Liquid-liquid equilibrium (LLE) phase behaviors for twenty ternary systems are examined by four lattice-based thermodynamic models, the Flory-Huggins model (F-H), the modified double lattice model (MDL), the modified double lattice model-chain length dependent (MDL-CL) and the Xin model, and compared with experimental data. Ternary systems are composed of simple molecule and polymer solutions, and are described according to Treybal classifications of Type 0, 1, 2 or 3. These types of phase behaviors can be influenced by the nature of the solvent or temperature, and accurate predictions are important in the separation process and to recover residual oils. The interaction energy parameters directly obtained from the LLE binary systems are used to predict the ternary systems. Applicable types of binary phase behavior and adjustable parameters for each model are tabulated. The vapor-liquid equilibrium (VLE) for polymer/solvent systems and the swelling equilibrium of the hydrogel system are described and the same interaction energy parameters from. the LLE binary systems were also used. The MDL-CL and Xin models provide better agreement with experimental data than other models. (C) 2014 Elsevier B.V. All rights reserved.