Analytical and numerical solutions of two-dimensional general rate models for liquid chromatographic columns packed with core–shell particles

Mechanistic Modeling of Preparative Column Chromatography for Biotherapeutics

Chromatography has long been, and remains, the workhorse of downstream processing in the production of biopharmaceuticals. As bioprocessing has matured, there has been a growing trend toward seeking a detailed fundamental understanding of the relevant unit operations, which for some operations include the use of mechanistic modeling in a way similar to its use in the conventional chemical process industries. Mechanistic models of chromatography have been developed for almost a century, but although the essential features are generally understood, the specialization of such models to biopharmaceutical processing includes several areas that require further elucidation. This review outlines the overall approaches used in such modeling and emphasizes current needs, specifically in the context of typical uses of such models; these include selection and improvement of isotherm models and methods to estimate isotherm and transport parameters independently. Further insights are likely to be aided by molecular-level modeling, as well as by the copious amounts of empirical data available for existing processes.

Fifty Years of Moment Technique for Dynamic Analysis of Chemical Reactor Parameters

Moment technique has been extensively used for the evaluation of the rate and equilibrium parameters in chemical reactors and also in adsorption vessels, for about five decades. Adsorption and reaction rate parameters, as well as axial dispersion constants, effective diffusivities within porous catalysts and heat and mass transfer coefficients were shown to be effectively evaluated by analyzing the moments of the response peaks, which could be obtained from pulse-response experiments performed in a reaction/adsorption vessel. A detailed review of chromatographic processes, involving moment analysis of adsorption equilibrium and rate constants in fixed beds, dynamic analysis of batch adsorbers, moment analysis of fluidized bed, slurry and trickle bed reactors are reported in this manuscript. Applications of the single-pellet moment technique, which was developed for the effective investigation of intrapellet rate and equilibrium processes, by eliminating the contributions of axial dispersion and external transport parameters, are comprehensively discussed. Recent studies for the analysis of reaction rate parameters using the TAP reactor approach, use of single pellet system for the investigation of catalytic and non-catalytic solid-gas reactions and extension of the moment technique to non-linear systems opened new pathways in reaction engineering research.