberia factory of Bahía of Huelva (Spain) in 2009, named PGS and from Chemical Group (GZT) factory of Gulf of Gabès (Sfax, Tunisia) in 2009, named PGT. In order to obtain a representative sample, the sampling was carried out in situ. 300 kg of each PG sample were mixed and homogenized in a mixer ENRICH, with 200 kg of capacity, then quartered successively up to obtain a representative sample of 1 kg, being subject of our experiments. After filtration and drying at 50 °C during 48 h, the chemical composition of PG, obtained by conventional methods, is listed in Table 1. The particles size was obtained by means of laser particle size analyzer Malvern Mastersize 2000 apparatus.

The diffractograms of PG samples were obtained using a X-ray diffractometer (Philips X'Pert PRO MPD) with Kα Cu radiation (40 mA current and 45 kV). The patterns of diffraction were obtained in a 2Θ scanning range from 5° to 80°, with 0.0167° and 0.6 s of scan step and time, respectively.

PG samples were subjected to differential thermal and thermogravimetric analysis (DTA and TGA) in an inert atmosphere (argon). Setaram Sensys Evolution 1500 DTA/TGA analyzer was used to measure and record the sample mass change with temperature over the course of the dehydration reaction. Thermogravimetric curves were obtained at heating rate of 10 °C/min between ambient and 650 °C in argon atmosphere (20 ml/ min) and the sample mass was between 45 and 50 mg.

The kinetic study of the dehydration of PG was performer with Differential Scanning Calorimetry (DSC) analysis. DSC experiments were performed on a Setaram Model mod 3D-EVO. Non-isothermal analysis was carried out at four different heating rates (5, 10, 15, and 20 °C/min) between ambient and 350 °C. Temperature calibration was achieved by using the ICTAC-recommended DSC standards. The precision of reported temperatures was estimated to be ±2 °C. Sample mass was about 60 mg and was placed in a 175 µl Al crucible sealed. All the experiments were conducted in an inert atmosphere, argon with a flow rate of 20 ml/min.

The reproducibility of the experiments is acceptable and the experiments data presented in this paper corresponding to the different operating conditions are the mean values of runs carried out two or three times.

Generally for PG degradation, it is assumed that the rates of conversion are proportional to the concentration of reacted material. The rate of conversion can be expressed by the following basic rate equation [Eq. 2]: d α d t   =   β d α d T   = k ( T ) . f ( α )

Where α is the degree of conversion of reaction, f(α) and k(T) are functions of conversion and temperature. In the DSC experiments, the Eq. [2] can be expressed by the following Eq. [3]: d α d t   =   d H d t . 1 ∆   H t o t a l

Where is d H d t is the heat flow above baseline and ΔHtotal the peak area of the reaction, expressed in mJ.

By combining Eqs. [2] and [3], the rate of conversion can be written in form [4]: d α d t   =   d H d t . 1 ∆ H t o t a l   =   k ( T ) . f ( α )

k(T) the temperature dependence of the rate of heat flow, is often modelled successfully by the Arrhenius Eq. [5]: k ( T )   =   A exp ( − E R T )

Where E is the activation energy, A the pre-exponential factor and R is the gas constant.

By combining the Eqs. [4] and [5], the reaction rate can be written as follow [6]: d α d t   =   A exp ( − E R T ) . f ( α )

Morphologically, both PG samples were yellowish brown color and relatively soft grains. The particle size of phosphogypsum were D₅₀=53 µm and D₅₀=83 µm for PGS and PGT, respectively. Chemically, the PG mainly consists of SO₃, CaO with low contents of SiO₂, Fe₂O₃, Al₂O₃ and P₂O₅ as well as traces of Na₂O, K₂O, TiO₂, F and 12–22% ignition loss (LOI). In addition to radionuclides such as ²²⁶Ra, ²¹⁰Pb, ²³⁸U and ⁴⁰K, the chemical analysis of PG is reported in Table 1.

Figure 1 reports the powder X-ray diffraction pattern of PG samples. As shown, PGS presents two maximum intensity diffraction peaks corresponding to calcium sulfate dihydrate (CaSO₄·2H₂O) (JCPDS 74-1433), calcium sulfate hemihydrate (CaSO₄·0.5H₂O) (JCPDS 81-1848) and anhihidryte (CaSO₄) (JCPDS 37-1496). The semi-quantification of the phases by the magnitude of the diffraction line intensity shows the presence of approximately 64% of CaSO₄·2H₂O; 33% CaSO₄·0.5H₂O and 3% of CaSO₄. These ratios are in accordance with the percentage of S and Ca obtained by the chemical analysis. The main diffraction peak of the PGT corresponds mainly to calcium sulfate dihydrate (CaSO₄·2H₂O) (JCPDS 74-1433). The gypsum content in the PGT is 94%, while the remainder is impurities.

The mineralogical composition of the PG depends strongly on its origin, the kind of acid phosphoric process used, environmental conditions of its storage and the age of the studied sample. Generally, PG could be composed by different ratios of three mineralogical phases of calcium sulfate. For example, the presence of these three phases has been described by Ma et al. (2010) (35) in their study of the reaction mechanism and the kinetic of the decomposition through a solid state by means of reaction with carbon, of a PG from Yunnan Gas and Chemical Engineering Company. Strydom et al. (1999) (36) establish for a PG from Omma Fertiliser's plant in Rustenburg, ratios determined through XRD of 16% CaSO₄ 2H₂O, 66% CaSO₄ 0.5H₂O and 15% γ-CaSO₄. López et al. (2011) (37), by studding a microencapsulation of a PG from Huelva Bay found only the presence of the gypsum and the hemihydrate phases and carbon. Cárdenas-Escudero et al. (2011) (38) reported that for a PG from the same zone, only the dihydrated phase was found.

Figure 2 shows the curves of TG, DTG and DTA obtained from heating the studied PG samples at 10 °C/min in argon atmosphere and open crucible.

The curves show two consecutive and much closed endothermic peaks between 144 °C and 175 °C for PGS sample (Fig. 2a) and 156 °C and 191 °C for PGT sample (Fig. 2b). The proximity of both signals makes difficult the mass loss assignation, reported in the TG curves for each one of the effect area. In the studied temperature range, an exothermic peak appears at a maximum temperature of 433 °C in the PGS sample and 465 °C in PGT sample. In the case of the exothermic peak, no mass loss was observed. The Table 3 reported the characteristic temperatures for each peak and its associated mass loss.

The first endothermic peak observed in the DTA/DTG curves is attributed to the gypsum dehydration reaction and the formation of the hemihydrate, according to the Eq. [12]. The second peak corresponds to the transformation of hemihydrate to anhydrate, according to the Eq. [13]. At temperatures near 400 °C, a slightly exothermic reaction occurs, in which the molecular structure of the soluble crystal (anhydrite III) irreversibly reorganizes itself into a lower insoluble energy state (anhydrite II or β-CaSO₄) (39–41) [Eq.14]. On the TG curve, no loss has been noticed at this temperature.

CaSO₄ 2H₂O→CaSO₄ 0.5H₂O+1.5H₂O  [12]

The difference in DTG and DTA profiles, among two PG, indicates the influence of sample origin, chemical composition and traces on dehydration behavior (28). The most obvious discrepancy is the temperature, at which gypsum begins to dehydrate. PGS begins to dehydrate at lowest temperature, while PGT dehydrate at highest temperature.

The TG curves analysis indicates that for the PGT sample, the mass loss observed between the ambient temperatures up to 500 °C is ≈17 wt%. This result is in accordance with the mass loss (LOI) obtained by the chemical analysis of the PG sample (Table 1), being the 12.8 wt% for the first peak and 4 wt% for the second one. Thus the mass loss is done according to a 3:1 rate. The two “jumps” of a 3:1 mass loss in TG curves are in accordance with the stoichiometry of the dehydration reactions: Eqs. [12] and [13].

For PGS sample, the total mass loss corresponding to the hydration reaction is 9.4 wt%, being the 4.7 wt% for the first peak and 4.7 wt% for the second peak, which means a relation of ≈1:1. In this case, it should be noted that in the initial PGS sample coexist the dihydrate and hemihydrate phases, which explains the relation of the identified mass loss.

Most literature reported that gypsum dehydration undergoes a two-step process, via hemihydrate (25, 28, 42–44), while some reports showed that γ-CaSO₄ is directly produced during gypsum dehydration of γ-CaSO₄ upon cooling with humidity air (45). Ball et al. (1969) (46) and Badens et al. (1998) (47) pointed out that both temperature and partial water pressure (P _H2O) controlled the product of dehydration. Lou et al. (2011) (48) reported that under non-isothermal conditions and in two steps, via hemihydrate in “autogenous P_H2O”, the dehydration of the gypsum contained in the “flue gas desulfurization gypsum (FGDG) occurs in one step (CaSO₄ 2H₂O→γ-CaSO₄), when the P_H2O is negligible.

The dehydration behavior may vary significantly among different gypsum types, such as natural gypsum and many kinds of chemical gypsum. Differences in crystalline characteristics and impurities appear to be the most important factor resulting in discrepancies of dehydration behavior (27).

Figure 3 shows the DSC curves obtained during the thermal dehydration of both studied PG samples at different heating rates (5, 10, 15 and 20 K/min) up to 350 °C.

The CaSO₄ 2H₂O reaction dehydration takes place into steps according to two endothermic peaks. The first peak is observed (depending on the heating rate) at T_p between 142 and 166 °C, for the PGS (Figure 3a) and between 151 and 163 °C for the PGT sample (Figure 3b). The second peak occurred at higher temperature, between 179 and 215 °C for the PGS sample and 186 and 207 °C for PGT sample. In both case and by increasing the heating rates, an increasing of the maximum of the degradation temperature is observed.

By considering the global dehydration reaction (step 1 and step 2), the Table 4 shows the maximums temperatures and the dehydration heat for each sample according to the heating rates. The dehydration heat was calculated from the integration of the area of the two endothermic peaks. The medium dehydration heats are 240.5 J/g and 535.2 J/g for the PGS and PGT samples, respectively, in accordance with the total mass loss (see section 3.2).

The results of the DSC curves obtained at different heating rates were used to calculate the activation energy of the dehydration reaction for the both PG samples. The activation energy was determined using Flynn-Wall-Ozawa (FWO), Friedman (FR) and ASTM E698 methods.

Firstly, the isoconversional Friedman method was used to calculate the activation energy for different conversion values. The plot of the variation of the ln ( dα dt ) in function of 1/T, for a constant f(α) at each conversion degree, αi, straight lines were obtained for each αi value for the slope (E/R), the activation energy value was obtained for each conversion degree αi (Figure 4).

The results of the activation energy for both PG samples are shown in Table 5 and 6. The means values of activation energy were 61.1 and 110.3 KJ/mol for PGS and PGT, respectively.

Secondly, FWO method is an integrated method, which is also independent of the degradation mechanism. Eq. [7] was used and the activation energy of the PGS and PGT was obtained from plot log(β) against 1/T at a fixed conversion with the slope such a line being 1.052E/R (Figure 5).

The values of activation energy of PGS and PGT are summarized in Table 5 and 6, respectively. The means valued of activation energy were 62.4 KJ/mol for PGS and 107 KJ/mol for PGT.

Finally, ASTM E698 method based on the assumption that the maximum of the DSC curves of a reaction is reached at the same conversion degree independent of the heating rate. The activation energy was obtained from plot of log(β) against 1/T with the slope of such a line being E/R. The values of the obtained activation energy of the both PG samples are summarized in the Table 5 and 6. The values of activation energy were 67.9 and 128.4 KJ/mol, for PGS and PGT, respectively.

Table 7 shows activation energy calculated by Coats-Redfern method for PGS and PGT at constant heating rate of 10 K/min. It was found that thermal dehydration mechanism of PGS is likely to be of first-order F1 type, because this mechanism presents the activation energy (62.6 kJ/mol) similar to the value obtained by FR isoconversional method (62.4 kJ/mol). It is clearly shows that the mechanism for PGT dehydration is proposed to be three-dimensional diffusion (D3) type. The activation energy of this mechanism was around 117.9 kJ/mol, which was similar to activation energy obtained by FR isoconversional method (107 kJ/mol).

The values of the activation energy are similar when calculated using the FR and FWO methods, while the ones obtained by the ASTM method are higher than the previous ones. Indeed, the ASTM method, using the results of TG curves, provides good kinetics results. However and in this case, it seems that using the results of the DSC curves, the results are very different to the ones obtained by the other calculation methods.

Thus the activation energy of the PG dehydration reaction, calculated from the global reaction (setp 1 and setp 2) varies depending on the calculation methods used between 61 and 63 kJ/mol for PGS sample and 107–118 kJ/mol for PGT samples.

The kinetics equations for PG dehydration is as follows [15], [16]: d α d t =  ​ 1.01  ​ ×  ​ 10 0.5 e − 62.61   ×   10 3 / R T ( 1  ​ −   α )  for PGS d α d t =  ​ 5.46  ​ ×  ​ 10 10 e − 117.9 ​  ×  ​ 10 3 / R T 3 ( 1 ​ −   α ) 2 ​ / ​ 3 2 ( 1 ​ − ( 1 ​ −   α ) 1 ​ / ​ 3 ) for PGT

Figure 6 shows the changes in the activation energy calculated by means of the Friedman method, according to the conversion degree for the global dehydration reaction of each studied PG sample.

It is clearly shows that the dehydration reaction takes place via a clearly two differentiated steps.

For PGS sample, the first step of the reaction occurs for 0.02≤α≤0.53, with an average value of activation energy of 68±6 kJ/mol and the second step for 0.53≤α≤0.99 with an average value of activation energy of 51±2 kJ/mol.

For PGT sample, the first step of the reaction occurs for 0.02≤α≤0.74, with an average value of activation energy of 110±6 kJ/mol and the second step for 0.74≤α≤0.99 with an average value of activation energy of 77±2 kJ/mol. In both PG samples, the first step of the reaction, corresponding to the formation of the hemihydrate, contributes most to activation energy of the global reaction of the dehydration than the second step, transformation of hemihydrate to anhydrate.

In the literature, there is a number of studies on kinetics dehydration of gypsum (25, 27, 43–49). In general, all the studies of the CaSO₄ 2H₂O dehydration through DTA or DTG show the presence of two endothermic peaks. However, the dehydration temperatures have been quite varied. This difference might be explained by the influence of nature as well as by the different origins of the samples. Although many studies about the decomposition of gypsum have been reported, we have not noticed any work about the kinetics of thermal dehydration of PG. The mechanisms involved in the dehydration of the PG are different from that of the natural gypsum, and some impurities in PG could influence the dehydration mechanism.

Comparing the experimental values of the activation energy obtained in this work to others values reported in the literature, we noted that the PGT is composed exclusively of gypsum and presents an activation energy comparable to that obtained by Elbeyli et al. (2004) (50) (95–114 kJ/mol) in their study the kinetic decomposition in non-isothermal conditions of a borogypsum composed by CaSO₄ 2H₂O. The values obtained in this work are also within the range of the values done by Lou et al. (2001) (48) when they study the kinetic dehydration of the flue gas desulphurisation phosphogypusm in variable conditions of partial water pressure (79–136 kJ/mol). Furthermore, Kontogeorgos and Founti (2012) (51) reported that the activation energy for the transformation of the calcium sulfate dihydrate into soluble calcium sulfate anhydrite III can be assumed to take place in three stages: nucleation (α<0.1 and E≈144 kJ/mol), nuclei growth (0.1<α<0.7 and E100 kJ/mol) and water molecule diffusion (α>0.7 and E83 kJ/mol).

The differences between these values and the values found in this paper could be attributed to the different origin of the raw material and/or the impurities.