Introduction

Phosphogypsum (PG) is a byproduct of phosphoric acid production industries generated from a wet process phosphoric acid (WPPA), with particle sizes generally ranging from 0.01 to 1 mm [1]. PG mainly consists of gypsum (CaSO4.2H2O), and contains some impurities such as silica (SiO2), phosphate, aluminum oxide, and heavy metals [2]. The WPPA is economic, but it generates a large amount of waste. The production of 1 ton of phosphoric acid generates approximately 3–5 tons of PG [3]. Morocco is one of the leaders of the phosphate and phosphoric acid industry in the world. The Moroccan Phosphates Board (OCP group) generates approximately 15 Mt of PG each year [4], and the annual production of PG worldwide is estimated to be 100–250 Mt [5]. However, 85% of this byproduct is usually disposed of into oceans or generally dumped in large stockpiles without any treatment [6]. The storage of PG causes environmental and human health problems due to the release of contaminants such as radionuclides in surface and underground water [7]. Corisco et al. confirmed the accumulation of heavy metals and radionuclides in Bryum sp. and Plantago sp. tissues growing naturally on PG piles [6]. The accumulation of cadmium in both plant tissues and edible parts has also been reported [8]. Therefore, there is an urgent need to develop a valorization process for this byproduct. Recently, different studies have attempted to valorize PG stockpiles in building materials that seems to be the largest field, such as brick cement or plasterboard [9]. In agriculture, PG is used as a source of calcium and sulfate for soil amendment [10, 11], or to extract valuable elements such as V, U, I2 and rare-earth elements [12, 13]. Moreover, it has also been used for the stabilization of bauxite residue [14]. Many researchers have studied the dissolution of PG in different areas including distilled water, seawater, and salt solutions [15]. Others have tried thermal decomposition in the presence of a solid fuel (coal or shale) to produce sulfur dioxide SO2 and the calcium oxide CaO [16]. However, the decomposition process requires high energy and generates toxic and corrosive gases such as CO, CO2, and SO2. For these reasons, researchers have focused on the conversion of PG under less-aggressive conditions. Ennaciri et al. transformed PG into lithium sulfate (Li2SO4) at 25 °C, using lithium carbonate (Li2CO3) with a concentration of 0.3 M [4]. Agli et al. produced potassium sulfate from PG using potassium chloride (KCl) at a concentration of 1,74 M [17]. Zemni et al. used sodium silicate (Na2SiO3) even with its high price to precipitate calcium ions [18].

The conversion of PG is also carried out by carbonation (CO2 bubbling) after dissolving PG in NaOH solution [19], and ammonia and CO2 have also been used [20]. The precipitation reaction of calcium in an aqueous system using carbonate reagent offers a high economic potential in the reuse of PG compared to other precipitation reagents such as NaOH, Na2SiO2, and KOH due to their high cost. Thus, in this study, the use of low-cost reagents was proposed. (NH4)2CO3 has been used in several studies to produce (NH4)2SO4 which can be used as a fertilizer (the Merseburg process) [21]. The kinetic parameters of the reaction process were estimated by Danielik et al. using a mathematical model. They found that the reaction proceeded in the liquid phase and not at the surface of the solid particles [22]. Kandil et al. obtained highly purified (NH4)2SO4 using the same process with an additional step of purification using sulfuric acid before conversion [23]. Sodium sulfate was also formed by reacting PG with sodium carbonate without further kinetic information. Mulopo et al. found that the conversion of PG into CaCO3 reached 98.5% after 105 min using a Na2CO3/PG molar ratio of 2 and slurry concentration of 5% [24]. Sodium sulfate has several applications such as the manufacture of detergents, the kraft process (papermaking), glass, and textile. The precipitated CaCO3 obtained from PG could be used in different areas such as in remediation of acid mine drainage to control wastes acidity [24], paper production, construction, and cement manufacturing [25, 26]. The phosphate industry can use this precipitate for flue-gas desulfurization or in other applications such as the recovery of radionuclides and rare-earth elements (REEs) [12]. In addition to the benefits derived from the production of Na2SO4, (NH4)2SO4, and CaCO3, the mineral carbonation process has more environmental benefits considering effective industrial waste management. Based on the conversion rate of PG, different models have been tested. The shrinking-core models (SCMs) describe how PG particles are converted into calcium carbonate, by determining the slowest step that controls the conversion reaction of PG [27,27,29].

This present work aims to investigate the conversion of PG using Na2CO3 and NH4HCO3 reagents. The effect of each of the following parameters including concentration, L/S ratio, contact time, and temperature on the conversion rate of PG was also studied. Shrinking-core models were applied to understand the kinetic mechanism of the conversion. Then, the economic feasibility of the conversion processes was discussed to develop an efficient process for the valorization of PG.

Materials and methods

Materials

The PG used in this study was provided by the OCP group (Moroccan fertilizer company), Jorf Lasfar, El Jadida, Morocco. Sodium carbonate (Na2CO3, 98.5 wt%) was supplied by Soda Solvay and ammonium bicarbonate (NH4HCO3, food grade) was provided by Weifang Zhenxing Coking CO., Ltd. Analytical reagent grade barium chloride (BaCl2, > 99 wt%) was purchased from Aromatic Chemicals-GB. It should be mentioned that the water used for all experiments was distilled water.

Conversion of PG

PG contains soluble and insoluble impurities that should be removed. PG purification was first performed by washing with distilled water to remove impurities prior to conversion. The L/S weight ratio of PG washing is 2. The mixture was stirred for 15 min at room temperature to remove impurities such as residual acids and organic matter [30]. The washed PG was dried overnight in the oven at 60 °C and crushed (Fig. 1). Then, PG was added to the reagent solution under vigorous stirring. The obtained slurry was filtered using filter paper (PRAT DUMAS). The precipitate was dried in an oven at 60 °C for 24 h. The filtrate was evaporated at 120 °C to form Na2SO4 and (NH4)2SO4 depending on the reagent solution used to convert washed phosphogypsum (WPG). The experimental factors and their levels are listed in (Table 1).

Fig. 1
figure 1

WPG dried and milled

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Table 1 Factors and levels of PG conversion experiments using sodium carbonate (X1) and using ammonium bicarbonate (X2)
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The general process consists of the conversion of calcium sulfate dihydrate present in phosphogypsum in aqueous medium. Calcium and sulfate ions combine by ion exchange with the appropriate reagent ions. Calcium ions precipitate in the form of CaCO3 and sulfates are released in the filtrate depending on the reagent used. However, PG was converted in the first process by sodium carbonate according to the reaction Eq. (1)

$$Na_{2} CO_{3} \left( {aq} \right){ }\, + \,{ }CaSO_{4} .2H_{2} O\left( s \right){ } \to { }Na_{2} SO_{4} \left( {aq} \right){ }\, + { }\,{ }CaCO_{3} \left( s \right){ }\, + \,{ }2H_{2} O\left( l \right)$$
(1)

The second process consists of the use of ammonium bicarbonate to convert PG according to the chemical reaction Eq. (2)

$$2NH_{4} HCO_{3} \left( {aq} \right)\, + \,{ }CaSO_{4} .2H_{2} O\left( s \right){ } \to { }(NH_{4} )_{2} SO_{4} \left( {aq} \right)\, + \,{ }CaCO_{3} \left( s \right)\, + \,{ }CO_{2} \left( g \right)\, + \,{ }3H_{2} O\left( l \right)$$
(2)

Since the solubility product of CaCO3 (Ks = 3.3 × 10–9 at 25 °C) is less than that of gypsum (Ks = 3.14 × 10–5 at 25 °C), the reactions in Eq. (1) and Eq. (2) move toward the direction of CaCO3 precipitation and the formation of Na2SO4 and (NH4)2SO4 products. The conversion rate of PG was determined by Eq. (3)

$$Conversion = { }m\left( {SO_{4}^{2 - } } \right)_{F} /m\left( {SO_{4}^{2 - } } \right)_{PG} \, \times \,100$$
(3)

Where m(SO42−)PG is the mass of SO42− in PG and m(SO42−)F is the mass of SO42− in the filtrate.

Characterization techniques

The analysis of crystalline phases was carried out with X-ray diffraction (XRD) D8 Advance Bruker, CuKα (1.5418 Å) radiation with a scan 2θ ranging from 5 to 70°. Data analysis phases were conducted using X’Pert High Score Plus software. The morphology was observed using scanning electron microscopy (SEM), FEI ESEM Quanta 450 FEG, and Fourier transform infrared spectroscopy (FTIR) using a JASCO 4600 spectrometer. The FTIR spectra were recorded in the region of 4000–400 cm−1 with a resolution of 4 cm−1.

Analytical techniques

pH was measured by a multiparameter WTW model 3630IDS. The sulfate concentration was measured by the gravimetric method according to the Indian Standard IS 3025. It involves the precipitation of barium sulfate (BaSO4) by the addition of barium chloride solution. The calcium concentration was determined by titration of excess ethylene glycol-bis (2-aminoethyl ether)-N, N, Nʹ, Nʹ-tetraacetic acid (EGTA) using calcium carbonate solution. The analysis of the major, minor, and trace elements was carried out using Inductively Coupled Plasma Optical Emission Spectroscopy (ICP–OES) Thermo Jarrell Ash IRIS Advantage and (ICP–MS) Perkin Elmer Nexion® 300X, and the samples to be analyzed are prepared in advance by a total dissolution of 1 g of sample in perchloric acid under 250 °C, and then, a filtration step was performed.

Results and discussion

PG treatment

The chemical composition of PG depends on several parameters, such as the origin of phosphate rock and the transformation process, which affects its purity, solubility, and conversion. Therefore, PG was washed with distilled water to reduce impurities. Moroccan PG is typically a gray-colored material mainly composed of dehydrated calcium sulfate (CaSO4.2H2O), PG has a fine grain size, and the crystals are tabular in shape and range in length from 40 to 200 µm, with percentages of 38, 42 and 19% for a median length of about 40, 120 and 200 µm respectively. Table 2 presents the chemical composition of PG. The initial pH (5 wt% slurry) of raw PG is 3.4. The acidic character of PG is due to the presence of water-soluble fluorinated compounds (H2SiF6, Na2SiF6, K2SiF6, and HF), traces of unwashed phosphoric and sulfuric acid and phosphoric salts [31]. After five cycles of washing, it was observed that the pH of PG increased to 5.1 which means that a part of the soluble acids was removed.

Table 2 Chemical composition of PG (Jorf lasfar)
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PG conversion

Concentration effect

The concentration effects of Na2CO3 and NH4HCO3 on the conversion of PG were studied to optimize the process. Figure 2 illustrates the conversion rate of PG at ambient temperature (22 °C) as a function of the concentration of Na2CO3 in the range of 0.2–0.8 M with a L/S Ratio of 10 at 60 min. As clearly seen, the conversion rate linearly increases with the concentration in the range of 0.2 to 0.6 M to reach the maximum value of 96.7%. The amount of 3.3% that could not be extracted is due to the insoluble sulfates which are complexed with other impurities such as radium and REEs. Moreira et al. used this property to remove radium and thorium from PG based on the difference in solubility, and radium sulfate (Ks = 3.66 × 10–11) is less soluble than calcium sulfate (Ks = 3.14 × 10–5) [32]. When the concentration exceeded 0.6 M, the conversion rate remains constant, since the PG in the solution is totally consumed. Therefore, it can be revealed that the optimum concentration is 0.6 M, which is equivalent to the stoichiometric conditions.

Fig. 2
figure 2

Effect of sodium carbonate and ammonium bicarbonate concentration on the conversion rate of PG

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The same variation behavior of the conversion as a function of the concentration (0.5–1.4 M of NH4HCO3 was obtained (Fig. 2). The conversion efficiency proportionally increased with concentration in the range of 0.5 to 1.2 M. As clearly seen, the maximum conversion value was found to be 95.6% at 1.2 M. For concentrations beyond 1.2 M, the conversion rate remained steady at 96.6%, indicating that the optimal concentration was 1.2 M, which is equivalent to a 3.3% excess of NH4HCO3. Therefore, in the next experiments, the amount of NH4HCO3 was fixed at 3.3% of the excess.

L/S ratio effect

Generally, the variation in the L/S ratio between PG and the conversion solution has an important effect on the conversion efficiency. A series of conversion experiments were carried out with L/S ratios from 7 to 15 using the corresponding stoichiometry of Na2CO3, while the other factors are kept constant at T = 22 °C and contact time at 60 min (Fig. 3). The results show that the conversion of PG proportionally increases with L/S in the range of 7–10. The highest value of 97.4% was achieved when the L/S ratio was 10. This could be ascribed to the decrease in diffusion resistance when the L/S ratio is increased. Then, with an increase in the L/S ratio from 10 to 15, the conversion rate was constant at a maximum of 97.4%. Therefore, the greatest L/S ratio of the conversion using Na2CO3 is 10. Figure 3 reveals the results when using NH4HCO3. Indeed, when the L/S ratio was increased from 7 to 10, the conversion rate rose from 75.3 to 92.9%, respectively. A steady conversion was obtained from 10 to 15. Referring to these results, the L/S ratio of 10 could be considered the optimum.

Fig. 3
figure 3

Effect of the L/S ratio on the PG conversion rate using sodium carbonate and ammonium bicarbonate

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Contact time effect and kinetics

The effect of contact time on PG conversion was studied in the range of 5 to 120 min keeping 10 as the L/S ratio for Na2CO3 (0.6 M) and NH4HCO3 (1.2 M) reagents. The results shown in (Fig. 4a) demonstrate that the conversion rate of PG increases with time and reaches a maximum of 95% after 60 min. The results of the conversion of PG using NH4HCO3 shown in (Fig. 4b) indicate that the conversion rate gradually increased in the range of 7 to 90 min and no further increase with extended time. Hence, the optimum contact time is 90 min.

Fig. 4
figure 4

Effect of reaction time on PG conversion rate using a sodium carbonate and b ammonium bicarbonate

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The conversion kinetics of PG provide more useful information about the rate-determining stage and the involved mechanism. PG conversion is a heterogeneous reaction between ions in the solution and solid particles of PG. For this typical reaction, shrinking-core models (SCMs) are the most common models used to describe the kinetic mechanism that controls the conversion. By applying SCMs, it is possible to identify the slowest step that is considered to be the rate-determining stage. The four models used, including the chemical reaction model [33], diffusion through the solid layer model, mixed model, and fluid diffusion model, are described using Eqs. 4–7, respectively [27]

$$1 - \left( {1 - {\text{X}}} \right)^{\frac{1}{3}} { }\, = \,{ }K_{1} {\text{t}}$$
(4)
$$1 - 2a/3 - \left( {1 - {\text{X}}} \right)^{\frac{2}{3}} \, = \,K_{2} t$$
(5)
$$1/3\ln \left( {1 - {\text{X}}} \right) - 1 + \left( {1 - {\text{X}}} \right)^{{\frac{ - 1}{3}}} \, = \,K_{3} t$$
(6)
$$1 - \left( {1 - {\text{X}}} \right)^{\frac{2}{3}} \, = K_{4} {\text{t,}}$$
(7)

where X is the PG conversion rate, and Ki is the experimental rate constant that can be calculated according to equations in the study [28]. t is the reaction time. External diffusion was not studied, because the stirring speed used was above 250 rpm. Mashifana et al. reported that with a high stirring speed, external diffusion has no effect on the fractional conversion of PG [29].

Figure 5 represents the four models applied to the conversion using Na2CO3. Table 3 lists the associated parameters of SCMs including the correlation coefficients (R2) and chemical rate constant (ki). The results presented in (Fig. 5c) show a plot of 1/3ln(1 − x) + (1 − x) − 1/3 − 1 vs. time and the correlation coefficients R2. All correlation coefficients were greater than 0.97 for 22, 40 and 60 °C. Therefore, the best model that fits the experimental results is the mixed model. This means that both interfacial reaction and diffusion through the product layer are the effective rate controlling the mechanism of PG conversion using Na2CO3.

Fig. 5
figure 5

Kinetic conversion of PG using Na2CO3 at different temperatures a chemical reaction model, b diffusion through the solid layer model, c mixed model, and d fluid diffusion model

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Table 3 Correlation coefficient R2 and rate constants Ki of shrinking-core models used
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Figure 6 displays the kinetic data plotted for SCMs of the conversion using NH4HCO3. Figure 6c shows a linear correlation of k3 and the conversion rate with correlation coefficients (R2) over 0.96. The proposed mixed model is in good agreement with the experimental data, attesting that the conversion of PG using NH4HCO3 is controlled by this model. Therefore, the model (Eq. (6)) can be used to properly describe the conversion process of PG using NH4HCO3. The conversion rate is also greatly affected by the size of the phosphogypsum particles. As the PG particle size decreases (similarly as the diffusion pores increase), the particle surface increases, which enhances the contact between the reagents and the PG particles. In addition, this promotes surface reaction and facilitates diffusion through the product layer, which increases the conversion rate.

Fig. 6
figure 6

Kinetic conversion of PG using NH4HCO3 at different temperatures a chemical reaction model, b diffusion through the solid layer model, c mixed model, and d fluid diffusion model

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Temperature effect

The influence of temperature on the conversion of PG was studied in the range of 22 to 90 °C to study the conversion of PG using Na2CO3. At room temperature and with an L/S ratio of 10, the conversion reaches 95%. Hence, the L/S ratio was fixed at 5 to investigate the conversion of a high amount of PG at high temperature. From the results shown in (Fig. 7), it is obvious that the conversion of PG increases with temperature up to reach a maximum of 96% at 55 °C. When the temperature was increased, the particles gained more energy; therefore, there was more collision between the reagents [23]. The conversion decreases with increasing temperature from 60 to 90 °C because of the CO2 released from the solution [34]. The conversion of PG using NH4HCO3 increases until it reaches a maximum of 98% at a temperature of 45 °C (Fig. 7). Then, the conversion highly decreased when the temperature was further elevated to more than 45 °C because of the solubility of both CO2 and NH3 which decreased as the temperature increased [35, 36].

Fig. 7
figure 7

Effect of temperature on the conversion rate of PG using sodium carbonate and ammonium bicarbonate

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The Arrhenius law (Eq. (8)) was used to describe the variation in the kinetic reaction as a function of temperature. A plot of the variation of ln(K3) as a function of 1/T is illustrated in (Fig. 8) using the apparent rate constant obtained from the mixed model

$$k\, = \,A . e^{{\frac{ - Ea}{{RT}}}}$$
(8)

where A is the pre-exponential factor, Ea is the activation energy (J mol−1), R is the universal gas constant (J mol−1 K−1), and T is the absolute temperature (K). The activation energy was calculated from (Fig. 8). The Ki value is inversely proportional to the temperature. The graph slope and intercept obtained were 3,4596 and 7,0563, respectively. The activation energy can be obtained by multiplying the slope value by a global gas constant, and the result is 28,4 kJ mol−1. On the other hand, the use of NH4HCO3 as a reagent leads to an activation energy of 37 kJ mol−1 (Fig. 8). These results are in accordance with the mixed model which is usually found to be in the range of 20–42 kJ mol−1 [37].

Fig. 8
figure 8

Arrhenius plot for conversion of PG using sodium carbonate and ammonium bicarbonate

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XRD analysis

Figure 9a presents XRD patterns of PG and the obtained products for the conversion process. PG is mainly composed of CaSO4.2H2O crystallized in the monoclinic system with space group C12/c1 (96–901-3168 COD, Crystallography Open Database). The precipitate was identified as calcite phase CaCO3 and a trace amount of quartz SiO2 was detected at 2θ equal to 26.6° (Fig. 9c). The formation of the precipitate can be explained by the reaction between Ca2+ and CO3.2− ions Eq. (9). Figures 9c, 10b show that under the optimum conditions for both processes, CaCO3 produced with a calcite phase with a spherical morphology composed of hexagonal blocks (JCPDS 96–901-6707). The product was calcite instead of vaterite because of the time impact on the polymorph of CaCO3. When the reaction time is longer the crystal phase, and the morphology went to calcite due to thermodynamic stability increases in the order of vaterite, aragonite, and calcite. The temperature has the same trend as the time effect and that was confirmed by Chen et al. [25]

$$Ca^{2 + } \left( {aq} \right) + CO_{3}^{2 - } \left( {aq} \right) \to CaCO_{3} \left( s \right)$$
(9)
Fig. 9
figure 9

XRD pattern of a PG, b crystallized Na2SO4, and c precipitated CaCO3 at 60 min as contact time

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Fig. 10
figure 10

XRD pattern of a crystallized (NH4)2SO4 , b precipitated CaCO3 at 90 min as contact time

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The XRD diffractogram of the salt obtained from the crystallized filtrate (Fig. 9b) indicates that it is mainly crystallized in the form of anhydrous sodium sulfate, Na2SO4 (96–900-4093, COD) in an orthorhombic system. Figure 10 shows the scenario in which different concentrations (1, 1.1, 1.2 and 1.3 M) were used to convert PG using NH4HCO3. Concentrations below 1.2 M shows signals of gypsum which confirms the partial conversion of PG. The total conversion of PG to Mascagnite (96–900-9883, COD) is evident in Fig. 10a using a concentration of 1.2 M. The formation of undesirable salts is due to the concentration of the reagents, when the reagent is used in insufficient quantity (NH4HCO3 1.1 M), the unreacted calcium ions will crystallize in the form of Koktaite. For Burkeite, their formation is due to the excess of the reagent Na2CO3 (0.7 M), in the same way the excess of carbonate combines with the sulfate and sodium ions to form Burkeite. These results confirm the optimal conditions of conversion.

FTIR analysis

The phosphogypsum, produced sodium sulfate, and ammonium sulfate were characterized by FTIR (Fig. 11), confirming the structure of the products obtained from the conversion of PG. The FTIR spectrum of PG (Fig. 11a) shows the presence of water molecules. Stretching vibration ʋO-H and bending vibrations δO-H are observed at 3545–3248 and 1686–1621 cm−1, respectively [38]. The vibration located at 2240–2115 and 1143–1113 cm−1 is attributed to the stretching vibration ʋO-S–O of SO42−. The bending vibration δ O-S–O is observed at 668–602 cm−1 [15]. Figure 11b shows the FTIR spectrum of the crystallized filtrate produced from PG using Na2CO3. The results indicate the presence of the strong sulfur–oxygen-stretching vibration ʋO-S–O of SO42− at 1090 cm−1 and bending vibration δO-S–O bands at 631–611 cm−1 [18]. The unmarked group of bands near 2200 cm−1 are the combination bands of the lower wavenumbers S–O [15, 18]. Moreover, the crystallized FTIR spectrum, displayed in Fig. 11c shows typical N–H vibrations. The bands observed at 2983 and 1606 cm−1, correspond to the ʋN-H stretching band and δN-H deformation band, respectively [39]. In conclusion, the FTIR results (Table 4) are in good agreement with those obtained by XRD analysis.

Fig. 11
figure 11

FTIR spectra of a PG, crystallized filtrate derived from PG conversion using b sodium carbonate and c ammonium bicarbonate

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Table 4 Allocation of the infrared vibration of the raw PG and leach filtrates
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SEM analysis

Figure 12 illustrates the morphological structure of PG and precipitated calcium carbonate. As seen in Fig. 12a, PG particles have a hexagonal crystal structure. This morphology depends essentially on the composition of PG (impurities, PO42− syncrystallized ions), condition of crystallization (nature of the rock, attack process, etc.). In addition, the morphology also depends on the size of these particles in the range of 20–200 µm. As observed by comparing SEM images of PG and precipitated CaCO3 particles, the morphology was changed. Figure 12b, c shows an SEM image of CaCO3 particles produced using Na2CO3 or NH4HCO3. As observed in these images, fine and agglomerated particles are obtained. However, the size of these particles ranges from 1 to 10 µm. In fact, impurities and trace elements contained in PG can modify the morphology and structure of precipitated particles according to Lu et al. [40]. SEM images Fig. 12e, f clearly show that the surface area of the PG particles was significantly affected by the reagent. It is clear from Fig. 12e that the surface area of the particles continues to gradually reduce as the conversion time increases. The fast evolution of the morphology also confirms the dominant effect of the chemical reaction on the particle surface after the diffusion of the reagent through the solid layer, and this is clearly apparent by the formation of the small calcium carbonate particle on the surface of the PG particles. Thus, this also indicates that the leaching kinetics is governed by the mixed controlled shrinkage-core model.

Fig. 12
figure 12

SEM images of a PG, b precipitate from the sodium carbonate process, c precipitate from the ammonium bicarbonate process, d evaporated filtrate of sodium sulfate, precipitated CaCO3 e at 30 min and f at 60 min

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Chemical composition of PG and products of the conversion

Table 5 represents the chemical analysis of the trace elements in the products. During the conversion process, the transfer factor of trace metals into the precipitated CaCO3 is high, approximately 90%. Hence, sodium sulfate and ammonium sulfate were obtained with high purity. Divalent metals such as Pb, Ni, Cu, Cd, and Zn can be easily incorporated into the precipitate because of adsorption on the precipitated particle surface. Moreover, the trapping phenomenon during precipitation is an effective mechanism for reducing metals mobility in aqueous systems, which causes them to be transferred into the precipitate [19]. The conversion of PG using carbonate solutions leads to the obtaining of Na2SO4 and (NH4)2SO4 products with fewer impurities. These results were also observed by other authors [41].

Table 5 Major and trace elements in PG and conversion products
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Economic feasibility

A preliminary analysis of the PG conversion process (Fig. 13) was conducted to investigate the economic viability of an industrial plant. The estimated capital expenditure for a 500 ton/day (180 000 tons/year) of phosphogypsum conversion plant is provided in (Table 6). The operating costs of each conversion process are discussed in Tables 7, 8. According to the process of conversion using sodium carbonate, 1 ton of PG can be treated by 0.57 ton of Na2CO3 (51.3$) to obtain 0.67 ton of CaCO3 (6.7 $) and 0.75 ton (93.7 $) of Na2SO4. This economic approach yields 7.49 M$ per year, with an ROI up to 69%. The second conversion process requires a high amount (0.94 ton) of ammonium bicarbonate for one ton of PG, which results in a net loss of approximately 31.35 $/ton (Table 9). Based on these results, the first process seems more economically valuable than the second one. This is due to the amount of ammonium bicarbonate needed to convert the totality of PG. Moreover, using ammonium carbonate is more efficient because of the stoichiometry condition of the reaction with CaSO4.2H2O. From the socioeconomic side, these processes remain environmentally sustainable for the management of PG waste and do not require complicated operation.

Fig. 13
figure 13

Flowsheet of the PG conversion process

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Table 6 Principal equipment description and cost
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Table 7 Operating cost of the first process
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Table 8 Operating cost of the second process
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Table 9 Determination of revenues
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Conclusion

In this work, a total conversion of PG using sodium carbonate and ammonium bicarbonate by precipitation of calcium carbonate was confirmed. Conversion kinetics under simulated experimental conditions are discussed, and Shrinking-core models are established. A possible conversion reaction mechanism is also proposed.

The kinetic results for both reactions showed that the conversion of PG was in accordance with the mixed model with equation \({\text{1/l}}n\left( {1 - a} \right) - 1\, + \,\left( {1 - a} \right)^{{\frac{ - 1}{3}}} \, = \,K_{3} t\), and the conversion reaction mechanism was controlled by the interfacial reaction and diffusion through the product layer. The Ea of PG conversion in Na2CO3 was 29.4 kJ mol−1. However, the use of NH4HCO3 as a reagent leads to an activation energy of 27.9 kJ mol−1. By comparing the activation energy of these two reactions, it can be determined that the conversion in NH4HCO3 is easier than that in Na2CO3. The precipitation of calcium does not require more demanding reaction conditions due to the amount of excess CO32− ions in the solution.

The economic study was carried out considering the main expenses namely chemicals and energy consumption. Therefore, the economic evaluation of the processes reveals that the conversion using sodium carbonate was economically viable. This is due to the low cost of the sodium carbonate reagents.