title: Irreversible and reversible reactive chromatography: analytical solutions and moment analysis for rectangular pulse injections.
abstract: This work is concerned with the analysis of models for linear reactive chromatography describing irreversible A→B and reversible A↔B reactions. In contrast to previously published results rectangular reactant pulses are injected into initially empty or pre-equilibrated columns assuming both Dirichlet and Danckwerts boundary conditions. The models consist of two partial differential equations, accounting for convection, longitudinal dispersion and first order chemical reactions. Due to the effect of involved mechanisms on solute transport, analytical and numerical solutions of the models could be helpful to understand, design and optimize chromatographic reactors. The Laplace transformation is applied to solve the model equations analytically for linear adsorption isotherms. Statistical temporal moments are derived from solutions in the Laplace domain. Analytical results are compared with numerical predictions generated using a high-resolution finite volume scheme for two sets of boundary conditions. Several case studies are carried out to analyze reactive liquid chromatographic processes for a wide range of mass transfer and reaction kinetics. Good agreements in the results validate the correctness of the analytical solutions and accuracy of the proposed numerical algorithm.
authors: Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad, Pakistan.
authors: Sameena
authors: S
authors: Bibi
authors: Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad, Pakistan; Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstrasse 1, 39106 Magdeburg, Germany. Electronic address: Shamsul.qamar@comsats.edu.pk.
authors: Shamsul
authors: S
authors: Qamar
authors: Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstrasse 1, 39106 Magdeburg, Germany.
authors: Andreas
authors: A
authors: Seidel-Morgenstern
mesh_terms: D000327:Adsorption; D000465:Algorithms; D002853:Chromatography, Liquid / Q000379:methods*; D007700:Kinetics; D008962:Models, Theoretical; D012996:Solutions
chemical_list: D012996:Solutions
keywords: Adsorption; Analytical solutions; Chromatographic reactors; Finite volume schemes; Irreversible and reversible reactions; Moments analysis