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Article

Optimal Design of Experiments for Liquid–Liquid Equilibria Characterization via Semidefinite Programming

1
Department of Chemical and Biological Engineering, ISEC, Polytechnic Institute of Coimbra, Rua Pedro Nunes, Quinta da Nora, 3030–199 Coimbra, Portugal
2
CIEPQPF, Department of Chemical Engineering, University of Coimbra, Rua Sílvio Lima, Pólo II, 3030–790 Coimbra, Portugal
3
Department of Statistics, London School of Economics, London WC2A 2AE, UK
*
Author to whom correspondence should be addressed.
Processes 2019, 7(11), 834; https://doi.org/10.3390/pr7110834
Received: 25 September 2019 / Revised: 27 October 2019 / Accepted: 6 November 2019 / Published: 8 November 2019
(This article belongs to the Section Chemical Processes and Systems)
Liquid–liquid equilibria (LLE) characterization is a task requiring considerable work and appreciable financial resources. Notable savings in time and effort can be achieved when the experimental plans use the methods of the optimal design of experiments that maximize the information obtained. To achieve this goal, a systematic optimization formulation based on Semidefinite Programming is proposed for finding optimal experimental designs for LLE studies carried out at constant pressure and temperature. The non-random two-liquid (NRTL) model is employed to represent species equilibria in both phases. This model, combined with mass balance relationships, provides a means of computing the sensitivities of the measurements to the parameters. To design the experiment, these sensitivities are calculated for a grid of candidate experiments in which initial mixture compositions are varied. The optimal design is found by maximizing criteria based on the Fisher Information Matrix (FIM). Three optimality criteria (D-, A- and E-optimal) are exemplified. The approach is demonstrated for two ternary systems where different sets of parameters are to be estimated. View Full-Text
Keywords: optimal design of experiments; approximate designs; semidefinite programming; liquid–liquid equilibria; ternary systems optimal design of experiments; approximate designs; semidefinite programming; liquid–liquid equilibria; ternary systems
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MDPI and ACS Style

Duarte, B.P.M.; Atkinson, A.C.; Granjo, J.F.O.; Oliveira, N.M.C. Optimal Design of Experiments for Liquid–Liquid Equilibria Characterization via Semidefinite Programming. Processes 2019, 7, 834. https://doi.org/10.3390/pr7110834

AMA Style

Duarte BPM, Atkinson AC, Granjo JFO, Oliveira NMC. Optimal Design of Experiments for Liquid–Liquid Equilibria Characterization via Semidefinite Programming. Processes. 2019; 7(11):834. https://doi.org/10.3390/pr7110834

Chicago/Turabian Style

Duarte, Belmiro P.M., Anthony C. Atkinson, José F.O. Granjo, and Nuno M.C. Oliveira. 2019. "Optimal Design of Experiments for Liquid–Liquid Equilibria Characterization via Semidefinite Programming" Processes 7, no. 11: 834. https://doi.org/10.3390/pr7110834

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