Analysis of linear reactive general rate model of liquid chromatography considering irreversible and reversible reactions

Abstract

A linear general rate model of two-component liquid chromatography is analyzed considering heterogenous reactions of types A→B and A⇄B. The model equations incorporate axial dispersion, external and intra particle pore diffusions, interfacial mass transfer, linear sorption kinetics, and first order heterogeneous chemical reactions. The solution methodology successively employs the Laplace transform and linear transformation steps to uncouple the governing set of coupled differential equations. The resulting system of uncoupled

Analysis of two‐dimensional models for liquid chromatographic reactors of cylindrical geometry

“…Our research group has solved analytically the linear one-dimensional (1D) and two-dimensional (2D) models of nonreactive and reactive chromatography. [11][12][13][14][15][16] The current work extends our previous analysis on 1D-GRM 17 to the analysis of linear two-component reactive 2D-GRM considering both axial and radial concentration gradients. Analytical solutions of the model for irreversible and reversible reactions are derived by applying the Hankel transformation, the Laplace transformation, the eigendecomposition technique, and the conventional solution technique for ordinary differential equations (ODEs).…”

“…In the latter case, where no initial radial gradients are introduced into the column, the solutions should converge to the solution of simpler 1D-GRM. 17 The classical mass balance equations for the bulk phase of adsorption are given as…”

“…The latter case results if is set equal to the radius of the column denoted by . In the latter case, where no initial radial gradients are introduced into the column, the solutions should converge to the solution of simpler 1D‐GRM . The classical mass balance equations for the bulk phase of adsorption are given as where for (), is the concentration of i th component in the bulk of fluid, is the concentration of the same component in the particle pores, u is the interstitial velocity, is the axial dispersion coefficient of i th component, and is the phase ratio with ε as the external porosity.…”

Analysis of Linear General Rate Model of Reactive Chromatography for Core–Shell Adsorbents

“…Recently, we have theoretically studied reactive liquid chromatopathy by considering different linear and nonlinear chromatographic models. [51][52][53][54][55][56] This paper is concerned with the analytical solutions of a two-component linear general rate model (GRM) for fixed-bed liquid chromatographic reactors packed with a spherical shaped core-shell particles. The model considers two-component mixture, irreversible and reversible reactions, axial dispersion, interfacial mass transfer, intraparticle diffusion, linear adsorption, and rectangular pulse injections.…”

“…It is an extension of our recent works on reactive chromatography considering fully porous particles. 55 Analytical solutions of the model equations are derived by simultaneously applying the Laplace transformation and eigen-decomposition techniques. 57,58 The numerical Laplace inversion is applied for back transformation of the solutions in the actual time domain.…”