## 1 Introduction
This strategy should be optimized using fixed-bed experiments. Several key parameters must be thoroughly investigated in fixed-bed adsorption experiments because they significantly influence the performance of the adsorbent. These include the feed concentration, flow rate (which determines the contact time), and bed height. Additionally, the characteristics of the matrix used for adsorbate recovery should not be overlooked. In particular, the presence of other competing elements within the matrix is a critical factor, especially in wastewater treatment, owing to its complex and variable composition. To the best of our knowledge, only a limited number of studies have investigated the removal of P from wastewater using calcined eggshells in fixed-bed column experiments. Some studies have combined eggshells with other wastes, such as corn stalks [12] and fly ash [13], to prepare low-cost adsorbents. However, these studies were conducted using simulated or pig wastewater. A recent study using rejected wastewater from an anaerobic sludge dewatering process (with an orthophosphate concentration of approximately 30 mg P/L) combined a submerged anaerobic membrane bioreactor and two adsorption columns (eggshell and seagrass as adsorbents). The eggshell was thermally treated at 900 \({}^{\circ}\)C for 30 min, and the seagrass was treated at 500 \({}^{\circ}\)C for 60 min. The column was operated in continuous mode, and high P removal efficiencies were obtained with eggshells (\(>\)90%) [14]. However, this study did not include the determination of breakthrough curves to obtain relevant parameters to scale up the process, such as the breakthrough time, stoichiometric time, and fraction of saturated bed (_FSB_) [15]. Alternatively, some studies have investigated the use of other low-cost adsorbents, such as biochar derived from wood residues [16] and biosolids pyrolysis [17], for P removal from wastewater. While these studies have shown promising results, none of them progressed to a scale-up design. Moreover, desorption is typically considered the final step for the exhausted adsorbent without exploring the potential of P recycling through soil application, an aspect that aligns closely with the goals of the present study. Specifically, no scientific studies to date have investigated the integration of the newly proposed struite precipitation approach (discussed before) with fixed-bed adsorption using calcined eggshells --a dual-P recovery system--to achieve P concentrations below regulatory limits and enable water for reuse. Thus, the main objectives of the present study were (i) to optimize the operating conditions of the adsorption process in the wastewater stream after chemical precipitation, specifically regarding the flow rate and column height; (ii) to analyze the impact of different feed concentrations and assess the feasibility of implementing the adsorption system independently of chemical precipitation; (iii) to evaluate the behavior of coexisting SO4\({}^{2-}\) ions under dynamic studies, given the interference observed in previous batch experiments [18]; and (iv) to develop a scale-up design of the adsorption column. Desorption tests were not performed, as the aim was to assess the potential use of the P-loaded adsorbent as a fertilizer in future agronomic experiments (which are beyond the scope of this work).