Bimolecular second-order reactions in spatially varying flows: Segregation induced scale-dependent transformation rates
Bimolecular second-order reactions in spatially varying flows: Segregation induced scale-dependent transformation rates
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DOI：
10.1029/96wr03687
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发表时间：
1997-04-01
影响因子：
5.4
通讯作者：
MirallesWilhelm, F
中科院分区：
文献类型：
--
作者：
Kapoor, V;Gelhar, LW;MirallesWilhelm, F
为了量化自然水文环境中的化学转化，需要了解它们与空间变化流量的耦合。考虑基本双分子二阶不可逆化学反应，其中任意点的转化率与该点两个不同物质的浓度乘积成正比（r(c(1), c(2)) = kappa c(1)c(2)，kappa 假设为常数）。将此类化学反应纳入水文输送模型时会出现问题，由于缺乏对流量所有细节的了解或计算限制，这些输送模型只能提供浓度场 (, ) 的空间平均值的估计，而不是不同物种浓度乘积的平均值 , 。然而，需要评估该空间平均值，以量化与空间平均浓度场相关的化学转化率（即，(r) 超过 bar = ）。对于一种物质在另一种物质的均匀背景下的脉冲输入，层流剪切流和非均匀多孔介质流的详细数值模拟表明，流动的空间变化导致小尺度浓度变化 c'(m) - c(m) - ； m = 1, 2) 不同物种呈负相关 (< 0)。这种小规模的溶质分离会产生依赖于尺度的转化，将平均浓度代入转化率表达式：r(, ) = kappa, 。偏析强度 /, ) 与流动变化和小规模混合机制（扩散/局部分散）密切相关。偏析强度的绝对值最初增加后，由于扩散的累积平滑作用，它随着时间缓慢减小。与水文问题一样，流量变异尺度特征的扩散时间尺度可能相当大；将平均浓度代入在充分混合的批次测试中确定的速率表达式可能会高估化学转化速率。
To quantify chemical transformations in natural hydrologic environments, their coupling with spatially varying flows needs to be understood. Consider the elementary bimolecular second-order irreversible chemical reaction for which the transformation rate at any point is proportional to the product of the concentrations of two distinct species at that point (r(c(1), c(2)) = kappa c(1)c(2), kappa assumed to be constant). A problem arises in incorporating such chemical reactions in hydrologic transport models, On account of a lack of knowledge of all of the details of flows, or computational limitations, these transport models can only provide estimates of spatial averages of the concentration fields (, ) and not the average of the product of the concentration of the different species, . However, that spatial average needs to be assessed to quantify the chemical transformation rate pertinent to the spatially averaged concentration field (i.e., (r) over bar = ). For an impulse input of one species in a uniform background of the other species, detailed numerical simulations in laminar shear flow and heterogeneous porous media flow show that the spatial variability of flow causes the small-scale concentration variations c'(m) - c(m) - ; m = 1, 2) of the different species to be negatively correlated ( < 0). This small-scale segregation of solutes gives rise to a scale-dependent transformation substituting the mean concentration into the transformation rate expression: r(, ) = kappa, . The segregation intensity /, ) is strongly related to both the flow variations and the small-scale mixing mechanisms (diffusion/local dispersion). After an initial increase in the absolute value of the segregation intensity, it slowly decreases with time due to the cumulative smoothing action of diffusion. As in hydrologic problems, the diffusion timescales characteristic to the flow variability scales can be quite large; substituting mean concentrations into rate expressions determined in well-mixed batch tests is likely to overestimate the chemical transformation rate.