A model for two-phase carbon dioxide transport with phase transfer in pipelines is presented. The stiffened-gas equation of state is used for calculating thermodynamical properties. The convergence and accuracy of two numerical methods – a centred multi-stage (MUSTA) scheme and an upwind Roe scheme – are compared. Results for the depressurization of a pipe, causing phase change and cooling, are presented, showing the importance of an accurate numerical method. The effect of a discontinuous sound velocity on the depressurization is discussed.