The safety of high pressure pipelines is nowadays routinely analysed using simple integral models to predict the nature of a release following a possible breach. Where two-phase flow may result, models making the assumption of homogeneous equilibrium between liquid and gas phases have been used successfully. In the case of a pipeline carrying carbon dioxide, however, solidification of a significant amount of the gas (owing to its high triple point pressure) is a distinct possibility, necessitating consideration of gas, liquid, and solid phases. This paper shows how integral models of two-phase flow can be generalised to accommodate the solid phase, and investigates some of the details of the flow where the triple point pressure occurs and partial solidification begins. It is shown that two-phase homogeneous equilibrium flow models may be generalised straightforwardly to cover the case of carbon dioxide, and some features are seen to emerge independently of more detailed flow modelling considerations. Crown Copyright (c) 2011 Published by Elsevier Ltd. All rights reserved.