Vertical movement of dispersed oil from the Deepwater Horizon spill, Gulf of Mexico

Rachel BeavinsAP Photo

Motivation

NOAA, 2010Revised: 16% chemically dispersed

Hopkinson et al, 2010Where did the dispersed oil go?• When will it surface (if ever)?• How long will it take for microbes to consume it?

Stokes’ AscentStokes’ settling

ws

(velocity upward, drag downward)

Stokes’ ascent

ws

Fd , Fg

Newton’s 2nd Law

Archimedes’ Principle

Stokes’ Law

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 mm 0.0018 9.61 days 2.0968 x 10-4 2.76 months

50 mm 4.5177 x 10-4 38.43 days 5.2419 x 10-5 11.04 months

10 mm 1.81 x 10-5 2.67 years 2.0968 x 10-6 23 years

Viscosity EffectsQuantified 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 mm 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 mm 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)

Biodegradation

Hazen et al 2010

Aim: Find equation for z(t) given that z(R(t))1. Find dR/dt2. Use ws (dz/dt) and dR/dt to find z(t)

BiodegradationAim: Find equation for z(t) given that z(R(t))1. Find dR/dt2. Use ws (dz/dt) and dR/dt to find z(t)

Integrate dR/dt: Substitute R into above:

Integrate twice:

Model resultsBiodegradation 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 days5.74 x 10-9 6.15 years surface 9.65 days5.74 x 10-8 7.38 months surface 10.05 days5.98 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 days5.74 x 10-9 3.08 years surface 39.84 days5.74 x 10-8 3.69 months 1441 n/a5.98 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/a5.74 x 10-9 7.38 months 115.3 n/a5.74 x 10-8 22.15 days 11.53 n/a5.98 x 10-7 2.13 days 1.12 n/a

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

Questions?

AP Photo

ReferencesAtlas, 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.