Interpretation of out-diffusion experiments on crystalline rocks using random walk modeling

Matrix diffusion in saturated rocks with very low permeability is one of the major mechanisms of solute transport. Laboratory out-diffusion experiments on rock samples may provide an estimate of the bulk diffusion coefficient. However, numerous results have shown that this average parameter does not really depict the complex mechanism of diffusion as a function of the internal heterogeneity of crystalline rocks. Two-dimensional images of the porosity distribution in a granite sample were obtained by impregnation with a radioactive resin and autoradiography. Some examples based on these images and synthetic images were used to perform numerical simulations of out-diffusion using two different random walk methods. The simulated shapes of the out-diffusion curves depend on the spatial distribution of the porosity and on the pore connectivity with the border of the sample. Such relations might explain the multiple nested slopes or the convex shapes often observed on real experimental curves.