Analyses of representative elementary volume for coal using X-ray μ-CT and FIB-SEM and its application in permeability predication model

The representative elemental volume (REV) study provides a bridge between macro and micro properties' research, which is critical for understanding and predicting the heterogeneous properties of a porous media. Permeability, one of the essential properties, dominates the capability of fluid flow in porous media, which is scale dependent and thus one of the most rationale way to predict macro scale permeability is to calculate the permeability at REV. Porosity is the most common parameter to determine REV, however, the porosity based REV works less satisfactory for complex pore system. In this work, we determined the REV based on fractal dimension, which is a fundamental parameter to characterize the complex pore network, and then the relation between fractal dimension and sample size was investigated extensively. We then determined and compared the REV from the porosity and fractal dimension that calculated from various sample sizes. Our results reveal that the relationship between fractal dimension-based REV and porosity-based REV can be classified as four cases, and the most common case is porosity declines if the domain is larger than fractal dimension-based REV size. The relation discussed above can be applied to existing fractal permeability models to predict the permeability at different scales.