Many theoretical treatments of transport in heterogeneous Darcy flows consider advection only. When local-scale dispersion is neglected, flux weighting persists over time; mean Lagrangian and Eulerian flow velocity distributions relate simply to each other and to the variance of the underlying hydraulic conductivity field. Local-scale dispersion complicates this relationship, potentially causing initially flux-weighted solute to experience lower-velocity regions as well as Taylor-type macrodispersion due to transverse solute movement between adjacent streamlines. To investigate the interplay of local-scale dispersion with conductivity log-variance, correlation length, and anisotropy, we perform a Monte Carlo study of flow and advective-dispersive transport in spatially-periodic 2D Darcy flows in large-scale, high-resolution multivariate Gaussian random conductivity fields. We observe flow channeling at all heterogeneity levels and quantify its extent. We find evidence for substantial effective retardation in the upscaled system, associated with increased flow channeling, and observe limited Taylor-type macrodispersion, which we physically explain. A quasi-constant Lagrangian velocity is achieved within a short distance of release, allowing usage of a simplified continuous-time random walk (CTRW) model we previously proposed in which the transition time distribution is understood as a temporal mapping of unit time in an equivalent system with no flow heterogeneity. The numerical data set is modeled with such a CTRW; we show how dimensionless parameters defining the CTRW transition time distribution are predicted by dimensionless heterogeneity statistics and provide empirical equations for this purpose.

中文翻译：

---

在具有局部尺度分散特征的异质介质中放大传输：流道、宏观延迟和参数预测


许多关于非均质达西流中输运的理论处理只考虑了平流。当忽略局部尺度的色散时，磁通量加权会随着时间的推移而持续存在;平均拉格朗日流速分布和欧拉流速分布彼此简单相关，并且与下面的水力传导率场的方差有关。局部尺度的色散使这种关系复杂化，可能导致最初的磁通量加权溶质经历较低的速度区域，以及由于相邻流线之间的溶质横向运动而出现泰勒型宏观色散。为了研究局部尺度色散与电导率对数方差、相关长度和各向异性的相互作用，我们对大规模、高分辨率多变量高斯随机电导率场中空间周期 2D 达西流中的流动和平流-色散传输进行了蒙特卡洛研究。我们观察所有异质性水平的流道并量化其程度。我们发现在放大系统中存在实质性有效延迟的证据，与流道增加相关，并观察到有限的泰勒型宏观分散，我们对此进行了物理解释。在释放的短距离内实现了准恒定的拉格朗日速度，从而允许使用我们之前提出的简化的连续时间随机游走 （CTRW） 模型，其中过渡时间分布被理解为在没有流异质性的等效系统中单位时间的时间映射。数值数据集使用这样的 CTRW 建模;我们展示了定义 CTRW 过渡时间分布的无量纲参数如何通过无量纲异质统计来预测，并为此提供了经验方程。