Chromatographic dynamic modelling

Diinnebier, G., Weirich, I., and Watt, K.-U. (1998) Computationally efficient dynamic modelling and simulation of simulated moving bed chromatographic processes with linear isotherms. Chem. Eng. Sci., 53, 2537-2546. 

Dunnebier, G., I. Weirich, and K. U. Klatt, Conputationally Efficient Dynamic Modeling and Simulation of Simulated Moving Bed Chromatographic Processes with Linear Isotherms, Chem. Engr. ScL, 53, 2537 (1998). 

In the interpretation and analysis of chromatographic data it is assumed that the system is linear. Kinetic and equilibrium parameters are determined by matching the experimental response curve to the dimensionless theoretical curve calculated from a suitable dynamic model for the system. The assumption of linearity is a valid approximation provided that the concentration change over which the response is measured is sufficiently small. In the linear regime the normalized response is independent of the magnitude of the perturbation, and variation of the pulse (or step) size therefore provides a simple and direct test of system linearity. 

Dynamic melting models provide results that are similar to those obtained from the chromatographic porous flow melting model in that the extent of ( Ra/ Th)... 

Liquid chromatography (LC) and, in particular, high performance liquid chromatography (HPLC), is at present the most popular and widely used separation procedure based on a quasi-equilibrium -type of molecular distribution between two phases. Officially, LC is defined as a physical method... in which the components to be separated are distributed between two phases, one of which is stationary (stationary phase) while the other (the mobile phase) moves in a definite direction [ 1 ]. In other words, all chromatographic methods have one thing in common and that is the dynamic separation of a substance mixture in a flow system. Since the interphase molecular distribution of the respective substances is the main condition of the separation layer functionality in this method, chromatography can be considered as an excellent model of other methods based on similar distributions and carried out at dynamic conditions. 

The literature data on the tortuosity factor r show a large spread, with values ranging from 1.5 to 11. Model predictions lead to values of 1/e s (8), of 2 (parallel-path pore model)(9), of 3 (parallel-cross-linked pore model)(IQ), or 4 as recently calculated by Beeckman and Froment (11) for a random pore model. Therefore, it was decided to determine r experimentally through the measurement of the effective diffusivity by means of a dynamic gas chromatographic technique using a column of 163.5 cm length,... 

There are three popular hypotheses. Two models propose extreme situations and each encompasses a substantial amount of chromatographic data. These two proposals are the ion-pair model and the dynamic ion-exchange model. The third view, which is broader in scope than the previous two concepts, accommodates both the extreme views without combining the two models. This proposal is the ion-interaction model. 

To obtain a simple interpretation of the experimental findings in IIC, theoretical chromatographers first adopted a stoichiometric strategy that pioneered this separation mode. Unfortunately, the reaction schemes of stoichiometric models in both the mobile phase (ion pair model) and stationary phase (dynamic ion exchange model) lack a firm foundation in physical chemistry because they are not able to account for the stationary-phase modification that results from the addition of the HR to the eluent, and they fail to properly describe experimental results, as pointed out by Bidlingmeyer et al. " Key insights on these retention models were also provided by... 

The use of thermogravimetric analysis (TGA) apparatus to obtain kinetic data involves a series of trade-offs. Since we chose to employ a unit which is significantly larger than commercially available instruments (in order to obtain accurate chromatographic data), it was difficult to achieve time invariant O2 concentrations for runs with relatively rapid combustion rates. The reactor closely approximated ideal back-mixing conditions and consequently a dynamic mathematical model was used to describe the time-varying O2 concentration, temperature excursions on the shale surface and the simultaneous reaction rate. Kinetic information was extracted from the model by matching the computational predictions to the measured experimental data. 

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