Diffusion in Crystalline Rocks

Summary

Laboratory experiments to determine the sorption and the rate of diffusion of cesium and strontium in pieces of granite have been performed. The effective diffusivity, Dp · εp was found to be 1-2 · 10−12 m2/2 for both cesium and strontium.

The diffusion of non-sorbing species in granites and other rock materials have been studied in laboratory scale. The non-sorbing species were iodide, tritiated water, Cr-EDTA and Uranine. In granites the effective diffusivities were determined to be 0.7–1.3 · 10−13 m2/s for iodide and 1.3–1.8 · 10−13 m2/s for tritiated water.

Electrical resistivity measurements in salt water saturated rock cores have been performed. The resistivity is measured in the saturated core and in the salt solution with which the core has been saturated. The ratio between these two resistivities has a direct relation to the ratio of the effective diffusivity for a component in the rock material and the diffusivity in free water for the same component.

The results from the electrical resistivity measurements and the experiments with diffusion of non-sorbing species are in fair agreement. The effective diffusivity for cesium and strontium (sorbing species) are, however, more than ten times higher than expected from the results of diffusion of non-sorbing species and the electrical resistivity measurements. This is interpreted as an effect of surface diffusion.

Abbreviations

A:

diffusion area m2

c:

concentration in bulk fluid mol/ℓ, cpm/ℓ, mg/ℓ

cp:

concentration in pore fluid mg/ℓ

D:

diffusion coefficient m2/s

De:

effective diffusion coefficient m2/s

Dp:

pore diffusivity m2/s

Dv:

diffusivity in water m2/s

kf:

parameter in Freundlich isotherm

ℓ:

thickness or length of a piece mm

N:

rate of transfer mol/s, cpm/s, mg/s

q:

concentration in the solid material mg/kg

Ro:

electrical resistivity in salt water Ωm

Rs:

electrical resistivity in salt water saturated rock sample Ωm

t:

time seconds, hours

x:

length coordinate

β:

exponent in Freundlich isotherm

δD:

constrictivity for diffusion

εp:

porosity of the materials

ρs:

density of the solid material kg/m3

τ:

tortuosity

ε·δD2:

formation factor

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Correspondence to K. Skagius.

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Skagius, K., Neretnieks, I. Diffusion in Crystalline Rocks. MRS Online Proceedings Library 11, 509 (1981). https://doi.org/10.1557/PROC-11-509

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