[M-AG24] Dynamics of radionuclides emitted from Fukuchima Dai-ichi Nuclear Power Plant in the environment

[MAG24-P06] Stochastic modeling of the migration of Cs-137 in soil considering a power law tailing in space

*Hiroki OKA¹, Yuko Hatano¹ (1.Department of Risk Engineering, Graduate school of Systems and Information Engineering, University of Tsukuba)

Keywords:Cs-137, Anomalous diffusion, Power law tailing in sace

We develop a theoretical model to reproduce the measured data of Cs-137 in the soil due to the Fukushima Daiichi NPP accident. The Advection Diffusion Equation (ADE) is proposed by He and Walling (1996) and has been used to predict migration in soil. This model shows Gaussian diffusion process called normal diffusion. However, We found that the concentration of Cs-137 has a discrepancy from ADE model, specifically in a deep part because the depth profiles have a power law tailing. The diffusion comes off ADE is called anomalous diffusion. Therefore, we improved ADE model in the following aspect. When Cs particle (or Cs solution) migrate in the soil, the diffusion coefficient should be the results of many processes in the soil. These processes include the effect of various materials which constitute the soil (clay, litter, sand), or the variations of pore size in the soil. Hence we regard the diffusion coefficient as the stochastic variable, we derive the model. Specifically, we consider the solution of ADE to be the conditional probability C(x, t | D) in terms of the diffusion coefficient D and calculate C(x, t) = ∫_(0~∞) C(x, t | D)*f(D)*dD, where f(D) is the probability density function of D. This model has a power law tailing in space like the space-fractional ADE.