Numerical Simulation Of Impregnation In Porous Media By Self-organized Gradient Percolation Method

TL;DR

This paper introduces a Self-organized Gradient Percolation (SGP) method for simulating impregnation in porous media, reducing computational costs and avoiding oscillations common in classical numerical approaches.

Contribution

The novel SGP algorithm leverages gradient percolation theory and an analytic initialization to efficiently simulate impregnation, outperforming traditional finite element methods in computational speed.

Findings

SGP reduces computational time compared to finite element models.

SGP avoids spurious oscillations in simulations.

Initial results in 3D are promising.

Abstract

The aim of this work is to develop a new numerical method to overcome the computational difficulties of numerical simulation of unsaturated impregnation in porous media. The numerical analysis by classical methods (F.E.M, theta-method, ...) for this phenomenon require small time-step and space discretization to ensure both convergence and accuracy. Yet this leads to a high computational cost. Moreover, a very small time-step can lead to spurious oscillations that impact the precision of the results. Thus, we propose to use a Self-organized Gradient Percolation (SGP) algorithm to reduce the computational cost and overcome these numerical drawbacks. The (SGP) method is based on gradient percolation theory, relevant to calculation of local saturation. The initialization of this algorithm is driven by an analytic solution of the homogenous diffusion equation, which is a convolution between a Probability Density Function (PDF) and a smoothing function. Thus, we propose to reproduce the evolution of the capillary pressure profiles by the evolution of the standard deviation of the PDF. This algorithm is validated by comparing the results with the capillary pressure profiles and the mass gain curve obtained by finite element simulations and experimental measurements, respectively. The computational time of the proposed algorithm is lower than that of finite element models for one-dimension case. In conclusion, the SGP method permits to reduce the computational cost and does not produce spurious oscillations. The work is still going on for extension in 3D and the first results are promising.