Evaluation of the probability of overflow from the Abadia de Goi & PRIME;as repository by the Fokker-Planck equation using the Trotter's formula

A model was constructed with the objective of developing the Fokker-Planck equation for the calculation of the reliability attributes required for risk-informed decision-making involved in the analysis of water infiltration inside the repository located in the Abadia de Goias municipality, in the metropolitan region of the city of Goiania. The solution of the Fokker-Planck equation was analytically obtained by the Trotter's method for a near surface repository. This solution provides the probability density and the probability functions for the height of the liquid (water + radionuclides) column, generated by the infiltrated water in the concrete crypt of the re-pository. The modeling was unidimensional, and the calculations were performed for the geometric center of the repository crypt, which is the place of greater sensitivity of occurrence of accidental scenarios. The concept of the present model can be extended to other places in the crypt without loss of generality. The developed model is appropriate to analyze the repository overflow, a kind of event that occurs when the height of the liquid column inside the repository reaches the value of the inner height of the concrete crypt of the facility. This accident scenario produces the greatest release of radioactive material to the region outside the repository and, conse-quently, it is responsible for the main radiological impact for both members of the public and the environment. Calculations performed for the Abadia de Goi'as repository indicated that the overflow probability for this facility is strongly dependent on the rainfall rate and also on the institutional time period, varying from about 3% with no rainfall penetration up 99% with the maximum rainfall rate for an institutional time period control of 300 yr. Such results can help making decisions on the problem of risk scenarios related to the disposal of radioactive waste.