In this work, the variability of regional-scale transport of inert solutes in heterogeneous confined aquifers of variable thickness is quantified by the variance of the displacement of a solute particle. In the traditional stochastic approach to solute transport at the regional scale, the variability of solute displacement is attributed to the variability of the transmissivity fields. In this work, however, variability in solute displacement is attributed to variability in hydraulic conductivity and aquifer thickness fields. A general stochastic methodology for deriving the variance of the displacement of a solute particle based on the convection velocity of solute particles, developed from the relationship between the two-dimensional depth-averaged solute mass conservation equation and the Fokker-Planck equation, is given. Assuming that the fluctuations in log hydraulic conductivity and log thickness of the confined aquifer are second-order stationary processes, a closed-form expression for the solute displacement variance in the mean flow direction is obtained for the case of advection-dominated solute transport. The results show that variation in hydraulic conductivity and aquifer thickness can lead to nonstationarity in the covariance of flow velocity, making longitudinal macrodispersion anomalous and increasing linearly with travel time at large distances.

中文翻译：

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非均质承压含水层中溶质颗粒位移的变化

在这项工作中，不同厚度的非均质承压含水层中惰性溶质的区域尺度输运的变异性通过溶质颗粒位移的方差来量化。在区域尺度溶质输运的传统随机方法中，溶质位移的变化归因于透射率场的变化。然而，在这项工作中，溶质位移的变化归因于水力传导率和含水层厚度场的变化。给出了一种基于溶质颗粒对流速度推导溶质颗粒位移方差的通用随机方法，该方法是根据二维深度平均溶质质量守恒方程和福克-普朗克方程之间的关系发展而来的。假设承压含水层测井导水率和测井厚度的波动为二阶平稳过程，对于平流主导溶质输运的情况，得到了平均流向溶质位移方差的闭式表达式。结果表明，水力传导率和含水层厚度的变化会导致流速协方差的非平稳性，使得纵向宏观离散异常并在大距离处随传播时间线性增加。