A Review of Critical Conditions for the Onset of Nonlinear Fluid Flow in Rock Fractures

Liyuan Yu,Richeng Liu,Yujing Jiang

doi:10.1155/2017/2176932

Liyuan Yu, Richeng Liu + Show 1 more

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https://doi.org/10.1155/2017/2176932

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Abstract

Selecting appropriate governing equations for fluid flow in fractured rock masses is of special importance for estimating the permeability of rock fracture networks. When the flow velocity is small, the flow is in the linear regime and obeys the cubic law, whereas when the flow velocity is large, the flow is in the nonlinear regime and should be simulated by solving the complex Navier-Stokes equations. The critical conditions such as critical Reynolds number and critical hydraulic gradient are commonly defined in the previous works to quantify the onset of nonlinear fluid flow. This study reviews the simplifications of governing equations from the Navier-Stokes equations, Stokes equation, and Reynold equation to the cubic law and reviews the evolutions of critical Reynolds number and critical hydraulic gradient for fluid flow in rock fractures and fracture networks, considering the influences of shear displacement, normal stress and/or confining pressure, fracture surface roughness, aperture, and number of intersections. This review provides a reference for the engineers and hydrogeologists especially the beginners to thoroughly understand the nonlinear flow regimes/mechanisms within complex fractured rock masses.

Highlights

Rock fracture network controls the main paths of fluid flow and contaminant migration in deep underground, and the estimation of permeability of fractured rock masses has been extensively studied during the past several decades in many geoengineering and geosciences such as CO2 sequestration, enhanced oil recovery, and geothermal energy development [1,2,3,4,5,6,7,8]
Before permeability estimation of fractured rock masses, the critical conditions for the onset of nonlinear flow such as critical Reynolds number and critical hydraulic gradient should be firstly calculated, below which the cubic law in conjunction with modifications is applicable for giving reasonable solutions and beyond which the complex Navier-Stokes equations rather than cubic law should be solved
This is the motivation of this work that summarizes the relative works on the evolution of critical conditions for the onset of nonlinear flow and provides a reference for those who are interested in this topic

Summary

Introduction

Rock fracture network controls the main paths of fluid flow and contaminant migration in deep underground, and the estimation of permeability of fractured rock masses has been extensively studied during the past several decades in many geoengineering and geosciences such as CO2 sequestration, enhanced oil recovery, and geothermal energy development [1,2,3,4,5,6,7,8]. When fluid flow is in the linear regime, each fracture in the two-dimensional DFNs is represented using a line segment [73], whereas when fluid flow enters the nonlinear regime and the NS equations are solved, the real geometry (void space) of each fracture that is formed with two walls should be incorporated, which to some extent increases the difficulty of establishing the models [36, 74] This work aims at providing a reference for engineers and researchers to quickly assess the magnitudes of critical Reynolds number or critical hydraulic gradient and to clearly understand the nonlinear flow mechanisms within complex fractured rock masses

Governing Equations of Fluid Flow in Fractures

Nonlinear Flow Characteristics of Rock Fractures

Findings

Conclusions