Solving hyperbolic conservation laws with active counteraction against numerical errors: Isothermal fixed-bed adsorption

On-line optimization of four-zone simulated moving bed chromatography using an equilibrium-dispersion model: I. Simulation study

“…The control unit with up to 40 cells per column could control the system up to 7500 theoretical plates. Compared to the theoretical plates of the plant the required numbers of cells for the optimizing control were two orders of magnitude smaller because the MC-AC scheme can compensate the numerical dispersion which is introduced by a low number of cells and can reproduce steep fronts with a rather low number of cells [14]. The model parameters estimated by the control unit were close to the true plant parameters.…”

“…With this scheme, steep concentration profiles can be quickly and accurately resolved with a rather small number of mixing cells. Details are given in reference [14].…”

“…Linearization is not applied. The algorithm is fast because a new solution algorithm is applied: The mixing cell with active counteraction (MC-AC) scheme [14] was used to accelerate the computation for updating the process model parameters and to search the optimized operating conditions in every control cycle corresponding to one port switching interval. Further, an additional concentration measurement in the recycle was considered, to allow tighter control.…”

Adaptive Interpolatory MOR by Learning the Error Estimator in the Parameter Domain

“…As a result, this problem is likely to have a slow Kolmogorov n-width decay. The batch chromatography equations are in fact a system of first-order hyperbolic PDEs [42]. It is known that for problems exhibiting hyperbolic characteristics or convection-dominance, the Kolmogorov n-width decay is slow [27].…”

On-line optimization of four-zone simulated moving bed chromatography using an Equilibrium-Dispersion Model: II. Experimental validation

“…We applied the concept to analyze the four-zone SMB process that has no system void volume and exploits columns with identical properties. Owing to the availability of the mixing cell with active counteraction (MC-AC) scheme that can provides accurate and rapid numerical solutions of the process model [12], the control unit can quickly estimate the model parameters and identify optimized operating conditions. However, practical application of this concept still requires further improvement to evaluate unavoidable system void volumes and monitoring strategies for dynamic optimization of a real SMB process.…”