Reduced-Order Modeling and ROM-Based Optimization of Batch Chromatography

A reduced basis method is applied to batch chromatography and the underlying optimization problem is solved efficiently based on the resulting reduced model. A technique of adaptive snapshot selection is proposed to reduce the complexity and runtime of generating the reduced basis. With the help of an output-oriented error bound, the construction of the reduced model is managed automatically. Numerical examples demonstrate the performance of the adaptive technique in reducing the offline time. The ROM-based optimization is successful in terms of the accuracy and the runtime for getting the optimal solution.

[1]  Bernard Haasdonk,et al.  Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation , 2012, SIAM J. Sci. Comput..

[2]  J. Hesthaven,et al.  Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations , 2007 .

[3]  Jörg Raisch,et al.  A hierarchical approach to optimal control of a hybrid chromatographic batch process* *Work has been done in the framework of the project “Methods from Discrete Mathematics for the Synthesis and Control of Chemical Processes”, DFG-FG 468 , 2009 .

[4]  M. Grepl Reduced-basis approximation a posteriori error estimation for parabolic partial differential equations , 2005 .

[5]  B. Haasdonk,et al.  REDUCED BASIS METHOD FOR FINITE VOLUME APPROXIMATIONS OF PARAMETRIZED LINEAR EVOLUTION EQUATIONS , 2008 .

[6]  Bernard Haasdonk,et al.  A training set and multiple bases generation approach for parameterized model reduction based on adaptive grids in parameter space , 2011 .

[7]  Peter Benner,et al.  Accelerating PDE Constrained Optimization by the Reduced Basis Method: Application to Batch Chromatography , 2015 .

[8]  N. Nguyen,et al.  An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations , 2004 .

[9]  Jens L. Eftang,et al.  An hp certified reduced basis method for parametrized parabolic partial differential equations , 2011 .

[10]  Anita M. Katti,et al.  Fundamentals of Preparative and Nonlinear Chromatography , 1994 .

[11]  Ahmed K. Noor,et al.  Reduced Basis Technique for Nonlinear Analysis of Structures , 1980 .

[12]  Sebastian Engell,et al.  Iterative set-point optimization of batch chromatography , 2005, Comput. Chem. Eng..