53
on 28 wave entrainment datasets, whereas r was calculated from the d v50 of the
Norwegian DeepSpill experiment. The model was tested against both laboratory
data and field measurements by a Holocam during the DWH spill (Li et al. 2015).
Both models provide a median volume diameter at very little computational cost.
As input parameters, both require the same information about the physical properties of the oil, oil exit velocity and exit diameter. Especially with regard to the
physical properties of “live” oil under deep-sea conditions (high pressure, low temperature), there are often no measured data, and the properties can only be calculated using empirical correlations (Lake and Fanchi 2006) or numerical models
(Gros et al. 2016). In addition, they have only been validated for “dead oil” in a
limited range of We and Oh and require extrapolation over several orders of magnitude beyond these limits to provide an estimation for a major spill like DWH.
The scaling laws described above only provide a steady-state volume median
diameter and no actual size distribution. However, as the size distribution may
differ widely for different blowout scenarios (Malone et al. 2018), information on
the spreading factor of the underlying distribution factor is of considerable
importance for a realistic near- and far-field modelling (see Vaz et al. 2020; Perlin
et al. 2020).
4.3.2 Mechanistic Modelling
A different approach by Zhao et al. (2014, 2017) uses a hydrodynamic model of the
jet to predict the complete drop size distribution. The Lagrangian model, called
VDROP-J, calculates the DSD of a small portion of the jet based on a population
balance of drop breakup and coalescence in a given time step. A single large drop
size is taken as initial input and tracked downstream while the jet widens and takes
in water, thereby reducing the oil fraction in the considered portion of the jet.
Breakage rate is determined stepwise by the probability of a drop to collide with a
turbulent eddy with sufficient energy to cause breakup of this drop; coalescence
rate is defined by the probability of two drops colliding and coalescing due to
turbulence.
As an outcome, this model provides the full DSD of a jet at different positions
downstream of the orifice, albeit at significant computational cost. Because the
DSD is directly calculated from the discharge conditions without the need for
upscaling by several orders of magnitude, it is less sensitive to miscorrelation of
experimental data than scaling-based models. However, a crucial point in the calculation of the DSD is turbulent dissipation rate in the jet, which can be seriously
affected by reactions and interactions of the multiphase flow of oil, gas, water and
possibly hydrates that are discharged in a major subsea spill like DWH, and which
are not yet fully understood.
4 Jet Formation at the Spill Site and Resulting Droplet Size Distributions
on 28 wave entrainment datasets, whereas r was calculated from the d v50 of the
Norwegian DeepSpill experiment. The model was tested against both laboratory
data and field measurements by a Holocam during the DWH spill (Li et al. 2015).
Both models provide a median volume diameter at very little computational cost.
As input parameters, both require the same information about the physical properties of the oil, oil exit velocity and exit diameter. Especially with regard to the
physical properties of “live” oil under deep-sea conditions (high pressure, low temperature), there are often no measured data, and the properties can only be calculated using empirical correlations (Lake and Fanchi 2006) or numerical models
(Gros et al. 2016). In addition, they have only been validated for “dead oil” in a
limited range of We and Oh and require extrapolation over several orders of magnitude beyond these limits to provide an estimation for a major spill like DWH.
The scaling laws described above only provide a steady-state volume median
diameter and no actual size distribution. However, as the size distribution may
differ widely for different blowout scenarios (Malone et al. 2018), information on
the spreading factor of the underlying distribution factor is of considerable
importance for a realistic near- and far-field modelling (see Vaz et al. 2020; Perlin
et al. 2020).
4.3.2 Mechanistic Modelling
A different approach by Zhao et al. (2014, 2017) uses a hydrodynamic model of the
jet to predict the complete drop size distribution. The Lagrangian model, called
VDROP-J, calculates the DSD of a small portion of the jet based on a population
balance of drop breakup and coalescence in a given time step. A single large drop
size is taken as initial input and tracked downstream while the jet widens and takes
in water, thereby reducing the oil fraction in the considered portion of the jet.
Breakage rate is determined stepwise by the probability of a drop to collide with a
turbulent eddy with sufficient energy to cause breakup of this drop; coalescence
rate is defined by the probability of two drops colliding and coalescing due to
turbulence.
As an outcome, this model provides the full DSD of a jet at different positions
downstream of the orifice, albeit at significant computational cost. Because the
DSD is directly calculated from the discharge conditions without the need for
upscaling by several orders of magnitude, it is less sensitive to miscorrelation of
experimental data than scaling-based models. However, a crucial point in the calculation of the DSD is turbulent dissipation rate in the jet, which can be seriously
affected by reactions and interactions of the multiphase flow of oil, gas, water and
possibly hydrates that are discharged in a major subsea spill like DWH, and which
are not yet fully understood.
4 Jet Formation at the Spill Site and Resulting Droplet Size Distributions