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Article

Phosphorus Control and Recovery in Anthropogenic Wetlands Using Their Green Waste—Validation of an Adsorbent Mixture Model

by
Juan A. González
1,
Jesús Mengual
2,* and
Antonio Eduardo Palomares
2
1
Institut Universitari d’Investigaciò d’Enginyeria de l’Aigua i Medi Ambient, Universitat Politècnica de València, Camí de Vera s/n, 46022 Valencia, Spain
2
Instituto de Tecnología Química, Universitat Politècnica de València—Consejo Superior de Investigaciones Científicas, Avenida de los Naranjos s/n, 46022 Valencia, Spain
*
Author to whom correspondence should be addressed.
Sustainability 2025, 17(13), 6153; https://doi.org/10.3390/su17136153
Submission received: 24 May 2025 / Revised: 27 June 2025 / Accepted: 29 June 2025 / Published: 4 July 2025

Abstract

The deterioration of freshwater ecosystems in anthropogenic wetlands is intensified due to phosphorus inputs from fertilizers applied in agricultural areas. In addition, managing the excess green waste generated in these ecosystems increases the complexity of the problem. To move towards a sustainable society based on the circular economy, the use of controlled combustion of green waste to obtain bioenergy—followed by the application of the resulting ash for phosphorus removal from freshwater bodies via adsorption processes—should be considered. Furthermore, those ashes could be used as natural fertilizers and incorporated into the cultivated fields. This paper presents a deep study of the adsorption of phosphorus ions using ashes from the main green waste produced in wetlands. Various experiments were conducted to determine the effects of different variables in the removal process. A double kinetic model was necessary to explain the presence of two different removal processes. The Langmuir model described the equilibrium isotherm data of both adsorbents through an endothermic process. Acidic pH in the initial solutions was preferred because it promotes phosphorus removal by calcium dissolution. The alkalinity did not have a substantial effect on the adsorbent capacity. Calcium was the element that had a more significant influence on the overall process. Finally, a removal study using blended materials was performed. A combined model was proposed and validated based on the original isotherm models for the pure materials.

1. Introduction

Continuous phosphorus discharges into water bodies, resulting from human activities such as agriculture, domestic effluents, or industrial wastewater, lead to water contamination. If the discharges are not controlled and limited, they can cause eutrophication of the aquatic environment. A concentration of more than 0.1 mgP·L−1 in bodies of water leads to eutrophication [1]. Eutrophication induces an overgrowth of phytoplankton, deteriorates water quality, reduces aquatic biodiversity, and accelerates water scarcity [2]. Esfandi et al. [3] report that 54% of lakes in Asia, 53% in Europe, 48% in North America, 28% in Africa, and 41% in South America are classified as eutrophic, according to the OECD lake classification scheme. For this reason, phosphorus in wastewater must be reduced, removed, and, if possible, recovered to prevent eutrophication. Phosphorus, primarily used in fertilizer production, was included on the European Union’s 2023 Critical Raw Materials List due to its supply risk and economic importance. Therefore, the development processes, technologies, and materials that enhance the safe recycling and reuse of this dissipated phosphorus are highly desirable as they support the sustainable recovery of critical elements from waste resources and contribute to a society based on the circular economy.
The water quality of anthropogenic wetlands, which combine natural vegetation with crops [4], is deteriorating due to urban and industrial growth as well as the farming practices around them [5]. These ecosystems suffer from drainage and pollution processes, especially for nutrients such as nitrogen and phosphorus [6,7], which contribute to a reduction in their total area [8,9]. These areas gradually transform into hypereutrophic systems with a predominance of cyanophytes, a lack of zooplankton, and an absence of submerged vegetation [10]. The influx of N and P from human daily life into water bodies has been estimated to be 1.5·105 kg of N and 1.1·103 kg of P annually worldwide [11]. Values of up to 1.4 mgP·L−1 have been reported in lakes with a high impact of human activity, e.g., Dianchi Lake, which far exceed the limit value leading to eutrophication [12]. These facts have promoted the proliferation of treatment systems using technologies integrated into the landscape [13,14,15]. In this sense, the constructed wetlands—engineered systems that use the natural functions of vegetation, soil, and organisms to treat and improve the water quality—represent a viable alternative. Constructed wetlands act as biofilters and can remove pollutants (such as organic matter, nutrients, pathogens, and heavy metals) from water [16]. Common reed, Phragmites australis, is one of the main wetland plant species used for phytoremediation in constructed wetlands [17,18]. This kind of system is straightforward to operate and only requires regular pruning of the vegetation to avoid organic matter and other pollutants being removed from the water and reincorporated into the water body.
In these anthropogenic wetlands, rice production is widespread. This activity is relevant for the sustainable maintenance of these ecosystems, balancing positive environmental impacts (landscape, water quality, and biodiversity), economic income for farmers, and the preservation of regional cultural heritage [19,20]. On the contrary, derived from this activity, rice straw is one of the most challenging materials to manage nowadays [21]. Burning the straw waste in the field has been the primary management method [22], promoting the reincorporation in the soil of specific nutrients present in those agro-wastes [23]. However, this practice can produce health problems [24,25] and is not preferred in the European Union Common Agricultural Policy. In situ and ex situ are other alternatives for managing agro-waste in these ecosystems. In situ options, such as soil incorporation, required strict control to avoid anaerobic decomposition, methane emissions, and sulfur toxicity [23,26]. Ex situ alternatives include composting and other biomaterial or bioenergy uses [27,28,29]. However, the necessary extraction of the biowastes has some drawbacks, such as poor demand, lack of specialized machinery for its extraction, and nutrient depletion of the soils. As a result, these ex situ alternatives attract little interest among farmers [23]. In this context, multi-stakeholder negotiations are recommended to promote sustainable development within these ecosystems [19].
Due to the large amount of green waste produced in anthropogenic wetlands—agricultural waste (e.g., rice straw) and natural biowaste (reed and other plant species)—the alternative use to obtain bioenergy through controlled combustion would be considered an effective management strategy. It would reduce air pollution impacts and retain part of its internal energy, 12.33 MJ kg−1 for rice straw and 18.90 MJ kg−1 for reed, which is necessary in this time of energy shortages and ambiguity [30,31,32,33]. In addition, in line with the new circular economy policies, the combustion process generates waste ashes from biowastes—which are rich in minerals—that could be returned to the fields by farmers, thereby increasing the attractiveness of biomass extraction.
Additionally, the bibliography reports the capacity of different kinds of ashes to remove pollutants in water by adsorption, including phosphorus [34,35,36,37,38,39,40,41]. Moreover, in the case of removing phosphorus, the product generated after adsorption treatment would have a high fertilizer value as it is enriched in this essential and non-renewable macronutrient critical for plant growth due to its higher phosphorus content [42,43,44]. This approach would extract phosphorus from the natural ecosystem, reduce the use of external phosphorus fertilizers in the nearby agricultural fields, and improve the profitability of this management strategy. Such potential would further increase farmers’ interest in adopting this option.
After these considerations and taking previous work as a starting point [45,46], the present work aims to conduct an in-depth study of the phosphorus removal from aqueous media by an adsorption process using materials derived from the green waste produced in anthropogenic wetlands, specifically ashes obtained after the energy recovery treatment of those biowastes. As a typical original material, rice straw—a widely produced agricultural waste in these ecosystems—and reed pruning—which commonly forms stands of beds around lagoons and rivers and is one of the main wetland plant species for phytoremediation—will be employed as representative source materials. The ashes will be obtained, processed, and subsequently tested for their phosphorus removal capacity. The kinetics of the removal process and the adsorption equilibrium will be analyzed and modeled. Particular attention will be paid to the effects of contact time, temperature, adsorbent dose, initial pH, alkalinity, and the presence of competing ions in the solution. Finally, blends of these materials for the same removal process will also be tested and modeled to approach the process that might occur in real treatment conditions.

2. Materials and Methods

2.1. Preparation and Characterization of Adsorbents

Both materials, the rice straw ash (RSA) and reed ash (RA), were obtained by combustion of raw materials in a muffle furnace at 823 K for 2 h and subsequent cooling, according to the Solid biofuels—Determination of ash content (ISO 18122:2022) standard [47]. Both materials presented an ash yield of around 6–15% by weight. Then, the ashes were washed with deionized water until the conductivity of the suspension was around 1000 μS·cm−1. Finally, the samples were dried at 378 K overnight in an oven, sieved with a 1 mm grid, and stored in hermetic containers in a desiccator.
Characterization of both adsorbents was performed using different techniques. The major and trace elements in the adsorbents were determined using the chemical analysis carried out in a Varian 715-ES ICP–optical emission spectrometer after solid dissolution in HNO3/HCl/HF aqueous solution. Elemental analysis of the samples (C, H, N, S) was performed on a Fisons EA 1108 CHNS-O. X-ray diffraction (PXRD) was performed to determine the crystalline nature of the adsorbents in a multi-sample Philips X’Pert diffractometer equipped with a graphite monochromator operating at 40 kV and 35 mA and using Cu-Ka radiation (λ = 0.1542 nm). The particle morphology of the samples was studied by field-emission scanning electron microscopy (FESEM) using a ZEISS Ultra5-55 microscope. Furthermore, textural properties were determined by N2 adsorption–desorption isotherms measured on a Micromeritics ASAP 2020 at 77 K.
The pH at the point of zero charge (pHPZC) was determined by the equilibrium technique. The pH of a series of aqueous solutions was adjusted using HCl 0.1 M or NaOH 0.1 M (until the initial required pH, pHinitial). Samples of adsorbents were mixed with 50 mL of each aqueous solution in a 100 mL stoppered conical flask and were stirred until reaching equilibrium at 293 K. Then, pH was again measured (pHfinal), and the pHPZC was determined through a plot of pHinitial versus pHfinal. The pHinitial varied from 1 to 12.

2.2. Batch Adsorption Experiments

Adsorption experiments were carried out in batch mode using different initial concentrations, C0 (5–150 mgP·L−1), of sodium phosphate dibasic (NaH2PO4) placed in a 100 mL stoppered conical flask with 50 mL of synthetic wastewater and different amounts of adsorbent, under stirring, in a temperature-controlled chamber during the selected time. The chosen temperatures were in the range of 283–303 K, typical values that can be found in most water bodies. Adsorption studies were performed with solid-to-liquid dose (D) varying from 0.5 to 24 g·L−1, depending on the capacity of the adsorbent used. Blank experiments, in the absence of phosphorus, were also performed to test the experimental methodology. After finishing the adsorption experiment, at time t, the solution was filtered through a glass microfiber filter (1.2 µm) and phosphate concentration, Ct (mgP·L−1), was determined according to the vanadomolybdophosphoric acid colorimetric method stated in the Standard Methods for the Examination of Water and Wastewater [48]. Also, the filtrate was used to determine pH, electric conductivity, and, in some cases, the dissolved calcium content. Calcium analysis was performed on a Scharlau Science flame photometer. A large number of experiments were performed for the same series, in which, randomly, some of them were repeated to check their reproducibility. In this sense, the errors determined at the different points ranged from minimum values of 2.5% to maximum values that, on rare occasions, reached 11.9%. The average error value obtained for the RSA was 7.2%, while for the RA it was 5.8%.
The amount of phosphorus adsorbed onto the adsorbent, qt (mgP·g−1), was calculated by the mass balance relationship represented by Equation (1) as follows:
q t = C 0 C t W V = C 0 C t D
where V (L) is the volume of the solution; W (g) is the weight of the adsorbent used; and D (g·L−1) is the adsorbent dose.
In addition, the percentage of phosphorus removal or removal efficiency, Premoval (%), was calculated according to the following equation:
P r e m o v a l % = C 0 C t C 0 × 100

2.3. Adsorption Kinetics

A kinetic study is required to understand the dynamics of adsorption over time. Several models can be used to express the mechanism of solute sorption onto a sorbent. Kinetics models show, at a constant temperature, the time dependence of the mass adsorbed per gram of adsorbent, qt (mg·g−1). Different kinetic models have been tested to determine the best fit. In this sense, three standard models used in the literature have been used, outlined as follows: the pseudo-first-order model [49]; the pseudo-second-order model [50]; and the Elovich model [51]. A more detailed description of the mathematical expressions for the rates of these models is given in the Supplementary Materials (Supplementary Data S1).
All these models have been fitted directly, without any linear graph transformation, to avoid violating the assumptions of linear regression [52,53]. The fitting of the models was performed using the least squares method.

2.4. Adsorption Isotherms

Adsorption isotherms show the relation between the total mass adsorbed per gram of adsorbent, qe (mg·g−1), and the solution concentration of adsorbate, Ce (mg·L−1), in the equilibrium, at constant temperature and pH [54]. Different isotherm models have been used to determine the adsorption capacity of adsorbents. Three of the most widely used models for the kind of process studied here have been used in this work: the Langmuir model [55], the Freundlich model [56], and the Temkin model [57]. A more detailed description of the mathematical expressions for these isotherm models is given in the Supplementary Materials (Supplementary Data S2).
Similar to the previous point, all these models have also been fitted directly, without any linear graph transformation, by the recommendations of other authors [53,58]. The models were fitted using the least squares method, following the recommendations of Tran and co-workers [54,59].

3. Results and Discussion

3.1. Characterization of Adsorbents

The physical and chemical properties of both adsorbents are shown in Table 1. The low value of the surface area, slightly higher in the reed ash, and the high percentage of the external area show that the adsorbents are not microporous materials. Thus, most adsorbent processes are expected to occur on the solid external surface. In this regard, the scanning electron micrograph images of both adsorbents, (Supplementary Data S3), show a non-crystalline and heterogeneous distribution of particles, with different sizes and shapes in the range of a few to several hundred micrometers.
The ashes are essentially inorganic, as observed in the low carbon content, indicating a correct raw material combustion process. Silicon oxide is the main component in both adsorbents, with low concentrations of other metal oxides such as iron, aluminum, or zinc. However, the presence of alkaline and alkaline–earth metal oxides is significant, with calcium and potassium mainly. An essential difference between both adsorbents is the calcium content in the reed ashes, about twice as much as rice straw ashes, at the expense of silicon content. The diffraction patterns of the ashes, (Supplementary Data S4), confirmed the low crystallinity of the treated samples. However, the presence of silica in the form of cristobalite in the rice straw ash is the main crystalline phase [60], whereas in the reed ash, the calcite phase appears due to its higher calcium content. In addition, in both pre-washed samples, a crystalline phase of sylvite appears, which is removed after washing. Since a large part of the potassium, an interesting raw material, is removed during the washing process, future studies should focus on its possible recovery from the wash water.
The basicity of the adsorbents can be observed in the determination of the pHPZC, (Supplementary Data S5), obtained for a dose of 10 g·L−1 for RSA and 1.5 g·L−1 for RA. This parameter is related to the surface adsorption ability and its active sites. Both materials show similar development, with a wide range in which the final pH remains constant regardless of the initial pH; for initial pH values ranging from 3 to 11, the final pH stabilizes around 10–11, indicating a strong buffering capacity of both adsorbents. The pHPZC values are around 10.9 and 11.6 for RSA and RA, respectively. These values are at the top of the typical range shown by metal oxides in the literature [61]. However, the higher calcium content in RA allows the same performance as RSA but with a dose more than six times lower.
When the pH is greater than pHPZC, the phosphate adsorption may be affected by the electrostatic repulsion and increasing competitive effect of OH-, while when the pH is lower, the sorbent surface is positively charged, favoring the adsorption of the phosphate anion [61]. The high pHPZC shown by the samples means that in most real situations, with water bodies pH below 10, the adsorption will be favored by the positive surface charge of the adsorbents.

3.2. Adsorption Kinetic Studies

Adsorption kinetic studies are essential for identifying the required equilibration time and the optimal contact time for isotherm adsorption experiments [58]. Kinetic phosphate adsorption experiments on both materials were performed at different temperatures: 283 K, 293 K, and 303 K. As an example, Figure 1 shows the kinetic results for 293 K.
As seen in Figure 1, the time needed to reach equilibrium is relatively long for both adsorbents, requiring more than a few days. It takes approximately 48 h to reach 95% of the maximum adsorption capacity at a temperature of 293 K for the RSA adsorbent and 60 h for RA. These values contrast with some shown in the literature for materials of a similar nature. For example, Mor and co-workers [60] studied the kinetics of phosphorus adsorption using rice husk ash for 60–240 min. This same time is used for the subsequent equilibrium study. However, that work does not show the typical evolution towards the equilibrium state, the maximum phosphorus removal value, and so this time interval should be taken cautiously. Lu and co-workers [36] studied the phosphate removal by fly ashes obtained from three coal-burning power plants. The time used for the adsorption isotherm determination was 6 h. However, the kinetic data shown in their work did not indicate that equilibrium was reached during that time, and phosphate was still being removed after 24 h. Compared to previous works, Grubb’s team [62] studied 96 h for the kinetics of phosphorus adsorption on fly ash obtained from an electrostatic precipitator, which is more similar to the values reported in this paper. Therefore, providing the specified timeframe in which the adsorption process approaches a proper equilibrium is necessary.
It can be seen that the final adsorption capacity is more than four times higher in the RA sample than in the RSA for all temperatures tested. Both adsorbent capacities increase with temperature (see Figure 1 and Supplementary Data S6).
Several kinetic models were used to test experimental data and to distinguish the possible kinetic differences between the two adsorbents. Table 2 shows the fitted parameters of the three studied kinetic models for both adsorbents and all temperatures, including the coefficients of determination (R2), calculated from the theoretical values predicted by the model regarding the true values obtained yteor = f(yexp). Figure 1 and (Supplementary Data S6) show the fitted curves obtained for the three models for each temperature.
Based on these results, the minimum time to reach a pseudo-steady state in adsorption could be around 3 and 4 days for RSA and RA, respectively. In this work, all the following experiments were performed to determine equilibrium processes during 4–5 days. In addition, higher temperatures increase the reaction rate, reaching the steady state before.
According to the fitting obtained, the Elovich model can be excluded for the RSA sample since it presents the most significant deviation from the experimental data, and the R2 values are farthest from one. However, the pseudo-first-order and pseudo-second-order models can reproduce this evolution better and have similar R2 values. By contrast, the situation for the RA sample is quite different; the pseudo-first-order and pseudo-second-order models are not appropriate, with overestimated values during the first day of adsorption and underestimated final equilibrium values, leading to R2 values farther from one. The Elovich model represents the evolution better, although the final trend presented by this model tends to continue growing. At the same time, in the experimental results, a stabilization of the value is appreciated. The R2 values are better than the other models, although they are still not close to one.
As noted, the development over time is also different between the two materials; after 5 h, the adsorption percentage reached for the RSA sample is around 25%, and for the RA, this is over 60%. However, adsorption stabilizes for the RSA sample for longer contact times, while an increase in adsorption is still visible but slower for the RA. These differences, mainly observed in the RA sample, suggest different adsorption processes and may indicate the possibility that the adsorption process involves two or more simultaneous reactions.
From an applied point of view, it is important to note that although the total equilibrium time for phosphorus removal ranged from 48 to 60 h, around 60% of the removal portion occurred within the first few hours of contact, mainly on the RA adsorbent. This suggests that, under real operating conditions, significant removal efficiency could be achieved in shorter times, particularly in continuous-flow systems in which the solid–liquid ratio is much higher. Future work should focus on these continuous systems and the estimation of their removal capacity in continuous processes.

3.2.1. Double Pseudo-First-Order Model

The main difference between the two adsorbents is the presence of more calcium in the reed ash sample, around double (Table 1). In relation, calcite appears as the main crystalline phase instead of sylvite in rice straw ash. Several works have studied the phosphorus interactions with pure calcite [63,64,65,66]. Those documents describe the kinetics of interaction by two simultaneous and independent reactions related to phosphate adsorption on the calcite surface and with the surface arrangement of phosphate clusters into calcium phosphate heteronuclei [64]. Those conclusions could agree with the kinetic behavior shown by the reed ash samples, in which a first quick removal process is observed, followed by a second, much slower removal step.
Considering this, the following equation represents the rate expression applied to a batch adsorption experiment for two independent pseudo-first-order processes:
q t = q e 1 e k 1 t + q e 1 e k 1 t
where k 1 and k 1 are the rate constants of the pseudo-first-order model; and q e and q e are the amount of solute adsorbed at equilibrium for each process. As the literature suggests, Equation (3) is the simplest model that allows for the representation of two independent processes. The following equation will give the maximum quantity adsorbed, overall adsorption, at equilibrium (qe).
q e = lim t     q t = q e +     q e
Table 3 shows the fitted parameters of the double pseudo-first-order model for both adsorbents and all temperatures. In the same way as before, the R2 values for each fit are calculated. Unlike the previous models, this has four fitting parameters, and so mathematically, the obtained fitting is expected to be better—as can be seen in the better R2 values obtained than the previous ones.

3.2.2. Model Discrimination—Validation of the Double Pseudo-First-Order Model

The double pseudo-first-order model fits the experimental results much better than other simpler models. However, this model has a larger number of parameters that could justify the better fit obtained. To check this possibility, the application of a statistical test is mandatory. The F-test statistic is commonly used in such cases. However, it is important to consider its limitations as it is only valid for nested models—models that can be derived from one another by imposing parametric restrictions. Not all of the models proposed in this study meet this criterion; therefore, alternative statistical tests must be employed. The tests used the corrected Akaike Information Criterion (AICc) [67,68], which is suitable for this kind of model [53]. A more detailed description of this method can be found in the Supplementary Materials (Supplementary Data S7).
The results for model discrimination according to the AICc are shown in Table 4. These values are presented as probabilities (AW) and Evidence Ratios (ER), referring to the model with the minimal AICc value.
According to Table 4, the most statistically probable model for the RSA adsorbent is the pseudo-first-order, since the double pseudo-first-order model, with better R2 values, has been penalized due to its higher complexity and higher number of parameters. In the case of the RA sample, the differences between models are much more significant. Even the greater complexity of the double pseudo-first-order model is compensated by the better fit obtained with the following plausible model (the Elovich model). Therefore, two simultaneous and independent reactions occur during the removal of phosphorus with reed ash samples—as indicated in the literature for pure calcite samples, which has also been observed. This complex model can accurately simulate the initial rapid elimination and later stabilization (Supplementary Data S8). Figure 2 shows the fitted curves obtained by the RSA sample’s pseudo-first-order model and the RA sample’s double pseudo-first-order model at the three temperatures tested, according to the model discrimination.

3.2.3. Effect of Temperature—Arrhenius Plot

Once the models describing the kinetic behavior of the samples have been selected and the rate constants for both adsorbents at different temperatures have been determined, it is possible to obtain the activation energy (Ea) of each process using the Arrhenius equation, which is shown below.
k = A     exp E a R T
This equation has been fitted directly without any linear graph transformation. The fitting was performed using the method of least squares. Figure 3 shows the Arrhenius plot obtained for the three kinetic constants and the accuracy of fit obtained, one for the RSA sample ( k 1 ) and two for the RA sample ( k 1 and k 1 ). The activation energy for the RSA sample was 24.7 kJ·mol−1, and the values for the RA sample were 3.2 kJ·mol−1 for k 1 (the slow process) and 15.6·kJ·mol−1 for k 1 (the fast process). This behavior of the activation energy—two processes with quite different values, one very low—was already observed in a study on the interaction of phosphorus with pure calcite [64]. In that work, the authors report values of <4 kJ·mol−1 for the slow process and ≈35 kJ·mol−1 for the fast one, considering that the material is different.

3.3. Adsorption Isotherm Studies

3.3.1. Effect of Temperature and Adsorbent Dose

Phosphate adsorption isotherms at three different temperatures for the RSA and RA adsorbents were determined, keeping both the adsorbent doses, 10 g·L−1 for RSA and 1.5 g·L−1 for RA, and the pH values, around 10 for RSA and RA, constant. The temperatures studied (283–303 K) cover the typical variation in water bodies.
The isotherms were studied using the three models presented before, as follows: Langmuir, Freundlich, and Temkin isotherm models. All the data were fitted directly to these models. The discrimination of the models was carried out using the same procedure described above, using the corrected Akaike Information Criterion (AICc). The main difference concerning the previous occasion is that all the tested models have the same number of parameters, and so the critical value is the sum of the squares of the regression residuals. Table 5 shows the results for model discrimination according to the AICc.
According to the data obtained, the Freundlich isotherm model can be excluded initially for the two samples because it presents the worst values. The lower-difference AICc value was obtained with the Langmuir isotherm model, which is around ten times more likely than the Temkin model for the RSA sample. In the case of the RA adsorbent, the differences between models are much more critical, showing the Langmuir model as the best statistically. Although the adsorbents used consist of mixtures of metal oxides—which could give rise to a heterogeneous surface—the fitting of the results obtained to a Langmuir isotherm shows that the adsorbent behaves as a homogeneous phase, which may indicate the relevance of one of these oxides to the removal process. Moreover, the existence of a limiting value at high equilibrium concentrations implies the need to assume a finite number of adsorption centers, typical of the Langmuir isotherm, which is not taken into account in the other models.
The fitted curves for the phosphorus removal with the Langmuir model for the two adsorbents are shown in (Supplementary Data S9). The continuous lines in the figure represent the fitted model obtained for each temperature. These lines are defined by the following equation, resulting from the combination of Equations (1), (2), and (S7):
P r e m o v a l % = C 0 D q e × 100 = C 0 D q m a x K L C e 1 + K L C e × 100
Figure 4 show the evolution of the Langmuir parameters with temperature for both adsorbents. As shown, an increase in temperature leads to an increase in adsorption capacity for both adsorbents, similar to that observed by other authors [42,60,65]. The maximum capacity of adsorption (qmax) increases with temperature for both samples, although in the case of RA, its value stabilizes at higher temperatures at around 22.6 mgP·g−1. In the case of RSA, the value increases linearly up to a value of 5.2 mgP·g−1 at 303 K. It is clear that the RA sample has more than four times the adsorption capacity of the RSA sample. These removal values are in agreement with those shown in the literature and can be considered suitable materials for this treatment, which show maximum adsorption capacities for untreated ashes in the order of or slightly higher than those obtained for the RSA sample (0.86–13.77 mgP·g−1) and clearly lower than that obtained with the RA sample [39,69,70,71,72,73]. Even the lowest value obtained for the RSA sample is higher than the one determined by Mor and co-workers for their activated rice husk ash, which has a capacity of 0.7 mgP·g−1 [60].
The Langmuir constant (KL) also increases with temperature for both materials, with a higher value for the RA sample, indicating a better affinity of the phosphate for the RA adsorbent. The Langmuir constant is the ratio between the adsorption and desorption rate constants. Assuming that KL is an equilibrium constant of the overall process during phosphorus adsorption, its temperature dependence can be used to determine the isosteric enthalpy of adsorption ( Δ H ¯ a d ) using the van’t Hoff equation.
ln K L 1 / T θ = Δ H ¯ a d R
According to Equation (7), the curve slope in a plot of ln KL versus 1/T is related to each adsorbent’s isosteric enthalpy of adsorption. The linearity of the KL curves obtained (Figure 4) is acceptable, and the calculated enthalpy values are 5.6 kJ·mol−1 and 11.7 kJ·mol−1 for the RSA and RA samples, respectively. These positive values indicate the endothermic nature of the global process during phosphorus removal.
The effect of adsorbent dose on phosphorus removal is shown in Figure 5. It can be seen that as the dose increases, the removal increases in both adsorbents as would be expected—there is a higher quantity of adsorbent for the same initial concentration of phosphorus, a higher decrease in its concentration at equilibrium, and thus, a higher removal of phosphorus. Again, it is clear that the RA material presents a higher removal efficiency than the RSA material, even at a low dose of adsorbent in a wide range of initial phosphorus concentrations. The experimental data were fitted to the Langmuir isotherm model similarly to before, and then Equation (6) was used to represent them.
Figure 5 is typical in the literature for determining the effect of adsorbent dose in the process. However, the conclusions reached by researchers with this kind of representation should be taken with caution because an increase in the dose necessarily increases the removal [60,74,75]. Figure 6 shows the effects of the adsorbent dose but now over the maximum adsorption capacity of both samples (qmax). This parameter was obtained from the Langmuir isotherm model fitted. In both cases, the increase in the adsorbent dose has a negative effect on the adsorption capacity of the materials, more significantly in the case of the RA adsorbent. However, the adsorption capacity of this material is much higher than that of the RSA sample. This behavior is not observed in Figure 5; hence, there is a need to choose the right kind of representation. The final pH variation observed during the increase in the dose used (around 10.1–10.5 for both materials) does not seem to be the main reason for reducing the maximum capacity (a study of the pH effect will be presented below). However, a linear variation in the conductivity with dose is observed. This could be explained as a reduction in the adsorption capacity due to competitive adsorption between phosphorus and other ions present in the solution by ion exchange or dissolution of part of the adsorbent components, reducing the availability of sites for phosphorus adsorption.

3.3.2. Effect of pH and the Presence of Other Ions in Solution

The pH of the aqueous solution is a crucial controlling parameter in adsorption processes. The degree of ionization and speciation of the adsorbate is strongly affected by pH. Hence, phosphate removal was studied using synthetic water containing 60 mgP·L−1 and the initial pH value was adjusted using HCl or NaOH, as required. The pH range tested was between 5 and 10 roughly, which covers typical pH values commonly found in urban wastewater streams and natural water bodies. In addition, alkalinity is the main parameter in water bodies that controls the liquid pH and its possible development. Given that adsorbents have a buffer capacity, (Supplementary Data S5), the effect of alkalinity in the adsorption process has also been studied. To achieve this, different dilutions of NaHCO3 were used to obtain solutions ranging from 0 mg·L−1 to 300 mg·L−1 of CaCO3.
Figure 7A shows the effect of initial pH on the adsorption capacity of both adsorbents for the four alkalinities tested. In all cases, an increase in the initial pH entails a decrease in the adsorption capacity, indicating that phosphorus removal is more efficient under acidic conditions. However, the loss of capacity is more relevant in the case of the RA adsorbent. Whereas the maximum loss in RSA is around 15.5%, the value for RA is about twice as much, 28.8%, in the pH range studied. In both materials, a possible effect of alkalinity on the removal capacity is not appreciable. In these cases, the alkalinity only slightly modified the final pH achieved. The carbonate ion does not seem to have any competitive effect on phosphorus removal under these operating conditions. Previous studies also show this variation in the pH [60,76,77]. These authors argue that adsorption is affected by the kind and ionic state of the functional group present in the adsorbent and the chemistry of the adsorbate solution. High pH leads to the dissociation of functional groups of the adsorbent, increasing the negative charge and, thus, decreasing the adsorption of the negative phosphate ion. Rathod and co-workers [78] indicate that at higher pH, the higher concentration of hydroxyl ions could compete with the phosphate ions for the sorption sites, decreasing phosphate removal.
However, due to the high buffer capacity of both adsorbents, the final pH obtained for the full range of initial pH studied is very close, (Supplementary Data S10). Then, it is difficult to explain the change in the adsorption capacity observed only for the above reasons. Another fact related to the evolution of the adsorbent behavior from initial to final pH could also be relevant to the results obtained. During the discussion of kinetic behavior, two phosphorus elimination processes have been observed in the RA sample, processes also reported in the literature (Section 3.2.1). The second process is related to the surface arrangement of phosphate clusters into calcium phosphate heteronuclei. Calcium in the solution is necessary for this process, resulting in the partial dissolution of the present one in the adsorbent. In addition, different authors conclude that these cations mainly accomplish phosphate fixation [36,39,79].
The hypothesis proposed in this work is that the acid solution could promote the dissolution of part of the basic calcium oxide in the adsorbent. Although the final pH was very close, the higher quantity of calcium dissolved increased the phosphate removed by precipitation. Figure 7B shows the calcium concentration in the equilibrium solution at different pH values and two different alkalinities. As can be seen, a lower initial pH leads to a higher final calcium concentration for both materials. In addition, the samples with the most elevated alkalinity—which reach lower final pH, (Supplementary Data S10)—also show higher calcium concentrations.
To confirm that the presence of calcium ions in solution has a positive effect on the adsorption capacity, experiments were performed using two different calcium concentrations, 10 mgCa·L−1 (10 Ca) and 40 mgCa·L−1 (40 Ca), from CaCl2·4H2O in the initial phosphate solution. The addition of salts modifies the ionic strength (I). To control this parameter, all experiments, including a blank without initial calcium, were conducted with a controlled ionic strength of around 2.20 mS·cm−1 using the required amount of NaCl to reach this value. Figure 8 shows the variation in the maximum adsorption capacity (qmax) for these experiments, obtained from the data fitting to the Langmuir isotherm. The effect of ionic strength is small; a slight variation is observed between the original and NaCl experiments (around 600 μS·cm−1 and 2.20 mS·cm−1, respectively). However, the addition of calcium ions has an appreciable positive effect on the capacity obtained, increasing its value to around 73% for RSA and 79% for RA in the highest calcium concentration tested (40 Ca), confirming the relevance of this cation in the phosphorus removal process.
Table 6 shows a detailed thermodynamic modeling analysis using Visual MINTEQ to estimate the saturation index (SI) of relevant calcium–phosphate mineral phases under the experimental conditions described. The modeling results indicate that the system is oversaturated with respect to hydroxyapatite, suggesting favorable conditions for its precipitation. This finding aligns with the observed trends in Figure 8 and supports the hypothesis that calcium availability enhances phosphate immobilization via mineral precipitation.
In addition to supporting the hypothesis proposed before, (Supplementary Data S11) show the distribution maps of FESEM images for the main components of both adsorbents. These samples were obtained after a batch adsorption experiment by filtration through a glass microfiber filter of the suspension. Then, the filter was dried at 353 K overnight, and the solid was recovered carefully. In both samples, it can be seen that the phosphorus is in the region occupied by calcium, much more evident in the RA sample, mainly because their distribution maps are similar and quite different from that of silicon. Other elements in lower concentrations, like aluminum and iron, which could also play a relevant role in the removal processes, show distribution maps that are more dispersed and not similar to phosphorus. This evidence is in line with all the previous results. They show the relative significance of calcium in solution and on the adsorbent surface in the phosphorus elimination process.

3.4. Adsorbent Blend—Combined Langmuir Adsorption Model

As stated in the introduction, using ashes from agro-wastes for phosphorus removal would increase the upstream combustion process’s profitability and align with the new circular economy and zero-waste policies. In addition, the possible further use of these materials, rich in phosphorus as a fertilizer, would enhance the environmental benefits. A potential problem with this kind of agricultural waste is its production seasonality and the presence of different kinds of waste. Thus, combining other ashes as an adsorbent could be a common practice. To study the effect of ash blend in the adsorption process and its mathematical modeling, experiments with both adsorbents blended were performed, and a combined Langmuir model was proposed ( q e + ). This combined model for mixtures of different adsorbents is shown in the following equation:
q e + = i w i   q e i = i w i q m a x i K L i C e 1 + K L i C e
where wi is the mass fraction of each adsorbent; and q e i is the Langmuir adsorption model for each adsorbent—dependent on the individual Langmuir parameters of each adsorbent. Logically, the sum of all the mass fractions of the different adsorbents that make up the mixture is equal to unity. In this model, it is assumed that there are no synergies or antagonisms between adsorbents; the mixture behaves as a linear sum; and that all adsorbents are in equilibrium with the same concentration of the solute.
The evolution of this model with equilibrium concentration is expected to be similar to that obtained with the simple Langmuir model. For this purpose, the derivative of the combined model can be determined, and its sensitivity to the change in this concentration can be analyzed (Equation (9)).
d q e + d C e = i w i q m a x i K L i 1 + K L i C e 2
The value of this equation is always positive—indicating an increase in the adsorption capacity with the equilibrium concentration—but with a decreasing slope, reaching a maximum value ( q m a x + ). This limiting value could be determined by applying Limits to the function when the equilibrium concentration tends to infinity, Equation (10).
q m a x + = lim C e q e + = i w i q m a x i
Since the blending model has an asymptotic maximum value, it may be of interest to try to simplify this model to an expression similar to that of the traditional Langmuir model, which could be represented by two parameters depending on the individual Langmuir constants of each adsorbent. In this sense, the equation of the simplified combined model would be as follows:
q e + = i w i   q e i = q m a x + K L + C e 1 + K L + C e
where K L + is an apparent Langmuir constant of the blending model. The determination of the apparent Langmuir constant can be obtained from Equation (11), resulting in the following expression:
K L + = i w i q e i i w i q m a x i q e i 1 C e
Unlike the true Langmuir constant, this apparent constant depends—for a given proportion of adsorbents—on the equilibrium concentration at which it is determined, varying between a maximum and minimum value. The limit values of this variable can be determined by the following equations, depending on the individual Langmuir parameters of each adsorbent present in the mixture. The variation in this parameter with equilibrium concentration is shown in (Supplementary Data S12).
lim C e 0 K L + = i w i q m a x i K L i i w i q m a x i
lim C e K L + = i w i   q m a x i i K L i i w i q m a x i     j j i K L j
In the case of the two adsorbents analyzed in this work, Equation (8) applied to the RSA and RA samples is equivalent to the following:
q e + = w RSA   q e RSA + w RA   q e RA = w RSA   q m a x RSA K L RSA C e 1 + K L RSA C e + w RA   q m a x RA K L RA C e 1 + K L RA C e
which, applying the Langmuir parameter values determined above (Section 3.3.1), gives us the following equation as a function of the mixing fraction:
q e + = 1 w RA   4.57 0.275 C e 1 + 0.275 C e + w RA   18.59 0.957 C e 1 + 0.957 C e
In the same way, the relationship of the maximum adsorption capacity of the combined model ( q m a x + ) with the parameters of the individual models as a function of the mixing fraction can be obtained, according to Equation (10), as outlined below:
q m a x + = w RSA   q m a x RSA + w RA   q m a x RA = 1 w RA 4.57 + w RA 18.59
To validate this proposed model, experiments were performed with a constant total dose of 5.0 g·L−1 of both adsorbents at 293 K. Four different mass fractions were tested. The results of the experiments and the fit obtained with Equation (16) are shown in Figure 9. This figure also shows the curve of the Langmuir isotherm for both pure adsorbents with their single data points.
It can be seen that the higher quantity of the RA adsorbent in the blend results in a higher adsorption capacity as expected. The data obtained are proportional to the relative amount of both adsorbents. These experimental points of the different mixtures of adsorbents are on a straight line for all ratios tested for the same initial phosphorus concentration. These curves result from the mass balance, provided that the adsorbent dose is kept constant. The equation of these straight lines is derived from Equation (1), which can be written as Equation (18). According to this equation, the slope of the straight lines is the inverse of the adsorbent dose used, and these lines only depend on the initial phosphorus concentration of each experiment. Indeed, this initial concentration corresponds to the intersection of the line with the x-axis.
q e = C 0 D 1 D C e
To validate the combined model, Figure 10A shows the relation between the capacity of adsorption for each equilibrium concentration and mass fraction, determined by Equation (16) ( q e t h e o r ), versus the capacity of adsorption determined experimentally for the same concentration and mass fraction ( q e e x p ). In addition, Figure 10B shows the maximum adsorption capacity for each mass fraction tested, obtained from theoretical Equation (17) ( q m a x + ), versus the same value obtained in a single fit to the Langmuir model of the experimental series for the same mass fraction ( q m a x S t d . ), in a similar way as in previous sections. As seen in both figures, all the values of the different series tested and the asymptotic values of maximum adsorption capacity have good linearity, with R2 near to unity, with a slight deviation from theoretical behavior. Therefore, the proposed non-competitive addition model for blending this kind of adsorbent is adequate and allows the overall behavior to be determined from the individual adsorption parameters obtained for each material.

4. Conclusions

Based on the results shown in this work, it can be concluded that ashes from rice straw and reed are effective in removing phosphorus from aqueous solutions and that the reed ash is around four times more effective than rice straw ash, even when applied at a sixfold lower adsorbent dose. The time required to reach equilibrium is relatively long; however, the reed ash shows two distinct processes, one faster than the other, as opposed to rice straw ash, in which only a single process is identified. A double pseudo-first-order model has been required to simulate the behavior of the reed ash, while a simple pseudo-first-order model was enough to simulate the behavior of the rice straw ash. Statistically, the double model is much more plausible than the models commonly used in the literature.
Phosphorus adsorption is an endothermic process in both materials, increasing the adsorption capacity with temperature. The Langmuir isotherm model can describe the observed behavior of both materials. A higher adsorbent dose leads to higher phosphorus removal rates, as expected. However, in both adsorbents, the quantity adsorbed per gram decreases with higher doses, indicating a lower adsorption capacity, possibly because of some kind of competitive adsorption or interaction due to the partial dissolution of the materials. The initial acid solutions positively affect the adsorption capacity for both materials, among others, due to the increase in calcium concentration in the solution. The higher calcium in the solution promotes the removal of phosphorus, possibly by assisting the precipitation step over the adsorbent surface in the form of some calcium phosphate. The presence of calcium ions in the solution strongly influences the removal process. The buffer capacity of the materials is very high; even with solutions with alkalinities around 300 mg CaCO3·L−1, the final pH is very close. The presence of sodium, chlorine, and carbonate ions does not significantly affect phosphorus adsorption.
Finally, the behavior of blended adsorbents could be successfully simulated based on the original isotherm models for the pure materials using a non-competitive additive approach depending only on their mixing ratio. These findings indicate that both materials, particularly reed ash, could be used as low-cost materials for phosphorus removal and recovery from water and wastewater.
Although the regeneration and reuse of the phosphorus-saturated ashes could be technically feasible, this option would require the use of chemical reagents, which would increase the cost and could also cause leaching of the active phases responsible for phosphorus removal. Therefore, the preferred strategy for managing the spent material is its direct application as a phosphorus-rich fertilizer. This approach not only enhances the economic viability of the proposed management solution but also contributes to the development of more sustainable and circular treatment practices.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/su17136153/s1.

Author Contributions

Conceptualization, J.A.G. and J.M.; methodology, J.A.G. and J.M.; characterization, A.E.P.; formal analysis, J.A.G., J.M., and A.E.P.; writing—original draft preparation, J.M.; writing—review and editing, J.A.G., J.M., and A.E.P. All authors have read and agreed to the published version of the manuscript.

Funding

This research was partially funded by the Spanish government—Ministerio de Ciencia, Innovación y Universidades, through project PID2021-122755OB-I00.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available upon substantiated request from the corresponding author.

Acknowledgments

The authors would like to acknowledge all who have directly or indirectly helped in carrying out this study. The financial support mentioned in the Funding Section is gratefully acknowledged.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Kinetics of phosphate removal by RSA (circles) and RA (triangles) at 293 K. Adsorbent dose (D): 10 g·L−1 (RSA), 2.5 g·L−1 (RA). Initial phosphate concentration (C0): 60 mgP·L−1.
Figure 1. Kinetics of phosphate removal by RSA (circles) and RA (triangles) at 293 K. Adsorbent dose (D): 10 g·L−1 (RSA), 2.5 g·L−1 (RA). Initial phosphate concentration (C0): 60 mgP·L−1.
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Figure 2. Kinetics of phosphate removal by RSA (circles) and RA (triangles) at different temperatures. Adsorbent dose (D): 10 g·L−1 (RSA), 2.5 g·L−1 (RA). Initial phosphate concentration (C0): 60 mgP·L−1.
Figure 2. Kinetics of phosphate removal by RSA (circles) and RA (triangles) at different temperatures. Adsorbent dose (D): 10 g·L−1 (RSA), 2.5 g·L−1 (RA). Initial phosphate concentration (C0): 60 mgP·L−1.
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Figure 3. Arrhenius plot for adsorption of RSA (circles) and RA (triangles) samples. k 1 (black); k 1 (blue); k 1 (red).
Figure 3. Arrhenius plot for adsorption of RSA (circles) and RA (triangles) samples. k 1 (black); k 1 (blue); k 1 (red).
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Figure 4. Effect of temperature on Langmuir adsorption parameters on RSA (circles) and RA (triangles) samples. Adsorbent dose (D): 10 g·L−1 (RSA), 1.5 g·L−1 (RA).
Figure 4. Effect of temperature on Langmuir adsorption parameters on RSA (circles) and RA (triangles) samples. Adsorbent dose (D): 10 g·L−1 (RSA), 1.5 g·L−1 (RA).
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Figure 5. Phosphorus removal for different doses on RSA adsorbent (circles) and RA adsorbent (triangles) at 293 K.
Figure 5. Phosphorus removal for different doses on RSA adsorbent (circles) and RA adsorbent (triangles) at 293 K.
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Figure 6. Effect of adsorbent dose at 293 K on Langmuir maximum adsorption capacity on RSA (circles) and RA (triangles) samples. Adsorbent dose (D): 10 g·L−1 (RSA), 1.5 g·L−1 (RA).
Figure 6. Effect of adsorbent dose at 293 K on Langmuir maximum adsorption capacity on RSA (circles) and RA (triangles) samples. Adsorbent dose (D): 10 g·L−1 (RSA), 1.5 g·L−1 (RA).
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Figure 7. Effect of initial pH on the adsorption of phosphorus onto RSA (circles) and RA (triangles) at 293 K. Adsorbent dose (D): 10 g·L−1 (RSA), 2.5 g·L−1 (RA). Alkalinity/(mgCaCO3·L−1): 0 (blue), 50 (green), 150 (orange), 300 (purple). (A) Over-adsorption capacity and (B) over-dissolved calcium at equilibrium.
Figure 7. Effect of initial pH on the adsorption of phosphorus onto RSA (circles) and RA (triangles) at 293 K. Adsorbent dose (D): 10 g·L−1 (RSA), 2.5 g·L−1 (RA). Alkalinity/(mgCaCO3·L−1): 0 (blue), 50 (green), 150 (orange), 300 (purple). (A) Over-adsorption capacity and (B) over-dissolved calcium at equilibrium.
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Figure 8. Effect of the presence of ions in solution on the maximum adsorption capacity for both materials at 293 K. Adsorbent dose (D): 10 g·L−1 (RSA), 1.5 g·L−1 (RA).
Figure 8. Effect of the presence of ions in solution on the maximum adsorption capacity for both materials at 293 K. Adsorbent dose (D): 10 g·L−1 (RSA), 1.5 g·L−1 (RA).
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Figure 9. Combined Langmuir isotherm model at 293 K for different ratios of both adsorbents. Adsorbent dose (D): 5.0 g·L−1.
Figure 9. Combined Langmuir isotherm model at 293 K for different ratios of both adsorbents. Adsorbent dose (D): 5.0 g·L−1.
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Figure 10. Validation of the combined Langmuir isotherm proposed model.
Figure 10. Validation of the combined Langmuir isotherm proposed model.
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Table 1. Physical and chemical properties of the adsorbent materials.
Table 1. Physical and chemical properties of the adsorbent materials.
SamplesRSARA
pHPZC10.911.6
BET surface area (m2 g−1)1217
   External surface area (%)7791
Elementary analysis (wt. %)
   Carbon1.191.41
   Nitrogen0.000.00
   Hydrogen0.210.15
   Sulfur0.070.41
Composition (wt. %)
   Si33.226.0
   Al0.70.5
   Fe1.10.8
   Mn0.10.3
   Mg2.83.2
   Ca6.713.1
   Na1.41.0
   K6.46.3
   P1.11.5
   Zn0.10.1
   Cu<0.05<0.05
Table 2. Typical kinetic models for phosphate adsorption over both materials at different temperatures.
Table 2. Typical kinetic models for phosphate adsorption over both materials at different temperatures.

Models

T (K)
RSA
283

293

303
RA
283

293

303
Pseudo-first-order
   qe (mgP g−1) 2.833.654.1713.715.216.9
   k1 (h−1) 0.0580.0620.1050.2170.3230.405
   R2 0.9860.9820.9840.9290.8700.811
Pseudo-second-order
   qe (mgP g−1) 3.284.284.7114.716.317.7
   k2 (g mgP−1 h−1) 0.0210.0170.0270.0200.0260.035
   R2 0.9850.9810.9840.9780.9530.947
Elovich
   a (mgP g−1 h−1) 0.3570.4641.07814.731.6232.1
   b (g mgP−1) 1.3260.9941.0250.4400.4290.519
   R2 0.9610.9550.9430.9790.9740.966
Table 3. Double pseudo-first-order model for phosphate adsorption over both materials at different temperatures.
Table 3. Double pseudo-first-order model for phosphate adsorption over both materials at different temperatures.

Model

T (K)
RSA
283

293

303
RA
283

293

303
Double pseudo-first-order
    q e (mgP g−1) 1.853.011.256.697.396.15
    q e (mgP g−1) 1.040.703.107.999.4511.9
    k 1 (h−1) 0.0380.0490.0310.0360.0360.039
    k 1 (h−1) 0.1190.1720.1460.6070.7760.944
   R2 0.9900.9850.9900.9940.9880.994
Table 4. Kinetic model discrimination: Akaike Information Criterion.
Table 4. Kinetic model discrimination: Akaike Information Criterion.

Model

N. Par. a
RSA
SSE b

AICc

ΔAICc
RA
SSE

AICc

ΔAICc
P-F c20.973−110.30.091.550.4136
P-S d21.049−107.52.727.8−15.670.0
Elovich23.046−68.441.817.8−37.548.0
DP-F e40.769−86.224.05.7−85.60.0
a Number of parameters; b total sum of the residuals; c pseudo-first-order model; d pseudo-second-order model; e double pseudo-first-order model.
Table 5. Isotherm model discrimination: Akaike Information Criterion.
Table 5. Isotherm model discrimination: Akaike Information Criterion.

Model

N. Par.
RSA
SSE

AICc

ΔAICc
RA
SSE

AICc

ΔAICc
L a21.399−119.00.023.0−11.20.0
F b24.211−73.046.1173.782.793.9
T c21.650−114.34.880.351.762.9
a Langmuir model; b Freundlich model; c Temkin model.
Table 6. Saturation index values (SI) and ion activity product (IAP) of several calcium phosphate minerals after equilibrium, as predicted by Visual MINTEQ modeling. Null SI values (red) indicate precipitation at apparent equilibrium. Ce = 60 mgP·L−1, T =293 K, pH = 10, and I = 0.01 N.
Table 6. Saturation index values (SI) and ion activity product (IAP) of several calcium phosphate minerals after equilibrium, as predicted by Visual MINTEQ modeling. Null SI values (red) indicate precipitation at apparent equilibrium. Ce = 60 mgP·L−1, T =293 K, pH = 10, and I = 0.01 N.
0 mg Ca·L−110 mg Ca·L−140 mg Ca·L−160 mg Ca·L−1
Minerallog Ksplog IAPSIlo IAPSIlog IAPSIlog IAPSI
Ca3(PO4)2 (amorphus 1)−25.5−41.0−16.3−33.7−9.1−33.7−9.1−33.7−9.1
Ca3(PO4)2 (amorphus 2)−25.3−41.0−13.5−33.7−6.3−33.7−6.3−33.7−6.3
Ca3(PO4)2 (beta)−28.9−41.0−11.6−33.7−4.3−33.7−4.3−33.7−4.3
Ca4H(PO4)3·3H2O−48.0−66.5−19.5−56.8−9.8−56.8−9.8−56.9−9.9
CaHPO4−19.3−25.5−5.9−23.1−3.5−23.1−3.5−23.1−3.6
CaHPO4·2H2O−19.0−25.5−6.3−23.1−3.9−23.1−3.9−23.1−3.9
Hydroxyapatite−44.3−56.5−12.1−44.30.0−44.30.0−44.30.0
Precipitated P(%) 0 6.6 24.6 39.9
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González, J.A.; Mengual, J.; Palomares, A.E. Phosphorus Control and Recovery in Anthropogenic Wetlands Using Their Green Waste—Validation of an Adsorbent Mixture Model. Sustainability 2025, 17, 6153. https://doi.org/10.3390/su17136153

AMA Style

González JA, Mengual J, Palomares AE. Phosphorus Control and Recovery in Anthropogenic Wetlands Using Their Green Waste—Validation of an Adsorbent Mixture Model. Sustainability. 2025; 17(13):6153. https://doi.org/10.3390/su17136153

Chicago/Turabian Style

González, Juan A., Jesús Mengual, and Antonio Eduardo Palomares. 2025. "Phosphorus Control and Recovery in Anthropogenic Wetlands Using Their Green Waste—Validation of an Adsorbent Mixture Model" Sustainability 17, no. 13: 6153. https://doi.org/10.3390/su17136153

APA Style

González, J. A., Mengual, J., & Palomares, A. E. (2025). Phosphorus Control and Recovery in Anthropogenic Wetlands Using Their Green Waste—Validation of an Adsorbent Mixture Model. Sustainability, 17(13), 6153. https://doi.org/10.3390/su17136153

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