A linearized non-isothermal general rate model for studying thermal effects in liquid chromatographic columns

Abstract

A linearized non-isothermal general rate model is formulated and analytically solved to quantify the effects of temperature variations in fixed-bed chromatographic columns. The model contains a set of four coupled partial differential equations (PDEs) accounting for energy transfer resistances, inner and outer particle-pore diffusions, and interfacial mass and axial dispersion. The Laplace transform, the eigenvalue-decomposition technique, and a conventional technique for the solutions of ordinary differential equations (ODEs) are jointly employed for the solution of the model equations. A few numerical test studies are considered to assess the impact of system parameters on the performance of packed-bed adsorption columns. To access the range of applicability and to get the scope of the appropriateness of calculated analytical results, the numerical results are also obtained by applying a high resolution finite volume scheme (HR-FVS). The analytical solutions obtained can be used as an invaluable tool for analyzing, optimizing, and upgrading the non-isothermal liquid chromatographic procedures.

Analysis of Liquid Chromatography Considering a Linear Single-Component Heterogeneous-Type Reactive General Rate Model

“…A high-resolution finite volume method is proposed with flux limitation in this section to construct the estimated results to examine the one-dimensional general rate model with a response of the heterogeneous reaction in the particle-phase equation. In prior publications, 3,14,15 we validated the order of accuracy for this method numerically analytically. The system is secondorder precise in both axial and radial coordinates.…”

“…In several industries, it is used in purification like food, pharmaceutical, and fine chemicals . There are various mathematical models with varying degrees of complexity accessible in the literature. , Among them, the most comprehensive and reliable mathematical model is the general rate model (GRM) used to describe the chromatographic profiles. Axial dispersion, advection, diffusion through an exterior layer encircling the sorbent particles, and intraparticle diffusion in the stagnant mobile phase within the particle pores are all included in this model.…”