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首页> 外文期刊>Water resources research >Modeling flow and transport in highly heterogeneous three-dimensional aquifers: Ergodicity, Gaussianity, and anomalous behavior-1. Conceptual issues and numerical simulations
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Modeling flow and transport in highly heterogeneous three-dimensional aquifers: Ergodicity, Gaussianity, and anomalous behavior-1. Conceptual issues and numerical simulations

机译：在高度异构的三维含水层中模拟流动和传输：遍历，高斯和异常行为-1。概念问题和数值模拟

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摘要

Uniform flow of mean velocity U takes place in a highly heterogeneous, isotropic, aquifer of lognormal conductivity distribution (variance σ_Y~2, integral scale I). A conservative solute is injected instantaneously over an area A_0 at x = 0, normal to the mean flow, in a flux-proportional mode. Longitudinal spreading is caused by advection by the fluid velocity and is quantified with the aid of the mass flux μ(t, x) through fixed control planes at x. An equivalent macrodispersivity is defined in terms of the traveltime variance. The flow and transport are solved numerically in three realizations of the conductivity field with σ_Y~2 = 2, 4, 8, respectively. The medium is modeled by a collection of a large number N = 100,000 of spherical inclusions whose conductivities are drawn at random. Transport is simulated by tracking 40,000 particles originating at a large injection area (A_0 approx= 2000 I~2) and for travel distance x ≤ 121 I. It is found that the mass flux has a highly skewed time distribution because of the late arrival of solute particles that are moving through low-conductivity blocks. The tail leads to large values of the equivalent macrodispersivity, which is highly dependent on cutoffs corresponding to the arrival of even 0.999 or 0.995 of the total mass. Furthermore, the tail is nonergodic, as it depends on the plume size. Transport appears to be anomalous in the considered interval, although by the central limit theorem it has to tend asymptotically to Fickianity and Gaussianity.
机译：平均速度U的均匀流动发生在对数正态电导率分布（方差σ_Y〜2，整数比例I）的高度非均质，各向同性的含水层中。在通量比例模式下，将保守的溶质瞬时注入到x = 0处的A_0区域，垂直于平均流量。纵向扩展是由流速对流引起的，并借助于在x处固定控制平面的质量通量μ（t，x）进行量化。等效的宏观分散度是根据旅行时间方差定义的。在电导率场的三个实现中分别用σ_Y〜2 = 2、4、8数值求解了流动和传输。该介质以大量N = 100,000的球形夹杂物的集合为模型，其电导率是随机绘制的。通过跟踪起源于较大注入区域（A_0大约= 2000 I〜2）且行进距离x≤121 I的40,000个粒子来模拟输运。发现由于通量的到来较晚，质量通量具有高度偏斜的时间分布。穿过低电导块的溶质颗粒。尾部导致较大的等效宏观分散度值，这在很大程度上取决于临界值，该临界值甚至相当于总质量的0.999或0.995的到来。此外，尾巴是非遍历的，这取决于烟羽的大小。在所考虑的时间间隔内，运输似乎是异常的，尽管根据中心极限定理，它必须渐近趋于Fickianity和Gaussianity。

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