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Abstract

In the last years the simulated moving bed technology has proven to be a powerful concept to separate isomers, in particular enantiomers. Due to the complex multicolumn arrangement, the design and optimization of this process is not a trivial task. The concept is often applied to achieve high purity outlet streams. Based on the assumption that the phase equilibria are established there is a powerful concept available to evaluate the feasibility of the process for highly efficient columns. However, in practice often lower purities are acceptable and cheaper columns can be applied. Rather than performing a complete optimization study, in such cases it is attractive to have in early development stages information available purpose of this paper to present a novel apporach to address this feasibility question based on discrete optimization, which permits the derivation of global infeasibility statements in conjunction with local feasible solutions. In order to achieve this, a mixed-integer linear program is constructed in such a way that its solution set contains all feasible solutions of the underlying non-linear optimization model. If the mixed-integer linear relaxation is infeasible, then it is guaranteed that the nonlinear model has no solution. In addition, an optimal solution of the mixed-integer linear relaxation can provide a feasible solution or a useful starting point for local optimization tools. Our approach for tackling the feasibility question is presented using capacity and separation factors for the separation of mixtures of fructose-dextran T9 and fructose-raffinose. A conventional 4 zone True Moving Bed (TMB) model is considered in conjunction with technically meaningful restrictions on the operating parameters. The apporach allows to prove lower bounds on the number of plates necessary to separate the mixtures for a specified purity requirement (e. g. 90 or 98 percent). It turns out, for instance, that for separating the mixture fructose-raffinose with a purity requirement of 98 percent (for both extract and raffinate outlets) twenty plates for each of the zones are provably not sufficient, whereas for twenty five plates per zone a solution is given which guarantees a purity of 94.5 percent for the fructose outlet. Several similar statements for other conditions or processes under consideration can be given as well.