A review of natural dispersion models

Abstract

Natural dispersion occurs when fine droplets of oil are transferred into the water column by wave action or sea turbulence. Small oil droplets (less than about 20 μm) are only somewhat stable in water and will remain for short periods of time. Large droplets tend to rise and larger droplets (more than 50 μm) will not stay in the water column for more than a few seconds. Depending on oil conditions and the amount of sea energy available, natural dispersion can be insignificant or it can temporarily displace a portion of the oil. Current models predict the amount of oil entering the water column, but do not deal with their stability or how long these droplets stay in the water column. The most commonly-used model is by Delvigne, who carried out experiments in a flume. Delvigne measured the droplets entering the water column using a simplified procedure. These data were then converted to a model to predict the entry of droplets into the water column. Delvigne recommended procedures to calculate the resurfacing of the dispersed droplets but no models have implemented these. A review of the mathematics of this procedure show that the Delvigne model might be adjusted to be more unit consistent and to correctly incorporate oil viscosity. The other models used include the Audunson and Mackay models. These models are also reviewed. The Audunson model is simple and does not incorporate any inputs other than the wind speed. Further, the Audunson model predicts that most slicks will dissipate within a day or a few days. The Mackay model predicts little natural dispersion. Although the Mackay model incorporates a sea state function, the effect of this is not as great as in other models. Several issues have been noted about all natural dispersion models. These are: 1 In all cases natural dispersion models predicted the input of droplets into the water column and suggestions were made about predicting rise and resurfacing, but this important second part was never implemented by anyone, 2 The natural dispersion predicted was measured as a temporary phenomenon - that is the instantaneous input of droplets into the water column. Their persistence was not measured. The equation was designed to yield only the temporary transport in the water. Later workers assumed that the natural dispersion portion was permanently dispersed. 3 The Audunson equation over-predicts natural dispersion, especially in cases of low sea states, 4 The inputs into the Audunson model and subsequently modeled are inadequate and consist only of the wind speed, the MacKay model has too much emphasis on oil slick thickness, 5 Many of the constants in all three models appear to be arbitrary and unnecessary in some cases, 6 Only in the case of the Delvigne model were there direct correlations to experimental data, the other models are largely constructs, and 7 The Delvigne and Mackay model reach somewhat similar conclusions, however the MacKay model has poor oil property inputs and no wind or a sea energy threshold. The models yield results that are not comparable and are in some cases orders-of-magnitude different. As an interim measure, it is recommended that natural dispersion not be included in spill models as the current dispersion models are weak and in any case, were intended for oil input and the resurfacing considerations were not included.