Evolution and persistence of cross‐directional statistical dependence during finite‐Péclet transport through a real porous medium
Evolution and persistence of cross‐directional statistical dependence during finite‐Péclet transport through a real porous medium
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通过真实多孔介质的有限佩克莱特传输过程中横向统计依赖性的演变和持久性
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发表时间：
2016
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通讯作者：
W. Nowak
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作者：
S. Most;B. Bijeljic;W. Nowak
完全饱和的复杂多孔介质中被动溶解化合物的传输经常表现出非菲克特征。最有趣的问题之一是确定可以将运输描述为统计独立过程的时间尺度。因此，我们研究进化机制，然后研究非 Fickianity 作为时间增加函数的减少。采用拉格朗日观点，我们通过分析真实多孔介质中的粒子轨迹，提供对流扩散过程的非线性关联分析，如对多丁顿砂岩三维图像的直接数值模拟所提供的。首先，我们分析了时间连续粒子位置增量之间的记忆效应以及纵向和横向粒子位置增量之间的相互依赖性，作为给定时间增量和连续时间增量之间的时间滞后的函数。其次，我们研究了佩克莱特政权对依赖性时间演变的影响。我们的主要发现是：（a）纵向和横向粒子位置增量之间的交叉依赖性在研究的时间增量范围内持续存在，尽管迄今为止这一方面已被忽略。 (b) 较低的佩克莱特数导致较弱的依赖性，然而，随着时间的推移，这种依赖性比较高的佩克莱特传输机制更持久。我们确认非菲克性来自与速度场异质性相关的空间相干性，速度场异质性将交叉依赖性和记忆引入到传输过程中。总的来说，我们表明记忆和交叉依赖在所有方向上和之间都是持久的，依赖是高度非线性的，发生在不同的时间尺度上，并且依赖于佩克莱特数。
Transport of passive, dissolved compounds in fully‐saturated complex porous media frequently exhibits non‐Fickian characteristics. One of the most interesting questions is to ascertain the time scales at which it is possible to describe transport as a statistically independent process. Therefore, we study the mechanisms for evolution and then the decrease of non‐Fickianity as a function of increasing time. Adopting the Lagrangian perspective, we provide a nonlinear copula analysis of advective‐diffusive processes by analyzing particle trajectories in a real porous media, as provided by direct numerical simulations on the three‐dimensional image of Doddington sandstone. First, we analyze the memory effects between time‐consecutive particle position increments and cross dependence between longitudinal and transversal particle position increments as a function of given time increments and time lags between consecutive time increments. Second, we investigate the influence of the Péclet regime on the temporal evolution of dependence. Our main findings are: (a) Cross dependence between longitudinal and transversal particle position increments is persistent over the investigated range of time increments, even though this aspect has been neglected up to date. (b) Lower Péclet numbers lead to a weaker dependence that is, however, more persistent over time than in higher‐Péclet transport regimes. We confirm that non‐Fickianity comes from spatial coherence associated with heterogeneities of the velocity field that introduce cross dependence and memory into the transport process. Overall, we show that memory and cross dependence are persistent in and among all directions, that the dependence is highly‐nonlinear, occurs at different temporal scales, and is dependent on the Péclet number.