22
Assuming spherical shape, valid for smaller dead oil droplets, the droplet terminal
velocity can be calculated as
v
gd
T =
2
18
∆ρ
η
(2.9)
where Δρ is the density difference between the oil and water, d is the particle diameter, and η is the of water dynamic viscosity. One consequence is that a spherical
droplet with twice the diameter would rise at four times the speed. Larger, nonspherical droplet rise can be estimated by similar empirical equations (Clift et al.
1978; Zheng and Yapa 2000). Whether the droplet reaches the surface or weathers
subsurface because of slow rise velocity depends critically on its initial size.
Calculating droplet size distribution is a challenging task. Hinze (1955) claimed
droplet breakup occurred due to two exclusive processes, laminar breakup and turbulent breakup. Laminar breakup occurs due to shear in the water phase. This tends
to twist and elongate the droplet until it breaks, usually into more or less equal size
droplets. Laminar breakup has been well studied in the literature, and the governing
equations in certain circumstances have closed solutions (Taylor 1934). Turbulent
breakup conversely occurs due to pressure variation within the droplet overcoming
a binding force. If the oil has a low viscosity, surface tension would be the dominant
force holding the droplet together, and the droplet breaks when the Weber number
exceeds a critical value. The droplet tends to burst and to generate daughter droplets
of non-equal sizes. If the oil has a high viscosity, shear forces within the droplet tend
to be the forces that resists breakup.
Currently, the research community is divided on the best technique for estimating droplet size distribution (Nissanka and Yapa 2018). One school of thought (Zhao
et al. 2014; Bandara and Yapa 2011) believes the best way is to begin with first
principles and dynamically determine size distribution by including transient populations in the calculation. These populations may further break up due to turbulence
but are resisted by interfacial tension and viscosity. They may also coalesce as some
droplets combine during the process. The results often show an initial bimodal
droplet distribution that evolves over time to a lognormal distribution. An alternative school of thought begins with the lognormal or similar distribution, fitting the
necessary model parameters using modified versions of Reynolds, Weber, and/or
other engineering numbers (Johansen et al. 2013).
Both of the new approaches consider the impact of reduced surface tension on
reducing mean droplet size, something not considered by classical methods
(Delvigne and Sweeney 1988). During DWH, surfactants were injected directly into
the outgoing plume in large amounts, and at least some evidence indicates that it
resulted in reduced surface oil expression due to a reduction in mean droplet size
(Zhao et al. 2014, 2015). However, turbulence was quite high in the exiting oil jet,
and some researchers claim that large energy dissipation at the release point was a
major influence on creating smaller droplets that would have occurred even without
massive surfactant use (Paris et al. 2012).
W. Lehr and S. A. Socolofsky
Assuming spherical shape, valid for smaller dead oil droplets, the droplet terminal
velocity can be calculated as
v
gd
T =
2
18
∆ρ
η
(2.9)
where Δρ is the density difference between the oil and water, d is the particle diameter, and η is the of water dynamic viscosity. One consequence is that a spherical
droplet with twice the diameter would rise at four times the speed. Larger, nonspherical droplet rise can be estimated by similar empirical equations (Clift et al.
1978; Zheng and Yapa 2000). Whether the droplet reaches the surface or weathers
subsurface because of slow rise velocity depends critically on its initial size.
Calculating droplet size distribution is a challenging task. Hinze (1955) claimed
droplet breakup occurred due to two exclusive processes, laminar breakup and turbulent breakup. Laminar breakup occurs due to shear in the water phase. This tends
to twist and elongate the droplet until it breaks, usually into more or less equal size
droplets. Laminar breakup has been well studied in the literature, and the governing
equations in certain circumstances have closed solutions (Taylor 1934). Turbulent
breakup conversely occurs due to pressure variation within the droplet overcoming
a binding force. If the oil has a low viscosity, surface tension would be the dominant
force holding the droplet together, and the droplet breaks when the Weber number
exceeds a critical value. The droplet tends to burst and to generate daughter droplets
of non-equal sizes. If the oil has a high viscosity, shear forces within the droplet tend
to be the forces that resists breakup.
Currently, the research community is divided on the best technique for estimating droplet size distribution (Nissanka and Yapa 2018). One school of thought (Zhao
et al. 2014; Bandara and Yapa 2011) believes the best way is to begin with first
principles and dynamically determine size distribution by including transient populations in the calculation. These populations may further break up due to turbulence
but are resisted by interfacial tension and viscosity. They may also coalesce as some
droplets combine during the process. The results often show an initial bimodal
droplet distribution that evolves over time to a lognormal distribution. An alternative school of thought begins with the lognormal or similar distribution, fitting the
necessary model parameters using modified versions of Reynolds, Weber, and/or
other engineering numbers (Johansen et al. 2013).
Both of the new approaches consider the impact of reduced surface tension on
reducing mean droplet size, something not considered by classical methods
(Delvigne and Sweeney 1988). During DWH, surfactants were injected directly into
the outgoing plume in large amounts, and at least some evidence indicates that it
resulted in reduced surface oil expression due to a reduction in mean droplet size
(Zhao et al. 2014, 2015). However, turbulence was quite high in the exiting oil jet,
and some researchers claim that large energy dissipation at the release point was a
major influence on creating smaller droplets that would have occurred even without
massive surfactant use (Paris et al. 2012).
W. Lehr and S. A. Socolofsky