The present paper aims to enhance the awareness of users of thermodynamic models on the impact that their accuracy may have in designing and operating units for the purification and compression of CO2-streams produced from capture technologies. After providing a review on the composition of streams produced by coal- or gas-fired plants with post-/pre-/oxy-combustion CO2 capture, coupled with different purification technologies, the paper quantifies the influence of equations of state accuracy in designing and operating CO2 purification and compression units. A comparison is made between the results obtained from the cubic Peng-Robinson model combined with either classical vdWlf (van der Waals one fluid) mixing rules (i.e. the standard Peng-Robinson equation of state) or with recently optimized advanced mixing rules incorporating residual-excess-Helmholtz-energy (a(res)(E,gamma)) models (EoS/a(res)(E,gamma) mixing rules). In detail, EoS/a(res)(E,gamma) mixing rules combine the residual contribution of the Wilson a(E,gamma) model and the formulation proposed by Lorentz, for the mixture co-volume term. It is shown that the improved accuracy of "PR + EoS/a(res)(E,gamma) mixing rules" in the representation of vapour-liquid equilibrium properties of CCS mixtures, with respect to the standard PR EoS, may lead to the design of a halved-height stripping column for the reduction of the oxygen content in the captured CO2 stream. Moreover, the paper shows the effect of the applied thermodynamic model on the definition of the pressurization level of the captured fluid and on the computed power required for its compression.