In this work, viscosity measurements of the ternary mixture [0.6511CH(4) + 0.0808C(3)H(8) + 0.2681CO(2)] were made over the temperature range (203-420) K and at pressures up to 31 MPa, with a combined overall standard uncertainty of 2.5%. The presence of CO2 or propane in the ternary mixture was found to always increase the viscosity relative to the constituent binary mixtures with larger differences observed at the highest density conditions: adding 26.8% mole fraction of CO2 to the binary mixture [xCH(4) + (1-x)C3H8] with x = 0.8888, increased the viscosity by up to 45%. Similarly, adding 8.1% mole fraction of propane to the binary mixture [xCH(4) + (1-x)CO2] with x = 0.7084, increased the viscosity by up to 23%; in this case, while the effect was apparent at lower temperatures, it was negligible at 370 K and above. The ternary mixture data were compared with the predictions of five models: corresponding states based approaches (ECS, SuperTRAPP and PFCT), the LBC model used widely by petroleum engineers, and a model (LJ) based on molecular dynamics simulations of Lennard Jones fluids. The relative deviations of the measured viscosities from those calculated by the five models exhibited a similar, systematic dependence on density, with stronger and larger systematic relative deviations observed at the lowest temperatures. The average absolute deviations from the measured viscosities were 2.5%, 6.4%, 8.0%, 4.2% and 3.9% for the ECS, ST, PFCT, LBC and LJ models respectively, with the ECS model providing a better representation of the data over the entire range. The present study reveals how well various engineering models can describe the viscosity of a multi-component mixture under supercritical conditions, which are of increasing interest in the energy industrial sector.