Polyethylene/n-pentane/carbon dioxide ternary systems have been modelled using the Sanchez-Lacombe lattice-fluid model. Phase diagrams have been generated at pressures up to 300 MPa and temperatures up to 460 K. The results show that the system may display two-phase or three-phase equilibrium depending upon the pressure. At a given temperature, the three-phase regions disappear with increasing pressure. Depending upon the pressure, calculations also predict the experimentally observed shifts from lower critical solution temperature to upper critical solution temperature type behaviours, which are illustrated in the ternary diagrams as shifts in the phase boundaries with temperature. It is further shown that for high-molecular-weight polymer samples the ternary calculations can be simplified by assuming that the polymer-lean phase is essentially free of polymer.