Equilibrium theory based design of simulated moving bed processes for a generalized Langmuir isotherm

In the frame of the local equilibrium theory of chromatography, design criteria for complete separation of binary mixtures in simulated moving bed (SMB) separations are developed, presented and discussed. These apply to systems, whose retention behavior is characterized by a generalized Langmuir isotherm. By allowing for negative terms in the denominator of the classical Langmuir isotherm, this newly introduced adsorption model captures a broad class of competitive or synergistic adsorption, including anti-Langmuir behavior for both adsorbates, and mixed cases where one species behaves in a Lagmuirian and the other in an anti-Langmuirian manner. By extending classical equilibrium theory results for the binary Langmuir isotherm, and by generalizing the approach followed earlier to derive SMB design criteria for the binary and multi-component Langmuir isotherm, exact algebraic equations for the boundary of the complete separation region in the operating parameter space are derived for all possible generalized Langmuir isotherm. The effect of changing feed composition on the shape of the complete separation region and on the position of the optimal operating point is analyzed and discussed.