Sorption Kinetic Models Research Articles

Amputation of phenol using barium embedded and Ba-HDTMA modified power station solid waste: Column dynamics

The aim of the study was to examine the adsorption capability of barium embedded and Surfactant modified zeolitic materials, which were synthesized from power station solid waste by microwave assisted alkaline hydrothermal reflux method. Power station solid waste and modified synthesized materials were characterized by XRF, PXRD, SEM, FTIR, TGA and BET-BJH instrumental methods. Batch Studies were performed to explore the outcome of various parameters such as pH (1–12), contact time (0–360min), Sorbent dose (0.2–10gL−1), initial sorbate concentration (50–300mgL−1) and temperature (30–60°C). Uptake of ionisable compounds is dependent greatly on pH. Batch sorption experiments showed that efficiency of MZCFA (24.19mgg−1) and SMZCFA (28.74mgg−1) is raised as compared to CFA (10.48mgg−1). Surface modification enhances phenol removal from aqueous solutions. Langmuir, Freundlich and Temkin isotherms have been studied, among them Langmuir isotherm is best suited. Pseudo-second-order was best fitted out of Pseudo-first-order, Pseudo-second-order and Intraparticle diffusion model for sorption kinetics. The breakthrough capacities acquired by column studies shows lower sorption capacity compare to batch studies. Regeneration studies were carried out using 0.5M NaOH and HCl solutions. The modified zeolitic materials enhanced the sorption of phenol from aqueous solution.

Biosorption of chromium(VI) using immobilized <i>Bacillius subtilis</i> and <i>Pseudomonas aeruginosa</i>

Heavy metals like chromium do contaminate the environment that comprises of soil, water and air. It affects the growth of flora and fauna which in turn affect human health negatively. Chromium could also bio-accumulate in plants and animals and this becomes dangerous for survival of human if adequate steps are not taken for treatment of industrial and agricultural wastes. Therefore, the batch removal of Cr (VI) from environment water bodies becomes necessary. Its removal from aqueous solution using immobilized Bacillus subtilis (IBBS), Pseudomonas aeruginosa (IPBS), mixed biomass (IMBS) and Alginate alone (IABS) was carried out. The conditions of influence of initial Cr (VI) concentrations, solution pH, contact time, biomass dosage and temperature were studied. The sorption kinetic models of Cr (VI) onto the biosorbents were examined with pseudo first-order, pseudo second-order, and Elovich kinetics respectively. It was found that the experimental conditions affected the extent of removal of Cr (VI) from aqueous solution. The higher the initial concentration, the larger the amount of Cr (VI) removed while the higher the temperature the lesser the amount removed. The optimum contact time and adsorbent dose for effective removal of Cr (VI) from aqueous solution were found to be 60 mins and 0.01 g respectively. Pseudo second-order kinetic model best correlates the experimental data. Among isotherm models studied, Freundlich adsorption isotherm model gave the best fit.Key Words: Chromium (VI), Adsorption Kinetics, Adsorption Isotherms, Spectrophotometric Determination, Immobilized Biosorbents

Removal of methylene blue from synthetic aqueous solutions with novel phosphoric acid-doped pyrazole-g-poly(glycidyl methacrylate) particles: kinetic and equilibrium studies

Fundamental investigations of the removal of methylene blue (MB) from aqueous solutions by synthesized orthophosphoric acid-doped pyrazole-g-poly glycidyl methacrylate (OPA-Py-g-PGMA) and poly (glycidyl methacrylate) (PGMA) particles of average size 71 and 40 μm, respectively, conducted under batch conditions. The kinetic and equilibrium results obtained for MB sorption with different initial MB concentrations onto synthesized OPA-Py-g-PGMA, and PGMA were analyzed. Kinetic modeling analysis with three different types of kinetic sorption models (pseudo-first-order, pseudo-second-order, simple Elovich, and intraparticle diffusion rate models) was applied to simulate the MB sorption data. The analysis of the kinetic data indicated that the sorption was a second-order process. An ion-exchange mechanism may have existed in the MB-sorption process with the synthesized OPA-Py-g-PGMA. The MB uptake by OPA-Py-g-PGMA and PGMA quantitatively evaluated with equilibrium sorption isotherms. To describe the isotherms mathematically, the experimental data of the removal equilibrium correlated with the Langmuir, Freundlich, Temkin, and Dubinin–Radushkevich (D–R) isotherm models, and the applicability of these isotherm equations to the sorption systems compared by the correlation coefficients. The maximum sorption capacities, determined from the Langmuir isotherm, were 15.15 and 8.67 mg/g at 25°C for OPA-Py-g-PGMA and PGMA, respectively. Moreover, diffusion mechanism of MB was described by different adsorption diffusion models. The diffusion rate equations inside particulate of Dumwald–Wagner and intraparticle models were used to calculate the diffusion rate. The actual rate-controlling step involved in the MB sorption process was determined by further analysis of the sorption data by the kinetic expression given by Boyd.

Kinetic model for sorption of divalent heavy metal ions on low cost minerals

A mathematical model is proposed that could predict the kinetic parameters for adsorption of divalent heavy metal ions (lead, copper and zinc) onto low-cost adsorbents such as pyrophyllite and rock phosphate using experimental data. The experiments were conducted with the initial concentrations of metal ions ranging from 10mg/L to 100mg/L. The mathematical model is based on the application of the Redlich-Peterson isotherm to mass transfer across the film surrounding the adsorbent. The developed non-linear sorption kinetic (NSK) mathematical model was solved using numerical integration by the trapezoidal method in Microsoft Excel along with the SOLVER function to obtain the best simulated values of the Redlich-Peterson constants A, B, r, the order of reaction n, and the film transfer coefficient α. Dissolution followed by precipitation was found to be the most probable mechanism responsible for heavy metal ion uptake by rock phosphate, while for pyrophyllite physical adsorption was governing mechanism at low concentrations (<100mg/L). The values of parameters A, B, r and α lie in the ranges of 0.015-23.2, 0.00003-3.09, 0.072-1, and 0.000057-52.8 [(L/mg)(n−1)/min], respectively, under different experimental conditions.

A proposed kinetic model for hydrogen sorption in MgH2

The role of ternary Mg–Nb oxides on H2 absorption and desorption properties of ball milled MgH2 is discussed on the basis of a kinetic model involving the formation of reaction pathways of ternary oxide species with easier splitting of H2 that facilitate the transport of H2 into the solid structure. The kinetic model comprised three key steps: dissociation of molecular hydrogen into H atoms, diffusion of H into Mg to form MgH2 during adsorption, and successive recombination of H–H on the surface of the additives during desorption to make a pathway for H2 sorption in the structure. The presence of transition metal oxides remarkably increases the H2 sorption rates of nano-structured MgH2, as determined by a volumetric Sievert apparatus. The H2 desorption rate increases with increasing temperature from 593 to 673 K and under the same conditions, the absorption rate decreases. The most promising results were obtained for Mg3Nb6O11-doped MgH2 nanoparticles. The MgH2/Mg3Nb6O11 system is completely dehydrogenated at 673 K under 0.1 MPa H2 and the samples fully rehydrogenated at 613 K under 2.5 MPa H2 pressure. Activation energies were obtained for MgH2/Mg3Nb6O11 mixture, and without additive (ball milled MgH2), to be 88 and 127 kJ mol−1, respectively, underlying the effect of the ternary additive.

Mathematical model of the water sorption kinetics of UBC

The water sorption kinetics of UBC (Upgraded Brown Coal) and its feedstock coals, including raw and dried coals, were investigated. A pseudo 1st order model was suitable for the desorption of raw coal, and a pseudo 2nd order and Elovich model was determined for both sorptions of the UBC and dried coal. This finding corresponded with the fact that the water adsorption status of the surface of the coal was modified through drying. The finding also indicated that the water sorption by the UBC and dried coal can be explained by similar kinetic models. These models were empirical, and the constants of the equations were determined from existing data. Therefore, the models cannot predict the sorption rate for given environmental conditions, such as temperature, relative humidity and initial moisture. To solve this problem, the Elovich model was converted by variable transformation to include the equilibrium moisture. The constants of the converted model could be determined for any given condition. The converted-Elovich model resembled the Langmuir model with regards to the driving force, although the force acted in a non-linear way, which was unlike the original Langmuir model. The reason why the constants could be determined was explained through this resemblance. Therefore, the converted-Elovich model was demonstrated to be effective not only in the fitting of existing data but also in the estimation of the sorption rate for any given conditions. The model was close to theoretical.

Water vapour sorption of wood modified by acetylation and formalisation – analysed by a sorption kinetics model and thermodynamic considerations

Abstract The water vapour sorption data of untreated (Wuntr), acetylated (Wac) and formaldehyde-treated (WFA) Scots pine (Pinus sylvestris L.) sapwood were analysed in terms of their sorption kinetics and were transformed into excess surface work (ESW) isotherms. The sorption kinetics were studied by fitting the non-linear parallel exponential kinetics (PEK) model to the experimental data in which the sorption kinetics curve is composed of two processes (fast and slow components). Wac and WFA showed evident differences in their sorption kinetics and their thermodynamic sorption behaviour. In contrast to acetylation, formalisation influenced both the extent of the slow sorption process and the shape of its pseudoisotherm. For Wuntr and Wac, it appears that some water associated with the slow process is adsorbed at sites for fast sorption newly generated upon swelling (previously postulated as extra water) and subsequently desorbed by the fast process. For WFA, the formation of extra water hardly occurs. ESW was reduced through acetylation with a constant factor over the whole hydroscopic range, whereas the ESW of WFA was reduced only after reaching the monolayer capacity compared to its control. The sorption behaviour of Wac was solely determined by cell wall bulking, whereas that of WFA was governed by the increased matrix stiffness due to cross-linking of the cell wall polymers.

Kinetics analysis of zinc sorption in fixed bed column using a strongly basic anionic exchange resin.

The aim of this study was to examine the capacity of anionic resins to remove zinc as zinc chloride complexes in fixed bed. The applicability of the kinetics models and the characteristics of the bed (sorption capacity, breakthrough curve, depth of the adsorption zone) were taken into account. The influence of the process parameters, such as resin quantity (bed height) and zinc initial concentration, on the removal process was also considered. The obtained results (Amberlite IRA410) were analyzed using sorption kinetic models such as Thomas, Adam-Bohart, and Clark, by linear regression analysis. Similarly, the concept of the mass transfer zone was applied in order to properly design the fixed bed adsorption process. By comparing various resins, the following series was depicted based on sorption capacities: Amberlite IRA410>Purolite A103S>Purolite NRW700>Purolite A400MBOH. The experimental data were in good agreement with the Clark model, while for the other models, lower correlation coefficients were obtained under the same experimental conditions. The MTZ height and rate of movement increased with increasing initial concentration.

The range of validity of sorption kinetic models

Several hundred papers are published yearly reporting liquid-phase adsorption kinetics data. In general the data is analyzed using a variety of standard models such as the pseudo first- and second-order models and the Intraparticle-Diffusion model. The validity of these models is often assessed empirically via their ability to fit the data, independently of their physicochemical soundness.The aim of the present paper is to rationalize the analysis of liquid-phase adsorption kinetics data, and to investigate experimental factors that influence the adsorption kinetics, in addition to the characteristics of the adsorbent material itself. For that purpose we use a simple Langmuir adsorption–diffusion model, which enables us to identify three dimensionless numbers that characterize the working regime of any batch adsorption experiment: an adsorption Thiele modulus, a saturation modulus, and a loading modulus.The standard models are found to be particular cases of the general adsorption–diffusion model for specific values of the dimensionless numbers. This provides sound physicochemical criteria for the validity of the models. Based on our modeling, we also propose a general yet simple data analysis procedure to practically estimate the diffusion coefficient in adsorbent pellets starting from adsorption half-times.

Transport of bromide and pesticides through an undisturbed soil column: A modeling study with global optimization analysis

The fate of pesticides in tropical soils is still not understood as well as it is for soils in temperate regions. In this study, water flow and transport of bromide tracer and five pesticides (atrazine, imazaquin, sulfometuron methyl, S-metolachlor, and imidacloprid) through an undisturbed soil column of tropical Oxisol were analyzed using a one-dimensional numerical model. The numerical model is based on Richards' equation for solving water flow, and the advection–dispersion equation for solving solute transport. Data from a laboratory column leaching experiment were used in the uncertainty analysis using a global optimization methodology to evaluate the model's sensitivity to transport parameters. All pesticides were found to be relatively mobile (sorption distribution coefficients lower than 2cm3g−1). Experimental data indicated significant non-conservative behavior of bromide tracer. All pesticides, with the exception of imidacloprid, were found less persistent (degradation half-lives smaller than 45days). Three of the five pesticides (atrazine, sulfometuron methyl, and S-metolachlor) were better described by the linear kinetic sorption model, while the breakthrough curves of imazaquin and imidacloprid were more appropriately approximated using nonlinear instantaneous sorption. Sensitivity analysis suggested that the model is most sensitive to sorption distribution coefficient. The prediction limits contained most of the measured points of the experimental breakthrough curves, indicating adequate model concept and model structure for the description of transport processes in the soil column under study. Uncertainty analysis using a physically-based Monte Carlo modeling of pesticide fate and transport provides useful information for the evaluation of chemical leaching in Hawaii soils.

Modeling Heavy Metal Sorption Kinetics Using Fractional Calculus

Heavy metals are commonly regarded as environmentally aggressive and hazardous to human health. Among the different metals, lead plays an important economic role due to its large use in the automotive industry, being an essential component of batteries. Different approaches have been reported in the literature aimed at lead removal, and among them a very successful one considers the use of water hyacinths for sorption-based operation. The modeling of the metal sorption kinetics is a fundamental step towards in-depth studies and proper separation equipment design and optimization. Fractional calculus represents a novel approach and a growing research field for process modeling, which is based on the successful use of derivatives of arbitrary order. This paper reports the modeling of the kinetics of lead sorption by water hyacinths (Eichhornia crassipes) using a fractional calculus. A general procedure on error analysis is also employed to prove the actual fractional nature of the proposed model by the use of parametric variance analysis, which was carried out using two different approaches (with the complete Hessian matrix and with a simplified Hessian matrix). The joint parameter confidence regions were generated, allowing to successfully show the fractional nature of the model and the sorption process.

Phosphated Cellulose as an Efficient Biomaterial for Aqueous Drug Ranitidine Removal

Crystalline cellulose chemically modified through a reaction with sodium trimetaphosphate (STMP) in an acidic or basic condition yielded Cel-P4 and Cel-P10. These phosphated solids were characterized by elemental analysis, X-ray diffraction (XRD), infrared (IR) spectroscopy, scanning electron microscopy (SEM), nuclear magnetic resonance (NMR) at the solid state for phosphorus nucleus and dispersive X-ray energy. The elemental results demonstrated that the phosphorylation reaction was more efficient in the basic medium, as supported by the amount of phosphorous content. The synthesized biomaterials decreased in crystallinity in comparison to the precursor cellulose, with an increase in roughness and present two distinct phosphorus environments in the formed structure. The phosphated cellulose in an alkaline condition was applied to sorb the drug ranitidine. This process was applied in varying pH, time, temperature and concentration. The best sorption kinetic model to fit the experimental data was the pseudo-second-order with a coefficient correlation of 0.8976, and the Langmuir isotherm model was the most adjusted to the variation in concentration. The efficient drug sorption has a low dependence on temperature, with maximum values of 85.0, 82.0 mg and 85.7 mg·g−1 for Cel-P10 at 298, 308 and 318 K, respectively. The best sorption occurred at pH = 6 with a saturation time of 210 min.

Determination of optimum isotherm and kinetic models for phosphate sorption onto iron oxide nanoparticles: nonlinear regression with various error functions

The aim of this study was to determine optimum kinetic and isotherm models for phosphate (P) sorption onto iron oxide nanoparticles through nonlinear regression analysis. Equilibrium batch experiments were conducted at the experimental conditions of initial P concentration = 0.5–20 mg/L, adsorbent doses = 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6 g/L, and shaking time = 24 h. Kinetic batch experiments were also performed at the experimental conditions of initial P concentrations = 1, 2, 4, 6, 8, and 10 mg/L, adsorbent dose = 0.6 g/L, and shaking time = 10 min–24 h. Six isotherm models (Langmuir, Freundlich, Temkin, Redlich–Peterson, Khan, and Sips) were used to analyze the equilibrium data through nonlinear regression analysis. Three kinetic models (pseudo-first-order, pseudo-second-order, and Elovich) were used to analyze the kinetic data through nonlinear regression. Error functions including the sum of the squared errors, hybrid fractional error function (HYBRID), average relative error, Marquardt’s percent standard deviation, and sum of the absolute errors (EABS) were used to minimize the error distribution between experimental data and predicted model fits in the optimization process. To compare the five error values, the results of each set were normalized and summed. Considering both coefficient of determination (R2) and Chi-square (χ2), the Redlich–Peterson (Freundlich) model was found to provide the best fit to the experimental data in the equilibrium model analyses, and the optimum parameter values were obtained by the HYBRID error function with the parameter values of KR/aR = 3.59–4.15 mg/g and g = 0.69–0.89 from the Redlich–Peterson model. Considering both R2 and χ2, the Elovich (or pseudo-second-order) model was found to provide the best fit to the kinetic data in the kinetic model analyses, and the optimum parameter values produced by the EABS error function with the parameter values of α = (3.60 × 105)–(4.80 × 106) mg/g/h and β = 4.43–13.07 g/mg from the Elovich model.

Facile preparation of oxine functionalized magnetic Fe3O4 particles for enhanced uranium (VI) adsorption

Abstract We present a study of uranium (VI) adsorption in aqueous solutions by magnetic oxine (ferroferric oxide/oxine composite). Batch experiments of uranium (VI) adsorption were conducted, investigating the significance of solution pH, contact time, ionic strength, and temperature on uranium sorption efficiency. The results suggest that maximum adsorption capacity is 125 mg g −1 when the initial uranium (VI) concentration is 50 mg L −1 at 298 K, displaying a mass transport property of the magnetic oxine for the removal of uranium (VI). The sorption was strongly dependent on pH and independent of ionic strength, indicating that the sorption was mainly dominated by inner-sphere surface complexation. The experimental data are analyzed using sorption kinetic models, revealing that the process follows a pseudo-second-order kinetic model. The thermodynamic parameters show that the process is endothermic and spontaneous. We demonstrate a fast, efficient and convenient material for the removal of uranium (VI) from aqueous solutions.

Long-wave Marangoni convection in a layer of surfactant solution

We consider the deformational mode of Marangoni instability in a heated layer of a surfactant solution with the Soret effect and the adsorption/desorption of surfactant molecules accounted for by using a linearized model of sorption kinetics. Linear stability analysis of the layer's quiescent base state reveals a competition between monotonic and oscillatory modes of the long-wave instability, as well as a strong stabilization due to surfactant adsorption. Based on these results, we carry out the derivation of a set of long-wave nonlinear evolution equations governing the spatiotemporal dynamics of the oscillatory mode of instability. Using a weakly nonlinear analysis of the evolution equations, we study pattern selection in the case of a 2D flow near the stability threshold of the system. We validate our theoretical predictions by a numerical solution of the evolution equations.

Reactive transport modeling of 90Sr sorption in reactive sandpacks

Strontium-90 (90Sr) is one of the most problematic radioactive contaminants in groundwater at nuclear sites. Although 90Sr is retarded relative to groundwater flow, it is sufficiently mobile and long-lived to require treatment in many hydrogeological settings. A detailed study was performed on the practicality of using granular clinoptilolite as a sandpack around groundwater wells where groundwater is contaminated with 90Sr and the water table must be lowered. The effectiveness of the reactive sandpack concept and the mechanisms controlling 90Sr attenuation was investigated by numerical analysis of data obtained from four in situ column experiments. The experiments spanned the range of pore-water velocities that would occur during radial flow through granular clinoptilolite sandpacks. A kinetic sorption model was required to adequately reproduce the experimentally observed 90Sr behavior. Calibrated first-order kinetic rates were correlated with pore-water velocities. After calibration, three sorption models were used to simulate 90Sr attenuation for four hypothetical pumping scenarios. Results show that a velocity-dependent kinetic model accurately simulates the observed early breakthrough for high pore-water velocities. The results indicate (1) that reactive sandpacks have good potential for in situ remediation and construction dewatering and (2) that quantitative modeling can aid in the design and application of this novel technique.

Moisture Sorption Kinetics of Switchgrass, Big Bluestem, and Bromegrass Biomass

<abstract><title><italic>Abstract.</italic></title> Moisture content of biomass is the most influential factor in biomass storage. Moisture sorption kinetics control the dynamic moisture condition of the biomass, thus affecting biomass storage, processing operations, and final utilization applications. Moisture sorption characteristics of switchgrass, big bluestem, and bromegrass, potential biomass feedstocks for the Northern Great Plains of the U.S., were studied. Study objectives were to determine the moisture sorption kinetics, mathematically model the sorption process using standard models, and evaluate the effect of temperature on moisture sorption. Moisture sorption experiments were conducted at temperatures of 20°C, 40°C, and 60°C and a fixed high relative humidity of 95% using a controlled-environment chamber. Standard moisture sorption kinetics models (exponential, Page, and Peleg) were used to analyze the experimental sorption characteristics of the feedstocks. Bromegrass had the highest moisture sorption rates and final moisture contents, followed by big bluestem and switchgrass. On average, at 20°C, 50% of moisture sorption completion occurred at 1.5, 1.9, and 1.7 h and 90% completion occurred at about 8.5, 13.4, and 12.8 h for switchgrass, big bluestem, and bromegrass, respectively. For the temperatures studied, on average 41% ±3%, 40% ±5%, and 39% ±1% of moisture sorption completion occurred in 1 h and 82% ±2%, 76% ±4%, and 73% ±1% completion occurred in 5 h for switchgrass, big bluestem, and bromegrass, respectively. Moisture sorption rates decreased very sharply during the first hour (≥78%) from their initial values and quickly plateaued thereafter. Increase in temperature increased the moisture sorption rates for all the biomass types tested. Both the Page and Peleg models effectively described the observed sorption characteristics for the selected biomass types (R² ≥ 0.96). The Arrhenius equation adequately described the temperature dependence of the model parameters (0.77 ≤ R² ≤ 1.00). Based on this study, the Peleg model in combination with the Arrhenius equation is recommended for moisture sorption predictions. Fitted moisture sorption kinetics models, developed nomograms, and combined prediction equations (R² ≥ 0.83) form baseline data essential for storage of the selected biomass types and various handling, conditioning, and processing operations.

Gold nanoparticle chitosan composite hydrogel beads show efficient removal of methyl parathion from waste water

Removal of pesticides from waste water is extremely important for the avoidance of serious health risks. We report an environmentally benign synthetic approach to prepare sorbent–hydrogel composite beads, composed of gold nanoparticles (GNP) embedded in a cross-linked biocompatible chitosan polymer matrix, for removal of the pesticide methyl parathion (MP). The equilibrium sorption and kinetic data, at different initial MP concentrations, are analysed using various sorption isotherm and kinetic models. It is observed that the sorption process can be best described by the Langmuir isotherm model and that pseudo second-order kinetics are followed throughout the studied concentration range. The monolayer capacity of the beads with and without the GNP composite are determined to be 58 μmol g−1 and 11 μmol g−1, respectively, suggesting the potential usefulness of the former for the removal of MP. The results show that the synthesized sorbent has good potential for pesticide removal.

Kinetic Sorption Study of Sucrose Osmotic Agent onto Granular Activated Carbon in Manipulated Osmosis Desalination System (MOD) Combined with a Solute Exchange Technique (SET)

The previous work elucidated that, the commercial granular activated carbon (GAC) with mesh (12-20) supplied by Sigma Aldrich Company in the UK has a capability to adsorb specific organic compounds such as sucrose from an aqueous solution. As well as other sucrose specifications such as; high solubility and non-toxicity, sucrose can be used as an osmotic agent in Manipulated Osmosis Desalination system (MOD) combined with a Solute Exchange Technique (SET). However, the sorption kinetic of sucrose onto granular activated carbon (mesh, 12-20) is investigated in this study. The sorption rates of sucrose (qt) onto GAC within 8 hrs contact time using three different GAC sample doses (5,10 and 30 g/l) at different shaking speed values (45,100.145 RPM) are determined. The sorption kinetic models: pseudo-first order, pseudo-second order, intraparticle diffusion and mass transfer were used for analyzing sucrose sorption by GAC. The finding showed that pseudo second order kinetic model was the most appropriate description of sucrose transport.

Comparative analysis of fixed-bed sorption models using phosphate breakthrough curves in slag filter media

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 (kT, q0, kYN, and τ) can easily be calculated from the Bohart–Adams model parameters (kBA 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 (kBA, N0, Z0, tb, and q0) for the fixed-bed systems.