54
4.3.3 Novel Applications of Energy Dissipation Metrics
to Understand Droplet Sizes from Experimental Data
To date, the prediction of live oil droplet size distributions has been treated with two
approaches: (i) the use of a modified Weber number scaling, proposed by Johansen
et al. (2013), and (ii) the use of Reynolds number, proposed by Aman et al. (2015).
In both cases, the studies define their respective dimensionless quantities based on
the physical conditions at the contact point of the blowout preventer (BOP) stack
and the seawater; that is, the internal oil pipe diameter was employed as the singular
property to define the length scale of the problem. This understanding clarifies why
both methods have failed to unify the available data: oil droplets are not created at
the exit point of the pipe, but rather in the near-field plume. As such, the research
community must understand and characterize turbulence at the point of droplet creation using a more fundamental basis of turbulence that can incorporate the known
contributions.
One such approach may be derived by evaluating both the turbulent kinetic
energy (TKE) and turbulence dissipation rate (TDR), which, respectively, describe
the energetic content of the eddies in the flow and the rate at which eddies transfer
TKE down the so-called energy cascade. As droplets are generated through the
transfer of TKE, the use of TDR-based scaling provides an attractive opportunity to
compare the available datasets. To this end, models must consider the three relevant
contributions to TDR in the context of a subsea blowout: (i) the momentum of the
gas/oil jet itself, defined between the exit of the pipe and the top of the near-field
plume; (ii) the additional momentum generated inside the BOP stack, where fluids
experienced an 84-bar orifice pressure drop imposed by the annular preventer within
a few diameters of the exit point; and (iii) additional turbulence introduced by the
evolution of free gas from live oil droplets. To date, computational fluid dynamics
(CFD) approaches have been unable to rationalize all three contributions together.
However, the first two contributions may be estimated from experimental laboratory
studies, to estimate the range of probable TDR in the field case.
Zhao et al. (2014) summarized experimental TDR estimates for single-phase jets
(the first contribution above), deriving a correlation as a function of jet exit diameter, velocity and distance into the plume. The study demonstrated that, within 10
diameters of the exit, the TDR remains constant and decreases monotonically thereafter; as such, the maximum TDR corresponding to the jet momentum may be conservatively estimated. This TDR method can be applied to data collected on the
apparatus at SINTEF, SWRI and TUHH (as described above). Through the use of
CFD to map stirred cells, Booth et al. (2018) have further demonstrated the ability
to correlate TDR for autoclave systems employed at the University of Western
Australia. For the range of volumetric flowrates reported in the DWH blowout and
for the relevant range of oil and gas properties, the TDR correlation from Zhao et al.
(2014) suggests a TDR range of between 10
−3
and 10
−5
m
2
s
−3
, which only represents the first contribution identified above. For reference, most autoclave
K. Malone et al.
4.3.3 Novel Applications of Energy Dissipation Metrics
to Understand Droplet Sizes from Experimental Data
To date, the prediction of live oil droplet size distributions has been treated with two
approaches: (i) the use of a modified Weber number scaling, proposed by Johansen
et al. (2013), and (ii) the use of Reynolds number, proposed by Aman et al. (2015).
In both cases, the studies define their respective dimensionless quantities based on
the physical conditions at the contact point of the blowout preventer (BOP) stack
and the seawater; that is, the internal oil pipe diameter was employed as the singular
property to define the length scale of the problem. This understanding clarifies why
both methods have failed to unify the available data: oil droplets are not created at
the exit point of the pipe, but rather in the near-field plume. As such, the research
community must understand and characterize turbulence at the point of droplet creation using a more fundamental basis of turbulence that can incorporate the known
contributions.
One such approach may be derived by evaluating both the turbulent kinetic
energy (TKE) and turbulence dissipation rate (TDR), which, respectively, describe
the energetic content of the eddies in the flow and the rate at which eddies transfer
TKE down the so-called energy cascade. As droplets are generated through the
transfer of TKE, the use of TDR-based scaling provides an attractive opportunity to
compare the available datasets. To this end, models must consider the three relevant
contributions to TDR in the context of a subsea blowout: (i) the momentum of the
gas/oil jet itself, defined between the exit of the pipe and the top of the near-field
plume; (ii) the additional momentum generated inside the BOP stack, where fluids
experienced an 84-bar orifice pressure drop imposed by the annular preventer within
a few diameters of the exit point; and (iii) additional turbulence introduced by the
evolution of free gas from live oil droplets. To date, computational fluid dynamics
(CFD) approaches have been unable to rationalize all three contributions together.
However, the first two contributions may be estimated from experimental laboratory
studies, to estimate the range of probable TDR in the field case.
Zhao et al. (2014) summarized experimental TDR estimates for single-phase jets
(the first contribution above), deriving a correlation as a function of jet exit diameter, velocity and distance into the plume. The study demonstrated that, within 10
diameters of the exit, the TDR remains constant and decreases monotonically thereafter; as such, the maximum TDR corresponding to the jet momentum may be conservatively estimated. This TDR method can be applied to data collected on the
apparatus at SINTEF, SWRI and TUHH (as described above). Through the use of
CFD to map stirred cells, Booth et al. (2018) have further demonstrated the ability
to correlate TDR for autoclave systems employed at the University of Western
Australia. For the range of volumetric flowrates reported in the DWH blowout and
for the relevant range of oil and gas properties, the TDR correlation from Zhao et al.
(2014) suggests a TDR range of between 10
−3
and 10
−5
m
2
s
−3
, which only represents the first contribution identified above. For reference, most autoclave
K. Malone et al.