Multi-scale Smoothed Particle Hydrodynamics model for flow and transport in unsaturated fractured porous media

本提案的主要目标是开发一种基于颗粒的多尺度建模工具，以模拟嵌入多孔基质中的非饱和裂缝中的流动和输运动力学。非饱和裂缝性多孔介质的流动和输运特征是水文地质学中最具挑战性的问题之一，对于裂缝性介质（核废料库）厚非饱和带入渗的量化、地下水补给和含水层脆弱性的预测等广泛应用具有重要意义。非饱和裂缝性多孔含水层的流动和输运动力学通常由强烈的非均质几何形状和水力性质的巨大差异决定。由于重力、惯性和毛细力、表面张力、润湿动力学和裂缝几何形状之间复杂的相互作用，裂缝中的流动动力学很难定量描述。小型实验室实验和数值模型通常是捕获高度非线性流动动力学和复杂界面运动的唯一可行方法。特别是，强变形界面对大多数基于网格的建模方法提出了挑战，这些问题可以很容易地通过基于粒子的模型来解决，因为粒子只是随着界面和/或自由表面移动，不需要复杂的前跟踪方案。在许多情况下，裂缝嵌入在多孔基质中，而多孔基质并不是一种不透水的介质。因此，基质-裂缝界面在多孔基质和裂缝之间形成了重要的连接，多孔基质提供了主要的储集空间，而裂缝则是通过气包带的主要水力通道。为了模拟这两个元素之间的耦合并模拟过程尺度上潜在的反馈机制，需要适当的建模方法来重现依赖于尺度的流动和运输过程。在模型离散化方面，由于孔喉和裂缝孔径相差几个数量级，使用单一建模方法无法详细求解孔隙空间和裂缝几何形状。因此，我们提出了一个适应的多尺度光滑粒子流体力学代码的发展。多孔基质内的流动和输运将通过经典的非饱和流动方法（如Richards方程）进行模拟，该方法将与裂缝中离散的自由表面流动动力学（例如吸附膜，液滴，溪流）相耦合。全耦合模型将嵌入到单个数值框架中，因此不需要管理求解程序和耦合方法的复杂组合。该模型将通过室内实验和数值实验进行验证，并用于研究复杂自由表面流动的影响以及基质-裂缝界面的润湿和输运动力学。

The main goal of this proposal is the development of a particle-based multi-scale modelling tool to simulate flow and transport dynamics in unsaturated fractures embedded in a porous matrix. The characterization of flow and transport in unsaturated fractured porous media remains one of the most challenging problems in hydrogeology and is of importance for a wide range of applications, such as the quantification of infiltration through thick unsaturated zones of fractured media (nuclear waste repositories), prediction of groundwater recharge and aquifer vulnerability. Flow and transport dynamics in unsaturated fractured porous aquifers are often dominated by a strong heterogeneous geometry and large contrasts in hydraulic properties. Flow dynamics in fractures are difficult to describe quantitatively because of the complex interplay between gravitational, inertial and capillary forces, surface tension, wetting dynamics and the fracture geometry. Small-scale laboratory experiments and numerical models are commonly the only feasible way to capture the highly non-linear flow dynamics and complex interface movements. In particular, strong deforming interfaces pose a challenge to most grid-based modelling approaches, problems that can easily be solved by particle-based models, as particles simply move with the interfaces and/or free surfaces and do not require complex front-tracking schemes. In many cases fractures are embedded in a porous matrix, which does not behave as an impervious medium. The matrix-fracture interface therefore forms an essential connection between the porous matrix, which provides the main storage and the fractures, that acts as the dominating hydraulic pathway through the vadose zone. To model the coupling between these two elements and to simulate the potential feedback mechanisms at the process scale, appropriate modelling approaches are required to reproduce the scale-dependent flow and transport processes. In terms of model discretization it is not feasible to resolve the pore-space and fracture geometry in detail using a single modelling approach as pore throat and fracture apertures are several orders of magnitude apart. Therefore we propose the development of an adapted multi-scale Smoothed Particle Hydrodynamics code. Flow and transport within the porous matrix will be simulated via classical approaches for unsaturated flow such as the Richards equation, which shall be coupled to the discrete free-surface flow dynamics (e.g. adsorbed films, droplets, rivulets) in the fracture. The fully-coupled model will be embedded in a single numerical framework and thus does not require the management of a complex combination of solver routines and coupling methods. The model will be validated by laboratory and numerical experiments and employed to study the effects of the complex free-surface flows and the wetting and transport dynamics at the matrix-fracture interface.