Multi-scale study of diffusion in composite grain–pore systems based on particles random walk

Abstract

This paper studies diffusion processes at different scales in two-dimensional (2D) composite media (grain–pore porous micromodels). To model diffusion, this study uses the random walk particle tracking (RWPT) method based on 2D analytical solutions in finite and semi-infinite domains with zero-flux boundary conditions (BC) at grain boundaries. The analytical solutions are developed using a method of images. Then, an RWPT combined to a Stop&Go algorithm is derived from these analytical solutions. The developed RWPT algorithm is then used to model diffusion processes inside the pores at the “microscopic” level (microscale), while the grain elements are assumed inaccessible to diffusion (zero-flux BC condition at the interface grain/pore). The composite medium, where the diffusion occurs, is a numerical micromodel made of periodic motifs of rectangular grains. Particles are initially located at the center of a pore, and diffuses in the periodic motifs micromodel (infinite domain). First, the grains are chosen square with different sizes to vary the porosity. Second, for constant porosities, the grains are elongated to study the effect of the anisotropy ratio on diffusion processes. Effective macroscale properties (porosities, effective diffusion tensors, tortuosities) are then calculated using moments of particles positions. The results obtained fit well with theoretical expectations and are in very good agreement with results found in the literature.

Keywords

• Composite media
• Diffusion
• Random walk particle tracking (RWPT)
• Discontinuities
• Analytical solutions
• Porous materials
• Zero flux