Rigorous Design of Complex Distillation Columns Using Process Simulators and the Particle Swarm Optimization Algorithm

We present a derivative-free optimization algorithm coupled with a chemical process simulator for the optimal design of individual and complex distillation processes using a rigorous tray-by-tray model. The proposed approach serves as an alternative tool to the various models based on nonlinear programming (NLP) or mixed-integer nonlinear programming (MINLP) . This is accomplished by combining the advantages of using a commercial process simulator (Aspen Hysys), including especially suited numerical methods developed for the convergence of distillation columns, with the benefits of the particle swarm optimization (PSO) metaheuristic algorithm, which does not require gradient information and has the ability to escape from local optima. Our method inherits the superstructure developed in Yeomans, H.; Grossmann, I. E.Optimal design of complex distillation columns using rigorous tray-by-tray disjunctive programming models. Ind. Eng. Chem. Res.2000, 39 (11), 4326–4335, in which the nonexisting trays are considered as simple bypasses of liquid and vapor flows. The implemented tool provides the optimal configuration of distillation column systems, which includes continuous and discrete variables, through the minimization of the total annual cost (TAC). The robustness and flexibility of the method is proven through the successful design and synthesis of three distillation systems of increasing complexity.

Tungsten coil atomic emission spectrometry combined with dispersive liquid–liquid microextraction: A synergistic association for chromium determination in water samples

A novel and environment friendly analytical method is reported for total chromium determination and chromium speciation in water samples, whereby tungsten coil atomic emission spectrometry (WCAES) is combined with in situ ionic liquid formation dispersive liquid–liquid microextraction (in situ IL-DLLME). A two stage multivariate optimization approach has been developed employing a Plackett–Burman design for screening and selection of the significant factor involved in the in situ IL-DLLME procedure, which was later optimized by means of a circumscribed central composite design. The optimum conditions were complexant concentration: 0.5% (or 0.1%); complexant type: DDTC; IL anion: View the MathML sourcePF6−; [Hmim][Cl] IL amount: 60 mg; ionic strength: 0% NaCl; pH: 5 (or 2); centrifugation time: 10 min; and centrifugation speed: 1000 rpm. Under the optimized experimental conditions the method was evaluated and proper linearity was obtained with a correlation coefficient of 0.991 (5 calibration standards). Limits of detection and quantification for both chromium species were 3 and 10 µg L−1, respectively. This is a 233-fold improvement when compared with chromium determination by WCAES without using preconcentration. The repeatability of the proposed method was evaluated at two different spiking levels (10 and 50 µg L−1) obtaining coefficients of variation of 11.4% and 3.6% (n=3), respectively. A certified reference material (SRM-1643e NIST) was analyzed in order to determine the accuracy of the method for total chromium determination and 112.3% and 2.5 µg L−1 were the recovery (trueness) and standard deviation values, respectively. Tap, bottled mineral and natural mineral water samples were analyzed at 60 µg L−1 spiking level of total Cr content at two Cr(VI)/Cr(III) ratios, and relative recovery values ranged between 88% and 112% showing that the matrix has a negligible effect. To our knowledge, this is the first time that combines in situ IL-DLLME and WCAES.