Onset Of Nonlinear Flow Research Articles

The Effect of Fracture Roughness on the Onset of Nonlinear Flow

AbstractIn fractures where surface fluctuations are large compared to their aperture (narrow fractures), the flow is forced to move in tortuous paths that produce additional viscous friction and are subject to inertia effects. We consider the relation between the magnitude of surface roughness and the onset of inertial effects in the pressure driving the flow through a single open fracture. We performed experiments systematically varying the average aperture of the open fracture and covering a wide range of Reynolds numbers. For each aperture, we analyze the data in terms of the Forchheimer equation and show that the critical Reynolds number, defined as the Reynolds number at which inertial effects contribute 10% of the total pressure losses, is highly correlated with the roughness of the surface. In particular, we show that significant inertial effects appear earlier as the relative importance of surface roughness increases. Finally, we present results showing that the magnitude of the deviations in the pressure field compared to a linear profile, taken at different points in the fracture along the flow direction, is directly related to the relative surface roughness of the fracture.

Experimental and numerical investigation on nonlinear flow behaviour through three dimensional fracture intersections and fracture networks

Abstract Fluid flow tests were conducted on four kinds of fracture intersections, namely straight fracture intersection, buckling fracture intersection, crossing fracture intersection and furcating fracture intersection. Corresponding numerical simulations were performed by solving the Navier-Stokes equations. The resultant flow force perpendicular to fracture walls were derived. The results show that at high hydraulic gradients the increased normal resultant force perpendicular to fracture walls will change the original flow direction and consequently cause the formation of eddies which triggers flow nonlinearity. Greater buckling angle and smaller crossing angle would result in the onset of nonlinear flow at a higher critical hydraulic gradient for the cases of buckling and crossing fracture intersections. The critical hydraulic gradient for the case of furcating fracture intersection depends on the absolute angle between furcating flow and the original flow direction. Based on the analyses, three nonlinear models for coefficient B in the Forchheimer law corresponding to three cases of fracture intersections are proposed, which are related to the fracture intersection angle and hydraulic aperture. These models are further validated using flow experimental data from a real fracture network created in a rock specimen with the corresponding fracture model constructed using the computed tomography (CT) method.

Relationship between the critical Reynolds number and aperture for flow through single fractures: Evidence from published laboratory studies

An evaluation of published laboratory studies of flow through single rough fractures was conducted to establish a relationship between aperture (2b) and critical Reynolds number (Rec) under controlled conditions for physically measured fractures. Of the relevant 47 published laboratory studies, only six reported physically measured apertures along with adequate hydraulic testing information to determine the corresponding Rec value and show that the fractures follow the cubic law reasonably well. Our analysis indicates a logarithmic relationship between 2b and Rec for cubic-law fractures in the reported aperture range (100–500 µm), consistent with theoretical and modeling studies. Discrete fracture network models used for simulating flow and transport in fractured rock aquifers require reliable values for 2b, usually obtained from the cubic law, using T values from straddle-packer hydraulic tests. The cubic law requires specification of the number of permeable fractures (N) in each test interval, but, distinguishing the permeable from the impermeable fractures is problematic. The relationship between 2b and Rec determined from the laboratory tests provides a fluid-mechanics basis for estimating the number of permeable fractures in straddle-packer tests. Constant-head step-tests carefully done with many steps provide precise identification of the flow rate at the onset of nonlinear flow, and numerous tests have shown that flow deviates from linearity at larger flow rates for larger values of transmissivity (T). A procedure was previously developed to relate N, 2b, and Rec using hydraulic test data, but this approach requires knowledge of the relation between 2b and Rec, thereby motivating this work.

Nonlinear Flow in Karst Formations

The variation of effective hydraulic conductivity as a function of specific discharge in several 0.2-m and 0.3-m cubes of Key Largo Limestone was investigated. The experimental results closely match the Forchheimer equation. Defining the pore-size length scale in terms of Forchheimer parameters, it is demonstrated that significant deviations from Darcian flow will occur when the Reynolds number exceeds 0.11. A particular threshold model previously proposed for use in karstic formations does not show strong agreement with the data near the onset of nonlinear flow.

Energy dissipation measures in three-dimensional disordered porous media

The onset of nonlinear flow was analyzed in three-dimensional random, porous granular systems with 60% porosity using a lattice-Boltzmann model. Quantitative analysis was based on participation numbers built on local kinetic energies and energy dissipation rates computed via nonequilibrium kinetic (viscous stress) tensors. In contrast to the kinetic energy participation number, which characterizes the onset of nonlinearity in terms of a transition from a locally concentrated to a dispersed distribution of kinetic energy densities, the nonequilibrium kinetic tensor participation number characterizes the onset of nonlinearity in terms of a transition from a dispersed to a locally concentrated distribution of energy dissipation densities as the flow rate increases. The transition characterized by the nonequilibrium kinetic tensor participation number occurred over a nearly equal or a narrower range of Reynolds numbers when compared to the transition characterized by the kinetic energy participation number.