Computation of the Mixing Energy in Rivers for Oil Dispersion

With the increase in transport of oil by rail, the probability of oil spills in rivers has increased. Traditionally, focus has been placed on oil slicks moving on the water surface. However, the density of bitumen oil carried by rail within and from Canada to the United States can exceed that of freshwater, causing this oil to get submerged in the water column. This also has the potential of forming oil particle aggregates (OPAs) upon interaction with suspended sediments. The energy-dissipation rate is a key parameter for predicting the formation of oil droplets, and for this purpose, expressions are developed to estimate the energy-dissipation rate at various depths in the river using easily measured quantities such as water depth, streambed slope, and streambed roughness. The formulation showed that for a stream 30 m wide with a natural slope of 1/1,000 and roughness height of 1.0 cm, the average and maximum energy-dissipation rates are 0.01 and 0.22 W/kg, respectively. The average value is comparable to spilling breakers of height around 0.3 m, and the maximum value is comparable to those obtained from plunging breakers of 0.30-m-high waves. The large average value suggests that breakup of droplets in streams is higher than in the open sea under regular waves.