Development of an Algorithm for Chemically Dispersed Oil Spills

Abstract

An algorithm utilizing four basic processes was described for chemical oil spill dispersion. Initial dispersion was calculated using a modified Delvigne equation adjusted to chemical dispersion, then the dispersion was distributed over the mixing depth, as predicted by the wave height. Then the droplets rise to the surface according to Stokes’ law. Oil on the surface, from the rising oil and that undispersed, is re-dispersed. The droplets in the water column are subject to coalescence as governed by the Smoluchowski equation. A loss is invoked to account for the production of small droplets that rise slowly and are not re-integrated with the main surface slick. The droplets become less dispersible as time proceeds because of increased viscosity through weathering, and by increased droplet size by coalescence. These droplets rise faster as time progresses because of the increased size. Closed form solutions were provided to allow practical limits of dispersibility given inputs of oil viscosity and wind speed. Discrete solutions were given to calculate the amount of oil in the water column at specified points of time. Regression equations were provided to estimate oil in the water column at a given time with the wind speed and oil viscosity. The models indicated that the most important factor related to the amount of dispersion, was the mixing depth of the sea as predicted from wind speed. The second most important factor was the viscosity of the starting oil. The algorithm predicted the maximum viscosity that would be dispersed given wind conditions. Simplified prediction equations were created using regression.