A joint velocity‐concentration PDF method for tracer flow in heterogeneous porous media
A joint velocity‐concentration PDF method for tracer flow in heterogeneous porous media
复制标题
非均质多孔介质中示踪剂流动的联合速度-浓度 PDF 方法
DOI：
10.1029/2010wr009450
复制
发表时间：
2010
影响因子：
5.4
通讯作者：
H. Tchelepi
中科院分区：
文献类型：
--
作者：
D. Meyer;P. Jenny;H. Tchelepi
污染物或示踪剂的局部浓度的概率密度函数（PDF）是涉及非均质地下地层中的流动的应用中的风险评估的重要组成部分。本文提出了一种新的求解高度非均质多孔介质中示踪剂渗流问题的速度-浓度联合PDF方法。PDF形式主义解释了平流输运、孔尺度分散（PSD）和分子扩散。低阶近似（LOA）通常使用微扰展开获得，通常会导致高斯单点速度PDF。此外，LOA为小的对数电导率变化提供了合理的近似值（即，σY2 < 1）。然而，对于较大的σY2，单点速度PDF显著偏离高斯分布，这一点已被多项蒙特卡罗（MC）模拟研究所证实。此外，拉格朗日速度统计数据表现出跨越广泛尺度的复杂相关性，包括由于优先流路形成而产生的长程相关性。在所提出的联合PDF方法中，非高斯PDF和复杂的长程相关性都使用马尔可夫速度过程（MVP）精确地表示。LOA方法可以通过假定浓度PDF的特定形状（例如，β PDF完全由浓度均值和方差表征）。这里提出的联合速度-浓度PDF方法不需要对边缘浓度PDF的形状进行任何闭合假设。欧拉联合PDF输运方程使用计算高效的基于粒子的方法进行数值求解。PDF方法用Caroni和Fiorotto（2005）的高分辨率MC参考数据进行了验证，这些数据用于速度场中的饱和输运，这些速度场在空间和时间上都是稳定的，适用于σY2 = 0.05、1和2以及Péclet数范围从100到10，000的区域。在参考MC计算和我们的PDF方法中，PSD均使用恒定的各向异性色散系数建模。
The probability density function (PDF) of the local concentration of a contaminant, or tracer, is an important component of risk assessment in applications that involve flow in heterogeneous subsurface formations. In this paper, a novel joint velocity‐concentration PDF method for tracer flow in highly heterogeneous porous media is introduced. The PDF formalism accounts for advective transport, pore‐scale dispersion (PSD), and molecular diffusion. Low‐order approximations (LOAs), which are usually obtained using a perturbation expansion, typically lead to Gaussian one‐point velocity PDFs. Moreover, LOAs provide reasonable approximations for small log conductivity variances (i.e., σY2 < 1). For large σY2, however, the one‐point velocity PDFs deviate significantly from the Gaussian distribution as demonstrated convincingly by several Monte Carlo (MC) simulation studies. Furthermore, the Lagrangian velocity statistics exhibit complex correlations that span a wide range of scales, including long‐range correlations due to the formation of preferential flow paths. Both non‐Gaussian PDFs and complex long‐range correlations are accurately represented using Markovian velocity processes (MVPs) in the proposed joint PDF method. LOA methods can be generalized to some extent by presuming a certain shape for the concentration PDF (e.g., a β PDF fully characterized by the concentration mean and variance). The joint velocity‐concentration PDF method proposed here does not require any closure assumptions on the shape of the marginal concentration PDF. The Eulerian joint PDF transport equation is solved numerically using a computationally efficient particle‐based approach. The PDF method is validated with high‐resolution MC reference data from Caroni and Fiorotto (2005) for saturated transport in velocity fields, which are stationary in space and time, for domains with σY2 = 0.05, 1, and 2 and Péclet numbers ranging from 100 to 10,000. PSD is modeled using constant anisotropic dispersion coefficients in both the reference MC computations and our PDF method.