Advection & Dispersion Modeling of Oil Spills

Some time ago I wrote an Oil Spill Advection modeling system for the company I was working for at the time. The system used a hindcast database of wind & current information (direction and speed) to predict the short-term and historic movement of oil spill incidents. It was used for emergency response purposes but was limited to only the advection (movement) component of the spill. NB: I will add a reference to this software in this blog once I dig up some old screen captures. The software ran under an ESRI GIS environment.

After one paticular emergency simulation exercise I decided that in some cases the advection component was just not good enough and we would need to add another dimension to the model in the form of the dispersion of hydrocarbons at the sea surface. I had attended an IMO Oil Spill Management course some time before and understood the basic inputs that govern dispersion and so I spent a couple of days (literally) working on this problem. I wanted to keep things simple and so I limited the dispersion modeling to the following inputs:

• The volume of hydrocarbon spilled.
• The period for which that hydrocarbon is spilled (volume / period = release rate).
  
• A classification of the type of oil / hydrocarbon spilled. This was based on a profile of the specific gravity or API (American Petroleum Institute) gravity of the hydrocarbon.
• Based on the above classification a linear "% degredation of persistent oil volume per hour" is determined based on a pre-determined degredation curve which in turn is based on various components (i.e. evaporation, dissolution, weathering and bio-degredation).
• Initial Spreading Coefficient (S) (classically derived from 3 interfacial surface tension components which were not available to me when I wrote the prediction model). Various literature indicates a valid range of 0.05 -> 0.2. Both extreme value ranges are therefore modeled by the software.
• Density derived from specific gravity.
• Viscosity (measured).
• Minimum thickness of oil slick (derived from the hydrocarbon type classification - various literature exists).
  
• Maximum spread radius for a given volume is calculated using the spreading coefficient, density, viscosity and the minimum thickness of a slick.
  
• Positional randomisation factor for each model step (instantaneous maximum randomisation at each step to account for sea-state and other factors).
• Propagated positional error (over time) = [time lapse] / n (meters).

Fig 1: Oil Spill Fates (Persistence) for different oil types over time. The graphic has been modified from it's original to show only generic hydrocarbon types.

A Pseudo-Lagrangian Dispersion Model was used with a "random step" method:

• Particle modeling method modified for limited input information.
• Uses base advection / spill trajectory for “movement” as a result of metocean effects.
• Models “spreading”.
• Models “degradation” as a result of evaporation, dissolution and weathering (derived from spill “fate” curves).
• Emulsification effects are indirectly considered in this model (via the spill "fate" curve).
  

The screen capture below shows the model output in terms of surface hydrocarbon density at a particular time-instance in the model:

Fig 2: Model output: Hydrocarbon density at a given time-step in the model. Certain details have been edited out to protect the location of the modeling exercise.