Estimation of equilibrium parameters using differential evolution in reactive extraction of propionic acid by tri- n-butyl phosphate

Abstract

The graphical and conventional optimization methods, used for the estimation of equilibrium parameters, do not guarantee the global optimum values. In this study, the equilibrium parameters are estimated using a well proven evolutionary based optimization routine [differential evolution (DE)]. For the estimation of stoichiometry and equilibrium constants, experiments are carried out for the reactive extraction of propionic acid using tri- n-butyl phosphate (TBP) dissolved in n-decane (inert diluent) and 1-decanol (modifier). The number of TBP molecules ( n) in the acid:TBP complex and equilibrium extraction constant ( K E) using 1:1 volume ratio of 1-decanol and n-decane as a diluent, are determined through proposed mathematical model using graphical methods as well as the differential evolution algorithm (DE, an optimization routine) and found that the predicted values of distribution coefficient ( K D) using DE are closely matching with the experimental values of K D. 1:1 complexes between TBP and acid are formed in most of the cases. The enthalpy and entropy of reactive extraction of propionic acid using TBP are also determined and found to be −12.47 kJ mol −1 and −32.42 J mol −1 K −1, respectively. The results of present study will be useful to intensify the recovery of propionic acid from fermentation broth (bio-separation) and aqueous waste stream.