Numerical solution of liquid‐phase multicomponent adsorption in fixed beds

Mansour, Awadh; Rosenberg, D.U. von; Sylvester, N. D.

doi:10.1002/aic.690280510

Cited by 47 publications

(18 citation statements)

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“…The finite difference method is a simple numerical procedure that can be directly applied to the solution of the entire model [42,44]. The finite difference method is a simple numerical procedure that can be directly applied to the solution of the entire model [42,44].…”

Section: Numerical Solutionsmentioning

confidence: 99%

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Mathematical Modeling and Scale-up of Liquid Chromatography

1995

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© Springer-Verlag Berlin Heidelberg 1995 Softcover reprin to the hardcover 1St edition 1995The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. PrefaceLiquid chromatography is no longer limited to chemical analysis. It has become an indispensable tool for the preparativeand large-scale purifications of proteins and other fine chemicals. So far, the scale-up of liquid chromatography relies mostly on trial and error and a few scaling rules that are more of a rule-of-thumb nature.This book provides numerical solutions to a series of general multicomponent rate models for liquid chromatography. The models consider dispersion, interfacial film mass transfer, intra particle diffusion, and nonlinear multicomponent isotherm, or the second order kinetics. The models can be used to simulate various chromatographic operations. They provide more realistic descriptions of preparative-and large-scale liquid chromatography than the equilibrium theory and plate models because various mass transfer mechanisms are included.The applications of the Fortran 77 codes for the models are explained. Parameter estimation for the models is discussed. The codes should be helpful in both the understanding of the dynamics of liquid chromatography and its scale-up. The codes are available to readers upon request by a letter, or preferably an electronic mail (to guting@ent.ohiou.edu).

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Section: Numerical Solutionsmentioning

confidence: 99%

“…This reflects that the dimensionless hold-up capacity of each component in the column is lower compared to the corresponding pure component case. 44 5.3.…”

Section: S21 Displacement Modementioning

confidence: 99%

Mathematical Modeling and Scale-up of Liquid Chromatography

1995

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“…A number of investigators have applied the pore diffusion model in conjunction with film resistance and various equilibrium expressions (38). It has been found, however, that pore diffusion coefficients calculated according to this model are frequently larger than corresponding free-liquid diffusivities.…”

Section: =Omentioning

confidence: 99%

Simulation and design models for adsorption processes

Weber¹,

Smith²

1987

Environ. Sci. Technol.

188

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Adsorption is a fundamental process for separating inorganic and organic contaminants from waters and waste waters. The most common environmental applications of this process are embodied in ion-exchange and activatedsarbon systems. Although such processes are generally capable of highly effective separations, the design and operation of specific systems is frequently complicated by the composition of waters and wastes and by the intricate matrix of interactions commonly associated with heterogeneous systems. These complications are particularly severe in applications involving the removal of specifically targeted organic compounds from complex mixtures, a circumstance encountered with increasing frequency as water decontamination requirements become more stringent.Adsorption system design traditionally has been based on information gained from pilot-plant test programs. The pilot-plant design approach acknowledges the system specificity of particular applications, but it does not lend itself easily to prediction of system responses to variables other than those specifically tested, nor to elucidation of design principles that can be e x t r a p lated to other applications.Mathematical process models can facilitate the design of full-scale systems simply by reducing the number of pilotscale tests required to evaluate various operating conditions and design parameters. Such models can generally be calibrated from simple and well-controlled bench-scale experiments, thus 1040 Environ. Sci. Technal.. Vai. 21. No. 11, 1987 U Q positioning pilot test programs principally for verification of design bases rather than for primary data development.Once verified, a process model can be used to examine conditions other than those directly measured. Such a model can also project adsorber response and sensitivity to a variety of circumstances that may be anticipated but not easily reproduced or experimentally simulated in the pilot program. The logistics, time, and expense normally associated with pilot-scale test equipment and programs make these important considerations.This paper provides an overview and analysis of certain contemporary elements and applications of adsorption process modeling. Included is a discussion that expands upon considerations initiated in a recent ES&T feature article that described processes for removing dissolved organic contaminants from water ( I ) . In addition, this paper lays a foundation for more detailed descriptions of research developments in adsorber modeling (2-4).The work is not exhaustive in that it makes no attempt to present and critique all models and approaches available. Rather, it focuses on the Freundlich and Ideal Adsorbed Solution Theory equilibrium models and a two-resistance, homogeneous-surface-diffusion dynamic model as examples that seem particularly suited for simulating adsorption processes and predicting their behavior in water and waste treatment applications. A discussion of modeling approaches and parameter estimation techniques that address environmental complexit...

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“…The mathematical analysis of nonlinear chromatography was studied by many authors including: Houghton (1963) on the effects of a polynomial isotherm on the shape of chromatographic response peaks with an infinite adsorption rate; Tien andThodos (1959, 1965) on ion exchange and adsorption kinetics in chromatography with the Freundlich isotherm equation; and Garg and Ruthven (1972) on computing the theoretical breakthrough curves for a molecular sieve chromatographic column using the pore diffusion model with the Langmuir isotherm equation. Many other nonlinear models using either the Langmuir equation or the Freundlich equation have also been reported for the adsorption of single-or multicomponent liquids in activated carbon chromatographic columns (Liapis and Rippin, 1978;Weber and Liu, 1980;Mansour et al, 1982;Seidel and Gelbin, 1986). However, previous studies on the nonlinear chromatography focused mainly on the prediction of breakthrough curves and the design of adsorbers for purifications.…”

Section: Introductionmentioning

confidence: 99%

Analysis of liquid chromatography with nonuniform crystallite particles

Yue

1990

AIChE Journal

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A mathematical analysis for the pulse responses of a liquid chromatographic column packed with crystal powders having a particle size distribution and a nonlinear adsorption isotherm is presented. The mathematical model is solved numerically by the orthogonal collocation method. Based on the parametric analysis of the model, the effects of a symmetrical and moderately asymmetric PSD on the LC responses are shown to be negligible in comparison with the effects of other parameters, such as isotherm nonlinearity, whose effects are much more profound. The simulated responses are compared with the experimental response data for an LC column packed with silicalite crystals, and a good agreement is found between the theoretical and experimental results. Using the nonlinear LC model, the simultaneous determination of nonlinear adsorption isotherms and intraparticle diffusivities from LC pulse responses is demonstrated for liquids in porous adsorbents. Y. S. Lin Y. H. Ma Chemical Engineering DepartmentWorcester Polytechnic Institute Worcester, MA 01609 IntroductionWith extensive applications of chromatographic techniques in bulk separations, purifications and physico-chemical parameter determinations (Conder and Young, 1979;Ruthven, 1984;Wankat, 1986), many mathematical models have been developed and solved for the mass transfer in chromatographic columns packed with porous particles. These studies include: the analytical solutions for the problems of chromatography with simpler mathematical models which neglect either axial dispersion or intraparticle diffusion (e.g., Rosen, 1952;Masamune and Smith, 1964); the modeling and analytical solutions for chromatography with the consideration of both intraparticle diffusion and axial dispersion (Deisler and Wilhem, 1953; Rasmuson and Nerenieks, 1980;Rasmuson, 1981); and the development of many more complex models for chromatography such as the macro-micropore diffusion models for the chromatographic columns packed with bidisperse structured adsorbents (Ma and Mancel, 1973;Hashimoto and Smith, 1973; Haynes and Sarma, 1973). Most of these models, however, were developed for gas chromatographic columns under the assumption of a linear adsorption isotherm.Nonlinear adsorption isotherms are more frequently encountered in liquid chromatographic systems. The mathematical

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Numerical solution of liquid‐phase multicomponent adsorption in fixed beds

Cited by 47 publications

References 28 publications

Mathematical Modeling and Scale-up of Liquid Chromatography

Mathematical Modeling and Scale-up of Liquid Chromatography

Simulation and design models for adsorption processes

Analysis of liquid chromatography with nonuniform crystallite particles

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