Transport in three-dimensionally heterogeneous aquifers: 2. Predictions and observations of concentration fluctuations
Transport in three-dimensionally heterogeneous aquifers: 2. Predictions and observations of concentration fluctuations
复制标题
三维非均质含水层中的输运：2.浓度波动的预测和观测
DOI：
10.1029/94wr00075
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发表时间：
1994
影响因子：
5.4
通讯作者：
L. Gelhar
中科院分区：
文献类型：
--
作者：
V. Kapoor;L. Gelhar
对于一个多维有限尺寸脉冲输入，给出了浓度方差守恒方程σc2的解析解。由于局部色散的耗散作用，在较大的时间内，σc是平均浓度的递减分数。科德角溴化物示踪剂显示出这种减少。对数电导率微尺度越大，局部色散作用越慢，预测的σc与平均浓度之比（即变异系数）随时间的下降速率越慢，在大时间内，反之亦然。变异系数随距离中心的远近而增大。σc2的产生率和耗散率之间的平衡与偏离质心的平均浓度场梯度的平方线性相关。对于局部色散为零的情况，σc是平均浓度随时间无界增长的倍数。纵向空间二阶矩和宏观色散对局部色散的包含/排除不敏感，因此不能区分两种不同情况下的浓度场。相反，σc2的时空演化是由局部色散的耗散作用奇异地决定的。为了评估含水层中的污染物浓度，需要对局部分散度进行测量，同时对水力传导率变化进行表征。
For a multidimensional finite-size impulse input, analytical solutions to the conservation equation for concentration variance σc2 are presented. Due to the dissipating action of local dispersion, at large times, σc is a decreasing fraction of the mean concentration. The Cape Cod bromide tracer exhibits this decrease. The larger the log conductivity microscale is, the slower is the action of local dispersion, and the slower is the predicted rate of decrease of the ratio of σc and the mean concentration (i.e., the coefficient of variation) with time, at large times, and vice versa. The coefficient of variation increases with distance from the center. A balance between the rates of production and dissipation of σc2 relates it linearly to the squared gradients of the mean concentration field, away from the center of mass. For the zero local dispersion case, σc is an unboundedly growing multiple with time of the mean concentration. The longitudinal spatial second moment and macrodispersivities are insensitive to the inclusion/exclusion of local dispersion and therefore do not differentiate between the concentration fields for the two different cases. In contrast, the spatial-temporal evolution of σc2 is singularly determined by the dissipating action of local dispersion. Measurements of local dispersivities need to be made along with a characterization of hydraulic conductivity variations to assess contaminant concentrations in aquifers.