A new criterion for determining the representative elementary volume of translucent porous media and inner contaminant

摘要

Representative elementary volume?(REV) is essential for measuring and quantifying the effective parameters of a complex heterogeneous medium. To overcome the limitations of the existing REV estimation criteria, a new REV estimation criterion?( χ i ) based on dimensionless range and gradient calculation is proposed in this study to estimate the REV of a translucent material based on light transmission techniques. Three sandbox experiments are performed to estimate REVs of porosity, density, tortuosity, and perchloroethylene?(PCE) plume using multiple REV estimation criteria. In comparison with? χ i , previous REV estimation criteria based on the coefficient of variation?( C V i ), the entropy dimension?(DI i ) and the relative gradient error?( ε g i ) are tested in REV quantification of translucent silica and the inner PCE plume to achieve their corresponding effects. Results suggest that the new criterion?( χ i ) can effectively identify the REV in the materials, whereas the coefficient of variation and entropy dimension ( F = - 2.01 × 10 - 12 + 1 2 π × 1.50 e - ( REV - 4.35 ) 2 2 ? 1.50 2 ) are not effective. The relative gradient error can make the REV plateau obvious, while random fluctuations make the REV plateau difficult to identify accurately. Therefore, the new criterion is appropriate for REV estimation of the translucent materials and inner contaminant. Models are built based on a Gaussian equation to simulate the distribution of REVs for media properties, whose frequency of REV is dense in the middle and sparse on both sides. REV estimation of the PCE plume indicates that a high level of porosity leads to a large value of mean and standard deviation for REVs of PCE saturation?( S o ) and PCE–water interfacial area?( A OW ). Fitted equations are derived from distribution of REVs for the PCE plume related to? d m (distances from mass center to considered point) and d I ?(distances from injection position to considered point). Moreover, relationships between REVs of the PCE plume and? S o are fitted using regression analysis. Results suggest a decreasing trend appears for S o -REV when S o ?increases, while A OW -REV increases with increasing? S o .