Moebius Franziska, Or Dani
Department of Environmental Systems Science, ETH Zurich, CH-8092 Zurich, Switzerland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Aug;90(2):023019. doi: 10.1103/PhysRevE.90.023019. Epub 2014 Aug 28.
The seemingly regular and continuous motion of fluid displacement fronts in porous media at the macroscopic scale is propelled by numerous (largely invisible) pore-scale abrupt interfacial jumps and pressure bursts. Fluid fronts in porous media are characterized by sharp phase discontinuities and by rapid pore-scale dynamics that underlie their motion; both attributes challenge standard continuum theories of these flow processes. Moreover, details of pore-scale dynamics affect front morphology and subsequent phase entrapment behind a front and thereby shape key macroscopic transport properties of the unsaturated zone. The study presents a pore-throat network model that focuses on quantifying interfacial dynamics and interactions along fluid displacement fronts. The porous medium is represented by a lattice of connected pore throats capable of detaining menisci and giving rise to fluid-fluid interfacial jumps (the study focuses on flow rate controlled drainage). For each meniscus along the displacement front we formulate a local inertial, capillary, viscous, and hydrostatic force balance that is then solved simultaneously for the entire front. The model enables systematic evaluation of the role of inertia and boundary conditions. Results show that while displacement patterns are affected by inertial forces mainly by invasion of throats with higher capillary resistance, phase entrapment (residual saturation) is largely unaffected by inertia, limiting inertial effects on hydrological properties behind a front. Interfacial jump velocities are often an order of magnitude larger than mean front velocity, are strongly dependent on geometrical throat dimensions, and become less predictable (more scattered) when inertia is considered. Model simulations of the distributions of capillary pressure fluctuations and waiting times between invasion events follow an exponential distribution and are in good agreement with experimental results. The modeling approach provides insights into the rich pore-scale dynamics of displacement fronts; these insights not only improve the basic understanding of these ubiquitous processes, but could shed light on solute dispersion and colloids mobilization at fronts and the mechanical consequences of passing fronts.
在宏观尺度上，多孔介质中流体驱替前沿看似规则且连续的运动是由众多（大多不可见）孔隙尺度的突然界面跳跃和压力脉冲推动的。多孔介质中的流体前沿具有尖锐的相间断以及作为其运动基础的快速孔隙尺度动力学特征；这两个特性都对这些流动过程的标准连续介质理论提出了挑战。此外，孔隙尺度动力学的细节会影响前沿形态以及前沿后方随后的相捕集，从而塑造非饱和带的关键宏观传输特性。该研究提出了一种孔隙喉道网络模型，重点在于量化沿流体驱替前沿的界面动力学和相互作用。多孔介质由一个连接的孔隙喉道晶格表示，这些喉道能够滞留弯月面并引发流体 - 流体界面跳跃（该研究聚焦于流量控制排水）。对于沿驱替前沿的每个弯月面，我们制定了局部惯性、毛细、粘性和静水压力平衡，然后针对整个前沿同时求解。该模型能够系统地评估惯性和边界条件的作用。结果表明，虽然驱替模式主要通过侵入具有较高毛细阻力的喉道而受到惯性力的影响，但相捕集（残余饱和度）在很大程度上不受惯性影响，限制了惯性对前沿后方水文特性的影响。界面跳跃速度通常比平均前沿速度大一个数量级，强烈依赖于喉道的几何尺寸，并且在考虑惯性时变得更难预测（更分散）。毛细管压力波动分布和侵入事件之间等待时间的模型模拟遵循指数分布，并且与实验结果吻合良好。该建模方法为驱替前沿丰富的孔隙尺度动力学提供了见解；这些见解不仅增进了对这些普遍存在过程的基本理解，还可能揭示前沿处的溶质弥散和胶体运移以及前沿通过的力学后果。
