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Longitudinal dispersion coefficients for numerical modeling of groundwater solute transport in heterogeneous formations

机译：非均质地层地下水溶质运移数值模拟的纵向扩散系数

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Most recent research on hydrodynamic dispersion in porous media has focused on whole-domain dispersion while other research is largely on laboratory-scale dispersion. This work focuses on the contribution of a single block in a numerical model to dispersion. Variability of fluid velocity and concentration within a block is not resolved and the combined spreading effect is approximated using resolved quantities and macroscopic parameters. This applies whether the formation is modeled as homogeneous or discretized into homogeneous blocks but the emphasis here being on the latter. The process of dispersion is typically described through the Fickian model, i.e., the dispersive flux is proportional to the gradient of the resolved concentration, commonly with the Scheidegger parameterization, which is a particular way to compute the dispersion coefficients utilizing dispersivity coefficients. Although such parameterization is by far the most commonly used in solute transport applications, its validity has been questioned. Here, our goal is to investigate the effects of heterogeneity and mass transfer limitations on block-scale longitudinal dispersion and to evaluate under which conditions the Scheidegger parameterization is valid. We compute the relaxation time or memory of the system; changes in time with periods larger than the relaxation time are gradually leading to a condition of local equilibrium under which dispersion is Fickian. The method we use requires the solution of a steady-state advection-dispersion equation, and thus is computationally efficient, and applicable to any heterogeneous hydraulic conductivity K field without requiring statistical or structural assumptions. The method was validated by comparing with other approaches such as the moment analysis and the first order perturbation method. We investigate the impact of heterogeneity, both in degree and structure, on the longitudinal dispersion coefficient and then discuss the role of local dispersion and mass transfer limitations, i.e., the exchange of mass between the permeable matrix and the low permeability inclusions. We illustrate the physical meaning of the method and we show how the block longitudinal dispersivity approaches, under certain conditions, the Scheidegger limit at large Péclet numbers. Lastly, we discuss the potential and limitations of the method to accurately describe dispersion in solute transport applications in heterogeneous aquifers.
机译：关于多孔介质中流体动力分散的最新研究集中在全域分散，而其他研究则主要集中在实验室规模的分散。这项工作着重于数值模型中单个块对分散的贡献。区块内流体速度和浓度的变化尚未解决，并且使用解析的数量和宏观参数来估算组合的扩散效果。无论将地层建模为均质还是离散为均质块均适用，但此处重点是后者。分散过程通常通过Fickian模型来描述，即通常通过Scheidegger参数化来确定分散通量与分辨浓度的梯度成比例，这是利用分散系数计算分散系数的一种特殊方法。尽管这种参数化是迄今为止在溶质传输应用中最常用的参数，但其有效性一直受到质疑。在这里，我们的目标是研究异质性和传质限制对块状纵向扩散的影响，并评估Scheidegger参数化在哪些条件下有效。我们计算系统的弛豫时间或内存；周期大于弛豫时间的时间变化逐渐导致局部平衡的条件，在该条件下色散为菲克。我们使用的方法需要求解稳态对流扩散方程，因此计算效率高，适用于任何非均质导水系数K场，而无需统计或结构上的假设。通过与矩量分析和一阶摄动法等其他方法进行比较，验证了该方法的有效性。我们研究了程度和结构上的非均质性对纵向弥散系数的影响，然后讨论了局部弥散和传质限制的作用，即渗透性基质与低渗透性包裹体之间的质量交换。我们说明了该方法的物理含义，并说明了在某些条件下大Pcletlet数下嵌段纵向分散性如何接近Scheidegger极限。最后，我们讨论了准确描述非均质含水层中溶质运移应用中分散的方法的潜力和局限性。

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