Universal scaling of spontaneous imbibition for water-wet systems
Universal scaling of spontaneous imbibition for water-wet systems
复制标题
DOI：
10.1029/2011wr011566
复制
发表时间：
2012-03-07
影响因子：
5.4
通讯作者：
Geiger, S.
中科院分区：
文献类型：
--
作者：
Schmid, K. S.;Geiger, S.
自发逆流自吸 (SI) 是许多多相流过程中的关键机制，例如非水相液体净化 (NAPL)、生物修复或二氧化碳储存。为了解释和升级实验室 SI 数据以及建模和预测目的，缩放组是一个重要的工具。如何制定通用标度群的问题已经争论了 90 多年。在这里，我们提出了第一个缩放组，该缩放组结合了两相达西模型中存在的所有参数对 SI 的影响。该组是通过将吸收的累积水相与归一化孔隙体积相关联，从唯一已知的自发渗吸精确解析解严格推导出来的。我们通过将其应用于 42 项已发表的水-油和水-空气实验的 SI 研究来证明该组的有效性，这些研究适用于各种粘度比、不同的材料、不同的初始水饱和度和不同的长度尺度。在所有情况下，水都是润湿相。我们的组作为一个“主方程”，其通用性允许严格预测过去 90 年来提出的大量专门缩放组的有效性。此外，我们的结果有力地证明了达西模型适合描述 SI，并且与假设相反，包括毛细管压力的动态效应对于逆流 SI 来说不是必需的。讨论了该组的两个关键应用：首先，该组可以作为双孔隙中使用的长期寻求的渗吸通用传输率其次，它是植物种子吸胀发芽模型中迄今为止缺失的比例常数。
Spontaneous, counter-current imbibition (SI) is a key mechanism in many multiphase flow processes, such as cleanup of nonaqueous phase liquids (NAPLs), bioremediation, or CO2 storage. For interpreting and upscaling laboratory SI data, and modeling and prediction purposes, scaling groups are an essential tool. The question of how to formulate a general scaling group has been debated for over 90 years. Here we propose the first scaling group that incorporates the influence of all parameters on SI that are present in the two-phase Darcy model. The group is derived rigorously from the only known exact analytical solution for spontaneous imbibition by relating the cumulative water phase imbibed to the normalized pore volume. We show the validity of the group by applying it to 42 published SI studies for water-oil and water-air experiments, for a wide range of viscosity ratios, different materials, different initial water saturations, and different length-scales. In all cases, water was the wetting phase. Our group serves as a "master equation'' whose generality allows the rigorous prediction of the validity of a large number of specialized scaling groups proposed during the last 90 years. Furthermore, our results give strong evidence that the Darcy model is suitable for describing SI, and that including dynamic effects in capillary pressure is not necessary for counter-current SI, contrary to what has been hypothesized. Two key applications of the group are discussed: First, the group can serve as the long sought after general transfer rate for imbibition used in dual-porosity models. Second, it is the so far missing proportionality constant in imbibition-germination models for plant seeds.