Cement is a practical material for constructing the geological disposal system of radioactive wastes. However, such materials alter groundwater up to 13 in pH around the repository, changing the permeability of natural barrier. So far, the authors have examined the relation of permeability change with dissolution process by flowing a high pH solution (NaOH, 0.1 mM) into a bed packed with amorphous silica particles. Here, the particle diameters were adjusted to a size fraction of 74 to 149 μm by sieving. Its specific surface area was estimated as 350 m2/g by the BET method using nitrogen gas. The experimental results showed that the permeability did not immediately change although the soluble silicic acid continuously flowed out of the packed bed.
This study proposes a new mathematical model considering the diffusion and dissolution processes in the inner pore of the particle. This model assumed that each packed particle (74 to 149μm in diameter) consists of the sphere-shaped aggregation of smaller particles (20 nm in diameter). OH− ions diffuse into the pore between such small particles, and simultaneously consumed by the reaction with small particles. The radius of the each packed particle (sphere-shaped aggregation of small particles) was defined by the length from the center of the aggregation to the region where the small particles still remains. Since the outer small particles more easily dissolve than inner small particles because of diffusion process of OH− ions, each packed particle gradually shrinks. The fundamental equations consist of a simple diffusion equation of spherical coordinates of OH− ions considering the reaction term, which is linked by the equation to describe the size change of small particles with time. Here, this model also considered a change (time and space) of the diffusion oefficient caused by the change of the porosity between small particles. Besides, the change of over-all permeability of the packed bed was evaluated by Kozeny-Carman equation and the calculated radii of packed particles. The dissolution rate constant already reported was used.
The calculated result was able to well describe the experimental result, though there was no fitting parameter in the comparison with the experiment results. While the flow paths of underground cannot be simply simulated by a packed bed, this approach suggested that the dynamic behavior of permeability in a natural barrier depends also on non-uniformity of dissolution processes in inner pores (secondary pores) of minerals.