Lagrangian modelling of reactive contaminant transport in the multi-component marine medium

Abstract

The particle-tracking method for transporting radionuclides in multicomponent ocean medium (water and multifractional suspended and deposited sediments) is considered using a probabilistic approach for simulating interaction processes between several states of radioactivity. The state transformations as a result of reactions of the first order were described using the master equation for the probability of the particle being in the given state. Transition probabilities between all possible states can be obtained from the numerical solution of the matrix master equation that is derived in the paper. In the first approximation, the Euler method was used to obtain a solution for the next time step. This approach can be applied to any linear system of equations describing phase transitions with any number of states, but it requires small values of the transition probabilities to ensure only a single-phase change during one time step. The paper also focuses on deriving the Lagrangian interface conditions between the water column and bottom deposition. To apply the probabilistic approach, the boundary conditions were considered as the reaction terms in a thin near-bottom interface layer in which boundary conditions were converted into source terms. For this layer, the corresponding master equation was derived to obtain transitional probabilities for particle states. The developed approaches were tested on numerical and analytical solutions of two test cases. It was found that the optimal thickness of the interface layer must be larger than the maximum vertical displacement of the particle during the one-time step, but it must be small enough to approximate the condition of uniform distribution of concentration in this layer.