55
experiments are performed between 10
−2
and 10
2
m
2
s
−3
, while most data from
pilot-scale jets corresponds to TDRs between 10
3
and 10
5
m
2
s
−3
.
The DWH jet was also influenced by a partially closed annular preventer, which
closely resembles a classical orifice and imposed an 84-bar pressure drop within a
few diameters of the exit point. This contribution of this orifice drop to the TDR has
largely been neglected to date. Kundu et al. (2016) provide a well-established
relation from fluid mechanics to estimate TDR contribution from a restricted
pressure drop:
ε
ρ
pd
c
Q
V
=
⋅
⋅
∆p
(4.10)
where ∆p is the permanent pressure drop applied by the restriction, Q is the volumetric flowrate through the restriction, ρ c is the continuous phase density and V is
the volume of energy dissipation (e.g. the volume of the BOP stack). With an 84-bar
pressure drop, an average fluid density of 700 kg/m
3
and a 2 m height of the BOP
stack with a 0.5 m internal diameter, this orifice contribution to TDR is estimated at
2700 m
2
s
−3
.
The third contribution above – from live oil degassing – has not been studied in
sufficient detail to quantitatively inform contributions to TDR. However, the first
two contributions identified above demonstrate the elegant rationale as to why
Weber- and Reynolds-based scaling arguments have failed to unify the available
data: such approaches severely underrepresent the turbulence of the Macondo
plume, because they only account for the first of two important contributions. That
is, the TDR contribution from the orifice pressure drop aligns well with the magnitude of TDRs captured at high mixing speed in autoclaves or in most pilot-scale jet
experiments. Importantly, neither Weber- nor Reynolds-based methods are able to
capture the additional TDR contributions from the orifice pressure drop, resulting in
the discrepancy of predicted droplet sizes heretofore.
4.4 Effects of Deep-Sea Blowout Characteristics
In case of a large-scale, deep-sea oil discharge from an uncontrolled well, several
factors must be considered in addition to the modelling approaches presented in
Sect. 4.3. These are mainly:
• Gaseous components (C 1 -C 5 , N 2 , CO 2 , H 2 S) dissolved in the crude oil (“live”
instead of “dead” oil).
• A multiphase flow (oil, gas, water) inside the borehole and at the wellhead.
• High hydrostatic pressure and low temperature of the surrounding seawater.
• Rapid pressure and temperature changes at the wellhead, inducing phase changes
in the oil.
4 Jet Formation at the Spill Site and Resulting Droplet Size Distributions
experiments are performed between 10
−2
and 10
2
m
2
s
−3
, while most data from
pilot-scale jets corresponds to TDRs between 10
3
and 10
5
m
2
s
−3
.
The DWH jet was also influenced by a partially closed annular preventer, which
closely resembles a classical orifice and imposed an 84-bar pressure drop within a
few diameters of the exit point. This contribution of this orifice drop to the TDR has
largely been neglected to date. Kundu et al. (2016) provide a well-established
relation from fluid mechanics to estimate TDR contribution from a restricted
pressure drop:
ε
ρ
pd
c
Q
V
=
⋅
⋅
∆p
(4.10)
where ∆p is the permanent pressure drop applied by the restriction, Q is the volumetric flowrate through the restriction, ρ c is the continuous phase density and V is
the volume of energy dissipation (e.g. the volume of the BOP stack). With an 84-bar
pressure drop, an average fluid density of 700 kg/m
3
and a 2 m height of the BOP
stack with a 0.5 m internal diameter, this orifice contribution to TDR is estimated at
2700 m
2
s
−3
.
The third contribution above – from live oil degassing – has not been studied in
sufficient detail to quantitatively inform contributions to TDR. However, the first
two contributions identified above demonstrate the elegant rationale as to why
Weber- and Reynolds-based scaling arguments have failed to unify the available
data: such approaches severely underrepresent the turbulence of the Macondo
plume, because they only account for the first of two important contributions. That
is, the TDR contribution from the orifice pressure drop aligns well with the magnitude of TDRs captured at high mixing speed in autoclaves or in most pilot-scale jet
experiments. Importantly, neither Weber- nor Reynolds-based methods are able to
capture the additional TDR contributions from the orifice pressure drop, resulting in
the discrepancy of predicted droplet sizes heretofore.
4.4 Effects of Deep-Sea Blowout Characteristics
In case of a large-scale, deep-sea oil discharge from an uncontrolled well, several
factors must be considered in addition to the modelling approaches presented in
Sect. 4.3. These are mainly:
• Gaseous components (C 1 -C 5 , N 2 , CO 2 , H 2 S) dissolved in the crude oil (“live”
instead of “dead” oil).
• A multiphase flow (oil, gas, water) inside the borehole and at the wellhead.
• High hydrostatic pressure and low temperature of the surrounding seawater.
• Rapid pressure and temperature changes at the wellhead, inducing phase changes
in the oil.
4 Jet Formation at the Spill Site and Resulting Droplet Size Distributions