EXTREQ-2 Software Package for Mathematical Modeling of Multicomponent Extraction Equilibria

ABSTRACT A description of the EXTREQ-2 software package for the MS Windows XP/Windows 7 operating system is presented. This package is designed for the mathematical modeling of extraction isotherms for a single component using mixtures of two extractants. The EXTREQ-2 program can automatically evaluate up to 6 extracted complex compositions simultaneously. The software allows selection of the composition of extracted complexes in synergistic and binary extraction, calculation of thermodynamic extraction constants and hydration parameters for each extracted complex, as well as determination of the equilibrium concentrations of the extracted complexes and extractants in the organic phase. The organic phase compositions obtained from all examined systems were found to be entirely consistent with the independent physicochemical analyses of the extracted complexes documented in previous studies in the literature. The EXTREQ-2 software suite employs a hybrid optimization approach to improve both user-friendliness and computational accuracy. Several optimization methods, including a Genetic Algorithm, Simulated Annealing, and “Pattern Searching”, were independently evaluated and tested. The following results were obtained: Simulated Annealing: 3.67% (calculation speed comparable to Nelder-Mead); Pattern Search: 7.74% (the fastest method); Genetic Algorithm: 3.38% (the slowest); Our utilized Nelder-Mead method: 3.29%. The EXTREQ-2 software package is capable solely of determining the composition of extractable substances within a given extraction system and calculating the thermodynamic parameters associated with every extraction reaction taking place in that system.