Temporal moments for transport with mass transfer described by an arbitrary memory function in heterogeneous media
Temporal moments for transport with mass transfer described by an arbitrary memory function in heterogeneous media
复制标题
异质介质中任意记忆函数描述的传质传输的时间矩
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
J. Carrera
中科院分区：
文献类型：
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作者：
Jian Luo;O. Cirpka;M. Dentz;J. Carrera
时间矩方程被推广用于线性传质下的传输，它已用于模拟各种小规模过程：动力学吸附、扩散到固定区域以及通过非均质含水层的传输。求解力矩方程在形式上与稳态输运方程相同，在计算上比通过积分瞬态通量浓度来评估瞬时力矩更有效。我们推导出通量集中矩的递归关系，它涉及记忆函数的矩，但不依赖于其形状。事实证明，如果低于 k 阶的矩相等，则两个传质模型具有相同的 k 阶矩。特别是，平均保留时间，即固定域中保留概率密度函数（pdf）的一阶矩，决定了浓度的第二时间矩。具有两个一阶速率系数的传质模型可以匹配具有预先描述的传质速率系数 pdf 的多速率模型所描述的第四时间矩。当记忆函数的第 (k-1) 个矩存在时，第 k 个时间矩是有限的。
Temporal moment equations are generalized for transport under linear mass transfer, which has been used to model a broad range of small‐scale processes: kinetic sorption, diffusion into immobile regions, and transport through heterogeneous aquifers. Solving the moment equations, which are formally identical to steady state transport equations, is computationally more efficient than evaluating the temporal moments by integrating the transient flux concentrations. We derive recursive relations for the moments of the flux concentration, which involve the moments of the memory function but do not dependent on its shape. It turns out that two mass transfer models have the same kth temporal moment if the moments of order lower than k are equal. Particularly, the mean retention time, i.e., the first moment of the retention probability density function (pdf) in the immobile domain, decides the second temporal moment of concentration. A mass transfer model with two first‐order rate coefficients can match up to the fourth temporal moment described by a multirate model with a predescribed pdf of the mass transfer rate coefficient. The kth temporal moment is finite when the (k‐1)th moment of the memory function exists.