The simulated moving bed process is increasingly used for the separation of binary mixtures. To ensure proper operation, the volumetric flow rates and the time interval must be exactly adjusted. This study presents a general method for determining the control variables for a dispersion-free SMB process. For noncompetitive Langmuir isotherms, explicit equations are derived for the case of complete separation. The proposed method allows both a good estimation of the time trajectories of the concentrations at the drains and the design of new applications for optimization and control of SMB plants.
IntroductionChromatographic processes have gained an important place in separation technology. They make use of the different adsorption strength of the single components of a multicomponent mixture. To achieve a continuous chromatographic separation, the theoretical concept of the true moving bed (TMB) was developed. A binary mixture dissolved into a solvent moves countercurrently to the solid phase. The velocities of the liquid and solid phase must be carefully selected so that the desired standing concentration profile is obtained. This can be done by using the "triangle theory" [1,2] or the "standing wave" design [3,4]. The SMB process is a practical implementation of a TMB process and was developed by the UOP company at the end of the 1950s [5]. Feeding and drains of the chromatographic columns are interconnected to a ring and cyclically switched in the direction of the solvent stream so that a countercurrent motion between liquid and solid phase is simulated. For the determination of the volumetric flow rates, the theory of the TMB process is still used. This is because a correctly adjusted TMB process has a real steady state profile while a SMB process only has a cyclically stationary state. Hence, a TMB process is mathematically simpler to analyze.The cyclic steady state of a SMB process for Henry isotherms was studied in [6]. Based on the knowledge of the ideal concentration profile of a SMB process in cyclic steady state, a new possibility to determine the flow rates for a given purity was introduced for the case of Henry isotherms [7]. Only the velocities of the four concentration fronts were examined and not the complete concentration profile. The key observation was that in cyclic steady state each concentration front moves exactly one column length during one time interval. This was already observed in [3] and used for the "standing wave" design. When applying this concept to a real SMB process the periodical time trajectories of the concentrations at the drains can be exactly determined. These are the quantities of interest since they determine the purities as well as a certain degree of robustness with respect to disturbances.In this study, the concept of [7] is extended to noncompetitive Langmuir isotherms. They can serve, for example, as a first-order approximation for the separation of Tröger bases [8] or of Ibuprofen [9]. It should be mentioned that a similar concept can be applied to more complicated ...