Time-Dependent Dispersion of Nonergodic Plumes in Two-Dimensional Heterogeneous Aquifers
Time-Dependent Dispersion of Nonergodic Plumes in Two-Dimensional Heterogeneous Aquifers
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二维非均质含水层中非穿经羽流随时间的扩散
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发表时间：
1997
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影响因子：
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通讯作者：
Dongxiao Zhang
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作者：
You‐Kuan Zhang;Dongxiao Zhang
在均匀平均速度μ和粒子位移的一阶近似下，在二维（2D）统计各向同性介质中计算非遍历羽流的随时间变化的二阶空间矩hZ(it)≡-hS （i0）和有效色散hγ(it)，定义为1/2μ id /idit，以研究初始羽流大小对hZ（it）和γ(it)的影响，其中为溶质羽流在质心附近的二阶空间矩hS（it）的集合平均值。hS（i0）为hS（it）的初值。研究发现，区域震源的长径比（ιd/ιd1）对非过流羽流的色散行为有重要影响，其中，ιd2和ιd1分别是震源正向和平行于μ的归一化长度（相对于测井-水力导电性相关尺度）。当ιd2/ιd1≥1时，纵向和横向秒空间矩iZd1d1和iZd2d2在早期均增大，在较大时间iZd1d1与时间成正比，或纵向有效色散γd1d1趋近于常数，而iZd2d2趋近于常数或γd1d1趋近于零。当ιd2/ιd1<1时，iZdiidii和γdiidii （ii=1,2）较早升高。然而，在后期，它们的行为方式根本不同：iZd1d1单调增加到接近常数，或者γd1d1逐渐减小到零，而iZd2d2达到峰值，然后减小到零，或者γd2d2低于零，即变为负值，然后再次增加到接近零。一阶理论结果与蒙特卡罗模拟结果的比较表明，对于初始尺寸较大的羽流，在非均匀介质中具有较好的一致性。
The time-dependent second spatial moment hZ(it)≡ –hS(i0) and the effective dispersivity hγ(it), defined as 1/2μ id /idit, of nonergodic plumes are evaluated in two-dimensional (2D) statistically isotropic media under a uniform mean velocity μ, and the first-order approximation of the particle displacement, to study the effect of initial plume size on hZ(it) and γ(it), where is the ensemble average of the second spatial moments, hS(it), of a solute plume about its center of mass, and hS(i0) is the initial value of hS(it). It is found that the aspect ratio ιd/ιd1 of an area source plays an important role in the dispersive behavior of a nonergodic plume, where ιd2 and ιd1 are the normalized lengths (with respect to the correlation scale of log-hydraulic conductivity) of the source normal and parallel to μ, respectively. When ιd2/ιd1 ≥ 1, both the longitudinal and transverse second spatial moments iZd1d1 and iZd2d2 increase at early time, and at large time iZd1d1 becomes proportional to time, or the effective longitudinal dispersivity γd1d1 approaches a constant while iZd2d2 becomes constant or γd1d1 approaches zero. When ιd2/ιd1<1, iZdiidii and γdiidii (ii=1,2) increase at early time. At late time, however, they behave in a fundamentally different manner: iZd1d1 increases monotonicly to approach a constant, or γd1d1 decreases gradually to zero while iZd2d2 reaches a peak and then decreases to zero, or γd2d2 falls below zero, i.e., becomes negative, and increases again to approach zero. Comparison of the first-order theoretical results with a Monte Carlo simulation shows good agreements for plumes with large initial sizes in less heterogeneous media.