A transient two-dimensional mathematical model for simulating the transport of radionuclide effluents from nuclear powered electric generating stations

A transient two-dimensional mathematical model for simulating the transport of radionuclide effluents from nuclear powered electric generating stations is presented.

The Eulerian fluid in discrete element (FLIDE) formulation employs the integral forms of the conservation principles of water mass and radionuclide mass in variable sized discrete elements that span the flow region. The transport of the radionuclide effluents are modeled in the water layer as suspended sediment and in the bottom layer as stationary resident sediment.

The contributions of vertical variations of the velocity components and radionuclide concentrations in the water layer are rigorously incorporated in the development of depth-averaged, two-dimensional transport fluxes by spatially integrating the conservation equations over the enclosure surfaces of the discrete elements. Horizontal transport of radionuclides in the bottom layer is not presented. A simple exchange model is used to approximate the formulation of mass transport of radionuclides between the dissolved/adsorbed state in the water layer and the dissolved/adsorbed state in the bottom resident sediment layer.

The resulting mathematical system is a system of weakly coupled, nonlinear, ordinary differential equations that are numerically integrated from arbitrarily specified initial conditions, by the Runge-Kutta-Gill method with a time step based on a stability criterion for explicit methods.

The mathematical model is applied to a hypothetical accidental release of radionuclide effluents at the San Onofre Nuclear Generating Station (SoNGs). Flow conditions in the region are modeled using field data, and the released radionuclide is Cesium 132.

During the simulation of a hypothetical accident condition at the San Onofre Generating Station the model showed that it readily takes into account the interaction of dissolved and adsorbed suspended sediment in the water layer and the dissolved and adsorbed resident sediment in the stationary bottom layer. Under high flow conditions, it showed the phenomena of the dissolved and adsorbed resident sediment in the stationary bottom layer being resuspended into the water layer, presenting a realistic simulation of natural conditions. At low flow conditions the settling of the dissolved and adsorbed suspended sediment in the water layer into the stationary bottom layer was modeled, thus giving an effective simulation of the vertical exchange between the two layers. Decay of the radionuclide contaminant is effectively modeled using the basic exponential decay form based on the radionuclides' half-life.