Direct simulation of heterogeneous diffusion and inversion procedure applied to an out-diffusion experiment. Test case of Palmottu granite

摘要

An out-diffusion laboratory experiment using a non-reactive tracer was fitted using the Time Domain Diffusion (TDD) method. This rapid particle tracking method allows simulation of the heterogeneous diffusion based on pore-scale images and local values of diffusivities. The superimposed porosity and mineral 2D maps act as computation grids to condition diffusion pathways. We focused on a Palmottu granite sample, in which the connected pore space has a composite microstructure with cracks linking microporous minerals and is above the percolation threshold.rnThree main results were achieved: (ⅰ) When compared to the fitting obtained with one coefficient (best mean square residual R=1.6x 10~(-2)), diffusion is shown to be suitably characterised with two coefficients related to cracks and microporous minerals (best R=6.5 x 10~(-4)), (ⅱ) rather than imposing a local apparent diffusion coefficient D_a independent of the local porosity Φ, a best fit is obtained by applying Archie's relationship D_a=D_0xG with G=Φ~m to each pixel of the calculation grids (G is the geometry-factor, D_0 is the diffusion coefficient in free fluid, and m is Archie's exponent), and (ⅲ) the order of magnitude of the fitted diffusion coefficient or Archie's exponents (m=0 for microcracks and m= 1.82 for microporous minerals) is physically realistic.