Analysis of a Two-Dimensional Nonequilibrium Model of Linear Reactive Chromatography Considering Irreversible and Reversible Reactions

Abstract

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.

Investigations on the Low Temperature Methanation with Pulse Reaction of CO

“…The moment analysis provides detailed information from less data as described by John et al [19] and Qamar et al [20]. According to pulse reaction experiments, the potential for the reduction of data points can be orders of magnitude.…”

Linearized non-equilibrium and non-isothermal two-dimensional model of liquid chromatography for studying thermal effects in cylindrical columns

“…The linear models are solvable analytically and several authors have derived the analytical solutions of linear onedimensional (1 D) models [27][28][29][30][31][32][33][34][35]. Moreover, the analytical solutions of linearized isothermal two-dimensional (2 D) models are also available in the literature [36][37][38][39]. It was found that the developed 2 D-models and their solutions are more flexible and general than the classical 1 D-models and their solutions.…”

“…Such a non-isothermal model is very useful for quantifying radial temperature gradients in those columns in which radial concentration gradients are significant. The Hankel and Laplace transformations are jointly used to obtain the Hankel-Laplace domains analytical solutions [36][37][38][39]. An accurate and efficient procedure of numerical Laplace inversion is applied to obtain solutions in the time domain [43].…”

Modelling diffusion and reaction for inert‐core catalyst in batch and fixed bed reactors

“…However, newly developed batch and fixed bed reactors with applications use inert‐core spherical particles, and those solutions are no longer valid to predict the concentration time relationship or the elution curves for inert‐core catalysts. Some investigations have been done for reactive chromatography for inert‐core adsorbents . It is therefore most desirable to develop a mathematical model and present the analytical solutions for batch and fixed bed reactors with inert‐core catalysts.…”

“…Some investigations have been done for reactive chromatography for inert-core adsorbents. [30][31][32] It is therefore most desirable to develop a mathematical model and present the analytical solutions for batch and fixed bed reactors with inert-core catalysts.…”