Fixed-bed kinetic sorption (Bohart–Adams, Thomas, Yoon–Nelson, Clark, Wolborska, and modified dose-response) models are commonly used to simulate breakthrough curves (BTCs) from fixed-bed systems. However, more caution should be taken in using these models. Some researchers misused the equation, which is a totally different type from the original model, as a simplified model. Others used the same equation expressed in different forms as an independent model. The aim of this study was to clarify the fixed-bed sorption models via comparative analysis using the phosphate BTCs in slag filter media. For the analysis, the breakthrough data for phosphate (initial phosphate concentration = 1.0 and 2.0 mg/L) sorption in fixed-bed columns (inner diameter = 2.5 cm and column length = 10, 20, and 30 cm) were obtained from the experiments. The original Bohart–Adams model was simplified in the literature to the convergent- and divergent-type models in order to be used for the BTC analysis. However, the divergent-type model, which is equivalent to the Wolborska model, should not be the type of Bohart–Adams model used, because it behaves totally different from the original model. Also, the Thomas and Yoon–Nelson models should not be used simultaneously with the Bohart–Adams model, because they are equivalent to the simplified convergent-type Bohart–Adams model, and the parameters of both of the models (k_T, q₀, k_YN, and τ) can easily be calculated from the Bohart–Adams model parameters (k_BA and N₀). The Bohart–Adams, Clark, and modified dose-response models could describe the BTCs relatively well with a high determination coefficient and a low chi-square coefficient. From this study, the Bohart–Adams, Clark, and modified dose-response models are recommended for the BTC analysis, because these models can provide useful design parameters (k_BA, N₀, Z₀, t_b, and q₀) for the fixed-bed systems.

This study investigated the applicability of algae (Hizikia fusiformis, Green gracilaria, and Codium fragile) for removing heavy metals (Cd²⁺, Cu²⁺, Ni²⁺, and Pb²⁺) from aqueous solutions. Among the algae, H. fusiformis was chosen as a bioadsorbent and modified with NaOH and HCl. The results showed that the biosorption capacity of H. fusiformis improved significantly after treatment with NaOH; however, H. fusiformis modified with HCl did not achieve the expected value. The NaOH treatment enhanced the biosorption of metals on the treated H. fusiformis because of the hydrolysis reaction producing carboxylic (–COOH) and hydroxyl groups (–OH). The kinetics for Cd²⁺, Cu²⁺, Ni²⁺, and Pb²⁺ biosorption well fitted to pseudo-first-order, pseudo-second-order, and Elovich models, with R² of >0.994. The Freundlich model provided a good fit for the equilibrium biosorption of Cd²⁺, Cu²⁺, and Ni²⁺ by both algae and the Langmuir model for Pb²⁺. The maximum biosorption of metals was in the order Pb²⁺ >> Cu²⁺ ≈ Ni²⁺ > Cd²⁺, with q_max of 167.73, 45.09, 44.38, and 42.08 mg/g, respectively. With an increase in the solution pH, metal biosorption was enhanced, and considerable enhancement was observed in the pH range of 2–4. Thus, H. fusiformis is expected to be considered a superior candidate for metal biosorption.