A three-dimensional model for quantification of the representative elementary volume of tortuosity in granular porous media

For most of aquifers with abundant groundwater resource, quantifications of tortuosity and corresponding representative elementary volume (REV) are very essential to improve the understanding of groundwater and contaminant transfers in porous media. In this study, a mathematical model of tortuosity based on the three dimensional (3D) microstructure of regular tetrahedron (RTM) is proposed to quantify tortuosity and corresponding REV of granular porous media. The calculated tortuosity using the new 3D RTM model agrees well with the measured tortuosity in experiment, indicating that the new 3D microstructure model is more appropriate to precisely delineate the tortuosity of granular porous media. Afterward, the new model is utilized to quantify the tortuosity of heterogeneous translucent silica. Moreover, corresponding REV is estimated using a criterion of relative gradient error (epsilon(i)(g)). Results suggest minimum tau-REV sizes most distribute in 0.0-5.0 mm and the bound of cumulative frequency above 80% is larger than 3.00 mm. The REV scale of tortuosity has its own rationality and superiority over that estimated by two-dimensional (2D) tortuosity model, implying the proposed 3D tortuosity model of RTM is helpful for understanding the tortuosity of flow paths in granular porous media and corresponding REV estimation of tortuosity. (C) 2017 Elsevier B.V. All rights reserved.