Piecewise linear regression: A statistical method for the analysis of experimental adsorption data by the intraparticle-diffusion models

Malash, Gihan F.; El-Khaiary, Mohammad I.

doi:10.1016/j.cej.2010.07.059

Cited by 295 publications

(160 citation statements)

References 14 publications

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“…Weber-Morris model. Weber-Morris model, which had been derived from the Fick's second law, assumes that the effect of the external mass transfer resistance is negligible, the direction of the diffusion is radial and the intraparticle diffusivity is constant [45,46]. This model was used to calculate the intraparticle diffusion rate constant.…”

Section: Sorption Kinetic Modelsmentioning

confidence: 99%

Cr(VI) sorption by using clinoptilolite and bacteria loaded clinoptilolite rich mineral

Erdoğan

Ülkü

2012

Microporous and Mesoporous Materials

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a b s t r a c tBatch sorption experiments were performed in order to understand the potential value of local clinoptilolite rich mineral and its bacteria loaded form in Cr(VI) sorption. The results indicated that Cr(VI) sorption capacities of the sorbents were increased after bacteria loading and the clinoptilolite rich mineral is a promising material in Cr(VI) sorption. Zeta potential and Fourier Transform IR (FTIR) analysis were performed to explain the possible mechanism involved in the Cr(VI) sorption. The results revealed that non-electrostatic forces played a significant role rather than the electrostatic forces. The existence of non-electrostatic forces was confirmed by the FTIR results.

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Section: Sorption Kinetic Modelsmentioning

confidence: 99%

Cr(VI) sorption by using clinoptilolite and bacteria loaded clinoptilolite rich mineral

Erdoğan

Ülkü

2012

Microporous and Mesoporous Materials

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“…Weber-Morris model, which had been derived from the Fick's second law assuming the effect of the external mass transfer resistance as negligible, the direction of diffusion as radial and no change in the concentration in the angular direction and the intraparticle diffusivity as constant (Malash and El-Khaiary, 2010;Weber and Morris, 1963), was used to calculate intraparticle diffusion rate constant. The model equation is given below:…”

Section: Intraparticle Diffusion Rate Constant (K D )mentioning

confidence: 99%

Ammonium sorption by Gördes clinoptilolite rich mineral specimen

Erdoğan

Ülkü

2011

Applied Clay Science

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Experimental and theoretical works were performed for the estimation of the effects of pH, initial concentration, agitation speed, particle size and temperature on the ammonium sorption by local clinoptilolite rich mineral specimen. The kinetic sorption data were analyzed using external mass transfer, intraparticle diffusion, pseudo first and second order kinetic models. Diffusion model results revealed that external film diffusion dominated at the very early stages of sorption process and then it was overcome by intraparticle diffusion. Pseudo-second order kinetic model correlated with the experimental data better than the pseudo first order kinetic model. Sorption isotherm model results indicated that the Langmuir isotherm fitted well to the experimental data. Thermodynamic parameters Gibbs energy change (ΔG), enthalpy change (ΔH) and entropy change (ΔS) were calculated. It was shown that the sorption process was exothermic and spontaneous. The value of the activation energy suggested that ammonium sorption by the clinoptilolite rich mineral specimen is likely due to physical interactions between the sorbent and the sorbate. Analysis of the cation exchange results revealed that ion exchange mechanism was not the only step which was effective in ammonium sorption.

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“…The number of linear segments and which points belong to each segment can be chosen visually; however, this is not a reliable practice. Recently, Malash and El-Khaiary (2010) showed that the results obtained by applying Piecewise Linear Regression (PLR) are more accurate than the ones obtained by using the visual determination. In this work, the number of linear segments (and the boundaries between then) of the mono-component kinetic data were estimated by using the PLR technique.…”

Section: Mono-component Systemmentioning

confidence: 99%

Biosorption study of Ni2+ and Cr3+ by Sargassum filipendula: kinetics and equilibrium

Seolatto

Martins

Tavares

et al. 2014

Braz. J. Chem. Eng.

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-In this work, the biosorption of Cr 3+ and Ni 2+ by Sargassum filipendula pre-treated with CaCl 2 was studied. Kinetic and equilibrium experiments were carried out for mono-and multi-component solutions in a batch reactor at pH 3.0 and 30 ºC. The results from the kinetic experiments showed that Cr 3+ adsorbs slower than Ni 2+ . This behavior was explained by means of a mechanistic analysis, which showed that Cr 3+ uptake presented three adsorption stages, whereas Ni 2+ adsorption presents only two. The mono-component equilibrium data, along with binary kinetic data obtained from mono-component experiments, showed that, although the kinetics for Cr 3+ removal are slower, the biomass had a stronger affinity for this ion. Almost all Ni 2+ is desorbed from the biomass as Cr 3+ adsorbs. The binary equilibrium data also presented this behavior. The binary data was also modeled by using modified forms of the Langmuir, Jain and Snoeyink, and Langmuir-Freundlich isotherms. However, the prediction obtained presented low accuracy. An alternative modeling with artificial neural networks was presented and the results showed that this technique could be a promising tool to represent binary equilibrium data. The main contribution of this work was to obtain experimental data for Cr 3+ /Ni 2+ adsorption, which is a system rarely found in the literature and that provides information that could be used in process modeling and simulation.

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Piecewise linear regression: A statistical method for the analysis of experimental adsorption data by the intraparticle-diffusion models

Cited by 295 publications

References 14 publications

Cr(VI) sorption by using clinoptilolite and bacteria loaded clinoptilolite rich mineral

Cr(VI) sorption by using clinoptilolite and bacteria loaded clinoptilolite rich mineral

Ammonium sorption by Gördes clinoptilolite rich mineral specimen

Biosorption study of Ni2+ and Cr3+ by Sargassum filipendula: kinetics and equilibrium

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