43 The models mentioned until now were developed with assumptions including one-dimensional, friction, isentropic, and homogeneous equilibrium, or non-equilibrium fluid flow. But it is possible, though very rare, to use the CFD technique to simulate the process in a pipe following failures of a CO2 pipeline, to describe the influences of non-isentropic on the decompressed CO2 pipeline.
In view of this, Elshahomi et al. (2015) [32] used the package ANSYS-Fluent (CFD model) to develop the gCCS decompression model for the depressurization process of a CO2 mixture flow in a broken pipeline. The gCCS model can solve the transient flows with an accurate EoS through user-defined functions (UDFs) and in three-dimensional geometries.
Particularly, this model can perform well the pressure and temperature drops as well as the transient phase during depressurization in the pipe. The model can also predict the curves of decompression wave speed in CO2 mixtures, which can be used to estimate fracture propagation in the pipelines [5].
44 5.2.2 Orientation of the release
Another important feature of the release is its orientation, especially in the near-field, i.e. x<100 m. The direction of the jet relative to the horizontal is an important modelling variable, influencing how the release develops after its expansion at ambient pressure.
Furthermore, recent experimental and modelling methods have indicated that the phase change of CO2 is relevant only for the near-field, while it is negligible at ground level when the downwind distance exceeds 100 m [21].
[1] Upward Leak
Figure 23. Upward loss of CO2 from a pressurized vessel.
During an upward release, the CO2 decompresses rapidly, leading to the formation of dry-ice particles and the subsequent condensation of the water from the entrainment air due to the lowering of the temperature, giving a characteristic white colour as can be seen from the figure above. The jet that comes out quickly heats up due to the friction with the surrounding air, giving enough energy to sublimate all the dry-ice particles into gas and avoiding the formation of a CO2 dry-ice bank on the ground [45].
[2] Downward Leak
For an above-ground pipeline, the leak can be downward-directed. As the jet imposes on the ground, a CO2 dry ice bank is formed, as illustrated in Figure 24, in the case of a vertical downward release from a pressurized vessel. After the spill, dry ice can sublimate, but given the low sublimation rate of gaseous CO2, around 2.5 gm-2s-1, this does not present a risk to surrounding people, unless wind speeds are too low [33].
45
Figure 24. a) The downward release of CO2 from the high-pressure vessel with the consequent formation of a dry-ice bank; b) The low concentrations of the gas in the air following the subsequent sublimation of solid CO2 from the bank surface during 14 days in
June [33].
[3] Horizontal Leak
The worst-case for the surrounding people to consider is that of a horizontal CO2 leak. In this case, if there is a release, for example from a pressurized vessel or even from a pipeline, the cloud will develop primarily horizontally, posing a very high risk for the surrounding area. The amount of CO2 present in the cloud can also vary, as the dry ice particles present could exit the cloud and fall to the ground, generating a new small source of CO2. However, given the difficulty in defining how much dry ice separates, conservatively it is usually assumed that this phenomenon does not occur, in this way the CO2 cloud will have a greater concentration [45].
The solid fraction of CO2 present in the horizontal jet affects its dispersion, leading to higher maximum concentrations near the source. Furthermore, the smaller the vapour fraction the larger the CO2 cloud itself and the further the cloud is propagated into a downwind direction. This can be explained by the effect given by gravity, as the density of the cloud increases as the solid mass fraction increases [46].
5.2.3 Solid CO2 particle snow-out (rain-out) and sublimation
In particular cases as downward release, the solid CO2 particles formed in the jet will rain out forming a dry ice bank on the ground, which will subsequently sublimate, and a consequent vapour cloud will be formed that disperses. The driving force for the sublimation of the dry ice is the heat transport from the subsoil, solar radiation and the wind blowing over the dry ice bank.
The rainout of solid CO2 particles was confirmed in a small-scale release test from the Sutton-Bonington Campus at the University of Nottingham [33]. In this study, a test was performed with the release of liquid CO2 from a supply tank with initial conditions of -15 °C and 2.3 MPa through a downward pointing drain valve, as shown in Figure 24 above. Mazzoldi et al. [33] developed a mathematical model to account for the sublimation rate of a dry ice bank formed from this downward vertical release of liquid CO2. The model describes the energy balance at the surface of dry ice bank on the ground, including short-wave radiation flux, long-wave radiation flux, sensible and latent heat flux, and heat flux from the ground. The simulation results of the sublimation rate were not validated against the experimental data.
46 In another study [34] a model for the analytical study of thermal and fluid-dynamic behaviour of a dry ice particle falling to the ground is presented. The model, based on the numerical solution of the equations of motion, the equation of convective mass and heat transfer, describes the kinematic and thermal mechanism affecting a dry ice particle generated in a pressurized release of carbon dioxide starting from the post-expansion conditions.
This analytical model proves that the effects related to solar radiation and relative humidity are negligible, in other words, they don’t affect considerably the quick process of sublimation of dry ice particles. Also, the ambient temperature has not an important role in the behaviour of thermal and fluid dynamics since the phenomena involved are extremely fast. On the contrary, the particle size and the air friction, related to the particle velocity, are not negligible when assessing flight particle sublimation. It was verified that, under Italian average weather conditions, the threshold particle diameter that discriminates a deposition on the ground coincides respectively with 150 μm in the case of slanting downwards releases, 120 μm for direct downwards releases and 650 - 700 μm for horizontal releases. So, these variables, in addition to the direction of the release and the local wind flow field, can discern the event of soil deposition of dry ice from releases with only atmospheric dispersion.
In experiments to study the two-phase flow of solid and vapour CO2 large-scale releases conducted from COOLTRANS research programme, CO2PipeHaz project and CO2PIPETRANS project, the rain out of the solid CO2 particles was not observed.
Also, in an experiment conducted by the COSHER Joint Industry Project, it was observed that, after a rupture of an underground pipeline, no dry ice bank was formed under those experimental conditions. As shown in the figure below, the break however caused a crater, with very cold stones, covered with a white thin coating that melts to water [5].
Figure 25. Photo of the crater and a broken pipe in the COSHER [5].
5.2.4 The momentum of the release
The momentum of the CO2 release is also an important factor to consider. A high-velocity jet will entrain ambient air more rapidly and thus may lead to different dispersion behaviour than a slow release.
One direct effect of the release speed is the shorter downwind distance reached by dangerous concentrations of the gas if compared with undisturbed releases, due to the high initial dispersion (jet-mixing effect). This means that in some cases, a consideration of a low momentum of the release may result in an excessive conservative assumption [44].
47 In particular, the cases, for high-pressure leakage, where a low momentum release could be expected are the following:
- horizontal releases from buried pipelines: these are expected to result in low momentum releases after impinging surrounding walls;
- a complete line rupture (guillotine-type failure): opposing releases are assumed to exert sufficient pressure upon one another to reduce significantly their momentum;
- presence of obstacles in front of the leak (e.g., buildings, trees), impingement releases;
- extremely quick sublimation of solid CO2 formed after a downward leakage [44].
In the case of small releases with low momentum and large releases with high momentum, it is necessary to consider the different effects that the wind speed causes.
- For small releases with low momentum, a high wind speed favours dispersion, as it improves mixing and transport.
- For large horizontal releases with high momentum, the wind pushes the cloud even further downstream, which is initially accumulated on the ground and dominated by the source moment, increasing the distances reached as the wind speed increases. In this case, the effect of the wind speed on the dispersion is limited, as it is much lower than the discharge speed [61].
5.2.5 Conservative release assumptions
Considering a conservative assumption, “worst-case scenario”, like a full-bore rupture, it is possible to simplify the model by adopting the maximum discharge rate, instead of the time-varying flow rate, underlining that in the quantitative risk assessment it is always necessary to consider the frequency of occurrence of a certain event.
In general, when modelling the release from the long CO2 pipelines is possible to approximate (in a suitable modelling software package) the discharge rate as a function of time with the average release rate over 20 seconds. Also, this assumption gives a conservative set of results. To be more precise and less conservative, a time-varying method has to be adopted, in case of a rapid variation in the CO2 flow rate [10].
Further conservative assumptions can be made by considering as a scenario the CO2 release by a full-bore horizontal rupture at ground level on flat terrain and with no solid formation on the ground.
Moreover, we have to highlight that in the reference [55] it was discovered that the consequence distances predicted in the case of a full-bore rupture assuming horizontal release are far from conservative if compared with a vertical release due to a full-scale pipeline fracture. This may be due to the lower release rate from a full-bore rupture compared to the explosive release rate due to a full-scale fracture, hence a study is necessary in order to control fracture propagation in high-pressure pipelines.