Self-organized gradient percolation method for numerical simulation of impregnation in porous media

Classical numerical methods (F.E.M, theta-method, etc.) applied to simulate unsaturated impregnation in porous media require high computational cost, which becomes prohibitive when the impregnation is coupled with other physics such as chemical reactions. To overcome the computational difficulties, we propose to use a drastically different approach based on a new method we call Self-organized Gradient Percolation. The deduced algorithm aims to calculate the local saturation during non-reactive impregnation in unsaturated conditions in a more efficient way in terms of computational duration and precision than previous methods. The initialization of this algorithm is driven by an analytic solution of the homogeneous diffusion equation, obtained by convolving a Probability Density Function (PDF) with a suitably chosen smoothing function. Thus, we reproduce the evolution of the capillary pressure profile by means of the evolution of the standard deviation of the PDF. This algorithm is validated by comparing theoretical, experimental and numerical results.