Theoretical analyses of nonaqueous phase liquid dissolution‐induced instability in two‐dimensional fluid‐saturated porous media
Theoretical analyses of nonaqueous phase liquid dissolution‐induced instability in two‐dimensional fluid‐saturated porous media
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DOI：
10.1002/nag.880
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发表时间：
2010-12
影响因子：
4
通讯作者：
Chong-bin Zhao;B. Hobbs;A. Ord
中科院分区：
文献类型：
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作者：
Chong-bin Zhao;B. Hobbs;A. Ord
本文研究了含溶质弥散效应的二维流体饱和多孔介质中非水相液体(NAPL)溶解引起的不稳定性的理论问题。在分析和克服了前人工作中的一些不足之后，提出了一个综合的无量纲数，称为赵数，它代表了一个有限域的NAPL溶解系统的主要驱动力和三种控制机制。进行了线性稳定性分析，得出了在平衡浓度与浓度之比趋于零时，极限情况下NAPL-溶解体系综合无量纲数的临界值。由此，建立了可用于评价有限域二维流体饱和多孔介质中平面NAPL溶解前锋不稳定性的理论判据。本文的理论结果不仅可以用来从理论上理解溶质弥散对有限域和无限域流体饱和多孔介质中NAPL溶解前沿不稳定性的影响，而且可以作为基准解，用于验证数值方法在二维流体饱和多孔介质中模拟NAPL溶解前沿形态演化过程的详细过程。版权所有©2009 John Wiley&Sons，Ltd.
This paper deals with the theoretical aspects of nonaqueous phase liquid (NAPL)‐dissolution‐induced instability in two‐dimensional fluid‐saturated porous media including solute dispersion effects.After some weaknesses associated with the previous work are analyzed and overcome, a comprehensive dimensionless number, known as the Zhao number, is proposed to represent the main driving force and three controlling mechanisms of an NAPL‐dissolution system that has a finite domain. The linear stability analysis is carried out to derive the critical value of the comprehensive dimensionless number of the NAPL‐dissolution system in a limit case as the ratio of the equilibrium concentration to the density of the NAPL approaches zero. As a result, a theoretical criterion that can be used to assess the instability of planar NAPL‐dissolution fronts in two‐dimensional fluid‐saturated porous media of finite domains has been established. Not only can the present theoretical results be used for the theoretical understanding of the effect of solute dispersion on the instability of an NAPL‐dissolution front in the fluid‐saturated porous medium of either a finite domain or an infinite domain, but also they can be used as benchmark solutions for verifying numerical methods employed to simulate detailed morphological evolution processes of NAPL‐dissolution fronts in two‐dimensional fluid‐saturated porous media. Copyright © 2009 John Wiley & Sons, Ltd.