Dynamic Models of Non-Reaction and Reactive Liquid Chromatography: Derivation of Analytical and Numerical Solutions

Abstract

Dynamic Models of Non-Reactive and Reactive Liquid Chromatography: Derivation of Analytical and Numerical Solutions Chromatography is an effective technique used in the analytical chemistry for separation, identification and quantification of mixture components. Reactive chromatography is an integrated process which combines chemical or biochemical reactions with the chromatographic separation. These techniques have gained wide recognition in petrochemical, fine chemical, pharmaceutical, bio-technical and food industries. This work is focused on the the analysis of linear models of non-reactive and reactive liquid chromatography incorporating both fully porous and the core-shell particles. The model equations incorporate axial dispersion, external and intra particle pore diffusions, interfacial mass transfer, and irreversible and reversible first order heterogeneous reactions. In most of the liquid chromatographic operations, the sample volume is very small (i.e. in microliters) and diluted. Thus, the current linear assumptions are valid. Semi-analytical solutions of the model equations are derived by successively applying the Laplace transformation and eigen-decomposition technique. To gain further confidence on the analytical results, a high resolution finite volume scheme (HR-FVS) is implemented to numerically investigate the same model equations. Analytical and numerical temporal moments of the elution profiles are presented. These moments can be used to further analyze the solute transport behavior. Moreover, relationships are derived among the essential kinetic parameters of different models considering core-shell particles. Such particles are helpful for rapid and better separation of complex mixtures with a reasonably low back pressure. Extensive case studies of practical interest are carried out to measure the effects of different kinetics and reaction parameters on the conversion and separation of sample components. The results obtained can be utilized to optimize the process and to estimate model parameters from the experimental results.