Introduction

Uranium (U) and its compounds are radioactive and toxic and can easily cause carcinogenesis in human cells and tissues [1, 2]. On the other hand, during the decay process of uranium, products radon (Rn) and radium (Ra) are released: 238U → 234Th → 234 Pa → 234U → 230Th → 226Ra → 222Rn. As known, Rn and Ra can instantly cause irreversible damage to the nervous system, blood circulation system and endocrine system [3]. The limit concentration of Rn in the living room is 200 Bq/m3 (National ecological and environmental standards, China, HJ 1212-2021), and the allowed concentration of 226Ra in the top 15 cm of soil is 0.18 Bq/m3 (Regulations on Radiation Protection for Uranium Processing and Fuel Manufacturing Facilities of China, EJ 1056-2005).

The uranium mining activities produce a large amount of U-contaminated water mainly including well-flushing wastewater, waste drilling fluid and tail liquid of leaching and ion exchange [4, 5]. The concentration of U in these waters varies from 0.5 to tens of mg/L, which is much higher than the limited concentration of 50 µg/L from the Regulations on Radiation Protection for Uranium Processing and Fuel Manufacturing Facilities of China (EJ 1056-2005) [6, 7]. Therefore, it is necessary to treat these U-contaminated waters using proper processes to avoid them spreading to the ecosystem and causing radioactive contamination in biosphere.

The immobilization process has been widely used in the treatment of water contaminated with heavy metals, e.g., As, Hg, Cr, and U [8,9,10,11]. In general, the immobilization process can be categorized into two types: first, soluble ions are added to react with heavy metals to form insoluble compounds [5, 12,13,14]. Second, an insoluble adsorbent was added to immobilize heavy metals with adsorption [15,16,17]. For U immobilization, calcium and phosphate were employed to immobilize U via mineralization, and autunite was extensively reported as the targeted mineral for U container [18]. The second type of process is usually employed to treat U-contaminated water. Adsorbents such as amorphous KAlSi3O8, activated carbon, amorphous calcium phosphates, and hydroxyapatite (HAP), has been extensively investigated in the uranium, thorium, cesium, and other radionuclides [19,20,21]. Among these adsorbents, HAP due to its good particle dispersion, ion-exchange characteristics and large specific surface area has been widely used at contaminants adsorption and was found to be a good adsorbent for U [22, 23]. Furthermore, HAP is often loaded with functional groups or metals (e.g., –NH2, Cu, Zn) and also substituted with Mg2+–, Sr2+–, and Fe3+– to increase the adsorption capacity of U [24,25,26].

However, with the wide use of HAP for U immobilization, the product of HAP-adsorbed U needs to be considered to evaluate the risk of secondary pollution after immobilization [27]. Usually, the adsorbent used is treated for regeneration or storage [28, 29]. Regardless of which method is used, the dissolution stability of the HAP-adsorbed U is the most significant factor in evaluating the possibility of regeneration or the risk of storage, directly determining the sustainability of U immobilization [30]. Moreover, it was found that the dissolved PO43− from HAP reacted with UO22+ to precipitate a stable P(V)–U(VI) compound on the surface of HAP particles when U was immobilized by HAP adsorption [5, 31], but the deep mechanism needs more explorations. The dissolution stability of HAP-adsorbed U has rarely been reported and requires further investigation.

The objective of this study was to investigate the dissolution stability of the product obtained from uranium immobilization with HAP while acquiring more information on the mechanism for U immobilization with HAP. U immobilization experiments were performed to obtain optimal conditions. Characterization of the product was conducted to identify the uptake mechanisms. The dissolution stability of the product was experimentally tested, and a thermodynamic model for the dissolution of the U mineral phase in the U immobilization product was developed to reveal the dissolution rules that determine the risk of secondary pollution and to design remediation strategies.

Experiments

Immobilization of U(VI) with HAP

First, simulated U-containing wastewater (U of 1.0 g/L) was prepared by dissolving U3O8 in 0.5 mol/L HNO3 aqueous solution.

Second, HAP (analytical reagent, AR) powder was mixed with 50 mL U solution in a reactor, and it was then placed in a digital thermostatic oscillator with a controlled oscillation frequency of 150 rpm and temperature of 25 °C for U immobilization. After the reaction, the slurry was filtered through a pore size of 0.22 μm to separate the residue and leachate. Subsequently, the residue was dried and collected for characterization. During the immobilization process, the initial solution pH was adjusted with HNO3 (0.1 mol/L) or NaOH (0.01 mol/L), the S/L ratio was controlled by the addition of HAP, and different initial U concentration solutions were prepared by diluting the 1.0 g/L simulated U-containing wastewater.

Third, raw HAP and residue sample were characterized with X-ray diffraction (XRD, D8-A25, BRUKER) and scanning electron microscopy-energy dispersive spectrometry (SEM‒EDS, Nova Nano SEM 450) as well as BET analyzer (ASAP 2460, Micromeritics). The leachate was analysed with an inductively coupled plasma-optical emission spectrometer (ICP‒OES, Agilent 5900 SVDV).

The immobilization capacity (Q, mg/g) and efficiency (R, %) of uranium were calculated by Eqs. (1) and (2):

$$Q = \frac{{\left( {C_{0} - C_{t} } \right) \times V}}{m}$$
(1)
$$R = \frac{{(C_{0} - C_{t} )}}{{C_{0} }} \times 100\%$$
(2)

where C0 (mg/L) is the initial concentration of U, Ct (mg/L) is the concentration of U at time t, V (L) is the volume of solution, and m (g) is the mass of HAP (g).

Dissolution stability of the immobilization product

The dissolution stability of the immobilization product that was obtained at an initial concentration of 14 mg/L, pH = 3, solid to liquid ratio (S/L) of 1 g/L and reaction time of 2 h and named HAP-U was evaluated experimentally by leaching tests. For the dissolution media, a buffer solution of HAc-NaAc with a pH of 4.93 was selected by referring to the toxicity characteristic leaching procedure (TCLP, US-EPA 1992) tests. According to the comparative experimental studies based on natural environmental conditions to which the immobilizing product HAP-U may be exposed, tap water (pH = 7.1), natural rainwater (pH = 5.6), and simulated acidic rain prepared with sulfuric and nitric acid solutions (pH = 5.0) were chosen for the dissolution stability evaluation tests. For the tests, the conditions were controlled at a solid-to-liquid mass ratio (S/L) of 1:20, leaching time of 24 h, and temperature controlled by a thermocouple. Intermittent sampling was completed during the tests, and the samples were filtered to determine the U concentration of the leachates by ICP‒OES and inductively coupled plasma‒mass spectrometry (ICP‒MS, Agilent 720ES).

Results and discussion

Effect of HAP immobilization conditions

Figure 1 shows the effect of immobilization time, S/L, pH, and initial U concentration on U immobilization with HAP. The immobilization efficiency of U increases significantly in the first 20 min and finally reaches an equilibrium of 90% at approximately 80 min (Fig. 1a). Hence, an immobilization time of 2 h was chosen for subsequent experiments to ensure a relatively high immobilization efficiency. When the S/L increases to 1.0 g/L, the immobilization efficiency is almost 100%. However, the immobilization capacity decreases with increasing S/L because the excessive dosage of HAP leads to the unsaturation of immobilized U on the HAP (Fig. 1b). With increasing pH, the immobilization efficiency and capacity show a tendency to increase first and then decrease and reach the top value at a pH of 2–3 (Fig. 1c).

Fig. 1
figure 1

a Concentration and immobilization efficiency of U as a function of immobilization time; b S/L, c pH, and d the initial concentration of U on the immobilization capacity and efficiency

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These results are attributed to competition between U and H+ during immobilization on the active sites of HAP particles at low pH [32]. When pH < 2, the increased H+ leads to decrease of immobilization capacity. The greater concentration of H+ created stronger competition with the U for the binding active sites on the adsorbents, which was unfavourable for the immobilization of the uranyl ions [33]. When the pH value was above 3.0, species of [UO2(OH)]+, [(UO2)2(OH)2]2+, [(UO2)3(OH)5]+ is stable in the system, causing the decreased immobilization capacity of uranium [34]. The specific surface area (SSA) of the raw HAP was determined to be 7.2 m2/g (Table S1), which was much lower than that reported in previous literature (Han et al., 78.42 m2/g) [31]. The pore volume and size were 0.043 cm3/g and 22.85 nm, respectively. However, the maximum uranium adsorption capacity in the literature is only twice of it in current research, whereas the SSA is almost ten times larger. When the initial U concentration is higher than 250 mg/L, the efficiency of U immobilization declines and the growth of immobilization capacity slows down, owing to that the active sites of HAP particles for U immobilization have been saturated (1d).

(Immobilization conditions: (a) initial U concentration of 14.0 mg/L, S/L of 2.5 g/L; (b) initial U concentration of 83.2 mg/L, immobilization time of 2 h, and pH of 3.0; (c) initial U concentration of 100 mg/L, S/L of 2.5 g/L, temperature of 25 °C, immobilization time of 2 h; (d) S/L of 2.5 g/L, pH of 3.0, and immobilization time of 2 h. All data are obtained through three replicated tests).

Theoretical analysis of the immobilization process

The immobilization capacity of U in the case of different initial U concentrations and optimal conditions of pH of 3.0, S/L of 1 g/L, and immobilization time of 2 h are shown in Table S1. Pseudosecond order kinetic model (Eq. 3) was applied to fit the immobilization results.

$$\frac{t}{{q_{t} }} = \frac{1}{{k_{{1q_{e}^{2} }} }} + \frac{t}{{q_{e} }}$$
(3)

where k1 is the immobilization rate constant (g/(mg∙min)), qt is the immobilization capacity at time t (mg/g), and qe is the immobilization capacity at equilibrium (mg/g).

The fitting results for pseudosecond order are shown in Fig. S1. The findings demonstrate that the correlation coefficient (R2) of the pseudosecond order kinetic model is above 0.99, indicating a linear relationship between the reaction rate and the concentration of U.

Since adsorption is a significant process of U immobilization on HAP, Langmuir (Eq. 4) and Freundlich (Eq. 5) isothermal adsorption models were used to study the thermodynamic mechanism of U immobilization on HAP. The immobilization capacity and concentration of U at equilibrium data were fitted according to these two models.

$$\frac{{C_{e} }}{{q_{e} }} = \frac{1}{{q_{m} }} \cdot C_{e} + \frac{1}{{q_{m} K_{L} }}$$
(4)
$${\text{ln}}q_{e} = \frac{1}{n}{\text{ln}}C_{e} + {\text{ln}}K_{{\text{F}}}$$
(5)

where KL (L/mg) denotes the equilibrium constant of the Langmuir model; KF (L/mg) denotes the equilibrium constant of the Freundlich model; Ce (mg/L) is the U concentration at equilibrium; qm is the maximum immobilization capacity (mg/g); qe (mg/g) is the immobilization capacity at equilibrium; and 1/n is an empirical constant.

The fitting results for the Freundlich and Langmuir models are shown in Fig. S2, and the characteristic parameters of these two models are summarized in Table S3. It can be concluded from the results that the Freundlich isothermal model is well fitted, indicating a multimolecular layer adsorption mechanism for U immobilization on HAP. Therefore, it can be speculated that the immobilized U on HAP exists as a covalent bond of P(V)-U.

Characterization of the immobilization product

Uranium of the immobilization product, HAP-U, obtained from the optimal conditions is homogeneously distributed on the map (Fig. 2a), and the relative content of U is 1.1% (Fig. 2b), indicating a well-immobilized performance of HAP. The XRD patterns of the HAP samples before and after U immobilization are shown in Fig. 2c. After U immobilization, the peaks of meta-autunite appeared on the HAP pattern, suggesting that during immobilization, uranyl ions reacted with Ca2+ and P(V), which were dissolved from the boundary layer of HAP particles to form meta-autunite, indicating that mineralization occurred when U was immobilized by HAP. Moreover, it has been reported that during the sorption of HAP, an ion exchange between heavy metal ions and Ca2+ happened, and then a new phase bearing the heavy metal formed [35]. According to the report of Han et al., a mineral phase of autunite was observed in the U immobilization product by using Bio-HAP as an adsorbent, which is consistent with the findings of the current research.

Fig. 2
figure 2

a EDS image and U, P, O, Ca mapping, and b EDS energy spectrum of the HAP-U sample; c XRD patterns of the HAP sample before and after immobilization. (HAP-U sample obtained at an initial U concentration of 83.2 mg/L, pH of 3, S/L of 1.0 g/L, and immobilization time of 2 h)

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Dissolution stability of the immobilization product

The results of the dissolution test for HAP-U in nitric acid (pH = 5.0), sulfuric acid (pH = 5.0), natural rainwater (pH = 5.6), and tap water (pH = 7.1) at different temperatures (30, 40, 50, and 60 °C) are summarized in Table S4. This result indicates that all the concentrations of dissolved U from the HAP-U were less than the ICP‒OES detection limit, 0.1 mg/L, and the dissolution rate was less than 1.0%, suggesting good stability of the immobilized product. The concentrations of U in the solutions from the TCLP test were determined with ICP‒MS, and all data are obtained through three replicated tests, and the standard deviation has been calculated. It can be seen from Fig. 3a that the results are shown in Fig. 3. The U concentration was as low as 34 μg/L after the 24 h TCLP test, which is close to the maximum U concentration (30 μg/L) regulated by the international drinking water standard (US EPA) and lower than the maximum U concentration (50 μg/L) by the Regulations on Radiation Protection for Uranium Processing and Fuel Manufacturing Facilities of China (EJ 1056–2005). The standard deviation of the U concentration is large in the first 12 h and then turns small in the later 12 h, which is attributed that the leaching was quite fast at the early stage and went to equilibrium at the later. In further, to evaluate the long term stability of the product, a 120 h dissolution test with the same lixiviant was conducted, shown as Fig. 3b. It can be seen that the U concentration increased rapidly in 18 h then trends to equilibrium, and the equilibrium value is approximately 38 μg/L. It can be therefore concluded that the U phase, meta-autunite, in the immobilized product, HAP-U, is highly stable in those media, indicating good dissolution stability, which is conducive to safe storage.

Fig. 3
figure 3

TCLP test for HAP-U at pH 4.93 for a 24 h and b 120 h

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Thermodynamic model for meta-autunite dissolution

The dissolution stability of the U immobilization product is directly related to the factors of the surrounding environment for product storage, especially pH and Eh. In general, the U immobilization products are stored in the U tailings pond, which is weakly acidic and oxidizing with a pH range of 5.5–6.5. Moreover, the dissolution stability of the U immobilization product in this study is essentially the dissolution stability of meta-autunite. Therefore, a thermodynamic analysis for meta-autunite dissolution in the oxidized and weakly acidic conditions of pH 5.5–6.5 was carried out to reveal the dissolution stability of the U immobilization product.

Solubility product

The dissolving reaction of meta-autunite at pH 5.5–6.5 is shown as Eq. (6):

$${\text{Ca}}\left( {{\text{UO}}_{{2}} } \right)_{{2}} \left( {{\text{PO}}_{{4}} } \right)_{{2}} \cdot{\text{3H}}_{{2}} {\text{O}} + {\text{2H}}^{ + } \to {\text{Ca}}^{{{2} + }} + {\text{2HPO}}_{{4}}^{{{2} - }} {\text{ + 2UO}}_{{2}}^{{{2} + }} + {\text{ 3H}}_{{2}} {\text{O}}$$
(6)

According to the van’t Hoff isothermal law (Eq. 7):

$$\Delta G^{\theta } = \Delta H^{\theta } - T\Delta S^{\theta } = - {\text{R}}T{\text{ln}}K$$
(7)

where ΔGθ (KJ/mol) is the standard reaction Gibbs free energy, ΔHθ (KJ/mol) is the standard reaction enthalpy of production, ΔSθ (J/(mol·K)) is the standard reaction entropy change, R is the constant (8.314 J/(mol·K)), T is the temperature (K), and K is the standard reaction equilibrium constant. The solubility product (Ksp) is equal to K because Eq. (6) reflects the dissolution process of meta-autunite.

The ΔHθ was calculated by the thermodynamic data (Table S5) to be 667.95 J/(mol k), suggesting an endothermicity of the dissolution reaction. In addition, the quantitative relationship between log Ksp and T was determined by Eq. 7, and the outcome is shown in Fig. S3. It is observed that log Ksp decreases with increasing temperature, and when T is 298 K, log Ksp is − 19.5, which is very close to the value of − 19.43 reported in previous literature [36].

Species distribution of U(VI) and P(V)

The chemical formulas and thermodynamic data for the calculations of the U(VI) and P(V) species are shown in Table S5, and all these data are from the Phreeq C program. The speciation diagrams for U(VI), P(V), and the coexistence of U(VI) and P(V) (Fig. 4) were drawn using a general calculation for the formula and the data in Table S5. It should be noticed that to simplify the calculation, Fig. 4 shows the major cations required but not all the U species. The dominant species are HPO42−, H2PO4−, (UO2)3(OH)5+, (UO2)4(OH)7+, UO2PO4− and UO2HPO4 in the U(VI)–P(V) aqueous system when the pH is 5.5–6.5. Therefore, the occurrence and transformation of these species are primarily considered in the subsequent development of the thermodynamic model.

Fig. 4
figure 4

Speciation diagram for a P(V); b U(VI) and c coexistence of P(V) and U(VI) at 25 °C

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Dissolution equilibrium of U from meta-autunite

Based on the dominating species, including HPO42−, H2PO4−, (UO2)3(OH)5+, (UO2)4(OH)7+, UO2PO4− and UO2HPO4, in the U(VI)–P(V) aqueous system with a pH of 5.5–6.5, all equilibrium formulas for the species were determined (see Table 1). The analysis of dissolution equilibrium of U from meta-autunite starts from Table 1.

Table 1 Equilibrium equations for the dominant species
Full size table

First, according to Eq. (6), the equilibrium constant of the dissolution reaction can be expressed as:

$$K = \frac{{a({\text{UO}}_{2}^{2 + } )^{2} *a({\text{HPO}}_{2}^{2 - } )^{2} *a({\text{Ca}}^{2 + } )}}{{a({\text{H}}^{ + } )^{2} }}$$
(14)

where ai (mol/L) is the activity of ion i.

The chemical equilibrium constants for Eqs. (8)–(13) are defined as KUP1, KUP2, KP1, KP2, KU1 and KU2, respectively, and they can be expressed as follows:

$$K_{{{\text{UP1}}}} = \frac{{a\left( {{\text{UO}}_{2} {\text{PO}}_{4}^{ - } } \right)}}{{a\left( {{\text{PO}}_{4}^{3 - } } \right)*a({\text{UO}}_{2}^{2 + } )}}$$
(15)
$$K_{{{\text{UP1}}}} = \frac{{a\left( {{\text{UO}}_{2} {\text{HPO}}_{4} } \right){ }}}{{a\left( {{\text{PO}}_{4}^{3 - } } \right)*a\left( {{\text{UO}}_{2}^{2 + } } \right)*a\left( {{\text{H}}^{ + } } \right)}}$$
(16)
$$K_{{{\text{P1}}}} = \frac{{a\left( {{\text{HPO}}_{4}^{2 - } } \right)}}{{a\left( {{\text{PO}}_{4}^{3 - } } \right)*a\left( {{\text{H}}^{ + } } \right)}}$$
(17)
$$K_{{{\text{P2}}}} = \frac{{a\left( {{\text{H}}_{2} {\text{PO}}_{4}^{ - } } \right)}}{{a\left( {{\text{H}}^{ + } } \right)*a\left( {{\text{HPO}}_{4}^{2 - } } \right)}}$$
(18)
$$K_{{{\text{U1}}}} = \frac{{a\left( {({\text{UO}}_{2} )_{3} \left( {{\text{OH}}} \right)_{5}^{ + } } \right)*a\left( {{\text{H}}^{ + } } \right)^{5} }}{{a({\text{UO}}_{2}^{2 + } )^{3} }}$$
(19)
$$K_{{{\text{U2}}}} = \frac{{a\left( {({\text{UO}}_{2} )_{3} \left( {{\text{OH}}} \right)_{7}^{ + } } \right)*a\left( {{\text{H}}^{ + } } \right)^{7} }}{{a({\text{UO}}_{2}^{2 + } )^{4} }}$$
(20)

The total activities of U and P in the system are defined as [U(VI)]T and [P(V)]T, respectively. According to mass conservation, [U(VI)]T and [P(V)]T are expressed as:

$$\left[ {{\text{U}}\left( \text{VI} \right)} \right]_{{\text{T}}} = a\left( {{\text{UO}}_{2}^{2 + } } \right) + a{\text{(UO}}_{{2}} {\text{PO}}_{{4}}^{ - } {)}+ a{\text{(UO}}_{{2}} {\text{HPO}}_{{4}} {)}+a{\text{((UO}}_{{2}} {)}_{{3}} {\text{(OH)}}_{{5}}^{ + } {)}+a{\text{((UO}}_{{2}} {)}_{{3}} {\text{(OH)}}_{{7}}^{ + } {)}$$
(21)
$$\left[ {{\text{P}}\left( \text{V} \right)} \right]_{{\text{T}}} = a\left( {{\text{H}}_{2} {\text{PO}}_{4}^{ - } } \right) + a\left( {{\text{HPO}}_{{4}}^{{{2} - }} } \right) + a\left( {{\text{UO}}_{2} {\text{PO}}_{4}^{ - } } \right) + a\left( {{\text{UO}}_{2} {\text{HPO}}_{4} } \right)$$
(22)

\(a({\text{UO}}_{2}^{2 + } )a\left( {{\text{PO}}_{4}^{3 - } } \right)\) and \(a\left( {{\text{H}}^{ + } } \right)\) are set as variables A, B and X, respectively, to simplify the calculation. According to Eqs. (15), (16), (19), (20) and (21), [U(VI)]T can be further expressed as:

$$\left[ {{\text{U}}\left( {{\text{VI}}} \right)} \right]_{{\text{T}}} = A + K_{{{\text{UP1}}}} AB + K_{{{\text{UP2}}}} ABX + \frac{{ K_{{{\text{U1}}}} A^{3} }}{{X^{5} }} + \frac{{K_{{{\text{U2}}}} A^{4} }}{{X^{7} }}$$
(23)

Similarly, according to Eqs. (15–18), and (12) can be further expressed as:

$$\left[ {{\text{P}}\left( \text{V} \right)} \right]_{{\text{T}}} = B + BK_{{{\text{P1}}}} X + K_{{{\text{P2}}}} K_{P1} BX^{2} + K_{{{\text{UP1}}}} AB + K_{{{\text{UP2}}}} ABX$$
(24)

As seen from Eq. (6), congruent dissolution of meta-autunite occurred in the pH range of 5.5–6.5, indicating the 1:1 molar ratio of U(VI):(P(V) and 1:2 molar ratio of Ca(II):U(VI) in the aqueous solution, as shown in Eqs. (25) and (26):

$$\left[ {{\text{U}}\left( \text{VI} \right)} \right]_{{\text{T}}} = \left[ {{\text{P}}\left( \text{V} \right)} \right]_{{\text{T}}}$$
(25)
$${2}\left[ {{\text{Ca}}\left( {\text{II}} \right)} \right]_{{\text{T}}} = \left[ {{\text{U}}\left( \text{VI} \right)} \right]_{{\text{T}}}$$
(26)

Combining Eqs. (23), (24) and (25), a relationship of A, B, and X is expressed as Eqs. (27), and (28) can be further obtained through a mathematical operation.

$$A + K_{{{\text{UP1}}}} AB + K_{{{\text{UP2}}}} ABX + \frac{{ K_{{{\text{U1}}}} A^{3} }}{{X^{5} }} + \frac{{K_{{{\text{U2}}}} A^{4} }}{{X^{7} }} = B + BK_{{{\text{P1}}}} X + K_{{{\text{P2}}}} K_{{{\text{P1}}}} BX^{2} + K_{{{\text{UP1}}}} AB + ABX$$
(27)
$$B = \frac{{ AX^{7} + K_{{{\text{U1}}}} A^{3} X^{2} + K_{{{\text{U2}}}} A^{4} }}{{(1 + K_{{{\text{P1}}}} X + { }K_{{{\text{P1}}}} K_{{{\text{P2}}}} X^{2} )X^{7} }}$$
(28)

[Ca(II)]T is expressed as Eq. (29) by substituting [U(VI)]T of Eq. (26) with Eq. (23).

$$\left[ {{\text{Ca}}({\text{II}})} \right]_{{\text{T}}} \,= \left[ {A + K_{{{\text{UP1}}}} AB + K_{{{\text{UP2}}}} ABX + \frac{{ K_{{{\text{U1}}}} A^{3} }}{{X^{5} }} + \frac{{K_{{{\text{U2}}}} A^{4} }}{{X^{7} }}} \right]$$
(29)

Equation (30) is obtained by processing Eq. (17) and Eq. (14):

$$A^{2} = \left[ {\frac{{KX^{2} }}{{\left[ {{\text{Ca}}\left( {{\text{II}}} \right)_{{\text{T}}} } \right](BK_{{{\text{P1}}}} X)^{2} }}} \right]$$
(30)

Then, Eq. (31) can be obtained by substituting [Ca(II)]T of Eq. (30) with Eq. (29):

$$A^{3} = \left[ {\frac{2K}{{\left[ {1 + { }K_{{{\text{UP1}}}} {\text{B}} + K_{{{\text{UP2}}}} {\text{BX}} + \frac{{ K_{{{\text{U1}}}} A^{2} }}{{X^{5} }} + \frac{{ K_{{{\text{U2}}}} A^{3} }}{{X^{7} }}} \right](BK_{{{\text{P1}}}} )^{2} }}} \right]$$
(31)

The relationship of A ~  X and B ~ X can be theoretically determined by processing Eqs. (28) and (31). Afterwards, the relationship of [U(VI)]T ~  X is obtained by replacing A and B of Eq. (23) with the obtained relationship A  ~  X and B ~  X. Therefore, [U(VI)]T can be expressed as:

$$\left[ {{\text{U}}\left( \text{VI} \right)} \right]_{{\text{T}}} = a\left[ {{\text{UO}}_{2}^{2 + } \left] { + { }10^{13.23} a} \right[{\text{UO}}_{2}^{2 + } \left] a \right[{\text{PO}}_{4}^{3 - } } \right] + 10^{19.59} a\left[ {{\text{UO}}_{2}^{2 + } \left] a \right[{\text{PO}}_{4}^{3 - } \left] a \right[{\text{H}}^{ + } } \right] + \frac{{ 10^{ - 15.55} a\left[ {{\text{UO}}_{2}^{2 + } } \right]^{3} }}{{a\left[ {{\text{H}}^{ + } } \right]^{5} }} + \frac{{ 10^{ - 21.90} a\left[ {{\text{UO}}_{2}^{2 + } } \right]^{4} }}{{a\left[ {{\text{H}}^{ + } } \right]^{7} }}$$
(32)

of which, \(a\left[ {UO_{2}^{2 + } } \right] = f_{1} \left( {a\left[ {H^{ + } } \right]} \right)\), \(a\left[ {PO_{4}^{3 - } } \right] = f_{2} \left( {a\left[ {H^{ + } } \right]} \right)\).

Because the ionic strength I in the dissolution aqueous system is extremely low, the activity coefficient of each ion is regarded as 1. The total U concentration is therefore equal to its activity.

$$c\left( {{\text{U}}\left( \text{VI} \right)} \right)_{{\text{T}}} = \left[ {{\text{U}}\left( \text{VI} \right)} \right]_{{\text{T}}}$$
(33)

Meanwhile, the relationship of pH ~ a(H+) is shown in Eq. (34).

$${\text{pH = }} - {\text{log}}a\left( {{\text{H}}^{ + } } \right)$$
(34)

Therefore, the relationship of c(U(VI))T ~ pH can be obtained through Eqs. (33) and (34):

$$c\left( {{\text{U}}\left( \text{VI} \right)} \right)_{{\text{T}}} = f\left( {{\text{pH}}} \right)$$
(35)

Theoretically, the c(U(VI))T–pH curve can be drawn by Eq. (35), but the formula is extremely complex; hence, a method of substitution, which sets the initial pH in the range of 5.5–6.5 with an interval of 0.1 (pH of 5.5, 5.6…6.5), was applied to calculate c(U(VI))T at each pH. Finally, the discrete points of [x = pH, y = c(U(VI))T] on coordinate were smoothly connected to present the c(U(VI))T–pH curve, shown as Fig. 5.

The concentration of dissolved U is generally extremely low at pH 5.5–6.5, and it is maintained at 4–5 µg/L when the pH is between 5.5 and 6.2. When the pH is higher than 6.3, c(U(VI))T increases significantly, and the equilibrium concentration of U is 48 µg/L at pH 6.5 (Fig. 5). These results are consistent with a general thermodynamic model for solubility calculations with varying pH values (2 − 6) using 100 μM U(VI) and 500 μM P(V), Ca2+, Mg2+, and Na+ [37]. Moreover, to verify the predictability of the dissolution model, a dissolution test for HAP-U was carried out. HAP-U samples were immersed in diluted nitric acid solutions of different pH values with an S/L of 0.05 g/L for 24 h. After testing, ICP‒MS was used to determine the concentration of total U in the solution, and the results are shown in Fig. 5, which are indicated with red dots. The experimental points strongly overlap with the model curves, indicating that the model has good predictability and is available to evaluate the dissolution stability of HAP-U products.

Fig. 5
figure 5

Total concentration of U at equilibrium as a function of pH

Full size image

In summary, this thermodynamic model adequately explains the extremely high dissolution stability of HAP-U, as well as the high efficiency of uranium immobilization with phosphates. This study provides a reference for future research on the dissolution stability of uranium immobilization products in phosphate systems and the long-term safe storage of products bearing uranium minerals. On the other hand, such a low U equilibrium concentration of meta-autunite dissolution is very meaningful for the extraction of U from seawater that contains approximately 3–7 µg/L U as well as the recovery of U from extremely low concentrations of U-containing solutions and suggests the possibility of U extraction or recovery by an immobilization process with phosphate.

Conclusion

Immobilization of U with HAP was experimentally investigated, and the optimal conditions were determined to be pH = 3, S/L of 1.0 g/L, initial U concentration of 150 mg/L, and immobilization time of 2 h. Under this condition, the immobilization efficiency and capacity of U were almost 100% and 105 mg/g, respectively. Theoretical analysis of the immobilization process showed that the kinetics of U immobilization on HAP fit the pseudosecond order kinetic model well, and the correlation coefficient (R2) was above 0.99. Moreover, the thermodynamic mechanism of U immobilization conformed to the Freundlich isotherm. The characterizations of the immobilization product, HAP-U, obtained under the optimal conditions indicated that meta-autunite formed through mineralization with the reaction between uranyl ions, Ca2+, and P(V) on the layer of HAP during immobilization. The tests of dissolution solubility for HAP-U indicated that the concentration of dissolved U from the HAP-U in HNO3 (pH = 5.0), H2SO4 (pH = 5.0), natural rainwater (pH = 5.6), and tap water (pH = 7.1) at different temperatures (30, 40, 50, and 60 °C) was below 0.1 mg/L, and further that in the TCLP test U was as low as 34 μg/L, suggesting an extremely high dissolution stability; HAP-U is therefore conducive to safe storage.

To reveal the dissolution behaviours of the U immobilization product, a thermodynamic model of the U mineral phase, meta-autunite, was developed. The log Ksp of the meta-autunite was calculated as − 19.5. The speciation diagram for P(V)-U(VI) in aqueous solution was drawn, and the dominant species were determined to be HPO42−, H2PO4−, (UO2)3(OH)5+, (UO2)4(OH)7+, UO2PO4− and UO2HPO4 at pH 5.5–6.5, which is close to the pH of the surrounding environment for product storage. The dissolution equilibrium of U from meta-autunite was specifically illustrated with thermodynamic calculations. The total concentration of dissolved U at equilibrium as a function of pH was revealed, which indicated that the concentration of dissolved U was extremely low at 4–5 µg/L at pH 5.5–6.2 and 48 µg /L at pH 6.5, and these results were further verified by dissolution tests. The outcome of this research provides possibilities for the extraction or recovery of U with an immobilization process from extremely low concentrations of U-containing solutions, especially seawater.