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

• Autor(a) principal: Duarte, Belmiro P. M.
• Data de Publicação: 2019
• Outros Autores: Atkinson, Anthony C., Granjo, José F. O., Oliveira, Nuno M. C.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Texto Completo: https://hdl.handle.net/10316/107314; https://doi.org/10.3390/pr7110834
• topic: optimal design of experiments; approximate designs; semidefinite programming; liquid–liquid equilibria; ternary 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.