Concentration variance and spatial covariance in second‐order stationary heterogeneous conductivity fields
Concentration variance and spatial covariance in second‐order stationary heterogeneous conductivity fields
复制标题
二阶平稳异质电导率场中的浓度方差和空间协方差
DOI：
10.1029/2001wr900009
复制
发表时间：
2001
影响因子：
5.4
通讯作者：
J. Vanderborght
中科院分区：
文献类型：
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作者：
J. Vanderborght
基于溶质粒子轨迹的一阶近似，在拉格朗日框架下推导了二阶稳态电导率场中均匀平均流驱动的对流色散输运的浓度方差和空间协方差。通过根据“反向”溶质轨迹概率分布定义特定位置x和时间t的浓度，可以大大简化大注入体积浓度（co）方差的近似。这是一个假想的微观的，不可分的溶质粒子的轨迹的概率，它在体积Δx中，在时间t，以x为中心，在溶质注入时，在注入体积V0中。在生成的二阶平稳电导率场中，通过输运模拟得出的浓度协方差验证了近似的浓度（co）方差。近似解相当好地再现了局部尺度分散和水导率的空间变异性对浓度（co）方差的影响。研究了水导率场的空间结构对浓度空间协方差的影响，以确定可以从浓度场结构明确确定的参数。对于给定的溶质羽流在平均流动方向上的扩散X11(t)、给定的loge转换后的导水率在横向方向上的空间相关长度Iƒ2和给定的局部尺度色散Dd，浓度协方差几乎不变，几乎不受协方差函数e和loge转换导水率方差σf2的各向异性的影响。因此，e和σf2不能从浓度场的空间结构中明确确定。横向到平均流动方向上的浓度方差和空间协方差主要由局部尺度分散的横向分量Dd22和横向到流动方向上的loge转换电导率的空间相关长度Iƒ2决定。这两个参数可以明确地从浓度（co）方差中得出。
The concentration variance and spatial covariance resulting from convective‐dispersive transport driven by a uniform mean flow in second‐order stationary conductivity fields was derived in a Lagrangian framework based on a first‐order approximation of solute particle trajectories. The approximation of the concentration (co)variances for large injection volumes is considerably simplified by defining the concentration at a certain location x and time t in terms of the “backward” solute trajectory probability distribution. This is the probability that the trajectory of a fictitious microscopic and indivisible solute particle, which is in a volume Δx centered around x at time t, was at the time of solute injection, t0, in the injection volume, V0. The approximated concentration (co)variances were validated against concentration covariances derived from transport simulations in generated second‐order stationary conductivity fields. The approximate solutions reproduced fairly well the effects of local scale dispersion and of the spatial variability of the hydraulic conductivity on the concentration (co)variance. The effect of the spatial structure of the hydraulic conductivity field on the spatial covariance of the concentrations was investigated in order to identify parameters that can be unequivocally determined from the structure of the concentration field. For a given spreading of the solute plume in the mean flow direction, X11(t), a given spatial correlation length of the loge transformed hydraulic conductivity in the transverse to flow direction, Iƒ2, and a given local scale dispersion Dd the concentration covariance was nearly invariant and hardly influenced by the anisotropy of the covariance function, e, and the variance, σf2, of the loge transformed conductivity. As a result, e and σf2 cannot be unequivocally determined from the spatial structure of the concentration field. The concentration variance and spatial covariance in the transverse to mean flow direction are predominantly determined by the lateral component of the local scale dispersion, Dd22 and by the spatial correlation length of the loge transformed conductivity in the transverse to flow direction, Iƒ2. These two parameters might be unequivocally derived from the concentration (co)variance.