Spectral properties of Bi-Langmuir isotherms

Flockerzi, Dietrich; Kaspereit, Malte; Kienle, Achim

doi:10.1016/j.ces.2013.09.045

Cited by 7 publications

(6 citation statements)

References 11 publications

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“…For thermodynamic reasons this should always be the case [29]. Explicit proofs for Langmuir isotherms were given in [29], for Bi-Langmuir isotherms in [7] and for the IAS theory for a large class of pure component isotherms in [17], Appendix B. Hence, the result of this Appendix does not only apply to mass action equilibria but is valid for any thermodynamically reasonable sorption equilibrium.…”

Section: Discussionmentioning

confidence: 99%

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Efficient simulation and equilibrium theory for adsorption processes with implicit adsorption isotherms – Mass action equilibria

Fechtner

Kienle

2017

Chemical Engineering Science

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An efficient method for the simulation of packed bed adsorbers is presented. It is based on equilibrium models and can be applied to any implicit adsorption isotherm. It uses a method of lines approach, avoids explicit differentiation of the adsorption isotherm, and exploits standard numerics for the simultaneous solution of the resulting ordinary differential and implicit algebraic equations. Application is illustrated for stoichiometric ion exchange, which also admits an analytical approach using equilibrium theory. Classical theoretical results from equilibrium theory are summarized, further extended and compared to the numerical calculations for different scenarios. Focus is on selectivity reversals and their influence on process operation. It is shown that the selectivity reversal may introduce multiple solutions.

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Section: Discussionmentioning

confidence: 99%

“…Classical equilibrium theory is for Langmuir isotherms [2] or ion exchange with constant separation factors [5]. More recently, extensions were given to Bi-Langmuir [6,7], generalized Langmuir [8], generalized Bi-Langmuir [9], and also to reactive systems with simultaneous phase and reaction equilibrium [10,11,12].…”

Section: Introductionmentioning

confidence: 99%

Efficient simulation and equilibrium theory for adsorption processes with implicit adsorption isotherms – Mass action equilibria

Fechtner

Kienle

2017

Chemical Engineering Science

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“…The term b 2 − 4ac can be reformulated such that it readily satisfies the last inequality in (A.7) The previous result of real and positive eigenvalues using only the assumption (A.2) cannot be extended to systems with more than two components, which is similar to the spectral results in [26]. For this purpose, a simple three component counter example using the Tóth isotherm…”

Section: Notation B Ijmentioning

confidence: 91%

“…For thermodynamic reasons this should always be the case as shown by Kvaalen et al [25] using displacement theory. Explicit proofs for Langmuir isotherms were given in [25], for Bi-Langmuir isotherms in [26] and for the IAS theory for a large class of pure component isotherms in [14]. In the Appendix these results are extended in two directions.…”

Section: Reformulation and Solution Strategymentioning

confidence: 99%

Efficient simulation and equilibrium theory for adsorption processes with implicit adsorption isotherms – Ideal adsorbed solution theory

Fechtner

Kienle

2018

Chemical Engineering Science

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Recently an efficient method for the simulation of packed bed adsorbers with implicit adsorption isotherms was presented. It uses a method of lines approach and exploits standard software for the simultaneous solution of the resulting differential algebraic equations (DAEs). Application was demonstrated for stoichiometric ion exchange. In the present paper, the approach is extended to systems described by the adsorbed solution theory. For that purpose, the relation between the differential index of the DAE system and the spectral properties of the underlying adsorption equilibrium is established. In particular, it is shown that real and positive eigenvalues of the Jacobian of the underlying conservation equations will lead to a differential index of one. It is further shown that real and positive eigenvalues of the Jacobian related to the IAST can be guaranteed for binary mixtures with any type of pure component adsorption isotherm or for multicomponent mixtures with certain restricted types of pure component isotherms. The new method is illustrated for different explicit and implicit pure component adsorption isotherms belonging to this class. It is compared with alternative solution approaches using the modified FastIAS method by Do and Myers and semi-analytical solutions from equilibrium theory.

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“…Wie von Flockerzi et al [25] gezeigt, ist dies für die Langmuir-Isotherme unabhängig von der Anzahl der Komponenten stets der Fall. Dies ist gegeben, wenn die Matrix J zwei unabhängige reelle Eigenwerte l 1 und l 2 besitzt.…”

Section: Theoretische Grundlagenunclassified

Vereinfachte Auslegung der simulierten Gegenstromchromatographie mittels des Hodographenraums

Kaspereit

Neupert

2016

Chemie Ingenieur Technik

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Auf der Basis der Gleichgewichtstheorie wird eine vereinfachte explizite Auslegungsmethode für die Chromatographie mit simuliertem Gegenstrom vorgeschlagen. Ihre Anwendbarkeit wird anhand des Hodographenraums für kompetitive Gleichgewichte mit variabler Selektivität, modifizierte Langmuir-, Bi-Langmuir-und Jovanovic-Adsorptionsisothermen, diskutiert. Bei der Validierung mittels Literaturdaten erreicht der Ansatz eine hohe Genauigkeit. Weiterhin wird gezeigt, dass in Systemen mit modifizierten und Bi-Langmuir-Isothermen grundsätzlich komplexe nichtlineare Phänomene auftreten können.A simplified and explicit shortcut method for the design of simulated moving bed processes is derived on the basis of equilibrium theory. The applicability of this approach is discussed using the hodograph plane for competitive adsorption equilibria with nonconstant selectivity, namely modified Langmuir-, Bi-Langmuir, and Jovanovic isotherms. The approach shows excellent accuracy when validated against literature data. Furthermore, it is demonstrated that systems described by modified or Bi-Langmuir isotherms may comprise complex nonlinear phenomena.

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Spectral properties of Bi-Langmuir isotherms

Cited by 7 publications

References 11 publications

Efficient simulation and equilibrium theory for adsorption processes with implicit adsorption isotherms – Mass action equilibria

Efficient simulation and equilibrium theory for adsorption processes with implicit adsorption isotherms – Mass action equilibria

Efficient simulation and equilibrium theory for adsorption processes with implicit adsorption isotherms – Ideal adsorbed solution theory

Vereinfachte Auslegung der simulierten Gegenstromchromatographie mittels des Hodographenraums

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