The Underwater Trajectory Behaviour of Heavy Oil Jet

The Underwater Trajectory Behaviour of Heavy Oil Jet In Cross-Flow From a Broken Surface Pipeline Portia Felix The University of the West Indies, St. Augustine Department of Civil and Environmental Engineering

OUTLINE • Introduction • State of the Art in Vertical Dispersion Oil Spill Modeling • Mathematical Model- The Navier-Stokes Equations • Numerical Results of the Research Model • Conclusion 2 ICon. ETech-2020, Faculty of Engineering, The UWI, St. Augustine, Trinidad and Tobago

INTRODUCTION 3 ICon. ETech-2020, Faculty of Engineering, The UWI, St. Augustine, Trinidad and Tobago

STATE OF THE ART IN VERTICAL DISPERSION OIL SPILL MODELING • The vertical downward movement of the oil (dispersion) hinges on theory that wave motion breaks up the surface oil slick into oil droplets of various sizes that is then transported vertically or entrained in the water column. 4 ICon. ETech-2020, Faculty of Engineering, The UWI, St. Augustine, Trinidad and Tobago

STATE OF THE ART IN VERTICAL DISPERSION OIL SPILL MODELING • Advection Dispersion 5 ICon. ETech-2020, Faculty of Engineering, The UWI, St. Augustine, Trinidad and Tobago

STATE OF THE ART IN VERTICAL DISPERSION OIL SPILL MODELING The modeling approach for vertical dispersion is as follows… • Most models are based on the combination of the Lagrangian particle approach and the random walk technique. • The Lagrangian method represents the transport of a surface oil slick as a large number of individual particles and their discrete path and mass are followed and recorded as functions of time. • To compute the movement of oil droplets in the water column some oil spill models use the random walk technique to follow the motion of the individual oil droplets. • Some models mention analytical curve fit methods used to model vertical dispersion. ICon. ETech-2020, Faculty of Engineering, The UWI, St. Augustine, Trinidad and Tobago 6

MATHEMATICAL MODEL- THE NAVIER-STOKES EQUATIONS This mathematical model represents that if a flow field is subjected to a temperature gradient, the density variation generated in the flow is due to the buoyancy forces, thereby inducing motion in the fluid ICon. ETech-2020, Faculty of Engineering, The UWI, St. Augustine, Trinidad and Tobago 7

THE NUMERICAL SOLUTION OF THE NAVIER STOKES EQUATIONS The Projection Step Method for Solving the Navier-Stokes Equations: This method was introduced by Chorin and Teman (1969) Iterative Process Compute an intermediate velocity field U* Step 1 Compute a pressure update Pn+1 by solving the Poisson Equation Step 2 Compute the new velocity Un+1 and pressure Pn+1 fields Step 3 ICon. ETech-2020, Faculty of Engineering, The UWI, St. Augustine, Trinidad and Tobago 8

NUMERICAL RESULTS OF THE RESEARCH MODEL • Buoyancy –Driven Flow Model: • Numerical Solution- Benchmark problem: • Problem definition • Flow in a differentially heated rectangular domain • Left and right walls are adiabatic • Top and bottom walls are maintained at temperatures Tc and Th respectively ICon. ETech-2020, Faculty of Engineering, The UWI, St. Augustine, Trinidad and Tobago 9

NUMERICAL RESULTS OF THE RESEARCH MODEL Another simulation showing the dense source moving horizontally 10 ICon. ETech-2020, Faculty of Engineering, The UWI, St. Augustine, Trinidad and Tobago

NUMERICAL RESULTS OF THE RESEARCH MODEL Another simulation showing the dense source moving horizontally 11 ICon. ETech-2020, Faculty of Engineering, The UWI, St. Augustine, Trinidad and Tobago

CONCLUSION • Satisfactory results were obtained for the numerical simulation of the 2 D buoyancy-driven numerical model when compared to the results of the standard benchmark problem. • Model sufficiently demonstrates that heavy oil can be immediately pushed beneath the water surface due to the momentum force and be suspended underwater and travel horizontally. This oil behaviour is significant because it illustrates the suspension of most of the heavy oil under the water surface in shallow water depth without a significant amount going to the sea bottom. This suggests that density changes between the oil and the water in the water column creates a sensitive density layer that allows the oil to remain suspended– neutrally buoyant. 12 ICon. ETech-2020, Faculty of Engineering, The UWI, St. Augustine, Trinidad and Tobago

THANK YOU! 13 ICon. ETech-2020, Faculty of Engineering, The UWI, St. Augustine, Trinidad and Tobago