Application of nature-inspired algorithms with generalized Pitzer-Debye-Huckel (PDH) refinement for liquid liquid equilibria (LLE) correlation in cyclic di-ether systems

Metaheuristic algorithms such as the genetic algorithm (GA) and cuckoo search (CS) algorithms have been widely used for phase equilibria computation. In the present work, correlation of the liquid-liquid splitting of 1,3-dioxolane + water and 1,4-dioxane + water mixtures using the buffers 3-n-morpholino-propanesulfonic acid (MOPS), 3-[4-(2-hydroxymethyl)-1-piperazinyl]-propanesulfonic acid (HEPPS), and the ionic-liquid (IL) tetra-methyl-ammonium 3-[4-(2-hydroxymethyl)-1-piperazinyl]-propanesulfonate [TMA][EPPS] is performed by the GA-NRTL, CS-NRTL, GA-UNIQUAC, and CS-UNIQUAC methods. Thermodynamically consistent binary interaction parameters are obtained after a rigorous investigation of the dimensionless excess Gibbs free energy of mixing G(M)(L)/RT topology thereby satisfying the Gibbs minor common tangent phase stability test. The results indicate that the GA-UNIQUAC method performs the best for correlating the biphasic regions with very high quantitative accuracies and well-resolved G(M)(L)/RT surface description. Furthermore, the UNIQUAC model is significantly enhanced by incorporating a thermodynamically consistent extended Pitzer-Debye-Huckel* (PDH*) contribution term considering weak electrostatic long-range interactions within the IL-rich phases.