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Marco Mazzotti - One of the best experts on this subject based on the ideXlab platform.
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Equilibrium Theory Analysis of a Binary Chromatographic System Subject to a Mixed Generalized Bi-Langmuir Isotherm
Industrial & Engineering Chemistry Research, 2015Co-Authors: Franziska Ortner, Simon Jermann, Lisa Joss, Marco MazzottiAbstract:In this study, an equilibrium theory solution for a binary system subject to a specific subclass of generalized bi-Langmuir Isotherm is derived. This solution provides a thorough understanding for the type of Isotherm investigated, which exhibits several interesting features. Depending on initial and feed compositions, the order of breakthrough and desorption changes at frontal analysis conditions, and a changing impact of component 1 (from competitive to cooperative) on the adsorption behavior of component 2 can be observed at displacement conditions. Furthermore, the equilibrium theory solution includes some rare transitions, such as semishock transitions with multiple shock and wave parts. Due to its interesting behavior, this Isotherm is able to accurately describe an experimental system investigated in the context of the delta-shock phenomenon. With the aid of the derived equilibrium theory solution, it was possible to identify several types of transitions and intermediate states, and to fit Isotherm...
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local equilibrium theory for the binary chromatography of species subject to a generalized Langmuir Isotherm 2 wave interactions and chromatographic cycle
Industrial & Engineering Chemistry Research, 2011Co-Authors: Arvind Rajendran, Marco MazzottiAbstract:The generalized Langmuir Isotherm model was recently developed to describe the competitive adsorption equilibria of a binary mixture [Mazzotti, M. Ind. Eng. Chem. Res. 2006, 45, 5332−5350]. This formalism captures the competitive effect of solutes that show either Langmuirian or anti-Langmuirian behavior. This results in four Isotherm types that show markedly different chromatographic behavior. The equilibrium theory of chromatography was developed in a previous work to study Riemann problems (saturation, elution, and the chromatographic cycle) that are of practical relevance [Mazzotti, M. Ind. Eng. Chem. Res. 2006, 45, 5332−5350]. This work focuses on the development of the equilibrium theory to account for wave interactions and is divided into two parts. In the first part, the theory of wave interactions is developed on the basis of the method of characteristics. It is shown that the rules developed for competitive Langmuir Isotherms can be extended to describe possible wave interactions in the case of ...
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Local Equilibrium Theory for the Binary Chromatography of Species Subject to a Generalized Langmuir Isotherm. 2. Wave Interactions and Chromatographic Cycle
Industrial & Engineering Chemistry Research, 2011Co-Authors: Arvind Rajendran, Marco MazzottiAbstract:The generalized Langmuir Isotherm model was recently developed to describe the competitive adsorption equilibria of a binary mixture [Mazzotti, M. Ind. Eng. Chem. Res. 2006, 45, 5332−5350]. This formalism captures the competitive effect of solutes that show either Langmuirian or anti-Langmuirian behavior. This results in four Isotherm types that show markedly different chromatographic behavior. The equilibrium theory of chromatography was developed in a previous work to study Riemann problems (saturation, elution, and the chromatographic cycle) that are of practical relevance [Mazzotti, M. Ind. Eng. Chem. Res. 2006, 45, 5332−5350]. This work focuses on the development of the equilibrium theory to account for wave interactions and is divided into two parts. In the first part, the theory of wave interactions is developed on the basis of the method of characteristics. It is shown that the rules developed for competitive Langmuir Isotherms can be extended to describe possible wave interactions in the case of ...
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Equilibrium theory based design of simulated moving bed processes for a generalized Langmuir Isotherm
Journal of Chromatography A, 2006Co-Authors: Marco MazzottiAbstract:In the frame of the local equilibrium theory of chromatography, design criteria for complete separation of binary mixtures in simulated moving bed (SMB) separations are developed, presented and discussed. These apply to systems, whose retention behavior is characterized by a generalized Langmuir Isotherm. By allowing for negative terms in the denominator of the classical Langmuir Isotherm, this newly introduced adsorption model captures a broad class of competitive or synergistic adsorption, including anti-Langmuir behavior for both adsorbates, and mixed cases where one species behaves in a Lagmuirian and the other in an anti-Langmuirian manner. By extending classical equilibrium theory results for the binary Langmuir Isotherm, and by generalizing the approach followed earlier to derive SMB design criteria for the binary and multi-component Langmuir Isotherm, exact algebraic equations for the boundary of the complete separation region in the operating parameter space are derived for all possible generalized Langmuir Isotherm. The effect of changing feed composition on the shape of the complete separation region and on the position of the optimal operating point is analyzed and discussed.
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Local Equilibrium Theory for the Binary Chromatography of Species Subject to a Generalized Langmuir Isotherm
Industrial & Engineering Chemistry Research, 2006Co-Authors: Marco MazzottiAbstract:The local equilibrium theory of chromatography is applied to binary systems subject to the generalized Langmuir Isotherm. This newly introduced adsorption Isotherm allows describing a variety of competitive and synergistic adsorption behaviors, by letting each of the two components be Langmuir-like or anti-Langmuir-like. It is shown that all four possible types of Isotherms (one of which is the classical competitive Langmuir Isotherm) share the key property that characteristics in the composition plane are straight lineshence, the application of the method of characteristics leads to explicit expressionsand the solution of Riemann problems, e.g., elution of a saturated column or adsorption on an initially clean column, boils down to the use of simple algebraic relationships. Similarities and differences among the four different cases are presented, analyzed, and discussed, including their physical legitimacy and thermodynamic consistency, particularly for the case where the first eluting component is anti...
T C W Poortvliet - One of the best experts on this subject based on the ideXlab platform.
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comparison of the linear van den berg ružic transformation and a non linear fit of the Langmuir Isotherm applied to cu speciation data in the estuarine environment
Marine Chemistry, 1995Co-Authors: L J A Gerringa, P M J Herman, T C W PoortvlietAbstract:Abstract Copper complexation measurements in estuarine organic-rich samples with differential pulse anodic stripping voltammetry (DPASV) and differential pulse cathodic stripping voltammetry (DPCSV) show a relatively large scatter in the data, due to a high organic matter content. Two methods for the estimation of the complexation parameters according to the Langmuir Isotherm are compared: the linear transformation of Van den Berg/Rǔzic and the non-linear method according to Wilkinson. For DPASV measurements in estuarine samples the values of the conditional stability constant (K′), estimated with the linearization method are systematically lower than those estimated with the Wilkinson method. The Van den Berg/Ružic linearization is more susceptible to outliers or data points that do not follow the model of the Langmuir Isotherm. For DPCSV measurements, where the data followed the Langmuir Isotherm more closely, this difference could not be demonstrated. The non-linear method is to be preferred because this method is more suited to the error structure of the data, which is of constant absolute magnitude. Moreover it offers the advantage that the standard error of the estimated parameters can be calculated consistently.
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Comparison of the linear Van den Berg/Ružić transformation and a non-linear fit of the Langmuir Isotherm applied to Cu speciation data in the estuarine environment
Marine Chemistry, 1995Co-Authors: L J A Gerringa, P M J Herman, T C W PoortvlietAbstract:Abstract Copper complexation measurements in estuarine organic-rich samples with differential pulse anodic stripping voltammetry (DPASV) and differential pulse cathodic stripping voltammetry (DPCSV) show a relatively large scatter in the data, due to a high organic matter content. Two methods for the estimation of the complexation parameters according to the Langmuir Isotherm are compared: the linear transformation of Van den Berg/Rǔzic and the non-linear method according to Wilkinson. For DPASV measurements in estuarine samples the values of the conditional stability constant (K′), estimated with the linearization method are systematically lower than those estimated with the Wilkinson method. The Van den Berg/Ružic linearization is more susceptible to outliers or data points that do not follow the model of the Langmuir Isotherm. For DPCSV measurements, where the data followed the Langmuir Isotherm more closely, this difference could not be demonstrated. The non-linear method is to be preferred because this method is more suited to the error structure of the data, which is of constant absolute magnitude. Moreover it offers the advantage that the standard error of the estimated parameters can be calculated consistently.
Somayeh Farzad - One of the best experts on this subject based on the ideXlab platform.
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kinetic modeling of the fischer tropsch synthesis in a slurry phase bubble column reactor using Langmuir freundlich Isotherm
Fuel Processing Technology, 2012Co-Authors: Ali Haghtalab, M. Nabipoor, Somayeh FarzadAbstract:Abstract We employed the Langmuir–Freundlich Isotherm for Fischer–Tropsch synthesis as a modification of the commonly used Langmuir Isotherm, because the Langmuir–Freundlich Isotherm can predict the adsorption of gases at solid absorbent more accurately than Langmuir Isotherm. Several mechanisms for kinetic modeling of the Fischer–Tropsch synthesis have been developed in which the Langmuir Isotherm is the basis of kinetic modeling of the catalytic reactions. Using Langmuir–Freundlich–Hinshelwood (LFH) model, the results of CO conversion in a slurry bubble column reactor show a very good agreement with the experiment. Moreover, we used fugacity instead of the pressure that leads to improve the accuracy of the new kinetic model. The fugacity term has been considered here by using Peng–Robinson Equation of State, modified by Gasem et al. The new kinetic model with fugacity is applied for modeling of a slurry bubble column reactor over the wide range of the reactor conditions of 523–563 K, 0.95–2.55 MPa and H 2 /CO ratio: 0.65–1.51. The results of the new kinetic LFH‐fugacity model shows the Average Absolute Deviation percentage (AAD%) of 4.25% for the CO conversion while this value is about 10.89% using the original equation based on Langmuir Isotherm.
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Kinetic modeling of the Fischer–Tropsch synthesis in a slurry phase bubble column reactor using Langmuir–Freundlich Isotherm
Fuel Processing Technology, 2012Co-Authors: Ali Haghtalab, M. Nabipoor, Somayeh FarzadAbstract:Abstract We employed the Langmuir–Freundlich Isotherm for Fischer–Tropsch synthesis as a modification of the commonly used Langmuir Isotherm, because the Langmuir–Freundlich Isotherm can predict the adsorption of gases at solid absorbent more accurately than Langmuir Isotherm. Several mechanisms for kinetic modeling of the Fischer–Tropsch synthesis have been developed in which the Langmuir Isotherm is the basis of kinetic modeling of the catalytic reactions. Using Langmuir–Freundlich–Hinshelwood (LFH) model, the results of CO conversion in a slurry bubble column reactor show a very good agreement with the experiment. Moreover, we used fugacity instead of the pressure that leads to improve the accuracy of the new kinetic model. The fugacity term has been considered here by using Peng–Robinson Equation of State, modified by Gasem et al. The new kinetic model with fugacity is applied for modeling of a slurry bubble column reactor over the wide range of the reactor conditions of 523–563 K, 0.95–2.55 MPa and H 2 /CO ratio: 0.65–1.51. The results of the new kinetic LFH‐fugacity model shows the Average Absolute Deviation percentage (AAD%) of 4.25% for the CO conversion while this value is about 10.89% using the original equation based on Langmuir Isotherm.
Hans Brix - One of the best experts on this subject based on the ideXlab platform.
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phosphorus adsorption maximum of sands for use as media in subsurface flow constructed reed beds as measured by the Langmuir Isotherm
Water Research, 2003Co-Authors: M Del Bubba, Carlos A. Arias, Hans BrixAbstract:The P-adsorption capacities of 13 Danish sands were studied by short-term Isotherm batch experiments and related to the physico-chemical characteristics of the sands. The maximum P-adsorption capacities (Q) and P-binding energy constants (b) were calculated using the Langmuir-Isotherm model. The Freundlich model was also used, but it was not useful for the description of adsorption phenomena per se since it fitted well P-removal data even if precipitation of P-salts occurred simultaneously. The Langmuir model described the data well (R2=0.90−0.99) when precipitation of phosphates did not occur and seems therefore to be useful for describing the adsorption processes per se. The relationships between maximum sorption capacities and physico-chemical characteristics of the sands were investigated using classical univariate and partial least squares regression analyses. Among the physico-chemical properties of the sands, Ca and Mg content, grain size, porosity, bulk density and hydraulic conductivity were significantly related (P<0.1) to the maximum adsorption capacity as estimated by the Langmuir model. Using the maximum P-adsorption capacities, it was estimated how long the P-removal can be sustained with the different sands in subsurface flow constructed reed beds. If the most efficient sand for P-adsorption was used, the adsorption capacity would be used up after about 1 year, while, for the less efficient sands, the P-retention would go on for about 2 months. This suggests that, in order to sustain a long-term P-removal in subsurface flow constructed reed beds, precipitation reactions of insoluble P-salts should be promoted. P-binding energy constants were not significantly related to the physico-chemical properties of the sands, except the Ca content, which showed, however, a low correlation coefficient.
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Phosphorus adsorption maximum of sands for use as media in subsurface flow constructed reed beds as measured by the Langmuir Isotherm
Water research, 2003Co-Authors: M. Del Bubba, Carlos A. Arias, Hans BrixAbstract:The P-adsorption capacities of 13 Danish sands were studied by short-term Isotherm batch experiments and related to the physico-chemical characteristics of the sands. The maximum P-adsorption capacities (Q) and P-binding energy constants (b) were calculated using the Langmuir-Isotherm model. The Freundlich model was also used, but it was not useful for the description of adsorption phenomena per se since it fitted well P-removal data even if precipitation of P-salts occurred simultaneously. The Langmuir model described the data well (R2=0.90−0.99) when precipitation of phosphates did not occur and seems therefore to be useful for describing the adsorption processes per se. The relationships between maximum sorption capacities and physico-chemical characteristics of the sands were investigated using classical univariate and partial least squares regression analyses. Among the physico-chemical properties of the sands, Ca and Mg content, grain size, porosity, bulk density and hydraulic conductivity were significantly related (P
L J A Gerringa - One of the best experts on this subject based on the ideXlab platform.
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comparison of the linear van den berg ružic transformation and a non linear fit of the Langmuir Isotherm applied to cu speciation data in the estuarine environment
Marine Chemistry, 1995Co-Authors: L J A Gerringa, P M J Herman, T C W PoortvlietAbstract:Abstract Copper complexation measurements in estuarine organic-rich samples with differential pulse anodic stripping voltammetry (DPASV) and differential pulse cathodic stripping voltammetry (DPCSV) show a relatively large scatter in the data, due to a high organic matter content. Two methods for the estimation of the complexation parameters according to the Langmuir Isotherm are compared: the linear transformation of Van den Berg/Rǔzic and the non-linear method according to Wilkinson. For DPASV measurements in estuarine samples the values of the conditional stability constant (K′), estimated with the linearization method are systematically lower than those estimated with the Wilkinson method. The Van den Berg/Ružic linearization is more susceptible to outliers or data points that do not follow the model of the Langmuir Isotherm. For DPCSV measurements, where the data followed the Langmuir Isotherm more closely, this difference could not be demonstrated. The non-linear method is to be preferred because this method is more suited to the error structure of the data, which is of constant absolute magnitude. Moreover it offers the advantage that the standard error of the estimated parameters can be calculated consistently.
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Comparison of the linear Van den Berg/Ružić transformation and a non-linear fit of the Langmuir Isotherm applied to Cu speciation data in the estuarine environment
Marine Chemistry, 1995Co-Authors: L J A Gerringa, P M J Herman, T C W PoortvlietAbstract:Abstract Copper complexation measurements in estuarine organic-rich samples with differential pulse anodic stripping voltammetry (DPASV) and differential pulse cathodic stripping voltammetry (DPCSV) show a relatively large scatter in the data, due to a high organic matter content. Two methods for the estimation of the complexation parameters according to the Langmuir Isotherm are compared: the linear transformation of Van den Berg/Rǔzic and the non-linear method according to Wilkinson. For DPASV measurements in estuarine samples the values of the conditional stability constant (K′), estimated with the linearization method are systematically lower than those estimated with the Wilkinson method. The Van den Berg/Ružic linearization is more susceptible to outliers or data points that do not follow the model of the Langmuir Isotherm. For DPCSV measurements, where the data followed the Langmuir Isotherm more closely, this difference could not be demonstrated. The non-linear method is to be preferred because this method is more suited to the error structure of the data, which is of constant absolute magnitude. Moreover it offers the advantage that the standard error of the estimated parameters can be calculated consistently.
