Chromatography stage model

For the solution of sophisticated mathematical models of adsorption cycles including complex multicomponent equilibrium and rate expressions, two numerical methods are popular. These are finite difference methods and orthogonal collocation. The former vary in the manner in which distance variables are discretized, ranging from simple backward difference stage models (akin to the plate theory of chromatography) to more involved schemes exhibiting little numerical dispersion. Collocation methods are often thought to be faster computationally, but oscillations in the polynomial trial function can be a problem. The choice of best method is often the preference of the user. 

Equilibrium stage model Adsorption chromatography for products with low molecular weights Accuracy only for single components or small differences in Ni for all components... 

Beltscheva, D., Hugo, P., and Seidel-Morgenstem, A. (2003) Linear two-step gradient counter-current chromatography analysis based on a recursive solution of an equilibrium stage model./. Chromatogr. A, 989, 31 5. 

The classic paper by Martin and Synge (1941) on liquid-liquid chromatography used an equilibrium-staged model with linear isotherms for the chromatographic column. Conparison of staged solutions with Eq. fl8-761 shows that the number of stages N is... 

The confusion that a combination of these different definitions can generate, together with the difficulties encoimtered in the determination of some of the column characteristics involved (particularly the internal and the external porosities) makes useful a careful consideration of these issues. Given the stage of sophistication that the modeling of chromatography has now reached, it is not possible to tolerate errors, confusions, or approximations in the definitions nor in the estimations of the critical parameters related to the porosities, the velocities, and the equilibrium constants, nor to accept that more errors be made in the estimation of these parameters than those that are always involved in any measurement process. 

Plate model A model of chromatography which assumes that the column is a series of stages in each of which equUibrimn between the stationary and the mobile phase is achieved. 

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