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A regularization method for the reconstruction of adsorption isotherms in liquid chromatography
Örebro University, School of Science and Technology. Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden; .ORCID iD: 0000-0003-4023-6352
Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, People's Republic of China.
Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
Örebro University, School of Science and Technology.ORCID iD: 0000-0003-0332-2315
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2016 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 32, no 10, article id 105005Article in journal (Refereed) Published
Abstract [en]

Determining competitive adsorption isotherms is an open problem in liquid chromatography. Since traditional experimental trial-and-error approaches are too complex and expensive, a modern technique of obtaining adsorption isotherms is to solve the inverse problem so that the simulated batch separation coincides with actual experimental results. This is a typical ill-posed problem. Moreover, in almost all cases the observed concentration at the outlet is the total response of all components, which makes the problem more difficult. In this work, we tackle the ill-posedness with a new regularization method, which is based on the fact that the adsorption isotherms do not depend on the injection profile. The proposed method transfers the original problem to an optimization problem with a time-dependent convection–diffusion equation constraint. Iterative algorithms for solving constraint optimization problems for both the equilibrium-dispersive and the transport-dispersive models are developed. The mass transfer resistance is also estimated by the proposed inverse method. A regularization parameter selection method and the convergence property of the proposed algorithm are discussed. Finally, numerical tests for both synthetic problems and real-world problems are given to show the efficiency and feasibility of the proposed regularization method.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2016. Vol. 32, no 10, article id 105005
Keywords [en]
chromatography; adsorption isotherm; inverse problem; regularization; convection-diffusion equation; adjoint problem
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-51923DOI: 10.1088/0266-5611/32/10/105005ISI: 000402976000005Scopus ID: 2-s2.0-85009212077OAI: oai:DiVA.org:oru-51923DiVA, id: diva2:957060
Funder
Knowledge Foundation, 20140179Swedish Research Council, 2015-04627
Note

Funding Agencies:

AForsk Foundation  15/497

STINT  IB2015-5989 

NSCF  11571311 

Available from: 2016-08-31 Created: 2016-08-31 Last updated: 2017-10-18Bibliographically approved

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Zhang, YeGulliksson, Mårten

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