Jet Formation at the Spill Site and Resulting Droplet Size Distributions

  • Karen MaloneEmail author
  • Zachary M. Aman
  • Simeon Pesch
  • Michael Schlüter
  • Dieter Krause


The size distribution of oil droplets and gas bubbles forming at the exit geometry of a deep-sea blowout is one of the key parameters to understand its propagation and fate in the ocean, whether with regard to rising time to the surface, drift by ocean currents, dissolution or biodegradation. While a large 8 mm droplet might rise to the sea surface within minutes or hours, microdroplets <100 μm may take weeks or months to surface, if at all. On the other hand, a microdroplet or bubble dissolutes faster due to its larger surface to volume ratio and is also more available for biodegrading bacteria. To be able to properly model these effects, it is necessary to understand the drop formation processes near the discharge point and to predict the evolving droplet size distribution (DSD) for the specific conditions.

In this chapter, the general breakup mechanisms and flow regimes of an oil-in-water jet are discussed in Sect. 4.1. Section 4.2 focuses on the different approaches to determine the DSD in the laboratory and field settings and critically reviews the existing datasets. State-of-the-art models for the prediction of the DSD of a subsea oil discharge are presented alongside a new approach based on the turbulent kinetic energy (TKE) in Sect. 4.3, while Sect. 4.4 takes a closer look at the specific effects of the deep sea on the DSD. Based on this, Sect. 4.5 discusses the advantages and limitations of subsea dispersant injection. Section 4.6 provides a summary of the chapter and gives an outlook to unresolved questions.


Jet formation Droplet size distribution Live oil Median drop size Flow regime Turbulent kinetic energy Turbulence Droplet breakup Near-field In situ measurements Dissolved gas Outgassing Phase change Dispersants 




Empirical coefficient in the modified Weber number scaling


Empirical coefficient in the modified Weber number scaling


Cumulative distribution function


Nozzle/discharge diameter


Sauter diameter


Median diameter of number distribution


Drop/particle diameter


Median diameter of volume distribution


Dispersant-to-oil ratio


Drop size distribution


Gauss error function


Exponential function


Interfacial tension


Scaling factor


Oil mass inside the nozzle


Ohnesorge number




Pressure drop at the nozzle


Volume flow rate


Reynolds number


Exit velocity of dispersed liquid phase


Viscosity number


Weber number


Modified Weber number



Spreading factor of the Rosin-Rammler distribution function


Turbulent energy dissipation rate


Turbulent energy dissipation rate caused by the exit velocity


Turbulent energy dissipation rate caused by pressure drop at the nozzle


Dynamic viscosity of dispersed liquid phase


Density of dispersed liquid phase


Density of continuous phase


Spreading factor of the log-normal distribution function


Interfacial tension (IFT) between dispersed liquid phase and continuous phase



This research was made possible by a from the Gulf of Mexico Research Initiative/C-IMAGE. Data are publicly available through the Gulf of Mexico Research Initiative Information and Data Cooperative (GRIIDC) at (DOIs: 10.7266/n7-jjqd-pa77, 10.7266/n7-eha7-tv03, 10.7266/N7V69H19, 10.7266/N77D2SM2).


  1. Adams EE, Socolofsky SA (2004) Review of deep oil spill modeling activity supported by the DeepSpill JIP and offshore operators committee: Final Report. 26 ppGoogle Scholar
  2. Ahmed TH (2010) Reservoir engineering handbook, 4th edn. Gulf Professional, OxfordGoogle Scholar
  3. Aman ZM, Paris CB, May EF, Johns ML, Lindo-Atichati D (2015) High-pressure visual experimental studies of oil-in-water dispersion droplet size. Chem Eng Sci 127:392–400. Scholar
  4. Belore R (2014) Subsea chemical dispersant research. In: Proceedings of the 37th AMOP technical seminar on environmental contamination and response, Canmore, AlbertaGoogle Scholar
  5. Booth CP, Leggoe JW, Aman ZM (2018) The use of computational fluid dynamics to predict the turbulent dissipation rate and droplet size in a stirred autoclave. Chem Eng Sci. In PressGoogle Scholar
  6. Boufadel MC, Gao F, Zhao L, Özgökmen T, Miller R, King T, Robinson B, Lee K, Leifer I (2018) Was the Deepwater Horizon well discharge churn flow?: implications on the estimation of the oil discharge and droplet size distribution. Geophys Res Lett 45:2396–2403. Scholar
  7. Boxall JA, Koh CA, Sloan ED, Sum AK, Wu DT (2012) Droplet size scaling of water-in-oil emulsions under turbulent flow. Langmuir 28:104–110. Scholar
  8. Brandvik PJ, Johansen Ø, Leirvik F, Farooq U, Daling PS (2013) Droplet breakup in subsurface oil releases – part 1: Experimental study of droplet breakup and effectiveness of dispersant injection. Mar Pollut Bull 73:319–326. Scholar
  9. Brandvik PJ, Davies EJ, Storey C, Leirvik F, Krause DF (2017) Subsurface oil releases – verification of dispersant effectiveness under high pressure using combined releases of live oil and natural gas, SINTEF report no: A27469. Trondheim Norway 2016. ISBN: 978-821405857-4Google Scholar
  10. Davies EJ, Brandvik PJ, Leirvik F, Nepstad R (2017) The use of wide-band transmittance imaging to size and classify suspended particulate matter in seawater. Mar Pollut Bull 115:105–114. Scholar
  11. Gros J, Reddy CM, Nelson RK, Socolofsky SA, Arey JS (2016) Simulating gas–liquid−water partitioning and fluid properties of petroleum under pressure: implications for deep-sea blowouts. Environ Sci Technol 50:7397–7408. Scholar
  12. Hsiang L-P, Faeth GM (1992) Near-limit drop deformation and secondary breakup. Int J Multiphase Flow 18:635–652CrossRefGoogle Scholar
  13. Jaggi A, Snowdon RW, Stopford A, Radović JR, Oldenburg TB, Larter SR (2017) Experimental simulation of crude oil-water partitioning behavior of BTEX compounds during a deep submarine oil spill. Org Geochem 108:1–8. Scholar
  14. Johansen Ø, Rye H, Melbye AG, Jensen HV, Serigstad B, Knutsen T (2000) Deep spill JIP - experimental discharges of gas and oil at Helland Hansen – June 2000, Technical ReportGoogle Scholar
  15. Johansen Ø, Brandvik PJ, Farooq U (2013) Droplet breakup in subsea oil releases--part 2: Predictions of droplet size distributions with and without injection of chemical dispersants. Mar Pollut Bull 73:327–335. Scholar
  16. Kundu PK, Cohen IM, Dowling DR (2016) Fluid mechanics, Sixth edition. Academic Press, OxfordGoogle Scholar
  17. Lake LW, Fanchi JR (2006) Petroleum engineering handbook. Society of Petroleum Engineers, RichardsonGoogle Scholar
  18. Lefebvre AH, McDonell VG (2017) Atomization and sprays, Second edition. CRC Press, Boca RatonCrossRefGoogle Scholar
  19. Lehr W, Socolofsky SA (2020) The importance of understanding fundamental physics and chemistry of deep oil blowouts (Chap. 2). In: Murawski SA, Ainsworth C, Gilbert S, Hollander D, Paris CB, Schlüter M, Wetzel D (eds) Deep oil spills: facts, fate, effects. Springer, ChamGoogle Scholar
  20. Lehr B, Aliseda A, Bommer P, Espina P, Flores O, Lasheras JC, Leifer I, Possolo A, Riley J, Savas O, Shaffer F, Wereley S, Yapa PD (2010) Deepwater Horizon Release: estimate of rate by PIV, July 21, 2010, Accessed on October 29, 2018.
  21. Li Z, Bird A, Payne JR, Vinhateiro N, Kim Y, Davis C, Loomis N (2015) Technical reports for Deepwater Horizon water column injury assessment: oil particle data from the Deepwater Horizon oil spill. Accessed 28 Sept 2018
  22. Li Z, Spaulding M, French McCay D, Crowley D, Payne JR (2017) Development of a unified oil droplet size distribution model with application to surface breaking waves and subsea blowout releases considering dispersant effects. Mar Pollut Bull 114:247–257. Scholar
  23. Maaß S, Wollny S, Voigt A, Kraume M (2011) Experimental comparison of measurement techniques for drop size distributions in liquid/liquid dispersions. Exp Fluids 50:259–269. Scholar
  24. Malone K, Pesch S, Schlüter M, Krause D (2018) Oil droplet size distributions in deep-sea blowouts: influence of pressure and dissolved gases. Environ Sci Technol 52:6326–6333. Scholar
  25. Masutani S, Adams EE (2001) Experimental study of multiphase plumes with application to deep ocean oil spills: final report to U.S. Dept. of the InteriorGoogle Scholar
  26. Ohnesorge WV (1936) Die Bildung von Tropfen an Düsen und die Auflösung flüssiger Strahlen. Z Angew Math Mech 16:355–358. Scholar
  27. Oldenburg TBP, Jaeger P, Gros J, Socolofsky SA, Pesch S, Radović J, Jaggi A (2020) Physical and chemical properties of oil and gas under reservoir and deep-sea conditions (Chap. 3). In: Murawski SA, Ainsworth C, Gilbert S, Hollander D, Paris CB, Schlüter M, Wetzel D (eds) Deep oil spills: facts, fate, effects. Springer, ChamGoogle Scholar
  28. Perlin N, Paris CB, Berenshtein I, Vaz AC, Faillettaz R, Aman ZM, Schwing PT, Romero IC, Schlüter M, Liese A, Noirungsee N, Hackbusch S (2020) Far-field modeling of a deep-sea blowout: sensitivity studies of initial conditions, bio-degradation, sedimentation and sub-surface dispersant injection on surface slicks and oil plume concentrations (Chap. 11). In: Murawski SA, Ainsworth C, Gilbert S, Hollander D, Paris CB, Schlüter M, Wetzel D (eds) Deep oil spills: facts, fate, effects. Springer, ChamGoogle Scholar
  29. Pesch S, Schlüter M, Aman ZM, Malone K, Krause D, Paris CB (2020) Behavior of rising droplets and bubbles – impact on the physics of deep-sea blowouts and oil fate (Chap. 5). In: Murawski SA, Ainsworth C, Gilbert S, Hollander D, Paris CB, Schlüter M, Wetzel D (eds) Deep oil spills: facts, fate, effects. Springer, ChamGoogle Scholar
  30. Reddy CM, Arey JS, Seewald JS, Sylva SP, Lemkau KL, Nelson RK, Carmichael CA, McIntyre CP, Fenwick J, Ventura GT, van Mooy BAS, Camilli R (2012) Composition and fate of gas and oil released to the water column during the Deepwater Horizon oil spill. Proc Natl Acad Sci 109:20229–20,234. Scholar
  31. Satter A, Iqbal GM (2016) Reservoir engineering: the fundamentals, simulation, and management of conventional and unconventional recoveries. Elsevier/Gulf Professional Publishing, AmsterdamGoogle Scholar
  32. Seemann R, Malone K, Laqua K, Schmidt J, Meyer A, Krause D, Schlüter M (2014) A new high-pressure laboratory setup for the investigation of deep-sea oil spill scenarios under in-situ conditions. In: Proceedings of the seventh International Symposium on Environmental Hydraulics, pp 340–343Google Scholar
  33. Socolofsky SA, Adams EE, Boufadel MC, Aman ZM, Johansen Ø, Konkel WJ, Lindo D, Madsen MN, North EW, Paris CB, Rasmussen D, Reed M, Rønningen P, Sim LH, Uhrenholdt T, Anderson KG, Cooper C, Nedwed TJ (2015) Intercomparison of oil spill prediction models for accidental blowout scenarios with and without subsea chemical dispersant injection. Mar Pollut Bull 96:110–126. Scholar
  34. Tang L (2004) Cylindrical liquid-liquid jet instability. Ph. D. ThesisGoogle Scholar
  35. Vaz AC, Paris CB, Dissanayake AL, Socolofsky SA, Gros J, Boufadel MC (2020) Dynamic coupling of near-field and far-field models (Chap. 9). In: Murawski SA, Ainsworth C, Gilbert S, Hollander D, Paris CB, Schlüter M, Wetzel D (eds) Deep oil spills: facts, fate, effects. Springer, ChamGoogle Scholar
  36. Wang CY, Calabrese RV (1986) Drop breakup in turbulent stirred-tank contactors. Part II: relative influence of viscosity and interfacial tension. Am Inst Chem Eng J 32:667–676. Scholar
  37. Zhao L, Boufadel MC, Socolofsky SA, Adams E, King T, Lee K (2014) Evolution of droplets in subsea oil and gas blowouts: development and validation of the numerical model VDROP-J. Mar Pollut Bull 83:58–69. Scholar
  38. Zhao L, Shaffer F, Robinson B, King T, D’Ambrose C, Pan Z, Gao F, Miller RS, Conmy RN, Boufadel MC (2016) Underwater oil jet: hydrodynamics and droplet size distribution. Chem Eng J 299:292–303. Scholar
  39. Zuzio D, Estivalezes J-L, Villedieu P, Blanchard G (2013) Numerical simulation of primary and secondary atomization. Comptes Rendus Mécanique 341:15–25. Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Karen Malone
    • 1
    Email author
  • Zachary M. Aman
    • 2
  • Simeon Pesch
    • 3
  • Michael Schlüter
    • 3
  • Dieter Krause
    • 1
  1. 1.Institute of Product Development and Mechanical Engineering DesignHamburg University of TechnologyHamburgGermany
  2. 2.Department of Chemical EngineeringUniversity of Western AustraliaPerthAustralia
  3. 3.Hamburg University of Technology, Institute of Multiphase FlowsHamburgGermany

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