Diffusion in reconstructed porous domains filled by two fluid phases

Abstract

In the present study, the tracer diffusion in porous media filled by a wetting and a non-wetting phase is investigated. The disordered porous structure of porous systems like random sphere packing, and the North Sea chalk, is represented by three-dimensional binary images. The random sphere pack is generated by a standard ballistic deposition procedure, while the chalk matrix by a stochastic reconstruction technique. Physically sound spatial distributions of the two phases filling the pore space are determined by the use of a simulated annealing algorithm, where the wetting and the non-wetting phases are initially randomly distributed in the pore space and trial-and-error swaps are performed in order to attain the global minimum of the total interfacial energy. The effective diffusivities of the resulting domains are computed by a random walk method. A parametric study with respect to the pore volume fraction occupied by each phase and the ratio of the diffusivities in the wetting and non-wetting phases, is performed. Furthermore, the dependence of the effective diffusivity on the porosity for chalk-like structures is examined.