FULL-BORE PIPELINE RUPTURE AS TRANSIENT FANNO' FLOW

摘要

Full-bore decompression of an initially highly pressurized pipe has been studied extensively in recent years. The main aim of this effort has been to estimate the speed of the decompression wave and its relationship to the speed of a travelling fracture in the pipe wall. It has been demonstrated that the speed of the decompression wave is influenced by the friction at the gas-solid interface, and also by the pipe size (diameter). The numerical value of the friction factor has been traditionally estimated using known relationships such as the Haaland formula. However, it has also been noticed that the friction factor calculated in this way has to be increased many-fold to achieve agreement between theory and experiment. To date, there is no physical justification for this increase. The present paper proposes an explanation by modelling the full-bore decompression as a 'transient Fanno' flow. The model development is based on the observation that the flow at the exit plane always tends to approach a 'choked' condition (sonic velocity). It is shown that a re-interpretation of the Fanno flow formula allows an estimation of the irreversibility, and therefore the friction factor, in the evolving flow. When averaged over space and time, the friction factor attains a value that need not be artificially adjusted. This value of the friction factor can be used in one-dimensional models of the decompression process. Also, the role of the 'second coefficient of viscosity' during the initial instants of the highly transient flow is examined.