This paper studies reactive extraction of formic (FA), acetic (AA), propionic (PA) and butyric (BA) acids from aqueous solutions by tri-n-butyl amine/diluent, with particular focus on proper optimization and modeling of extraction equilibria. The uptake capacities of amine/diluent and diluent alone approximate the following order: oleyl alcohol>octyl acetate>diisobutyl ketone and BA>PA>AA approximate to FA. An intrinsic optimization structure has been applied to the description of optimum extraction field of relevant systems, based on analyzing the variation profiles of separation ratio R and synergistic enhancement SE factors through the derivative variation method. We present new solvation molecular models extended-linear solvation energy relation (e-LSER), SPR1 and SPR2 (solvation probability relation), and an extension to group-contribution approach A-UNIFAC (Association-UNIFAC). A-UNIFAC predicts phase equilibria using new group interaction parameters regressed from vapor-liquid equilibrium data. The e-LSER model involves eight descriptors used for expressing solvent effects. By performing SPR1 and SPR2, we are able to scale up the probability range and activation energy of solvation effect. The strength of acid-amine association is calculated with chemodel. e-LSER, A-UNIFAC, SPR and chemodel simulate accurately the observed performance with average deviations inferior to 4.8%, 24.1%, 0.8% and 16.2%, respectively. (c) 2017 Curtin University and John Wiley & Sons, Ltd.