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 (χⁱ) 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 χⁱ, previous REV estimation criteria based on the coefficient of variation ($C_{\mathrm{V}}^i$ ), the entropy dimension (DIⁱ) and the relative gradient error (${\mathit{\epsilon }}_{\mathrm{g}}^i$ ) are tested in REV quantification of translucent silica and the inner PCE plume to achieve their corresponding effects. Results suggest that the new criterion (χⁱ) can effectively identify the REV in the materials, whereas the coefficient of variation and entropy dimension ($F=-\mathrm{2.01}\times {\mathrm{10}}^{-\mathrm{12}}+\frac{\mathrm{1}}{\sqrt{\mathrm{2}\mathit{\pi }}\times \mathrm{1.50}}{e}^{-\frac{(\mathrm{REV}-\mathrm{4.35}{)}^{\mathrm{2}}}{\mathrm{2}\cdot {\mathrm{1.50}}^{\mathrm{2}}}}$ ) 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.

Column experiments were conducted to investigate the effects of ion type, ion strength, humic acid (HA), and nanometer alumina (NA) particles on the transport of hexavalent chromium (HC) in saturated porous media. A one-dimensional model is developed to simulate the migration of HC affected by NA particles. The results show that nano-alumina particles would enhance the mobility of HC in saturated porous media. However, the influence of NA on the migration of HC in porous media is complex. When the concentration of NA reaches 30 mg/L, HC has minimum retention parameter and best mobility. The transport of HC also is affected by ion strength and ion type. Higher ionic strength would decrease the retention of HC and enhance its mobility. Compared with sodium ion, calcium ion has larger effects on the transport of HC. Moreover, HA can improve the mobility of HC in saturated porous media, but the corresponding promoting effect decreases with the increase of HA concentration. As nanometer contaminants and HC come into the subsurface environment, findings from this study elucidate the key factors and processes controlling the transport of HC in porous media, which can promote the prediction and assessment of HC in the groundwater system.

Oases are vital habitat areas for both humans and wild plants and animals in desert areas of arid Northwestern China. The efficient management of oasis water resources, especially groundwater resources, is very important for the environmental sustainability and economic development of the region. Pumping wells play a vital role in the oasis groundwater supply; therefore, optimizing the layout of these wells is essential for water resource management. In this study, we present a novel optimization methodology that implements a genetic algorithm and nonlinear programming model for the layout of pumping wells. The methodology was tested and evaluated in the real oasis case study of Qira Oasis located in southern Xinjiang Province, China. The optimization result shows that only 68 pumping wells are required for irrigation purposes of Qira Oasis, and this layout reduces the number of current pumping wells strongly by 59%. Thus, a large number of pumping wells can be closed to save resources. The optimizing method presented in this research is mathematically general and can be applied to other oasis areas without any obstacles. This method can provide decision-makers and managers with key information to ensure the optimal management and safety of valuable groundwater resources in oases.