This thesis describes the fundamental extension, development and testing of a
mathematical model for predicting the transient outflow following the failure of
pressurised pipelines. The above encompasses improvements to the theoretical basis and
numerical stability, reduction in the computational runtime and the modelling of
fracture propagation with particular reference to CO2 pipelines.
The basic model utilises the homogeneous equilibrium model (HEM), where the
constituent phases in two-phase mixtures are assumed to be in thermodynamic and
mechanical equilibrium. The resultant system of conservation equations are solved
numerically using the Method of Characteristics (MOC) coupled with a suitable
Equation of State to account for multi-component hydrocarbon mixtures.
The first part of the study involves the implementation of the Finite Volume Method
(FVM) as an alternative to the MOC. In the case of gas and two-phase hydrocarbon
pipeline ruptures, both models are found to be in excellent accord producing good
agreement with the published field data. As compared to the MOC, the FVM shows
considerable promise given its significantly shorter computation runtime and its ability
to handle non-equilibrium or heterogeneous flows.
The development, testing and validation of a Dynamic Boundary Fracture Model
(DBFM) coupling the fluid decompression model with a widely used fracture model
based on the Drop Weight Tear Test technique is presented next. The application of the
DBFM to an hypothetical but realistic CO2 pipeline reveals the profound impacts of the
line temperature and types of impurities present in the CO2 stream on the pipeline’s
propensity to fracture propagation. It is found that the pure CO2 and the postcombustion
pipelines exhibit very similar and highly temperature dependent propensity
to fracture propagation. An increase in the line temperature from 20 – 30 oC results in
the transition from a relatively short to a long running propagating facture. The situation
becomes progressively worse in moving from the pre-combustion to the oxy-fuel stream. In the latter case, long running ductile fractures are observed at all the
temperatures under consideration. All of the above findings are successfully explained
by examining the fluid depressurisation trajectories during fracture propagation relative
to the phase equilibrium envelopes.
Finally, two of the main shortcomings associated with previous work in the modelling
of pipeline ruptures are addressed. The first deals with the inability of Oke’s (2004)
steady state model to handle non-isothermal flow conditions prior to rupture by
accounting for both heat transfer and friction. The second removes the rupture plane
instabilities encountered in Atti’s (2006) model when simulating outflow following the
rupture of ultra high pressure pipelines. Excellent agreement between the new nonisothermal
model predictions and the published data for real pipelines is observed