Propagation of concentration fronts (non-linear waves) in chromatographic processes is a result of both kinetic effects and phase equilibrium behavior of the system. However, equilibrium theory [1, 2], can reveal characteristic patterns in the process that stem from thermodynamics because dispersive kinetic effects are eliminated, and it should be considered a powerful tool for analysis and design of chromatographic processes. While it should be noted that predictions from equilibrium theory represent limiting cases that cannot necessarily be realized in practice, its application appears particularly promising when considering complex chemical processes with additional degrees of freedom due to highly-integrated structures (like reactive chromatography and combined separations), or non-isothermal conditions.

After a short overview on fundamentals of equilibrium theory for chromatographic processes, as a first example separations by Simulated-Moving-Bed (SMB) chromatography will be considered. It has been shown that lowering the purity requirements on SMB processes can be beneficial when considering a combination of SMB with other separation techniques [3]. However, prediction of optimum operating parameters so far is possible only from expensive optimizations of numerical models. Here, the application of equilibrium theory to derive simplified design expressions will be discussed.

As a second application, analysis of reactive chromatography is discussed. In particular, equilibrium theory can be used to analyze whether thermodynamic constraints allow complete conversion and separation of the products for a given stoichiometry and elution order, or is a reactive azeotrope formed that elutes through the column unchanged [4].

Finally, non-isothermal operation of a chromatographic reactor is studied. In this case, additional degrees of freedom have to be taken into account. Due to the adsorption enthalpies and the heat of reaction, additionally moving thermal waves are developed in the column [5]. Like for chromatographic reactors, such thermal waves can also be described in the framework of equilibrium theory. In particular, we present how the approach can be used to analyze the coupling between the propagation velocities of concentration and temperature fronts.

[1] H.-K. Rhee, R. Aris, and N.R. Amundson. First-Order Partial Differential Equations, Vol. I, Dover, 2001. [2] H.-K. Rhee, R. Aris, and N.R. Amundson. First-Order Partial Differential Equations, Vol. II, Dover, 2001. [3] M. Kaspereit, et al. J. Chromatogr. A 1092 (2005) 55-64. [4] S. Grüner and A. Kienle. Chem. Engng. Sci. 59 (2004) 901-918. [5] T. Sainio, Ion-exchange Resins as Stationary Phase in Reactive Chromatography, Acta Universitatis Lappeenrantaensis 218, Lappeenranta, 2005