Phosphorus recovery from aqueous solutions using Bioclastic Granules (Lithothamnium calcareum)

Against the growing world demand for food and the possibility of recovering some nutrients, this work focused on the evaluation of the use of Bioclastic Granules (BG) from the algae Lithothamnium calcareum as sorbent material for the removal/recovery of phosphorus from aqueous solutions. The main variables that affect the sorption process, pH, initial concentration of phosphate, and GB, as well as the contact time, were evaluated. The effect of pH was very significant, obtaining the best results of PO43− removal at pH 5. In the coarser granulometric fractions (+ 106 − 150 and + 210 − 300 μm), the best removals were observed (around 75%). Regarding the initial PO43− concentration in the solutions, the highest removal (in the range of 74 to 78%) was observed in the lowest concentrations (5 to 70 mg L−1) and the best uptake (10 to 14 mg g−1) at higher concentrations (200 to 420 mg L−1). The PO43− sorption data fitted the Freundlich model well, with kF of 1.35 L mg−1 and n of 2.43. A qmax of 14.35 mg g−1 was obtained using the Langmuir model. Regarding the sorption data over time, a better fit to the pseudo-first-order kinetic model was observed, obtaining a calculated qeq of 6.56 mg g−1 and a k1 of 0.0073 min−1. The incorporation of PO43− ions in the GB structure was confirmed through the characterization results before and after the sorption experiments using X-ray fluorescence (FRX) and scanning electron microscopy (SEM) techniques.


Introduction
Contamination of water resources by different pollutants such as PAHs (Onydinma et al. 2021), trace metals (Ukaogo et al. 2022), NOM (Feng et al. 2022), and nutrients such as N and P (Salo and Salovius-Laurén 2022) ends up producing adverse effects on human health, configuring as direct or indirect precursors of different diseases. An important impact has been the acceleration of artificial eutrophication with the increase of nutrient concentration and organic matter, mainly of phosphate compounds, that tend to enlarge the biological production in rivers, lakes, and reservoirs (Martín-Hernández et al. 2022).
Recently, the water treatment system of Guandu, which is responsible for most of the potable water destined for the population of the Metropolitan Region of Rio de Janeiro, suffered from the introduction of phosphorus and other nutrients in its water. Those contaminants come from effluents that are discarded without receiving proper treatment, being from either domestic and/or industrial origin, arising from river dos Poços and Ipiranga, both rivers that disembogue at the river Guandu, near the catchment point called Guandu lake. This guarantees the ideal nutritional portion, so, in periods of intense solar radiation, algae and cyanobacteria can produce residual substances giving an unpleasant taste and odor to the water, such as Geosmin (trans-1, 10 dimethyl-trans-9 decalol) and 2-MIB (2-methylisobomeol) (Kim et al. 1997). In addition, certain species produce, under specific circumstances, substances that present risk to human health (Volschan 2022).
The sanitary sewers constitute the main anthropogenic source of phosphorus in natural waters. According to Larsen and Gujer (1996), some sanitary effluents, when submitted to a previous separation, can present a composition with up to 50% of phosphorus. The compound is inserted through extremely concentrated detergents along with fecal matter itself, which is rich in proteins (Piveli 2015). Other industrial effluents contribute as well to the contamination of waters with phosphorus, many times due to an intrinsic inefficiency of the treatment process. Biological systems remove phosphorus in low amounts, using it in the production of biomass through cell growth of heterotrophic bacteria, or even in mixed cultures involving microalgae and bacteria synergistically (Ahmed et al. 2022). On the other hand, physicochemical systems tend to be inefficient when the concentration of phosphorus is low. In addition, there is a problem on generating a huge amount of sludge containing metals in general (Tchobanoglous et al. 2016).
The phosphorus utilized in agricultural practices is normally obtained from phosphate rock mines that are being depleted in an alarming rate due to an increase in demand of this mineral (Lamont et al. 2019). Phosphorous shortages have very important implications for global food security; therefore, it should be analyzed in a broader and more integrated sustainability context, providing alternative sources of phosphorus supply, such as its recovery from effluents (Neseta and Cordell 2012). According to the Food and Agriculture Organization (FAO 2021), growth in the middle-class population increases the consumption of products, whose production demands a higher quantity of grains and water, increasingly pushing agricultural systems. Some treatment methods to reduce waste in food production and distribution, thus valuing the waste generated in this chain, are already well known, such as composting, anaerobic and aerobic digestion, and the production of biofertilizers (O'Connor et al. 2021). These methods produce waste that can reduce the loss of fertile soils and water pollution, as these end up being deposited in landfills. However, in many cases, these residues have a more acidic pH and lack other trace elements necessary for plant nutrition (Reyes-Torres et al. 2018;Facchin et al. 2013). Given the context, the necessity of research and implementation of innovative techniques becomes clear.
Brazil needs to develop its own technologies for the obtainment of raw material and new fertilizers geared towards the geoclimatic and pedologic conditions of our soils. In these circumstances, the continental limestone (known as marine bioclastic limestone) emerges as an alternative of soil conditioner or nutrients carrier (Veneu 2017). The Bioclastic Granule (BG) is an important mineral resource due to its versatility with the possibility of being utilized as animal feed supplement, human nutrition, pharmacology/cosmetics, biotechnology (Briand 1976), on agriculture as a fertilizer and soil corrector (Blunden et al. 1997;Lima et al. 2002;Melo and Furtini Neto 2003), and most recently, on the treatment of water and effluents (Gray et al. 2000;Veneu et al. 2017;Caletti 2017;Veneu et al. 2017;Almeida 2018;Veneu et al. 2018a, b;Nogueira 2019;Melo et al. 2019;Silva et al. 2021). Wu et al. (2020) highlights the importance of investigating selective phosphate sorption by certain sorbents that can be reused after the process, adding to the ice a high concentration of phosphate. It is possible to observe, despite verified technical work and relevant information about the material, that technical literature has an insufficient amount of information and data that could elucidate, in a more consistent way, the application of the enriched Bioclastic Granule as a soil additive. Through the retention/adsorption of some elements contained in effluents, especially phosphorus, the Bioclastic Granule could be posteriorly utilized as a fertilizer/soil conditioner.
The present study evaluated the capacity and efficiency of Bioclastic Granules (BG) from Lithothamnium calcareum algae limestone to act as a sorbent material for the treatment of aqueous solutions containing PO 4 3− ions.

Bioclastic Granules and reagents
A sample of approximately 5 kg of Bioclastic Granules (Lithothamnium calcareum) was provided by the company Oceana Minerals LTDA with different particle sizes (+ 210 − 300 μm; + 106 − 150 μm; + 53 − 75 μm, and − 38 μm). A bar mill followed by separation in series was utilized for the obtainment of these particles. Initial tests with synthetic effluents were realized with solutions prepared with the salt KH 2 PO 4 (99%) provided by Sigma-Aldrich in deionized water.

Sorption batch experiments
Factors affecting BG sorption rate and uptake capacity were studied on a bench scale. All assays were performed in 250-mL Erlenmeyer flasks, employing 150 mL of solution containing ions of PO 4 3− , rotation velocity of 250 rpm in a horizontal platform (CIENLAB CE-720).
Succeeding the sorption tests, the BG were deposited through a digital bench centrifuge (CIENTEC CT-6000), rotating in 5000 rpm, in falcon tubes of 50 mL. The supernatant was filtered with a membrane of cellulose acetate with a pore size of 0.45 μm (Unifil). For determination of phosphate (PO 4 3− ), an ion chromatograph with conductivity detector model 930 Compact IC Flex from Metrohm was used. Removal and sorption capacity were calculated through Eqs. (1) and (2), respectively. All assays were performed in triplicate.
where R is the removal of PO 4 3− ions (%), q is the uptake capacity of PO 4 3− ions (mg g −1 ), C i is the initial PO 4 3− concentration (mg L −1 ), C eq is the PO 4 3− concentration at equilibrium (mg L −1 ), V is the volume of the solution containing the PO 4 3− ions (L), and M is the mass of the BG (g). The following variables were determined: (i) initial pH, (ii) sorbent concentration, (iii) initial concentration of phosphate, (iv) particle size, and (v) contact time. Table 1 shows the experimental conditions employed in sorption tests with synthetic effluents.

Langmuir isotherm
The Langmuir isotherm described initially to predict the adsorption of gaseous molecules in a solid is widely used for aqueous systems involving the sorption of ions in different sorbent materials (Foo and Hameed 2010;Chen et al. 2022). Langmuir (1918) proposed this model with the following hypotheses: (i) monolayer adsorption; (ii) uniform adsorption force on the surface of the homogeneous adsorbent; and (iii) no steric hindrance or lateral interaction between the adsorbed molecules, even at M adjacent sites. Basically, the Langmuir isotherm equation has a hyperbolic form, given by Eq. (3): where q is the amount of PO 4 3− retained in the solid at equilibrium (mg g −1 ), q max is the Langmuir parameter relative to sorption capacity (mg g −1 ), k L is the Langmuir constant relative to sorption energy (L mg −1 ), and C eq is the PO 4 3− concentration in solution at equilibrium (mg L −1 ).

Freundlich isotherm
The Freundlich isotherm model (Freundlich 1906) assumes that the sorbent material has a heterogeneous surface composed of several types of sorption sites that saturate during the process, culminating in an exponential decrease in sorption energy. The Freundlich isotherm model (Eq. (4)) is considered appropriate to describe both multilayer sorption and can, therefore, be applied to non-ideal systems (Zand and Abyaneh 2020).
where q is the amount of PO 4 3− retained in the solid at equilibrium (mg g −1 ), C eq is the PO 4 3− concentration in solution at equilibrium (mg L −1 ), k F is a constant that indicates sorption capacity (L mg −1 ), and n is the constant that indicates sorption strength (L mg −1 ). Dubinin and Radushkevich (1947) proposed the D-R isotherm model (Eq. (5)) which represents the adsorption of vapors and gases on microporous solid surfaces, such as activated carbon, through a pore-filling mechanism. Through the Polanyi potential (Eq. (6)), one can get an idea of the adsorption energy distribution. The Dubinin-Radushkevich (D-R) model assesses the nature of the adsorption and is more general than the Langmuir isotherm, since it assumes a smooth surface or a constant adsorption potential.

Dubinin-Radushkevich isotherm
where q is the amount of PO 4 3− retained in the solid at equilibrium (mg g −1 ), q max is the maximum sorption capacity of the sorbent (mg g −1 ), B is the constant related to the adsorption energy (mol 2 kJ −2 ), is the Polanyi potential (kJ mol −1 ), R is the universal gas constant (0.008314 kJ mol −1 K −1 ), T is the absolute temperature (K), and C eq is the PO 4 3− concentration in solution at equilibrium (mg L −1 ).
The sorption energy value (kJ mol −1 ) is related to the constant B, as shown in Eq. (7). It is defined as the change in free energy when 1 mol of PO 4 3− is transferred from infinity, inside the solution, to the solid surface, and is related to the sorption phenomenon that happens in the sorbent/solute system (Wang et al. 2007). If E s < 8 kJ mol −1 , the adsorption process is of a physical nature; if 8 kJ mol −1 < E s < 16 kJ mol −1 , adsorption occurs by ion exchange; if 16 kJ mol −1 < E s , adsorption is of a chemical nature.
where E s is the mean sorption free energy (kJ mol −1 ).

Temkin isotherm
The Temkin equation model (Eq. (8)) has been proposed to describe the adsorption of hydrogen on platinum electrodes within acidic solutions (Febrianto et al. 2009). In this model, the effect of indirect solute/sorbent interactions on the adsorption isotherms is considered, assuming that the drop in heat of adsorption is linear due to the coverage of the layer by the solute/sorbent and nonlogarithmic interactions (Basha et al. 2008).
where q is the PO 4 3− amount retained in the solid at equilibrium (mg g −1 ), C eq is the concentration of PO 4 3− in the equilibrium solution (mg L −1 ), T is the absolute temperature (K), R is the universal gas constant (0.008314 kJ mol −1 K −1 ), A is the Temkin isotherm constant (L mg −1 ), and b is the constant related to the heat of sorption (kJ mol −1 ).

Pseudo-first-order model
The pseudo-first-order kinetic model was initially introduced by Lagergren (1907) at the end of the nineteenth century. According to Ho and McKay (1999), the model can be used in the form of Eq. (9).
Equation 10 is obtained by integrating Eq. (9) from t = 0 to t = t and qt = 0 to qt = qt: where q eq is the amount of PO 4 3− retained in the solid at equilibrium (mg g −1 ), q is the amount of PO 4 3− retained in the solid at time "t" (mg g −1 ), and k 1 is the pseudo-first-order reaction velocity constant (g mg −1 min −1 ).

Pseudo-second-order model
The pseudo-second-order kinetic model was introduced in the mid-1980s (Blanchar et al. 1984), but it became popular when Ho and McKay (1999) when evaluating several results of works by different authors, obtained a better correlation of the experimental data when used this model. The pseudosecond-order model is represented by Eq. (11): Equation 12 is obtained by integrating Eq. (11) from t = 0 to t = t and qt = 0 to qt = qt: where q eq is the amount of PO 4 3− retained in the solid in equilibrium (mg g −1 ), q is the amount of PO 4 3− retained in the solid at time "t" (mg g −1 ), and k 2 is the pseudo-secondorder reaction velocity constant (g mg −1 min −1 ).

X-ray fluorescence
Elementary semi-quantitative chemical determination of the Bioclastic Granule samples before and after the sorption process was performed by X-Ray fluorescence spectrometry in a PanAnalytical equipment, model AXIOS MAX, using the standardless method for reading the samples. These samples were prepared by melting at a dilution of 1 to 10 using as flux lithium tetraborate (Li 2 B 4 O 7 ) from Maxxifluxi and 0.07 g of lithium iodide (LiI) release agent.

Scanning electron microscopy
The micrographs of the Bioclastic Granules before and after the sorption process were obtained in a scanning electron microscope (SEM) FEI Quanta 400, equipped with a Bruker Xflash 4030 Energy Scattered X-Ray Spectrometry (EDS) System to evaluate the morphology of the particles. The acquisition and processing of the data generated by the EDS were performed using Brucker's ESPRIT software version 9.1. The samples were dried in an oven for 24 h at a temperature of 60 °C and deposited on carbon adhesive tapes supported on metallic disks where they were finally covered with a micrometric gold film from evaporation in a metallizing chamber, thus enabling the conduction of electric current.

Results and discussion
Initial pH effect Figure 1 shows the final concentration and PO 4 3− uptake in the pH range of 5 to 8. It is possible to notice with the increase in the pH value, the final concentrations increased gradually going from 24.1 to 36.7 mg L −1 , respectively. Uptake decreased gradually from pH 5 to 7, with values of 7.7 mg g −1 in pH 5 and 6.4 mg g −1 in pH 7. Percent removal decreases from the range of 76-63.8% (pH 5 to 7) to 32% (pH 8); in this value, the highest concentration in solution was observed (68.9 mg L −1 ) and lowest uptake (3.2 mg g −1 ). The slightly acidic condition of the system leads to a high dissociation of CaCO 3 in the surface of the granules, consequently, better sorption of the ions PO 4 3− .
According to Sondi et al. (2009), the surface of the minerals of carbonate in contact with water suffers coordination reactions with species in solution, such as Ca 2+ , CO 3 2− , HCO 3− , and CaHCO 3 + . In accordance with a few authors, systems composed by different types of limestones presented a final pH value in the range of 7.5 to 8.0, due to the buffer capacity of the carbonate system, once the predominant specie is the HCO 3− (Aziz et al. 2008;Sdiri et al. 2012). Figure 2 shows the speciation diagram log C as a function of pH, built in the computational program computational (MEDUSA-Make Equilibrium Diagrams Using Sophisticated Algorithms, 32 bits).
In fact, as observed in Fig. 2 2− , and Ca 5 (PO 4 ) 3 OH. In this study, in the condition of slightly alkali pH (7 to 8.3), it is possible to suggest that the concentration of the species Ca 2+ , Ca(OH) 2 , HCO 3− , CO 3 2− , PO 4 3− , and HPO 4 2− increases in the surface of the Bioclastic Granules, working in favor of precipitate formation as hydroxyapatite Ca 5 (PO 4 ) 3 OH, and others:  Laurence (1991), studying solubility of different calcium phosphates in a ternary system (Ca(OH) 2 , H 3 PO 4 e H 2 O), observed that in slightly acidic regions, every phosphate is more soluble. In regions of slightly alkali pH, the solubility of the calcium phosphates decreases in the following order: hydroxyapatite > tetracalcium phosphate > tricalcium phosphate > calcium hydrogen phosphate > monocalcium phosphate. According to Wu et al. (2020), the protonated phosphate anions interact with the hydrogen bond receptors with selective ions, such as Ca 2+ , which produces phosphate complexes. It is observed that other anions, in solution, such as CO 3 2− also had such capacity; however, this anion differs in the capacity of donating a pair of nonbonding electrons remaining in the: PO 4 3− > CO 3 2− order. Therefore, the predominant mechanism in GB phosphate sorption is spherical complexation, inner sphere complexation via bonding variations process, in which the hydrated CO 3 2− groups on the surface are substituted for PO 4 3− anions. As stated by Wu et al. (2020), the inner sphere complexation involves a stronger interaction than an external sphere, as observed in carbonate. However, additional mechanisms, such as electrostatic attraction, and/or precipitate might coexist in the sorption process.

Particle size effect
In Fig. 3, it is possible to observe the concentration in solution and uptake of PO 4 3− in the granulometric range of − 38; + 53 − 75; + 106 − 150; and + 210 − 300 μm. The size increase of the Bioclastic Granule particles has a positive effect in PO 4 3− removal. In fraction − 38 μm, the values of removal and uptake were less expressive, corresponding to 49.4% and 4.0 mg g −1 , respectively. From the fraction + 53 − 75 to + 106 − 150 μm, an increase in removal and uptake can be noticed, with values of 6.5% and 4.6 mg g −1 and 75.6% and 6.1 mg g −1 , respectively. In the larger size (+ 210 − 300 μm), the results remain practically the same to the anterior size (+ 106 − 150 μm). This is a curious behavior, once that sorbents with less particle sizes usually presents greater available superficial areas for sorption and are more susceptible to dissolution in comparison to larger particles. Ayoub et al. (2019) evaluated PO 4 3− removal by a dolomite (CaMg(CO 3 ) 2 from south Beirut, Lebanon) in fixed bed column systems and observed how the particle size affected the removal. According to the authors, the best result was reached in the finest fraction 75 μm (97%), but in the larger ones + 75 − 105 and + 175 μm, the removal was also high, corresponding to the values of 90.3% and 93.7%, respectively. Kasprzyk and Gajewska (2019) evaluated a residue of opoka (enriched carbonate with silicon) pre-processed at a temperature of 700 °C in the removal of PO 4 3− and observed a high capacity of uptake (45.6 mg g −1 ) applying particles up to 2.0 mm in size.
What has been observed in the study may be related to the low variation of surface BET of micropores between different fractions (1.44 and 2.81 m 2 g −1 ), suggesting that dissolution reactions of CaCO 3 do not increase with reduction in particle size, in other words, exposition of more binding sites for the formation of new crystals from micropores.

Bioclastic Granule concentration effect
The concentration of the granules is an important factor that determines the necessary amount of sorbent to remove a specific amount of PO 4 3− in solution. According to Wu et al. (2020), one of the alternatives for treating effluents containing phosphorus is chemical precipitation; however, the need to introduce metal salts into high concentrations brings an inconvenience that is the high generation of sludge and the incorporation of these metals into the sludge. In fact, as we can see in Fig. 4, as BG concentrations increased from 1 to 20 g L −1 , the removal gradually increased from 13.7% (1 g L −1 ) to 70.7% (20 g L −1 ). However, unlike the chemical precipitation process by metals, the process of phosphorus sorption generates a highly enriched material with macronutrients (Ca, Mg, and P) that can be reused as fertilizers. The uptake responded in opposition to the concentration, with the increase in the concentration of Bioclastic Granules, the values decreased significantly, from 12.5 mg g −1 (1 g L −1 ) to 3.2 mg g −1 (20 g L −1 ).
The increase in the removal efficiency with the increase in the initial concentration of the granules is probably due to the greater amount of active sorption sites and Ca 2+ , Ca(OH) 2 , and CaOH + ions released in solution. Wu et al. (2020) describes that the presence of calcium and magnesium generally increases the phosphate removal capacity through surface precipitation (co-precipitation of Ca-P and Mg-P). Some studies describe that the solubility of hydroxyapatite begins to decrease from pH 4.1, initiating the formation of this species in solution (Aljerf and Choukaife 2017; Choukaife and Aljerf 2017). Some species of soluble hydroxides in the pH range under study may promote the formation of more stable solid species, since they serve as precipitation nuclei at the solid-solution interface. In real processes, higher concentrations of Bioclastic Granules (BG) are applied to ensure complete removal of PO 4 3− in effluents, once the limits stablished by responsible organs be satisfied. Caletti (2017) applicating BG for the treatment of raw leachate observed that an increase in the initial concentration of the granules was necessary to reach expressive values in removal. According to the author, with 40 g L −1 of the granules, it was possible to remove around 81.5% of phosphorus of the effluent.
These results suggest that the sorbent's concentration must be taken into consideration when utilizing materials based on CaCO 3 with the final objective of controlling cost/ benefit. Both uptake capacity and efficiency of removal of PO 4 3− ions are equally important in the process of sorption. The concentration of 10 g L −1 of Bioclastic Granules was maintained in the following tests.

Initial concentration of PO 4 3− effect
The rate that the ions are removed from the liquid phase to solid phase is generally described in comparison with their initial concentration, making it a very important variable of the process. Sorption tests were realized utilizing Bioclastic Granules and different solutions with initial concentrations of PO 4 3− in the range of 5 to 420 mg L −1 . Table 2 shows the values for the removal and uptake of PO 4 3− ions with the different initial concentrations at pH 5.0; BG concentration of 10 g L −1 ; particle size: + 106 − 150 μm; temperature: 25 °C; contact time: 6 h. As shown in Table 2, the PO 4 3− ions present a similar behavior, with the increase in the initial concentration from 5 to 70 mg L −1 , the removal values remain practically the same, in the range of 74 to 78%. In the concentration of 100 mg L −1 , removal decreases gradually from 66 to 34% in the initial concentration of 420 mg L −1 . Kasprzyka et al. (2018) noticed a similar pattern in this study, applicating a bentonite modified with lanthanum (Phoslock®) for the removal of phosphorus in concentrated solutions, varying from 5 to 100 mg L −1 . According to the authors, removal was practically the same (> 95%) in all different concentrations.
The uptake values, with the increase in PO 4 3− concentration in solution, also increase gradually, going from 0.38 (5 mg L −1 ) to 14.3 mg g −1 (420 mg L −1 ). The fact that an increase of ions PO 4 3− in solution does not significantly increase the removal rates may be associated with the epitaxial growth of a fine layer of calcium phosphate crystals in the surface of the granules, during the process of sorption. This layer may prevent the CaCO 3 dissolution, forming a stagnation layer, impeding the creation process of new precipitation nucleus and, posteriorly, new crystals. A few authors describe that the proportion of calcite and aragonite that composes the material may also interfere. The aragonite, for instance, has sorption capabilities much higher than calcite (Prieto et al. 2003;Cubillas et al. 2005;Köhler et al. 2007).
In accordance with Veneu (2017), it is always necessary to identify the maximum potential of saturation of a sorbent, so the tests may be realized in the highest initial solute concentration as possible. This value of maximum uptake of saturation can be calculated through adsorption isotherms.

Sorption isotherms
The adsorption isotherms were built with data of the equilibrium, aiming the determination of important parameters, for instance, the theoretical saturation capacity of the Bioclastic Granules for the PO 4 3− ions and the type of mechanism in the sorption process. The tests were realized in the initial concentrations of 5 to 420 mg L −1 with the final objective of obtaining the maximum saturation capacity of the BG. Figure 5 shows the experimental data of the quantity of PO 4 3− ion in sorption (q in mg g −1 ) as a function of the concentration (mg L −1 ) of these ions in solution. The dashed lines show the isotherms profiles generated through the model of Langmuir, Freundlich, Dubinin-Radushkevich (D-R), and Temkin. Table 3 contains the parameters obtained from the models of isotherms, and the respective correlation coefficients.
In Fig. 5, the profile of PO 4 3− uptake data can be observed, being similar to the "L" type, in other words, Langmuir's type. This isotherm is used for solids with relatively small external surfaces and when the relation between solute concentration in solution and in sorption decreases with the increase of solute (Aljerf 2018). They present with a concave curve, suggesting a progressive saturation of the solid, what, in this case, may be related to a stagnation.
Based on the values obtained and shown in Table 3, the PO 4 3− sorption data were better suited to the Langmuir (R 2 = 0.965) and Freundlich (R 2 = 0.961) models. According to the images obtained with the SEM, it was possible to observe that the surface of the BG after sorption does not present a well-defined monolayer as recommended by the Langmuir model, which can be justified initially by the sorption of PO 4 3− at the interface, thus forming this monolayer, and as the crystals are formed, a second stage begins, that of crystal growth, the formation of more heterogeneous solids, as recommended by the Freundlich model, culminating in very close correlation coefficients comparing the two models.
In face of this statement, the q max values obtained through the Langmuir model (q max = 14.35 mg g −1 ) and Dubinin-Radushkevich (10.97 mg g −1 ) may be treated cautiously. The values of q max represent the maximum of sorption capacity when the surface of the sorbent is completely covered (Aljerf 2018). High k L values would indicate a high affinity between the PO4 3− ions and the Bioclastic Granules, reflecting in a steep isotherm curve. However, it was not observed, with a low value of k L (0.0248 L mg −1 ) as expected, once that sorption through precipitation mechanism and crystal growth is not as fast as the adsorption mechanism.
According to Wang et al. (2007), the average free energy in sorption E s is related to the type of sorption. For values of E s < 8 kJ mol −1 , which is the case in this study, that presents the value of E s = 0.1 kJ mol −1 , what might be good, once the enriched granules will be utilized posteriorly as a soil fertilizer.
In the Freundlich model, k F represents a measurement relative to the adsorption capacity, and n is related to the adsorption intensity; in other words, values > 1 indicate that the ions are not going through a favorable sorption process. In Table 3, it is possible to observe that the value of n (2.43 L mg −1 ) demonstrates a good distribution of PO 4 3− ions in the BG. According to Frimmel and Huber (1996), a relatively light inclination n > > 1 indicates that the intensity of sorption is high in every concentration range of the study, while a steeper inclination (n < 1) means that the intensity of sorption is only high in high concentrations, decreasing at lower ones. In fact, as previously discussed, in the concentrations of 5 to 70 mg L −1 of PO 4 3− , the most significant removals were obtained, although they had lesser uptake, characterizing an n > > 1 and a light inclination isotherm. 3− ions sorption isotherm (pH: 5.0; initial concentration of the BG: 10 g L. −1 ; particle size: + 106 − 150 μm; temperature: 25 °C; contact time: 6 h) Table 3 Parameters obtained from the isotherm models and their correlation coefficients As observed in Table 3, the sorption data of PO 4 3− by the Bioclastic Granules adjust well to Temkin model, with values of the constants A and b of 0.52 L mg −1 and 1.0 kJ mol −1 , respectively. In this study, this high correlation coefficient for the Temkin isotherm may have occurred due to a linear dependency of heat of sorption in relation to the nucleation process and the growth of heterogenous crystals in a layer formed in the surface of the Bioclastic Granules. Kasprzyk et al. (2021) evaluated three distinct materials for the phosphorus removal, in bentonite modified with lanthanum (Phoslock®), a byproduct of powder carbonate rock, with a high content of silicon (Rockfos®) and a residue of water treatment (DWTR) with different contents of Fe and Mn. According to the authors, the three materials showed sorption data that adjust well to the Freundlich model, with correlation coefficients of 0.92, 0.99, and 1.00, respectively. The values of q max obtained through the isotherm model of Langmuir were 158.7 mg g −1 for Phoslock®, 256.4 mg g −1 for Rockfos®, and 6.9 mg g −1 for DWTR. Kong et al. (2018) obtained a sorbent material for phosphorus ions from a calcined sludge at 800 °C with different proportions for CaCO 3 :sludge (0:1, 1:2, and 1:1). According to the authors, the sorption data for the three proportions adjust well to Langmuir model, presenting a R 2 = 0,999, while the calculated coefficients through the Freundlich model were < 0.70. The values of q max for the relation 0:1, 1:2, and 1:1 were 22.04, 116.82, and 97.56 mg g −1 , respectively.

Sorption kinetics
One of the main information that we may obtain from the kinetic studies of sorption is the sorption rate. It determines the necessary contact time with the surface of the sorption and solution, and with that information, it is possible to scale the size of the reactor. According to Davis et al. (1987), sorption rates of ions prevenient of minerals based on calcium carbonate are generally characterized by process that depend on the physicochemical nature of the material and ions in the process of sorption, with a half-life varying from a few minutes to even days.
The experimental uptake data (q) were applied in the kinetic models of pseudo-first and pseudo-second order for the verification of the order and sorption velocity of the PO 4 3− ions and the BG. Figure 6 shows the experimental data of uptake through time, with the corresponding lines of the models of pseudo-first and pseudo-second order for the sorption of PO 4 3− ions. Figure 6 shows a gradual growth in the uptake values, with an initial value of 0.54 mg g −1 in the first 15 min, rising to 53.2 mg g −1 in the mark of 180 min. From that point on, the uptake varies in the range of 53 to 57 mg g −1 until the mark of 360 min, suggesting a reduction on the sorption rate in that period of the reaction. In fact, the sorption rates of PO 4 3− ions in the Bioclastic Granules are related with interaction with species as Ca 2+ , CaOH + , Ca(OH) 2 , HCO 3 − , and HPO 4 2− , that depend on the pH of the solution. The early stages of the sorption process are quicker due to reactions in the surface of the sorbent, while slower process in the final stages occur due to a structural diffusion and recrystallization in the surface of the BG.
This behavior observed in the sorption process in respect to the recrystallization rate of ionic solids is consistent with the surface model proposed by Lahann and Siebert (1982) that includes a hydrated calcium carbonate layer in the disordered surface of the calcite that crystallizes over the calcite. The existence of this stage is supported by experimental observations that shows that dissolution and precipitation of calcite rates are generally controlled by a surface reaction instead of a diffusion of the reactants (Nancollasg and Reddy 1971). Table 4 shows the kinetic parameters obtained with the utilization of pseudo-first-and pseudo-second-order models for the PO 4 3− . It is possible to verify that the kinetic data obtained adjusted well to the kinetic models, with R 2 > 0.97. However, the kinetic model of pseudo-first-order presents a R 2 value of 0.979 and, consequently, a calculated q e value (6.56 mg g −1 ) closer to the one obtained experimentally (5.88 mg g −1 ), and a k 1 value of 0.0073 min −1 . Kasprzyk et al. (2021) evaluating a calcium carbonate based by product for the removal of phosphorus related that the pseudo-first-order model presented a good correlation coefficient and q e and k 1 values of 7.9 mg g −1 and 0.0013 min −1 , respectively. Chen et al. (2014) evaluating the application of a ceramic biomaterial calcite/montmorillonite/starch based (1:1:1) for the removal of PO 4 3− observed that in the early stages of sorption, the ions entered the sorption process in the external surface of the sorbent with a high rate of sorption. Posteriorly, the sorption in the external surface reached a saturation stage. According to the authors, when the sorption data was applied to a pseudo-first model, a R 2 of 0.979, q e of 9.5 mg g −1 , and a k 1 of 0.017 min −1 were obtained. Table 5 shows obtained values of the oxides of the constituents of the Bioclastic Granules through X-ray fluorescence (XRF). The calcium oxide represents 45.7% of the material, in smaller proportions, magnesium oxide (MgO-5.6%), and silicon oxide (SiO 2 -2.7%). The remaining oxides represent slightly less than 2.2% of the material. Approximately 43.8% of the material was eliminated in the process by fire loss. Vila (2012) obtained similar percentages of fire loss (43.5-45.3%) for different aragonite-based biomaterials, attributing this percentage to organic matter and water.

X-ray fluorescence
Several authors obtained similar compositions to the ones found in this research for carbonated minerals. Silva et al. (2010) characterize two biomaterials (oyster shells and mussels); it contained majorly CaO, corresponding to 56.1% of oyster shells and 53.8% of mussels. The remaining oxides represent less than 1% of their composition. Zeng et al. (2003) evaluating the removal of P in two volcanic soils observed that it was possible to incorporate about 0.566 to 0.909 mgP g −1 of volcanic soils that had high levels of SiO 2 (42.4 to 47.2%), Al 2 O 3 (11.2 to 12.9%), and Fe 2 O 3 (9.53 to 7.74%) and low contents of CaO (2.21 to 1.58) and MgO (0.908 to 0.791). According to Table 4, it was possible to remove about 8.29 mgP g −1 of GB (equivalent to 1.9% P 2 O 5 ) and a reduction in the contents referring to loss on fire, CaO and MgO, evidencing a redistribution of elements in the chemical structure of BG as a function of the sorption of PO 4 3− on the surface of the material.
According to Gubernat et al. (2020) phosphorus adsorbent materials must have elements such as Ca, Mg, Fe, and Al that end up functioning as phosphorus binders. The mechanism of phosphate sorption by Fe and Al can occur through the exchange of ligands, and for Ca and Mg, the removal of phosphates is carried out through the precipitation of poorly soluble calcium phosphates or struvite (Wu et al. 2006).

Scanning electron microscopy
With the objective of evaluating the morphology of the Bioclastic Granule particles before and after the process of sorption with PO 4 3− , scanning electron microscopy analysis was made. In Fig. 7A, C, a particle of the granule can be observed before and after the sorption process, respectively. In Fig. 7A, the particle presents an irregular surface, with the predominance of cavities of different sizes and small fragments inside and in its radius. After sorption, the particle presents different clear crystalline solids, that disorderly grows from its nucleus, giving birth to a new crystalline phase in the surface of the Bioclastic Granules.
As reported by Davis et al. (1987), among the main mechanisms of reaction of an aqueous solute with the surface of a pre-existing solid phase, the adsorption and precipitation are considerably similar; they still differ in their geometry. The adsorption is generally bidimensional, while precipitation in a surface is tridimensional. Sposito (1984) describes the term precipitation as being a process that implicates on the growth of a new solid phase that propagates in a molecular unity repeatedly in three dimensions. Farley et al. (1985) utilized the term surface precipitation to describe a multilayer adsorption process, what may include the formation of an ordinated solid solution as the growing phase of a crystal. In this study, the PO 4 3− apparently forms precipitates in the surface of Table 4 Kinetic parameters obtained from the kinetic models of pseudo-first-and pseudo-second-order for the sorption of PO 4 3− ions with the Bioclastic Granules Pseudo-first-order Pseudo-second-order q eq exp (mg g −1 ) q eq (mg g −1 ) k 1 (min −1 ) R 2 q eq (mg g −1 ) k 2 (g mg −1 min −1 ) R 2 6.5652 0.0073 0.979 9.2130 0.0006 0.973 5.88 the Bioclastic Granules, originating a multilayer sorption process that forms a new ordinated solid solution followed by the growth of a new crystal as stated in Fig. 7C. In Fig. 7B, D, spectrums obtained in the surface of a Bioclastic Granule particle by dispersive energy X-ray can be observed, before and after sorption with PO 4 3− ions, respectively. In Fig. 7D, before the sorption process, the spectrum presents three sharp peaks referring to the elements, Ca, O, and C, characteristic of the mineral CaCO 3 , besides peaks of the elements Mg and Au that were utilized in the metallization process. After sorption with ions PO 4 3− (Fig. 7D), the three expressive peaks of Ca, O, and C practically maintained unaltered, but a new one of P appeared, evidencing a kind of exchange mechanism between HCO 3 − and HPO 4 2− ions that appear in the spectrum in the form of P and reduction of C and O elements after the sorption process.

Conclusions
Based on the results, it can be concluded that at pH 5, GB presented the most expressive values of removal (76%). In general, when the initial concentrations of PO 4 3− were increased from 5 to 420 mg L −1 , the highest removal (76.4%) was observed at the concentration of 5 mg L −1 and the highest uptake (14.3 mg g −1 ) at a concentration of 420 mg L −1 . The sorption data fitted well to the Langmuir isotherm models (R 2 = 0.965) showing q max values of 14.35 mg g −1 and k L of 0.0248 L mg −1 and Freundlich (R 2 = 0.961) showing k F values of 1.35 L mg −1 and n of 2.43. The uptake data best fitted the pseudofirst-order kinetic model (R 2 = 0.979) and calculated q eq of 6.56 mg g −1 and k 1 of 0.0073 min −1 . Regarding characterization, the Bioclastic Granules have a chemical 3− with an increase of × 500; and D spectrum after sorption composition predominantly in the form of CaO (45.7%), followed by MgO (5.6%) and SiO 2 (2.7%). After the sorption process, it was possible to verify a P 2 O 5 content corresponding to 1.9%. The SEM associated with the EDS showed that the GB has a very irregular surface, with a predominance of cavities of different sizes that are later filled by small precipitation nuclei that evolve into small crystals on the surface of the GB presenting element P in its composition.