Upscaling of the advection–diffusion–reaction equation with Monod reaction
Upscaling of the advection–diffusion–reaction equation with Monod reaction
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DOI：
10.1016/j.advwatres.2009.05.009
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发表时间：
2009-08
影响因子：
4.7
通讯作者：
F. Heße;F. Radu;M. Thullner;S. Attinger
中科院分区：
文献类型：
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作者：
F. Heße;F. Radu;M. Thullner;S. Attinger
人们已经充分认识到，需要可靠的模型来研究污染物在地下的反应性运移。这些模型的预测能力取决于对多孔介质中污染物对微生物的生物利用度的准确描述。在影响生物利用度的许多其他因素中，扩散传质过程可能限制基质在孔隙尺度上的利用度，从而大大降低有效降解率。在这项研究中，我们使用了解析和数值相结合的方法来提高单孔内表面催化的monod型反应速率，以获得更大规模的有效速率表达式。结果表明，在放大描述中，Monod动力学导致了反应和扩散限制之间的浓度依赖过渡。严格地说，有效速率抑制不遵循monod型动力学。然而，我们可以提出适当的有效参数关系，它提供了一个可接受的近似降解动力学使用有效的monod型反应速率。
The need for reliable models for the reactive transport of contaminants in the subsurface is well recognized. The predictive power of these models is determined by the accurate description of bioavailability of contaminants to microorganisms in porous media. Among many other factors influencing bioavailability, diffusive mass transfer processes may limit the substrate availability at the pore scale and hence reduce the effective degradation rate considerably. In this study we used a combination of analytical and numerical methods to upscale surface catalyzed Monod-type reaction rates within a single pore, to obtain effective rate expression at a larger scale. Results show that in the upscaled description Monod kinetics lead to a concentration dependent transition between a reaction and diffusion-limited regime. Strictly, the effective rate repression does not follow Monod-type kinetics. However, we can present appropriate effective parameters relations, which provide an acceptable approximation of degradation dynamics using an effective Monod-type reaction rate.