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Modeling of nonlinear multicomponent chromatography

  • T. Gu
  • G. -J. Tsai
  • G. T. Tsao
Chapter
Part of the Advances in Biochemical Engineering/Biotechnology book series (ABE, volume 49)

Abstract

In the age of rapid development of biotechnology, preparative and large scale chromatography becomes more and more popular. Unlike analytical chromatography, dispersion and mass transfer effects are often significant in preparative and large scale chromatography. Concentration overload often leads to nonlinearity of the system. The study of nonlinear chromatography becomes more and more demanding. Much work has been done in the past two decades, but many topics of practical importance still need to be tackled. In this chapter, a review is given on different models for chromatography. This chapter provides a brief review of different mathematical models for non-linear chromatography. A general multicomponent rate model, which accounts for various mass transfer mechanisms and nonlinear isotherms is presented. This comprehensive model is a very powerful tool for the study of the dynamics of nonlinear multicomponent chromatography. This chapter also presents an efficient numerical method for the solution of the model and its numerous extensions. As an example, the model is used for the study of some interesting effects of isotherm characteristics of the displacer on the optimization of stepwise displacement.

Keywords

Displacement Development Nonlinear Isotherm General Rate Model Nonlinear Chromatography Size Exclusion Effect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

ai

constant in Langmuir isotherm for component i, biC i

bi

adsorption equilibrium constant for component i, kai/kdi

Bii

Biot number of mass transfer for component i, kiRp/(εpDpi) or kiRp/(ε pi a Dpi)

Cbi

bulk phase concentration of component i

Cfi

feed concentration profile of component i, a time dependent variable

C0i

concentration used for nondimensionalization, max{Cfi(t)}

Cpi

concentration of component i in the stagnant fluid phase inside particle macropores

Cpis

concentration of component i in the solid phase of particle (mole adsorbate/unit volume of particle skeleton)

C1

adsorption saturation capacity for component i (mole adsorbate/unit volume of particle skeleton)

¯C

adsorption saturation capacity based on the unit volume of the bed

¯Ci

concentration of component i in the stationary phase based on the unit volume of the bed

Ci

concentration of component i in the fluid phase based on the unit volume of the bed

cbi

= Cbi/C0i

cpi

= Cpi/C0i

cpis

= C pi s /C0i

ci

= C i /C0i

Dbi

axial or radial dispersion coefficient of component i

Daia

Damköhler number for adsorption, L(kaiC0i)/v

Daid

Damköhler number for desorption, Lkdi/v

Fiex

size exclusion factor for component i, ε pi a p

ki

film mass transfer coefficient of component i

kai

adsorption rate constant for component i

kdi

desorption rate constant for component i

L

column length

N

number of interior collocation points

Ne

number of quadratic elements

Ns

number of components

PeLi

Peclet number of axial dispersion for component i, vL/Dbi

R

radial coordinate for particle

Rp

particle radius

r

R/Rp

t

time

v

interstitial velocity

Z

axial coordinate

z

Z/L

εb

bed void volume fraction

εp

particle porosity

εpia

accessible particle porosity of component i

ηi

dimensionless constant, εpDpiL / R p 2 v

ξi

dimensionless constant for component i, 3Biiηi(1−εb)/εb

τ

dimensionless time, vt/L

τimp

dimensionless time duration for a rectangular pulse of the sample

φ

Lagrangian interpolation function

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • T. Gu
    • 1
  • G. -J. Tsai
    • 2
  • G. T. Tsao
    • 3
  1. 1.Department of Chemical EngineeringOhio UniversityAthensUSA
  2. 2.Lederle LaboratoriesPearl RiverUSA
  3. 3.Laboratory of Renewable Resources Engineering, 1295 Potter CenterPurdue UniversityWest LafayetteUSA

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