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tion model (VDROP-J), DB_VDROPJ_untreated and DB_VDROPJ_treated.
VDROP-J predicts initial stabilized size distribution for the droplets and gas bubbles
(Zhao et al. 2014). We used the DSD for the liquid droplets as reported in Gros et al.
(2017), with the range of droplets of 1–8000 m for the untreated oil and 1–2400 m
for the SSDI-treated oil. It has been discussed, however, in Sect. 11.2 that the DSD
from the diving observations during the DWH incident indicated a maximum droplet size of approximately 400 μm. Nevertheless, we included these options of larger
droplets predicted by the jet-droplet formation model VDROP-J to allow model
validation and comparison of corresponding far-field modeling results against those
done with more conservative DSD estimates.
11.3.3 Model Output and Post-processing Variables
The CMS model output consists of trajectory files that contain the following variables at a specified output frequency (2 hours) for each released droplet: droplet
horizontal (latitude, longitude) and vertical (depth) location, its average density and
average droplet diameter, and whether the droplet is still suspended in a water column. Averaging is done across multiple fractions within each droplet. The postprocessing algorithm outlined below translates these output variables into oil
concentrations or oil mass in each grid box of a 3D output grid. To compute the
sedimented oil mass, only particles that have been landed (no longer transported by
the flow) are accounted for. These oil mass or oil concentrations could be used for
the quantitative analysis and model verification.
An estimated 4.9 million of stock tank barrels or about 730,000 tons of gas and
oil mixture were spilled into the GoM during the 87-day period of relief efforts
(McNutt et al. 2012b; Griffiths 2012). A total of 3.132 million droplets are released
by the CMS model during the 87 days of the simulated DWH incident, which need
to represent the total amount of crude oil that spilled into the water from the oil well.
To conserve the oil mass balance of the total spilled oil, the droplet mass is scaled
up to obtain a representative amount of oil for each droplet.
The CMS model generates a uniform DSD at the droplet release time. Droplet oil
mass, m, is computed as m = (π/6)ρd
3
, where π=3.14, ρ is the droplet average density, and d is the droplet diameter. If the probability density function (PDF) of a
continuous random variable d, P(d), is known on a range of diameters d min to d max ,
then the PDF of the oil mass, P(m), could be determined by employing a change-ofvariable technique for a random variable (Pishro-Nik 2014). Knowing the oil flow
rate and the number of released droplets, we could further use the P(m) to determine
a fraction of oil that each droplet needs to represent to achieve the mass balance;
under a uniform DSD assumption, this amounts to 233 kg for each released droplet
regardless of its size.
These values differ for the DSD corresponding to the untreated oil and for the
treated oil (Sect. 11.3.1), and we assume the droplets in the same bin represent similar mass of oil per droplet. Furthermore, while the size and mass of released droplets
N. Perlin et al.
tion model (VDROP-J), DB_VDROPJ_untreated and DB_VDROPJ_treated.
VDROP-J predicts initial stabilized size distribution for the droplets and gas bubbles
(Zhao et al. 2014). We used the DSD for the liquid droplets as reported in Gros et al.
(2017), with the range of droplets of 1–8000 m for the untreated oil and 1–2400 m
for the SSDI-treated oil. It has been discussed, however, in Sect. 11.2 that the DSD
from the diving observations during the DWH incident indicated a maximum droplet size of approximately 400 μm. Nevertheless, we included these options of larger
droplets predicted by the jet-droplet formation model VDROP-J to allow model
validation and comparison of corresponding far-field modeling results against those
done with more conservative DSD estimates.
11.3.3 Model Output and Post-processing Variables
The CMS model output consists of trajectory files that contain the following variables at a specified output frequency (2 hours) for each released droplet: droplet
horizontal (latitude, longitude) and vertical (depth) location, its average density and
average droplet diameter, and whether the droplet is still suspended in a water column. Averaging is done across multiple fractions within each droplet. The postprocessing algorithm outlined below translates these output variables into oil
concentrations or oil mass in each grid box of a 3D output grid. To compute the
sedimented oil mass, only particles that have been landed (no longer transported by
the flow) are accounted for. These oil mass or oil concentrations could be used for
the quantitative analysis and model verification.
An estimated 4.9 million of stock tank barrels or about 730,000 tons of gas and
oil mixture were spilled into the GoM during the 87-day period of relief efforts
(McNutt et al. 2012b; Griffiths 2012). A total of 3.132 million droplets are released
by the CMS model during the 87 days of the simulated DWH incident, which need
to represent the total amount of crude oil that spilled into the water from the oil well.
To conserve the oil mass balance of the total spilled oil, the droplet mass is scaled
up to obtain a representative amount of oil for each droplet.
The CMS model generates a uniform DSD at the droplet release time. Droplet oil
mass, m, is computed as m = (π/6)ρd
3
, where π=3.14, ρ is the droplet average density, and d is the droplet diameter. If the probability density function (PDF) of a
continuous random variable d, P(d), is known on a range of diameters d min to d max ,
then the PDF of the oil mass, P(m), could be determined by employing a change-ofvariable technique for a random variable (Pishro-Nik 2014). Knowing the oil flow
rate and the number of released droplets, we could further use the P(m) to determine
a fraction of oil that each droplet needs to represent to achieve the mass balance;
under a uniform DSD assumption, this amounts to 233 kg for each released droplet
regardless of its size.
These values differ for the DSD corresponding to the untreated oil and for the
treated oil (Sect. 11.3.1), and we assume the droplets in the same bin represent similar mass of oil per droplet. Furthermore, while the size and mass of released droplets
N. Perlin et al.