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

A two-dimensional nonlinear and non-equilibrium model of liquid chromatography is numerically approximated to simulate the dynamics of multi-component mixtures in a fixed-bed isothermal liquid chromatographic reactor. The mathematical model is formed by a system of nonlinear convection-diffusion-reaction partial differential equations coupled with differential and algebraic equations. A semi-discrete high resolution finite volume scheme is applied to solve the model equations. The scheme is second order accurate in axial and radial coordinates. The resulting system of ordinary differential equations is solved by a second order accurate Runge-Kutta method. The proposed scheme capably captures narrow peaks and sharp discontinuities in the concentration profiles. Radial gradients were not considered in the pervious studies which are particularly important in the case of non-perfect injections. Several test problems of heterogeneously catalyzed reversible reactions are carried out. The considered case studies include three and four-component elution assuming hypothetical injections of the reactants in inner or outer sections of the column inlet cross-section. The developed numerical algorithm and results are useful tools for further improvements in reactive chromatography.

This article presents semi-analytical solutions and analytical temporal moments of a two-dimensional non-equilibrium transport model of linear reactive chromatography considering irreversible (A → B) and reversible (A ⇋ B) reactions. The model is formed by a system of four coupled partial differential equations accounting for linear advection, longitudinal and radial dispersions, rate of variation of the local concentration of each component in the stationary phase, local deviation from equilibrium concentrations, and first order chemical reactions in both liquid and solid phases. The solution process successively employs Hankel transformation, Laplace transformation, and linear transformation steps to uncouple the governing set of coupled differential equations. The resulting uncoupled systems of ordinary differential equations are solved using an elementary solution technique. The numerical Laplace inversion is applied for back transformation of the solutions in the actual time domain. To analyze the effects of different kinetic parameters, statistical temporal moments are derived from the 1 Hankel and Laplace transformed solutions. The current solutions extend and generalize the recent solutions of a two-dimensional non-equilibrium single-solute transport model for non-reactive liquid chromatography. Analytical results are compared with the numerical solutions of a high resolution finite volume scheme for two sets of boundary conditions. Several case studies are carried. Good agreements in the results verify both the correctness of the analytical solutions and accuracy of the suggested numerical algorithm.

This article is concerned with the numerical approximation of a nonlinear model describing the two-dimensional non-equilibrium transport of multi-component mixtures in a chromatographic column. The model consists of nonlinear convection-diffusion partial differential equations coupled with some differential and algebraic equations. Due to the unavailability of analytical solutions for nonlinear models, numerical solution techniques are the only tools to get accurate solutions. A semi-discrete high resolution finite volume scheme is extended to solve the model equations numerically. The scheme is second order accurate in axial and radial coordinates. The accuracy of the scheme is guaranteed by applying a second order accurate Runge-Kutta method to solve the resulting system of ordinary differential equation. The considered radial gradients were typically ignored in pervious studies. They can be relevant in particular in the case of non-perfect injections. The effects of possible rate limitations of the mass transfer in the radial direction are studied assuming hypothetical injections in outer or inner sections of the column inlet cross-section. The case studies consider single-component, two-component and three-component elution. The developed numerical algorithm is an efficient tool to study the effects of mass transfer kinetics on the shape of elution profiles.

This article presents semi-analytical solutions of a linear general rate model for fixed-bed liquid chromatographic reactors packed with core-shell particles. The model considers axial dispersion, interfacial mass transfer, intraparticle diffusion, linear adsorption, heterogeneous irreversible and reversible reactions, and injection of rectangular pulses. The Laplace transformation and eigen-decomposition technique are simultaneously applied to derive analytical solutions. The numerical Laplace inversion is applied for back transforming solutions in the actual time domain. A high resolution finite volume scheme is used to numerically approximate the model equations. Different case studies of reactive chromatography are considered to analyze the effect of core radius fraction on the elution profiles.