Modeling the flow regime near the source in underwater gas releases

Abstract

Recent progress in calculating gas bubble sizes in a plume, based on phenomenological approaches using the release conditions is a significant improvement to make the gas plume models self-reliant. Such calculations require details of conditions Near the Source of Plume (NSP); (i.e. the plume/jet velocity and radius near the source), which inspired the present work. Determining NSP conditions for gas plumes are far more complex than that for oil plumes due to the substantial density difference between gas and water. To calculate NSP conditions, modeling the early stage of the plume is important. A novel method of modeling the early stage of an underwater gas release is presented here. Major impact of the present work is to define the correct NSP conditions for underwater gas releases, which is not possible with available methods as those techniques are not based on the physics of flow region near the source of the plume/jet. We introduce super Gaussian profiles to model the density and velocity variations of the early stages of plume, coupled with the laws of fluid mechanics to define profile parameters. This new approach, models the velocity profile variation from near uniform, across the section at the release point to Gaussian some distance away. The comparisons show that experimental data agrees well with the computations.

Keywords

underwater gas releases / bubble plumes / near source conditions / plumes/jets / oil and gas spill models

References

[1] Bandara UC, Yapa PD. Bubble sizes, breakup, and coalescence in deepwater gas/oil plumes. Journal of Hydraulic Engineering, 2011, 137(7): 729-738

[2] Cederwall K, Ditmars JD. Analysis of air-bubble plumes, 1970

[3] Clift R, Grace JR, Weber ME. Bubbles, drops, and particles, 1978, New York, USA: Academic Press

[4] Cloete S, Olsen JE, Skjetne P. CFD modeling of plume and free surface behavior resulting from a sub-sea gas release. Applied Ocean Research, 2009, 31: 220-225

[5] Delnoij E, Lammers FA, Kuipers JAM, van Swaaij WPM. Dynamic simulation of dispersed gas-liquid two-phase flow using a discrete bubble model. Chemical Engineering Science, 1997, 52(9): 1429-1458

[6] Dhotre MT, Smith BL. CFD simulation of large-scale bubble plumes: Comparisons against experiments. Chemical Engineering Science, 2007, 62(23): 6615-6630

[7] Drew B, Charonko J, Vlachos P. Liquid entrainment by round turbulent gas jets submerged in water. ASME-JSME-KSME 2011 Joint Fluids Engineering Conference, 2011, 2723-2731

[8] Fabregat A, Dewar WK, Ozgonkmen TM, Poje AC, Wienders N. Numerical simulations of turbulent thermal, bubble and hybrid plumes. Ocean Modelling, 2015, 90: 16-28

[9] Falcone AM, Cataldo JC. Entrainment velocity in an axisymmetric turbulent jet. Journal of Fluids Engineering, 2003, 125(4): 620-627

[10] Fannelop T, Sjoen K. Hydrodynamics of underwater blowouts. 18th Aerospace Sciences Meeting, 2015

[11] Ferentinos, J. Infield System, 2013. Global offshore oil and gas outlook. Presented at the Gas/Electric Partnership.

[12] Hill BJ. Measurement of local entrainment rate in the initial region of axisymmetric turbulent air jets. Journal of Fluid Mechanics, 1972, 51(4): 773-779

[13] Hirst E. Analysis of buoyant jets within the zone of flow establishment, 1971

[14] Hussain NA, Narang BS. Simplified analysis of air-bubble plumes in moderately stratified environments. Journal of Heat Transfer, 1984, 106(3): 543-551

[15] Hussain NA, Siegel R. Liquid jet pumped by rising gas bubbles. Journal of Fluids Engineering, 1976, 98(1): 49-56

[16] Johansen. DeepBlow–a Lagrangian plume model for deep water blowouts. Spill Science & Technology Bulletin, 2000, 6(2): 103-111

[17] Kobus HE. Analysis of the flow induced by air-bubble systems. Coastal Engineering Conference, London, 1968, 2: 1016-1031

[18] Lima Neto IE. Modeling the liquid volume flux in bubbly jets using a simple integral approach. Journal of Hydraulic Engineering, 2012, 138(2): 210-215

[19] Liro CR, Adams EE, Herzog HJ. Modeling the release of CO₂ in the deep ocean, 1991

[20] McDougall TJ. Bubble plumes in stratified environments. Journal of Fluid Mechanics, 1978, 85(4): 655-672

[21] McGinnis DF, Lorke A, Wüest A, Stöckli A, Little JC. Interaction between a bubble plume and the near field in a stratified lake. Water Resources Research, 2004, 40(10): W10206

[22] Milgram JH. Mean flow in round bubble plumes. Journal of Fluid Mechanics, 1983, 133: 345-376

[23] Mudde RF, Simonin O. Two-and three-dimensional simulations of a bubble plume using a two-fluid model. Chemical Engineering Science, 1999, 54(21): 5061-5069

[24] Nissanka ID, Yapa PD. Calculation of oil droplet size distribution in an underwater oil well blowout. Journal of Hydraulic Research (IAHR), 2016, 54(3): 307-320

[25] Olsen JE, Skjetne P. Current understanding of subsea gas releases: A review. Canadian Journal of Chemical Engineering, 2016, 94: 209-219

[26] Shealy DL, Hoffnagle JA. Beam shaping profiles and propagation. Applied Optics, 2006, 45(21): 5118-5131

[27] Simiano M. Experimental investigation of large-scale three dimensional bubble plume dynamics, 2005, Zurich: Swiss Federal Institute of Technology

[28] Simiano M, Zboray R, Cachard F d, Lakehal D, Yadigaroglu G. Comprehensive experimental investigation of the hydrodynamics of large-scale, 3D, oscillating bubble plumes. International Journal of Multiphase Flow, 2006, 32(10-11): 1160-1181

[29] Smith BL. On the modelling of bubble plumes in a liquid pool. Applied Mathematical Modelling, 1998, 22(10): 773-797

[30] Socolofsky SA, Bhaumik T, Seol D. Double-plume integral models for near-field mixing in multiphase plumes. Journal of Hydraulic Engineering, 2008, 134(6): 772-783

[31] Sokolichin A, Eigenberger G, Lapin A. Simulation of buoyancy driven bubbly flow: Established simplifications and open questions. American Institute of Chemical Engineers Journal, 2004, 50(1): 24-45

[32] U.S. Energy Information Administration (US EIA), 2014. Brazil. International energy data and analysis. https://www.eia.gov/beta/international/analysis_includes/countries_long/Brazil/brazil.pdf.

[33] Wüest A, Brooks NH, Imboden DM. Bubble plume modeling for lake restoration. Water Resources Research, 1992, 28(12): 3235-3250

[34] Yapa PD, Dasanayaka LK, Bandara UC, Nakata K. A model to simulate the transport and fate of gas and hydrates released in deepwater. Journal of Hydraulic Research, 2010, 48(5): 559-572

[35] Zhao L, Boufadel MC, Socolofsky SA, Adams E, King T, Lee K. Evolution of droplets in subsea oil and gas blowouts: Development and validation of the numerical model VDROP-J. Marine Pollution Bulletin, 2014, 83(1): 58-69

[36] Zheng L, Yapa PD, Chen F. A model for simulating deepwater oil and gas blowouts -Part I: theory and model formulation. Journal of Hydraulic Research, 2003, 41(4): 339-351