ROSA

4 Oil spill model

The ROSA simulation of oil spillage accidents in rivers is able to simulate reality, with a view to providing quantitative answers to what-would-happen-if questions in terms of:

quantitative description of oil slick movement in space and time and
water quality as a distribution of oil pollutant concentrations in water body.

To accomplish the above needs ROSA has been equiped with a number of oil dispersion model as described below.

4.1 The surface oil slick equations

To keep track of the surface slick the marker fluid is introduced. The value of the marker is used to distinguish between surface water and oil.

The marker distribution is supposed to obey the advection/diffusion equation:

dCo/dt + d(us.Co)/dx + d(vs.Co)/dy =

d(Dx.dCo/dx)/dx + d(Dy.dCo/dy)/dy

Where:

x, y, t = space and time variables;
Co = area marker of oil in the surface layer;
us, vs = components of surface drift velocity;
Dx, Dy = surface diffusion coefficients.

To track the slick originated from spill site cell, the Co value is put to unity for that cell. The boundary values for all time intervals are zero. The location of oil slick/water interface is deduced from the distribution of Co taking into account of the mass balance of surface oil as explained in Section 6.2

An alternative technique is to track individual oil parcels in a Lagrangian framework. This technique, embodied in GENTRA, is also available for ROSA users being beyond the scope of this paper.

4.2 The surface oil dispersion equations

The conservation equation for oil in the surface layer is written as:

dCs/dt + d(us.Cs)/dx + d(vs.Cs)/dy =

d(Dx.dCs/dx)/dx + d(Dy.dCs/dy)/dy +


     alfa.Vb.Cv    -    gamma.Cs   -   Co.Se  -       Ds
     ----------      --------------  -----------   ----------
     source from     dispersion in   evaporation   shoreline
     suspended       suspended layer               deposition

In above:

x, y, t = space and time variables;
Cs = volume of surface oil per unit area;
us, vs = components of surface drift velocity;
Dx, Dy = surface diffusion coefficients;
alfa = a coefficient representing probability of an oil dropled in the mixed layer reaching the water surface;
Vb = the buoyant velocity of suspended oil globules;
gamma = a coefficient describing the rate at which the surface oil is dispersed into the water ;
Co = area concentration of oil in the surface layer;
Se = rate of evaporation and dissolution per unit area of the surface slick and
Ds = effect on the distribution of surface oil by shoreline deposition and entraimment.

4.3 The suspended oil dispersion equations

The oil concentration distribution is described, for "shallow water" river flow, by conservation equation as follows:

d(Cv.h)/dt + d(u.Cv.h)/dx + d(v.Cv.h)/dy =
d(d(h.Dx.Cv)/dx)/dx + d(d(h.Dy.Cv)/dy)/dy +


        gamma.Cs     -     alfa.Vb.Cv      -     betta.Cv
     --------------        ----------           --------------
     dispersion in         source from          bed depositon
     suspended layer       suspended

in which,

Cv = depth averaged volumetric concentration of oil in the suspended layer;
h = depth of flow;
u, v = components of depth-averaged river currents;
betta = a coefficient defining the rate of net oil deposition on the river bed per unit area.