A solute flux approach to transport in heterogeneous formations: 1. The general framework
A solute flux approach to transport in heterogeneous formations: 1. The general framework
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DOI：
10.1029/91wr03086
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发表时间：
1992-05
影响因子：
5.4
通讯作者：
G. Dagan;V. Cvetkovic;A. Shapiro
中科院分区：
文献类型：
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作者：
G. Dagan;V. Cvetkovic;A. Shapiro
非均质地层中的溶质运移一般用滞留浓度C（x，t）表示，并将其视为随机空间函数。本研究调查的替代表示q，溶质质量通量在一个点的控制平面垂直于平均流量。这种表示法适用于许多现场应用，其中感兴趣的变量是通过控制表面排出的溶质的质量。建立了一个计算q和相关的总溶质排放量Q和质量M的统计矩的一般框架。当x为平均流的方向时，溶质粒子在y = η，z = η和行进（到达）时间τ处穿过控制平面。相关的预期溶质通量值与η、τ和τ的联合概率密度函数（pdf）g1成比例，而q的方差取决于两个粒子的相同变量的联合pdf g2。反过来，η、τ和τ的统计矩通过随机常微分方程系统依赖于速度分量的统计矩。对于一个稳定的速度场，忽略孔隙尺度弥散的影响，问题的一个主要简化导致了随机变量η，τ和τ的独立性。因此，η和η的pdf可以独立于τ导出。概述了几种求取η、τ和τ统计矩的近似方法。本文第二部分将对这些方法进行探讨，以便有效地推导出总溶质流量和质量的方差，而第三部分将讨论速度方差对η、τ和τ矩的非线性影响
It is common to represent solute tranport in heterogeneous formations in terms of the resident concentration C(x, t), regarded as a random space function. The present study investigates the alternative representation by q, the solute mass flux at a point of a control plane normal to the mean flow. This representation is appropriate for many field applications in which the variable of interest is the mass of solute discharged through a control surface. A general framework to compute the statistical moments of q and of the associated total solute discharge Q and mass M is established. With x the direction of the mean flow, a solute particle is crossing the control plane at y = η, z = ζ and at the travel (arrival) time τ. The associated expected solute flux value is proportional to the joint probability density function (pdf) g1 of η, ζ and τ, whereas the variance of q is shown to depend on the joint pdf g2 of the same variables for two particles. In turn, the statistical moments of η, ζ and τ depend on those of the velocity components through a system of stochastic ordinary differential equations. For a steady velocity field and neglecting the effect of pore-scale dispersion, a major simplification of the problem results in the independence of the random variables η, ζ and τ. As a consequence, the pdf of η and ζ can be derived independently of τ. A few approximate approaches to derive the statistical moments of η, ζ and τ are outlined. These methods will be explored in paper 2 in order to effectively derive the variances of the total solute discharge and mass, while paper 3 will deal with the nonlinear effect of the velocity variance upon the moments of η, ζ and τ