A Theoretical Study on the Governing Laws for Fluid Transport in Rough Fractures

地球上地壳中各种规模的天然岩石裂隙都存在。它们在地质介质中的地下水运动、溶质运移和废物分离方面发挥着重要作用。描述裂隙岩石中流体流动和质量传输的特征取决于我们对流体如何通过单个裂隙传输的了解。然而，被两个粗糙表面包围的裂缝中的流体流动是复杂的。关于粗糙裂隙的立方定律和雷诺方程的有效性的重要问题已经被许多人研究过。一般的结论是，三次定律只能提供流量的定性描述，雷诺方程不适用于粗糙的裂缝，需要在更好的控制流动定律中考虑孔径和曲折的影响。本研究的主要目的是(1)系统地探索和量化裂缝粗糙度、弯曲度和流动通道的形成对控制流动规律的影响，以及(2)通过对流体运移机理的了解，建立更好的粗糙裂缝控制流动规律。具体地说，我将试图实现以下目标：(1)开发一种合理的方法来表征天然岩石的裂缝几何形状，(2)研究生成的裂缝和剖面化裂缝中沟道化流动路径的形成，(3)检验修正的雷诺方程有效的条件，(4)识别从Darcian流动到非Darcian流动的过渡流动状态，以及(5)构建更好的控制规律，捕捉粗糙裂缝中流体运移的主要特征。我将采用一系列理论方法，并利用现有的实验室实验数据来实现这些目标。数值求解雷诺方程、修正的包含局部开度和弯曲度几何变量的雷诺方程和Navier-Stokes方程，数值模拟粗糙裂缝中的流体流动。格子Boltzmann方法将用于模拟复杂几何裂缝中的线性和非线性流体运移。这项拟议的研究代表了一项全面的理论尝试，旨在研究粗糙岩石裂隙中流体运移的支配规律。

9804789GeNatural rock fractures exist at all scales in the earth's upper crust. They play a major role in groundwater movement, solute transport, and waste isolation in geologic media. Characterizing fluid flow and mass transport in fractured rocks depends on our knowledge of how fluid transports through individual fractures. Yet fluid flow in fractures bounded by two rough surfaces is complex. Important questions on the validity of the cubic law and the Reynolds equation for rough fractures have been studied by many. The general conclusions are that the cubic law can only provide a qualitative description of flow rate, the Reynolds equation is not valid for rough fractures and effects of aperture and tortuosity need to be included in better governing flow laws. The primary goals of this research are (1) to systematically explore and quantify the effects of fracture roughness, tortuosity, and the formation of flow channeling on governing flow laws, and (2) to develop a better governing flow law for rough fractures by understanding the fluid transport mechanisms. Specifically, I will attempt to achieve the following objectives: (1) develop a rational method to characterize fracture geometry of natural rocks, (2) investigate the formation of channelized flow paths in generated and profiled fractures, (3) examine the conditions under which the modified Reynolds equation is valid, (4) identify the transitional flow regime from Darcian to non-Darcian flow, and (5) construct a better governing law that captures the dominant features of fluid transport in rough fractures. I will employ an array of theoretical approaches and utilize the existing lab experimental data to achieve these objectives. The Reynolds equation, the modified Reynolds equation including geometric variables of local aperture and tortuosity, and the Navier-Stokes equations will be solved numerically to simulate fluid flow in rough fractures. The Lattice Boltzmann method will be used for simulating both linear and non-linear fluid transport in fractures with complex geometries. The proposed research represents a comprehensive theoretical attempt to examine the governing laws for fluid transport in rough rock fractures.