Bajaj Allianz Life Insurance Company - Insurer Innovation Award 2024
Deepwater modeling
1. Vertical movement of dispersed oil from the
Deepwater Horizon spill, Gulf of Mexico
Rachel Beavins
AP Photo
2. Motivation
NOAA, 2010Revised: 16% chemically dispersed
Hopkinson et al, 2010
Where did the dispersed oil go?
• When will it surface (if ever)?
• How long will it take for microbes to consume it?
4. Hindered Ascent
http://www.filtration-and-separation.com/thickener/sld005.htm
Critical concentration
m ~ 5 (Richardson and Zaki, 1954)
Particle size
Stokes' ascent
(m/s)
Time to
surface
Hindered
ascent (m/s)
Time to
surface
100 µm 0.0018 9.61 days 2.0968 x 10-4 2.76 months
50 µm 4.5177 x 10-4 38.43 days 5.2419 x 10-5 11.04 months
10 µm 1.81 x 10-5 2.67 years 2.0968 x 10-6 23 years
w =
−2R2
g(ρd − ρs )
9µ
(1−
c
cs
)m
5. Viscosity Effects
Quantified how high concentration of small spheres
affect the viscosity of the solution:
Concentration of small spheres
Particle
size
Hindered
ascent (m/s)
Time to
surface
Velocity (m/s)
5% by volume
Time to
surface
Velocity (m/s)
10% by
volume
Time to
surface
100 µm 2.0968 x 10-4 2.76 months 1.86 x 10-4 3.12 months 1.67 x 10-4 3.45 months
50 µm 5.2419 x 10-5 11.04 months 4.66 x 10-5 12.42 months 4.19 x 10-5 13.8 months
μ solution = μ solvent (1+2.5Φ)
w =
−2R2
g(ρd − ρs )
9[µ(1+ 2.5φ)]
(1−
c
cs
)m
6. Biodegradation
Hazen et al 2010
Aim: Find equation for z(t) given that z(R(t))
1. Find dR/dt
2. Use ws (dz/dt) and dR/dt to find z(t)
dm
dt
=
dm
dR
×
dR
dt
dR
dt
=
dm dt
dm dR
m = 4
3
πρd R3 dm
dR
= 4πρd R2
dm
dt
= f (R,ρd ,b)
dm
dt
= R2
b
dR
dt
= −
R2
b
4ρd πR2
= −
b
4ρd π
7. BiodegradationAim: Find equation for z(t) given that z(R(t))
1. Find dR/dt
2. Use ws (dz/dt) and dR/dt to find z(t)
Integrate dR/dt: Substitute R into above:
Integrate twice:
R = −
b
4ρd π
+ R0
d2
z
dt2
= A− Bt
z = At2
− 1
6
Bt3
+ ws0
t + z0
8. Model results
Biodegradation Rate (kg m-2 s-1 )
100 μm
Total consumption time Position above ocean floor (m) Time to surface
5.74 x 10-10 61.5 years surface 9.61 days
5.74 x 10-9 6.15 years surface 9.65 days
5.74 x 10-8 7.38 months surface 10.05 days
5.98 x 10-7 21.26 days 1106 n/a
Biodegradation Rate (kg m-2 s-1 )
50 μm
Total consumption time Position above ocean floor (m) Time to surface
5.74 x 10-10 30.76 years surface 38.55 days
5.74 x 10-9 3.08 years surface 39.84 days
5.74 x 10-8 3.69 months 1441 n/a
5.98 x 10-7 10.63 days 138.3 n/a
Biodegradation Rate (kg m-2 s-
1 )
10 μm
Total consumption time Position above ocean floor (m) Time to surface
5.74 x 10-10 6.15 years 1153 n/a
5.74 x 10-9 7.38 months 115.3 n/a
5.74 x 10-8 22.15 days 11.53 n/a
5.98 x 10-7 2.13 days 1.12 n/a
9. Implications
• Large particles biodegrade slowly and surface quickly
• Small particles biodegrade quickly and mostly remain in
the fluid column
• Many factors will contribute to the ultimate fate of the oil
• Oil will likely persist for months, if not years
5.74 x 10-8 (kg m-2 s-1 ) 5.74 x 10-9 (kg m-2 s-1 )
Joye 2010
10. Questions?
AP Photo
References
Atlas, R.M. (1981), Microbial degradation of petroleum hydrocarbons: an environmental perspective, Microbiological Reviews, 45,
180-209.
Bartha, R. (1986), Biotechnology of petroleum pollutant biodegradation, Microb. Ecol., 12, 155-172.
Einstein, A. (1911), A new determination of molecular dimensions, Annals of Physics, 19, 289-306.
Hopkinson, C., Brandes, J., Joye, S., Lee, R., and M. Sun., 2010, Outcome/guidance form Georgia Sea Grant Program: current status
of BP oil spill, Georgia Sea Grant.
Joye, S. (2010), Gulf oil blog, University of Georgia, September 5.
Lubchenco, J., McNutt, M., Lehr, B., Sogge, M., Miller, M., Hammond, S., and W. Conner (2010), Deepwater Horizon/BP oil budget:
what happened to the oil?, NOAA.
Richardson, J.F., and Zaki, W.N. (1954), Sedimentation and fluidisation: Part I, Trans. Inst. Chem. Eng., 32, 35-53.
