• Biotechnology and Bioprocess Engineering:BBE
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• v.11 no.1
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• pp.61-66
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• 2006

The simple Langmuir isotherm is frequently employed to describe the equilibrium behavior of protein adsorption on a wide variety of adsorbents. The two adjustable parameters of the Langmuir isotherm - the saturation capacity, or $q_m$, and the dissociation constant, $K_d$ - are usually estimated by fitting the isotherm equation to the equilibrium data acquired from batch equilibration experiments. In this study, we have evaluated the possibility of estimating $q_m$ and $K_d$ for the adsorption of bovine serum albumin to a cation exchanger using batch kinetic data. A rate model predicated on the kinetic form of the Langmuir isotherm, with three adjustable parameters ($q_m,\;K_d$, and a rate constant), was fitted to a single kinetic profile. The value of $q_m$ determined as the result of this approach was quantitatively consistent with the $q_m$ value derived from the traditional batch equilibrium data. However, the $K_d$ value could not be retrieved from the kinetic profile, as the model fit proved insensitive to this parameter. Sensitivity analysis provided significant insight into the identifiability of the three model parameters.

• Advances in environmental research
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• v.3 no.2
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• pp.131-149
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• 2014

Two different model selection indices, the Akaike information criterion (AIC) and the coefficient of determination ($R^2$), are used to discriminate competing isotherm equations for aqueous pollutant removal systems. The former takes into account model accuracy and complexity while the latter considers model accuracy only. The five types of isotherm shape in the Brunauer-Deming-Deming-Teller (BDDT) classification are considered. Sorption equilibrium data taken from the literature were correlated using isotherm equations with fitting parameters ranging from two to five. For the isotherm shapes of types I (favorable) and III (unfavorable), the AIC favors two-parameter equations which can easily track these simple isotherm shapes with high accuracy. The $R^2$ indicator by contrast recommends isotherm equations with more than two parameters which can provide marginally better fits than two-parameter equations. To correlate the more intricate shapes of types II (multilayer), IV (two-plateau) and V (S-shaped) isotherms, both indices favor isotherm equations with more than two parameters.

• Resources Recycling
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• v.27 no.4
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• pp.65-69
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• 2018

In solvent extraction, extraction isotherm represents the relation between the equilibrium concentration of metal in the aqueous and organic phase. McCabe-Thiele diagram on which extraction isotherm and operating line are constructed provides valuable information on the mass transfer operation. When the equilibrium constant of a solvent extraction reaction is known, the calculation method to obtain extraction isotherm was introduced. Kresmer equation by which the number of extraction stages can be calculated when the distribution coefficient is constant was introduced.

• Environmental Engineering Research
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• v.22 no.4
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• pp.384-392
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• 2017

Mango shell (MS) and mango shell activated carbon (MSAC) was used to adsorb crude oil from water at various experimental conditions. The MSAC was prepared by carbonization at $450^{\circ}C$ and chemical activation using strong $H_3PO_4$ acid. The adsorbents were characterized with Fourier Transform Infrared spectroscopy. Investigations carried out included the effects of parametric variations of different adsorbate dose, adsorbent dose, time, temperature, pH and mixing speed on the adsorption of crude oil. The equilibrium isotherm for the adsorption process was determined using Langmuir, Freundlich, Temkin and Dubinin Radushkevich isotherm models. Temkin isotherm was found to fit the equilibrium data reasonably well than others. The result demonstrated that MSAC was more effective for crude oil adsorption than raw mango shell. Optimum conditions were also presented. The enhanced effect from activation was justified statistically using Analysis of Variance and Bonferroni-Holm Posthoc significance test. The pseudo first order kinetics gave a better fit for crude oil adsorption with both MS and MSAC.

• Journal of Hydrogen and New Energy
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• v.16 no.4
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• pp.307-314
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• 2005

In this work, a static volumetric method was experimentally implemented to measure the adsorption isotherm of hydrogen and methane by the activated carbon. The equilibrium data of stationary phase and mobile phase were correlated into the Langmuir, Freundlich, Langmuir-Freundlich, and Toth isotherms, respectively. In addition, the comparison between prediction and experimental data was made. By a nonlinear regression analysis, the experimental parameters in the equilibrium isotherms were estimated and compared. Then, the linear and quadratic equations for pressure and temperature to adsorption amounts were expressed. The adsorption amounts were increased with the pressure increase and the temperature decrease.

• Environmental Engineering Research
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• v.16 no.2
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• pp.55-60
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• 2011

The removal of hexavalent chromium from aqueous solutions onto modified holly sawdust was studied at varying initial hexavalent chromium concentrations, adsorbent doses, pHs and contact times. The removal of hexavalent chromium from aqueous solutions increased with increasing adsorbent dosage and contact time. The percentage of hexavalent chromium removed from the aqueous solutions decreased with increasing hexavalent chromium concentration and pH of the solution. The kinetics of the adsorption of hexavalent chromium onto modified holly sawdust was analyzed using pseudo first-order and pseudo second-order models. The pseudo second-order model described the kinetics of adsorption of hexavalent chromium. The Langmuir and Freundlich isotherm models were used for modeling of the adsorption equilibrium data. The Langmuir isotherm model well described the equilibrium data for the removal of hexavalent chromium by modified holly sawdust. The obtained maximum adsorption capacity was 18.86 mg/g at pH 7. The results showed that modified holly sawdust can be used as a low cost adsorbent for the treatment of aqueous solutions containing chromium.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2002.04a
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• pp.122-126
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• 2002

Contaminant transport in porous media is characterized by solving an advection-dispersion equation(ADE). The ADE can cover equilibrium phenomena of interest, which include sorption, decay, and chemical reactions. Among these phenomena, sorption mechanism is described by several types of sorption isotherm. If we assume the sorption isotherm as linear, the solution of ADE can be easily procured. However, if we consider the sorption isotherm as non-linear isotherm like a Dual Reactive Domain Model (DRDM), the resulting differential equation becomes non-linear. In this case, the solution of ADE cannot be easily acquired by an analytic method. In this paper, we present the numerical analysis of ADE using a DRDM. The results reveal that even if sorption data may be fitted well using linear or non-linear isotherm, the characteristics of contaminant transport of the two cases are different from each other. To be concrete, the retardation of linear isotherm has stronger effect than that of the DRDM. As the non-linearity of sorption isotherm increases, the difference of retardation effects of the two cases becomes larger. For a pulse source, the maximum concentration of the linear model is higher than that of the DRDM, but the plume of the DRDM moves faster than that of the linear model. Behaviors of contaminant transport using the DRDM are consistent with common features of a linear model. For instance, biodegradation effect becomes larger as time goes by The faster the seepage velocity is, the faster the plume of contaminant moves. The plume of the contaminant is distributed evenly over overall domain in the event of high dispersion coefficient.

• Journal of Environmental Science International
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• v.29 no.8
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• pp.827-835
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• 2020

Zeolite material having XRD peaks of Na-A zeolite in the 2θ range of 7.18 to 34.18 can be synthesized from the waste catalyst using a fusion/hydrothermal method. The adsorption rate of Mn ions by a commercial Na-A zeolite and the synthesized zeolitic material increased as the adsorption temperature increased in the range of 10 ~ 40℃. The adsorption of Mn ion were very rapid in the first 30 min and then reached to the equilibrium state after approximately 60 min. The adsorption kinetics of Mn ions by the commercial Na-A zeolite and the zeolitic material were found to be well fitted to the pseudo-2^nd order kinetic model. Equilibrium data by the commercial Na-A zeolite and the zeolitic material fit the Langmuir, Koble-Corrigan, and Redlich-Peterson isotherm models well rather than Freundlich isotherm model. The removal capacity of the Mn ions by the commercial Na-A zeolite and the zeolitic material obtained from the Langmuir model was 135.2 mg/g and 128.9 mg/g at 30℃, respectively. The adsorption capacity of Mn ions by the synthesized zeolitic material was almost similar to that of commercial Na-A zeolite. The synthesized zeolitic material could be applied as an economically feasible commercial adsorbent.

• Advances in environmental research
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• v.1 no.2
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• pp.143-151
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• 2012

Nitrate removal from aqueous solution was investigated using $ZnCl_2$ and phosphoric acid activated carbon developed from pomegranate peel with particle size 0.4 mm. Potassium nitrate solution was used in batch adsorption experiments for nitrate removal from water. The effects of activated carbon dosage, time of contact, and pH were studied. The equilibrium time was fond to be 45 min. Two theoretical adsorption isotherms namely Langmuir and Freundlich were used to describe the experimental results. The Langmuir fit the isotherm with the theoretical adsorption capacity ($q_t$) was fond 78.125 mg g-1. Adsorption kinetics data were modeled using the pseudo-first, pseudo-second order, and intraparticle diffusion models. The results indicate that the second-order model best describes adsorption kinetic data. Results show activated carbon produced from pomegranate is effective for removal of nitrate from aqueous solution.

• Journal of Korean Society of Environmental Engineers
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• v.33 no.8
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• pp.606-616
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• 2011

The objectives of this study were to evaluate the applicability of adsorption models for adsorption properties of adsorbents. For this study, adsorption experiment of $NO_3^-$ ion using anion exchange resin has been investigated under adsorption equilibrium and kinetic in bach process. Adsorption equilibrium experiment were carried out that two conditions is change of adsorbate concentration and change of adsorbent weight. Experiment results have been analyzed by adsorption isotherm models, energy models and kinetic models. Under the condition of change of adsorbate concentration was best described by Sips and Redlich-Perterson isotherm models. However case of change of adsorbent weight was described by Langmuir isotherm models. It seems reasonable to assume that isotherm model was dominated by multiple mechanism according to experiment condition.