Modeling of the pseudo-colloids migration for multi-member decay chains with a arbitrary flux boundary condition in a fractured porous medium

A deep geologic disposal is the prime option for the long-term isolation of high-level radioactive waste (HLW) in many countries. For deeply located repositories, a radionuclide released from a failed waste container moves through the engineered and natural barriers before it reaches a biosphere. The pseudo-colloid which a radionuclide is adsorbed on a moving natural humic or fulvic colloid can be generated in a fractured porous medium. The size of a colloid is in general in the order of a hundred nanometer so that its migration velocity in a fracture is higher than that of a radionuclide due to the hydrochromatic effect. A large colloid cannot diffuse easily into a surrounding rock. Also, there are many kinds of actinides and these actinides have decay chains. In this analysis, the canonical form solution is derived for a pseudo-colloid and a solute in a fracture and a surrounding rock with a realistic inlet boundary condition with multi-member decay chains. It is used the Fortran based a computational code which uses a special subroutine for the inversion of Laplace transform. Consequently, the role of the pseudo-colloid in the fractured porous medium is important and also their decay chains aren’t neglected in the performance assessment of the HLW.