The group contribution equation of state (GC-EOS) has been used in several published works to correlate or predict the high-pressure phase equilibria of a variety of systems of practical interest. Nevertheless, quantitative and even qualitative disagreement among predictions and experimental data has been detected in mixtures of CO2 with heavy compounds, such as triglycerides, when operating at high pressure. For instance, phase split up to indefinitely high pressures has been computed, when the observed experimental behavior shows full miscibility at sufficiently high pressure. In the present work, we study the influence on calculated critical lines and solubilities (Pxy diagrams) of the group-based interaction parameters k(ij), for the interactions of CO2 with both, the triglyceride (TG) group and the paraffinic groups. Based on such study, we propose a parameterization procedure that improves upon the conventional parameter regression practice. The distinguishing feature of such procedure is the repeated observation of the global phase equilibrium behavior, studying in particular the effect of the group-group interaction parameters on critical lines, on the composition of the phases at equilibrium along liquid-liquid-vapor lines, and on selected isothermal or isobaric phase equilibrium diagrams. For the case of the non-randomness parameter, we use a universal positive value, more consistent with its physical meaning. (C) 2009 Elsevier B.V. All rights reserved.