Defining and Validating Convergence Criteria for the Determination of Representative Elementary Volume in Porous Media

Abstract

The representative elementary volume (REV) is a fundamental concept in the study of porous media, describing the minimum volume at which a material property can be considered statistically representative of the whole. Determining an REV is essential for linking pore-scale measurements, often obtained from high-resolution imaging, to continuum-scale models used in engineering and geoscience. In particular, accurate REV identification of porosity and tortuosity is critical, as these parameters govern transport processes such as flow, diffusion, and conductivity in porous structures. This work presents a systematic methodology for identifying REVs based on a threshold criteria designed to reduce computational demands. An REV is defined as the volume in which at least 80% of 100 randomly sampled subdomains yield porosity or tortuosity values within 20% of the overall average. The method was applied to both synthetic datasets and real samples provided by Dong and Blunt, with subdomain volumes ranging from 10^3 to 100^3 voxels [1]. Of the 12 real samples analyzed, 7 satisfied the proposed criteria, and REVs were identified for both porosity and tortuosity. Samples that met the criteria exhibited smaller average pore sizes and higher porosity ratios, while outliers were explained using pore size distribution data. To further assess robustness, predicted tortuosity values obtained using the correlation proposed by Tomadakis and Sotirchos were compared with ground truth measurements [2]. Several samples failed to reproduce the true values, indicating that even when an image contains an REV, it may not be internally self-consistent. While this may appear contradictory, it reflects the distinction between the stability of averaged values across subdomains and predictive accuracy of empirical correlations. The results of this work demonstrate that REVs can be identified from relatively small fractions of the total image volume given that certain conditions are met, offering a balance between accuracy and computational efficiency. This framework provides a flexible approach for porous media characterization, with direct implications for hydrogeology, petroleum recovery, fuel cell design, and filtration technologies.