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The behavior of effective rate constants for bimolecular reactions in an asymptotic transport regime

机译:渐进转运体系中双分子反应的有效速率常数的行为

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Previous research has shown that rate constants measured in batch tests (κ) may over-predict the amount of product formation when used in continuum models, and that these rate constants are often much greater than effective ones (λ~(eff)) determined from upscaling studies. However, there is evidence that mixing is more important than the rate constants when using upscaled models. We use a numerical two-dimensional pore-scale porous medium with an approach similar to an experimental column test, and focus on the scenario of the displacement and mixing of two solutions with irreversible bimolecular reactions. Break-through curves of multiple cross-sectional averaged concentrations are analyzed for conservative and reactive transport, as well as the segregation of reactant species along the cross-sections. We compute effective parameters for the continuum scale in order to better understand the impact of using intrinsic rate constants in upscaled models. For a range of Damkohler numbers (Da), we compute effective reaction rate parameters and a reaction effectiveness factor; the latter is described by an empirical formula that depends on the Damkohler number and captures the upscaled system behavior. Our pore-scale results also confirm the segregation concept advanced by Kapoor et al. (1997). We find that for Da > 1, λ~(eff)?κ, and yet the relative difference in total mass transformation between the pore-scale simulation and what is predicted by the upscaled continuum model using κ is about 10%. The explanation for this paradox is that the early transition of the regime from rate-limited to mixing-limited results in a model that is relatively insensitive to the rate constant because mixing controls the availability of reactants. Thus, the reaction-rate parameter used in the model has limited influence on the rate of product computed.
机译:先前的研究表明,在连续模型中使用时,批次测试(κ)中测得的速率常数可能会高估产品形成的数量,并且这些速率常数通常远大于由以下公式确定的有效值(λ〜(eff))。升级研究。但是,有证据表明,在使用放大模型时,混合比速率常数更重要。我们使用数值二维孔尺度多孔介质,其方法类似于实验柱测试,并重点研究了具有不可逆双分子反应的两种溶液的置换和混合情况。分析了多个横截面平均浓度的穿透曲线,以进行保守和反应性转运,以及反应物沿横截面的分离。我们计算连续量表的有效参数,以便更好地了解在上规模模型中使用内在速率常数的影响。对于一系列的Damkohler数(Da),我们计算有效的反应速率参数和反应效率因子。后者由经验公式描述,该经验公式取决于Damkohler数并捕获了高级系统行为。我们的孔尺度结果也证实了Kapoor等人提出的分离概念。 (1997)。我们发现,对于Da> 1,λ〜(eff)?κ,而孔尺度模拟与使用κ的扩展连续谱模型预测的总质量转换之间的相对差异约为10%。这种矛盾的解释是,该方案从速率限制到混合限制的早期转变导致了一个对速率常数相对不敏感的模型,因为混合控制了反应物的可用性。因此,模型中使用的反应速率参数对计算出的产物速率的影响有限。

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