Multi-scale simulation of deep-sea oil plume trajectory

Oil plumes emerging from accidents at deep-sea oil gushers pose threats in terms of economic, ecological and environmental disasters (Bjorndal et al., 2011) in local as well as in global scales. Despite the state of the art oil recovery methods, 70% of the spilled oil remains trapped inside the sea for a very long term (Kerr et. al., 2010). Hence, methodologies to obtain detailed information about the trajectory of the three dimensional oil plumes is extremely important from the perspectives of better recovery and dispersion of spilled oil. Till date, the observations and predictions on the nature of oil plume behavior have come up with inconsistency and confusions (Barker, 2011). Hence, multi-physics based simulations and better visualizations are needed for understanding the growth and dynamics of the oil plume starting from the event of the wellhead accident. Difficulties in oil spill simulation arise due to the fact that the oil jet diameter spans over a wide range of length-scales at different levels of height inside the sea. The wellhead is usually of inches (centimeters) in diameter whereas oil spreads over hundreds of kilometers on the ocean-surface. Therefore, it is impossible to define flow parameters like Reynolds number or Froude number for the entire oil plume spanning over the depth of the ocean. Moreover, different types of instabilities are observed at different heights of the oil-jet Depending on the ambient flow conditions and pressure and inertia of the jet. Most of the numerical models have considered only few hundred meters depth from the ocean surface (Zheng and Yapa, 1997; Chen and Yapa, 2002), where the jet diameter is at least of few hundred meters and did not predict the near well head dynamics of the oil plume. The present paper represents a multi-scale modeling for the oil plume, where the near wellhead jet has been simulated in a centimeter scale domain up to 60 meters of height and the upper domain is simulated in a meter scale telescopic mesh spanning up to 50 km width of the ocean. Two different sets of Cartesian meshes have been used for that. Near well-head mesh contains 4.6 million cells with a minimum grid spacing of 0.005 m. The upper domain is considered as a telescopic mesh (Figure 1) that contains 4 million cells starting with a span-wise width of 1 m and stretched to 500 meters. Hycom prediction (Ref 6) of the ocean current shows that the cross-flow is negligible in the vicinity of the ocean bed (around 1500 m height). The oil jet rises due to high pressure and buoyancy effect where its diameter spans from 2 inches at the well head to few meters at 60 m height. Cross-flow boundary conditions are provided to the upper domain to model the effects of north-south and east-west ocean currents with turbulent boundary layer velocity profile. Velocity and species fraction at the outflow plane of the lower domain is interpolated to meter-scale grids of the inlet plane of the upper domain. The numerical model solves Navier-Stokes equation in an Eulerian framework in presence of buoyancy and Coriolis terms. An in-house parallel-multiblock-multispecies CFD solver has been used. An overall accuracy of second order is maintained in spatial flux splitting algorithms and time integration schemes. Oil and water are considered to be two different species with negligible inter-species mass diffusion. The turbulence in the ocean current has been addressed using a large-eddy simulation technique that directly resolves the large energy carrying energy carrying and models the effects of smaller dissipative scales using dynamic Smagorinsky models (Smagorinsky, 1963). The large eddy simulation model has already been tested for several applications involving wide range of flow conditions. This methodology has been validated for a simpler jet in cross flow simulation at Reynolds number 5000 with available DNS data (Muppidi and Mahesh, 2007), where satisfactory agreement has been obtained in terms of mean jet trajectory (Figure 2). Higher exit pressure and buoyancy at the lower domain produces turbulence and instability in the oil jet resulting into jet bifurcation that can be seen via different peaks of axial velocity 30m above the wellhead (Figure 3), which has not been reported in earlier studies. The oil plume is observed to bend due to cross flow of oceanic currents at the upper domain (Figure 4). Timescales of oil-jet instabilities has been found out in both domains and correlated using velocity structure functions. However, the undulation of ocean surface and air effects has not been considered in the current study. The present method can be extended for studying pinch off and droplets formations from the oil jet using a surface evaluation algorithm, where the scale of simulation can be re-sized down to the droplet scales and further improved to capture physics of hydrate formations and dispersant activities.

References: 1. Kerr, R.A., 2010, A Lot of Oil on the Loose, Not So Much to Be Found.Science 329 (5993): 734–5. 2. Bjorndal, K.A., Bowen, B.W., Chaloupka, M., Crowder, L.B., Heppell, S.S., Jones, CM., Lutcavage, M.E., Policansky, D., Solow, A. R.,and Witherington, B. E.,2011, Better Science Needed for Restoration in the Gulf of Mexico, Science, 331, 537-538. 3. Chen F., and Yapa, P.D., 2002, A model for simulating deepwater oil and gas blowouts – Part II: Comparison of numerical simulations with “Deep-spill” field experiments. Journal of Hydraulic Research, Vol 41, 353-365 4. Zheng, L., and Yapa, P. D., 1998, Simulation of oil spills from underwater accidents II: Model verification, Journal of Hydraulic Research, Vol 6, 35119-134. 5. Barker, C. H., 2011, A Statistical Outlook for the Deepwater Horizon Oil Spill, Geophysical Monograph Sereis, 195, 237-244 6. http://hycom.org/ 7. Smagorinsky J., 1963, General circulation experiments with the primitive equations. I: The basic experiment. Monthly Weather Review, 91, 99-165. 8. Muppidi, S., and Mahesh, K., 2007, Direct numerical simulation of round turbulent jets in crossflow, Journal of Fluid Mechanics, 574, 59-84