Assessment and Future Directions of Nonlinear Model Predictive ...

476 A. Küpper and S. EngellFig. 2. Flowchart of the Hashimoto processflow chart of the SMB plant operated at the Universität Dortmund. The portsfortheexternalfeedandeluentinletsaswellastheextractandraffinateoutletscan be connected to each single chromatographic column (1-8). Each reactor(9-12) can be placed in front of each chromatographic column.Accurate dynamic models of multi-column continuous chromatographic processesconsist of dynamic models of the single chromatographic columns and ofthe tubular reactors and the node balances which describe the connections ofthe columns and of the switching of the ports. The chromatographic columnsare described accurately by the general rate model which accounts for all importanteffects of the column, i.e. mass transfer between the liquid and solidphase, pore diffusion, and axial dispersion. It is assumed that the particles ofthe solid phase are uniform, spherical, porous (with a constant void fraction ɛ p ),and that the mass transfer between the particle and the surrounding layer ofthe bulk is in a local equilibrium. The concentration of component i is given byc i in the liquid phase and by q i in the solid phase. D ax is the axial dispersioncoefficient, u the interstitial velocity, ɛ b the void fraction of the bulk phase, c eqithe equilibrium concentration, k l,i the film mass transfer resistance, and D p,ithe diffusion coefficient within the particle pores. The concentration within thepores is denoted by c p,i . Furthermore, it is assumed that u and c i are uniformlydistributed over the radius. The following set of partial differential equations forthe separators and the tubular reactors can be obtained from a mass balance