Prediction of calcium phosphate generation and behaviors of metals during phosphorus recovery using a modified thermodynamic model

Phosphorus is a vital element for humans, animals, and all plants. However, economically exploitable rock resources of phosphate will be depleted in the mid-21st century (Steen 1998; Pindine et al. 2021). Most of the phosphate rock is converted into fertilizer, but only 20% of the applied phosphate fertilizer is consumed by plants and animals and a large amount of phosphorus is discharged into natural water bodies (Peng et al. 2018b). Phosphorus in sewage and industrial wastewater is not only a kind of nutrient pollutant responsible for serious eutrophication in enclosed water bodies (besides nitrogen) but also a reservoir of phosphorus resources. With a relatively high concentration in fruit and vegetable wastewater (200–400 mg·L⁻¹), phosphorus can be recovered and reused by the selected adsorbents (Qin et al. 2022). To recover phosphorus in human urine (150–250 mg·L⁻¹) and reject water after sludge dewatering (approximately 150 mg·L⁻¹), seawater was used as a precipitant to form struvite (Dai et al. 2014; Shaddel et al. 2020). But with a relatively low concentration (typically 5 mg·L⁻¹) in sewage, it is difficult to recover directly, although the recovered phosphorus from sewage can satisfy 15–20% of the world's demand for phosphorus (Yuan et al. 2012). The pretreatment by the membrane and microbial fuel cells has great potential for phosphorus recovery because of the enrichment of phosphorus (Peng et al. 2018a), but other participating ions are also concentrated at the same time, which could have a negative effect on the recovery. It is reported that phosphorus in sewage was recovered by fluidized bed crystallization of vivianite after biofilm enrichment (Zhou et al. 2022). By the worldwide application of the enhanced biological phosphorus removal (EBPR) process, phosphorus is transferred to excess sludge. Phosphorus could be recovered from sewage sludge or the ash of incinerated sewage sludge (Cornel & Schaum 2009; Cieślik & Konieczka 2017). Enhanced phosphorus recovery can be carried out using the released phosphorus from sewage sludge with anaerobic-based treatment (Yu et al. 2021), thermal (Meng et al. 2019), and thermochemical treatment (Galey et al. 2022), or using the extracted phosphorus from sewage sludge ash with the wet chemical extraction (Boniardi et al. 2021) and the electrodialytic process (Guedes et al. 2014). The major challenge for phosphorus recovery from sewage sludge or sewage sludge ash is the higher concentration of metallic ions than that in sewage caused by bio-adsorption of sewage sludge, and the pretreatment with ion-selective nanofiltration could be an effective way to remove multivalent metal cations (Schütte et al. 2015). Although the phosphorus recovery from sewage sludge or sewage sludge ash is promising for resource recovery, it costs a lot for waste disposal. It is better to reduce the generation of excess sludge and recover the resource from sewage, not from sewage sludge.

In order to reduce excess sludge generation and recover phosphorus from the sewage simultaneously, a kind of advanced sewage treatment process combined with excess sludge reduction and phosphorus recovery (SRPR process) has been developed by incorporating a sludge ozonation unit and a phosphorus crystallization unit into an A/O process (Saktaywin et al. 2005, 2006; Nagare et al. 2008; Tsuno et al. 2008) or an A/A/O process (Tsuno et al. 2008; Qiang et al. 2015). In this advanced SRPR process (Supplementary material, Figure S1), a part of excess sludge (60–80% in this study) was introduced into the sludge ozonation unit, where excess sludge was treated by ozone to decompose cells and obtain soluble organic product and phosphate, and then ozonated sludge (0.67–0.93% of influent in this study) was fed into the A/O process together with influent and untreated return sludge. In the A/O process, phosphate concentration at the end of anaerobic tank reached a relatively high level caused by anaerobic phosphate release and phosphate inflow from raw sewage as well as ozonated sludge. The mixed liquid with relatively high phosphate concentration was partly drawn out of the A/O process at the end of anaerobic tank and separated solid by settlement tank, and then the soluble orthophosphate in the supernatant of anaerobic tank (SAT) in the A/O process, was partly introduced into the phosphorus crystallization unit (P-cry unit) for recovery. Finally, the supernatant of crystallization unit was returned to the aerobic tank of the A/O process. It is one of the advantages of the SRPR process to use SAT for more effective phosphorus recovery because of concentrated phosphorus (typically 20 mg·L⁻¹, approximately 5 mg·L⁻¹ from influent, less than 1 mg·L⁻¹ from ozonated return sludge since its flowrate was less than 1% of raw sewage, and others from anaerobic phosphorus release) but the same level of metallic ions compared to that in raw sewage. If not from SAT, it is reported that the phosphorus in raw sewage could be recovered by 29% from the supernatant of ozonated sludge (Qiang et al. 2015). It should be noted that simultaneous chemical precipitation to remove phosphorus with the addition of iron or aluminum salts is not necessary in this SRPR process. Limited by the ammonia concentration in sewage, calcium phosphates, but not struvite, were generated as the product during phosphorus recovery by the addition of calcium ions and pH adjustment.

As for calcium phosphates, hydroxyapatite (HAP) is the most stable species at normal temperature and pressure. However, its formation will reach equilibrium very slowly over a very much longer time (from a minimum of 1 month to a number of years) than any used in the experiments (Ferguson & McCarty 1971; Musvoto et al. 2000a; Celen et al. 2007; Cao & Harris 2008). In the actual experimental period (30 min in this study), HAP cannot be the main product although many researchers reported as listed in Table 3 by Peng et al. (2018a). In this paper, the possible composition of generated calcium phosphates was discussed based on both thermodynamic considerations and experimental results.

Furthermore, in the P-cry unit of the advanced SRPR process, some may co-precipitate with calcium phosphates, which both decrease the purity of the recovered phosphorus product and affect the accumulation of metals in the advanced sewage treatment process. However, only a few studies have focused on both metals and phosphorus with the objectives of maximizing both P crystal production and their quality (Guney et al. 2008; Keller et al. 2022). In this study, the behavior of metals during phosphorus recovery was examined, and the improvement of not only the phosphorus recovery rate but also its quality was studied by optimizing operational conditions without an additional separation process. For this purpose, the behaviors of K, Mg, Ca, Al, Fe, Cr, Mn, Ni, Cu, Zn, and Ba were investigated with the measured results in batch and continuous experiments as well as thermodynamic simulation.

In this study, phosphorus recovery by calcium phosphates was investigated by both the laboratory and pilot experiments and a thermodynamic model for the advanced SRPR process. As the thermodynamic model predicts the final equilibrium state, it was modified to be applied to the short-term precipitation for actually used cases. Phosphorus recovery and the behavior of metals are discussed using the modified thermodynamic model under operational conditions of pH ranging from 8.0 to 10.0 and molar ratio of Ca/P ranging from 1.67 to 5. The optimized operational conditions were finally obtained which maximized both phosphorus recovery efficiency and quality of the recovered product (minimum of metals co-precipitation).

Thermodynamic modeling is very helpful for understanding the formation of calcium phosphates and their competition with other precipitates, and has been adopted as a powerful tool by many researchers, even though it cannot explain reaction kinetics. Phosphorus crystallization of HAP (Song et al. 2002b) and magnesium ammonium phosphate MAP, (Wang et al. 2006; Song et al. 2015) was investigated using PHREEQC, a fully developed thermodynamic software. Phosphorus recovery by ferric phosphate precipitation from wastewater was examined by PHREEQC and an additional case study (Zhang et al. 2010). Phosphate behavior and the fate of counter ions during hydrothermal carbonization of sewage sludge were investigated by thermodynamic model (Ovsyannikova et al. 2019). Celen et al. (2007) used Visual MINTEQ, a chemical equilibrium model, to predict amendments required to precipitate phosphorus as struvite in liquid swine manure. Phosphorus recovery by MAP from digested sewage sludge using raw seawater (Shaddel et al. 2020) and magnesium salts (Keller et al. 2022) as magnesium source was investigated with thermodynamic models to prevent the co-precipitation of heavy metal ions.

As the initially formed metastable precursors, the generation of the first class of the species (DCPD and ACP) is reported to be a relatively fast process (Musvoto et al. 2000a), while the growth of the second class (the more thermodynamically stable species of DCP, TCP or HAP) takes a much longer time – from a minimum of one month to a number of years (Ferguson & McCarty 1971; Musvoto et al. 2000a; Celen et al. 2007; Cao & Harris 2008).

Without consideration of reaction kinetics, the actual products and composition of calcium phosphates, generated in the operation time range (30 min in this study) during phosphorus recovery, were not able to be predicted by thermodynamic calculation only. However, if the generation of the first class (DCPD and ACP) is fast enough to reach the metastable state in the above reaction time, this metastable state can be predicted by thermodynamic calculation without consideration of the second class (DCP, TCP, and HAP), since its growth is very slow and only generates a very small fraction as discussed above.

Furthermore, it should also be considered that DCPD and ACP generation does not reach full equilibrium under a low pH and a low Ca/P molar ratio for precipitation in as short a period as 30 min. Thus, a correction equation was incorporated based on the experimental results in this study.

Besides calcium phosphates, other important precipitates are calcium carbonates and magnesium carbonates since carbonate could compete with phosphate for calcium ions. Several kinds of minerals are related to calcium carbonates and magnesium carbonates. These include aragonite (CaCO₃), calcite (CaCO₃), vaterite (CaCO₃), dolomite [CaMg(CO₃)₂], huntite [CaMg₃(CO₃)₄], and magnesite (MgCO₃). It has been reported that the presence of Mg²⁺, phosphate, and dissolved organics decreased the precipitation rate of CaCO₃ (Meyer 1984; Musvoto et al. 2000b; Celen et al. 2007) and that dolomite also exhibited a slow precipitation rate (Mamais et al. 1994; Celen et al. 2007). No more than a tiny fraction of these two kinds of precipitate could generate in a reaction time of only 30 min and they were not considered in this study, while huntite and magnesite were included during thermodynamic modeling.

In this study, precipitation experiments of both batch tests (case 1 and case 2) and continuous operations of a pilot-scale reactor of the advanced SRPR process (case 3) were carried out to investigate the phosphorus recovery by calcium phosphates. The corresponding experimental conditions in the three cases are listed in Table 1. In case 1, the test water was prepared by ultrapure water (UPW) and contained only calcium ions and phosphates. In case 2 and case 3, supernatant from the outflow of the anaerobic tank (SAT) in A/O process (Supplementary material, Figure S1) was employed as the source water. A pilot-scale sequencing batch reactor (SBR) was run as an A/O process using artificial sewage, which only contained essential metals for microorganism growth (Saktaywin et al. 2005) in cases 2-1 and 3-1 (low metal level), while containing typical metal composition similar to actual sewage (Asai et al. 2005) in cases 2-2, 2-3, and 3-2 (high metal level).

In all batch tests, phosphate was fixed at 20 mg-P·L⁻¹ as the designed inlet concentration of phosphorus to the recovery unit. The different molar ratio of Ca/P was obtained by the adjustment of the calcium concentration, while pH was adjusted by the addition of 1-N NaOH. Besides the batch tests, continuous operation of the advanced SRPR process (Supplementary material, Figure S1) was carried out for about 2.5 months in case 3-1 and 7 months in case 3-2 with two sub-phases (phase 2 and phase 3). More details of the material and methods of experiments are shown in the first part of the Supplementary material.

Besides the above batch investigation, the continuous operations of the advanced SRPR process were carried out with two kinds of artificial sewage, which resulted in relatively low and high metals content in the SAT, i.e., the inflow to the P-cry unit, for cases 3-1 and 3-2, respectively.

The phosphorus recovery rate in continuous experiments using an SAT with low metals content (case 3-1) was 77.1 ± 5.3% under pH of 8.3–9.1 and a Ca/P molar ratio of 2.6–3.3, which was almost the same as that of the batch test.

As for the experimental results of continuous operation using an SAT with high metal content in case 3-2, phosphate was shown to recover more than 90% under pH of 9.0–9.5 and a Ca/P molar ratio of 3–5 (Supplementary material, Figure S3(a)). Higher Ca/P molar ratio and pH in case 3-2 than that in case 3-1 contribute to higher phosphorus recovery rate. In comparison with batch tests under a pH of 9.0 and a Ca/P molar ratio of 4.0, the results of phosphorus recovery and co-precipitation of metals in continuous experiments were in accordance with those in the batch test for phosphorus and most metals, but not for barium, copper, iron, and aluminum (Supplementary material, Figure S3(b)). The bio-adsorption of sewage sludge was assumed to contribute to the removal of barium, copper, iron, and aluminum since batch experiments were carried out with filtrated SAT, while pilot continuous experiments with settled SAT, which contained suspended solids of activated sludge.

As discussed above, the generation of the first class of calcium phosphates (DCPD or ACP) was considered during thermodynamic modeling, and their generation reactions were shown in Equations (1) and (2), respectively. Their corresponding solubility products, reported in the literature, are shown in Figure 1.

During thermodynamic modeling of phosphorus recovery, the following aspects need to be considered: (1) all precipitated solids besides the above calcium phosphates and calcium carbonates; (2) all soluble species, such as H⁺, OH⁻, H₂O, H₃PO₄, ⁠, ⁠, ⁠, H₂CO₃, ⁠, ⁠, NH₃, ⁠, and all metallic ions; (3) the equilibrium equations of all soluble and precipitated species mentioned above, the mass balance of all elements, and the charge balance of solution; and (4) the effects of temperature, activity, and alkalinity.

In this study, the fully developed free software, Visual MINTEQ (Allison et al. 1991), was employed as a tool for thermodynamic calculation. All the factors mentioned above were dealt with by the software, except for the modification of the database to exclude the species with a slow generation rate (HAP, TCP, DCP, OCP, all CaCO₃, and dolomite). ACP was not originally included in the database of Visual MINTEQ (version 3.0 and released in April 2010) but was added to the database with the solubility product constant (pK_s = 26.52) and the molar ratio of calcium and phosphate (Barat et al. 2008).

In batch experiments, it was found that all measured molar ratios of Ca/P in the precipitates were in the range of 1.0–1.5, which was lower than 1.67 (molar Ca/P in HAP). The lower molar ratio of Ca/P indicated HAP was not the main component in generated calcium phosphates with a reaction time of 30 min as discussed above, while the mixture of ACP (Ca/P = 1.5) and DCPD (Ca/P = 1.0) had a high possibility of being the precipitated product. If only ACP and DCPD were contained in the recovery product, in case 1, their generation amounts and ratios in the product were calculated by actual measured calcium and phosphate according to the mass balance of Ca and P. Corresponding calculations can be carried out in cases 2-2 and 2-3 after considering the co-precipitation of calcium by carbonate. It is confirmed that magnesium precipitated only with carbonate by huntite and magnesite according to thermodynamic calculation results. Thus, precipitated calcium by carbonate could be obtained from the measured magnesium precipitation amount and the molar ratio of Ca/Mg in precipitates according to thermodynamic calculation results.

The comparison of the measured P recovery rate and the calculated one, after correction by Equation (5), is shown in Figure 5(c), which indicates that calculated results accorded well with measured ones after correction (R² = 0.900 for P recovery rate).

The final predicted ratio of calcium in the precipitates with correction of the thermodynamic calculation by Equation (6) was compared to the measured results as shown in Figure 5(d). After correction, the model was able to predict calcium behavior very well (R² = 0.980).

To clarify the behavior of metals with the actual inlet concentrations of the P-cry unit in the advanced SRPR process, the thermodynamic calculation was carried out using actual inflow metal concentrations and initial phosphate concentration of 20 mg-P·L⁻¹ for both batch tests (case 2-2 and case 2-3).

The comparison of the precipitation ratios of metals between measured results and those of thermodynamic calculation with different pH and molar ratio of Ca/P of 3.0 in case 2-3 is shown in Figure 6(b), which was similar to that in Figure 6(a). These results showed the limitation of thermodynamic modeling that should be paid attention to for the actual application of thermodynamic modeling.

Thermodynamic modeling results showed that not only phosphorus recovery efficiency but also recovered product purity depends on the operational conditions (pH and molar Ca/P). In case 2-2, increased initial calcium concentration contributed to the generation of huntite and other precipitates under the calculation conditions, which led to the increased amount of impurity (co-precipitated solid besides for ACP and DHCP) with an elevated Ca/P molar ratio (Supplementary material, Figure S4(a)). In case 2-3, when pH was more than 8.5, the amount of impurity significantly increased as pH level rose, resulting in a clear decrease of the P ratio in the recovered product (Supplementary material, Figure S4(b)).

In the application of the modified thermodynamic model, the phosphorus recovery efficiency and behavior of metals as well as their effects on the quality or purity of recovered product with a pH of 8–10 and a Ca/P molar ratio of 1.67–5 were predicted. Thermodynamic calculation results indicated that more than 90% of phosphorus could be recovered under any of the following conditions: pH = 8.5 and Ca/P ≥ 4 or pH = 9 and Ca/P ≥ 3 or pH = 9.5 and Ca/P ≥ 2 (Supplementary material, Figure S5(a)). However, with the increase of pH and molar ratio of Ca/P, the percentage of recovered phosphorus in the product decreased from about 20 to 10% (Supplementary material, Figure S5(b)), since the amount of impurity very noticeably increased from about 2 to 70 mg/L (Supplementary material, Figure S5(c)).

Phosphorus contents in the recovered product clearly decreased as both pH and the molar ratio of Ca/P increased. Thus, an overly high pH or molar ratio of Ca/P should be avoided considering the generation of impurity or the co-precipitation of metals. On the other hand, a pH of 9.0 and a Ca/P molar ratio of 3.0 were essential operational conditions for a recovery rate of more than 80% phosphorus according to experimental results (Supplementary material, Figure S2 and Figure 2). From the perspective of maximizing both phosphorus recovery efficiency and the quality or purity of recovered product, a pH of 9.0 and a Ca/P molar ratio of 3.0 were found to be the optimized operational conditions for phosphorus recovery with calcium phosphates in the advanced SRPR process where the content of the influent metal was at the level of actual municipal sewage.

In this study, phosphorus recovery by calcium phosphate and behaviors of metals were simulated by a modified thermodynamic model, in which precipitated phosphate and calcium were modified by incorporating correction equations, and the precipitated product was assumed to be ACP and DCPD only to simulate the short-term precipitation of calcium phosphates based on the experimental results and literature review. The modified thermodynamic model was verified with the experimental results of both batch tests and continuous experiments. Finally, phosphorus recovery and the behavior of metals were predicted by the modified thermodynamic model for the actual application of advanced sewage treatment process. The following main results are obtained:

• Batch experimental results indicated that phosphorus recovery efficiency decreased with the increase in metal content and more than 80% phosphorus can be recovered with a Ca/P molar ratio of 3.0 and a pH of 9.0 for SAT containing a high metal level.

• According to measured calcium and phosphate precipitation ratios, it was confirmed that HAP was not the main product in recovered phosphate, while the mixture of ACP and DCPD had a high possibility.

• A precipitated molar ratio of Ca/P in the recovered product was augmented with an increase in the initial Ca/P molar ratio or pH. Correspondingly, the ACP ratio in the recovered product increased while the DCPD decreased.

• ACP generation without the negative effect of other metals and carbonate in case 1 was more than that with metals and carbonate existing in case 2.

• The precipitated metal content, i.e., the impurity in the recovered product, clearly increased with an increase in both pH and the molar ratio of Ca/P for SAT with high metal contents.

• According to experimental results, the following correction equations were proposed with R² of 0.900 for phosphorus recovery rate and 0.980 for calcium precipitation rate.

  

  

  

From the perspective of maximizing both the efficiency of phosphorus recovery and elevated quality or purity of recovered product, co-precipitation of metals should be controlled at a low level, it was concluded that a pH of 9.0 and a Ca/P molar ratio of 3.0 were the optimized operational conditions for phosphorus recovery with calcium phosphates in the advanced SRPR process where the content of the influent metal was at the level of actual municipal sewage.

This work was supervised by Prof. Hiroshi TUSNO in Lake Biwa Environmental Research Institute and Prof. Hideaki NAGARE in Okayama University.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.