Two-Dimensional General Rate Model of Liquid Chromatography Incorporating Finite Rates of Adsorption–Desorption Kinetics and Core–Shell Particles

Abstract

A two-dimensional general rate model of liquid chromatography incorporating slow rates of adsorption−desorption kinetics, axial and radial dispersions, and core−shell particles is formulated. Radial concentration gradients are generated inside the column by considering different regions of injection at the inlet. Analytical solutions are obtained for a single-component linear model by simultaneously utilizing the Laplace and Hankel transformations for the considered two sets of boundary conditions. These linear solutions are useful for simulating liquid-chromatographic columns with diluted or small-volume samples and those in which radial concentration gradients are significant. To gain further insight into the process, analytical moments are also deduced from the Laplace−Hankel-domain solutions. For situations of concentrated and large-volume samples, which are not solvable analytically, formulation of nonlinear models is necessary. In this study, a semidiscrete, high-resolution, finite-volume scheme is extended to approximate the resulting nonlinear-model equations for multicomponent mixtures. The performance of the column is analyzed by implementing a specified criterion of performance. A few numerical case studies are conducted to inspect the effects of the model parameters on the elution profiles.

The use of predictive models to develop chromatography-based purification processes

“…General rate model Lieres and Andersson (2010) Two-dimensional general rate model Brhane et al (2019) Lumped rate model Leweke and Lieres (2018) Transport dispersive model Piątkowski et al (2003) Equilibrium dispersive model Guiochon et al (2006) Thomas model (kinetic model) Cavazzini et al (2002) Reactive-dispersive model Golshan-Shirazi and Transport model Qamar et al (2020) Adsorption kinetic models Reference…”

“…Whereas the inter-particle mass balance accounts for convection, dispersion and film mass transfer, the intra-particle mass balance represents pore diffusion processes inside the mostly spherical particles of the stationary phase and the sorption of colloid i to the surface, which is defined by the corresponding isotherms. The calculation becomes more complex if the two-dimensional general rate model (GRM2D) is used, which includes a radial coordinate to consider non-axial transport resulting from inhomogeneous resin packing or dispersion at the frits of the column inlet ( Brhane et al, 2019 ). This mass transport model is already implemented in some modeling software 3 .…”

Recent advances in modelling and control of liquid chromatography

“…This can be an oversimplification for preparative or process chromatography, where the larger columns (commonly loaded manually) are prone to nonhomogeneous packing causing radial velocity and temperature gradients or non-homogeneous sample injection. Hence, two dimensional (radial and axial) transport models, although not yet the standard, are by no means the exception [44,45].…”

“…This assumption seems valid for small molecules but is commonly adopted without justification. The more advanced general rate models (GRMs) account for mass transfer effects by incorporating transfer resistance, surface diffusion, adsorption-desorption kinetics, and pore diffusion [45,49]. This is achieved by two additional equations describing the radial solute concentration profiles inside the porous particles (Figure 2c) and the mass transfer between the stationary and mobile phases at the stationary particle surfaces.…”

Desarrollo y producción recombinante de un péptido bloqueador de TNF para el tratamiento de trastornos autoinmunes inflamatorios.

“…Es capaz de predecir fenómenos de interacción entre proteínas, así como el efecto de diferentes condiciones de proceso y propiedades de las fases estacionarias sobre la separación de proteínas. Para cada componente de una mezcla (proteínas, péptidos, sales u otros reactivos) el modelo consiste en un conjunto de dos ecuaciones diferenciales parciales (PDE) que describen el movimiento de las proteínas y el desplazador (fase móvil) a través del lecho y dentro de las partículas de la fase estacionaria [50,149,165].…”