scholarly journals Quantitative Estimates of Nonlinear Flow Characteristics of Deformable Rough-Walled Rock Fractures with Various Lithologies

Processes ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 149 ◽  
Author(s):  
Qian Yin ◽  
Lixin He ◽  
Hongwen Jing ◽  
Dong Zhu
Keyword(s):  
Nonlinear Coefficient ◽  
Flow Regimes ◽  
Confining Pressure ◽  
Nonlinear Flow ◽  
Hydraulic Pressure ◽  
Rock Fractures ◽  
Flow Process ◽  
Wide Range ◽  
Fracture Closure ◽  
Hydraulic Aperture

The existence of surface roughness, various contact conditions and the occurrence of flow nonlinearity make the flow process in natural rock fractures more complicated. To evaluate the fluid flow regimes in deformable rough-walled rock fractures, a great many hydromechanical tests were conducted on nine real fractures artificially produced from a wide range of lithological diversity. For fractures with a certain JRC (fracture roughness coefficient) value, the confining pressure varied from 5 to 20 MPa, and the hydraulic pressure was increased from 0.4 to 6.0 MPa. The experimental results display that (i) regression analyses of the raw experimental data indicate that the Forchheimer’s law provides a perfect description for flow process through the fractures. The coefficients of viscous and inertial pressure drops undergo a growth of 2–3 orders of magnitude with an increase in the confining pressure; (ii) the hydraulic aperture decreases by approximately 87.41–92.81% as the confining pressure increases, and experiences a decrease of 1.52–2.96 times with the JRC values. A power-law function is used to evaluate the hydraulic aperture as a function of the nonlinear coefficient. The nonlinear coefficient decreases with increasing hydraulic aperture; (iii) using Forchheimer equation, the critical Reynolds number Rec was successfully assessed by choosing E percentage (generally 10%) of the nonlinear effect as the critical value between the linear and nonlinear flow regimes. The obtained Rec steadily increases with increasing confining pressure, while it diminishes with the JRC values; and (v) the transmissivity decreases as the pressure gradient increases. Additionally, transmissivity also exhibits a decreasing trend with both the confining pressures and JRC values due to fracture closure and tortuous and channeling flow paths in rougher fractures, and the rate of its decrease for a smaller confining pressure (5, 10 MPa) is more significant.

scholarly journals Hydromechanical Investigations on the Self-propping Potential of Fractures in Tight Sandstones

2021 ◽  
Author(s):  
Chaojie Cheng ◽  
Harald Milsch
Keyword(s):  
Mechanical Properties ◽  
Surface Roughness ◽  
Fractured Rock ◽  
Confining Pressure ◽  
The Self ◽  
Fracture Aperture ◽  
Wall Displacement ◽  
Fracture Closure ◽  
Hydraulic Aperture ◽  
Tensile Fractures

AbstractThe hydromechanical properties of single self-propping fractures under stress are of fundamental interest for fractured-rock hydrology and a large number of geotechnical applications. This experimental study investigates fracture closure and hydraulic aperture changes of displaced tensile fractures, aligned tensile fractures, and saw-cut fractures for two types of sandstone (i.e., Flechtinger and Fontainebleau) with contrasting mechanical properties, cycling confining pressure between 5 and 30 MPa. Emphasis is placed on how surface roughness, fracture wall offset, and the mechanical properties of the contact asperities affect the self-propping potential of these fractures under normal stress. A relative fracture wall displacement can significantly increase fracture aperture and hydraulic conductivity, but the degree of increase strongly depends on the fracture surface roughness. For smooth fractures, surface roughness remains scale-independent as long as the fracture area is larger than a roll-off wavelength and thus any further displacement does not affect fracture aperture. For rough tensile fractures, these are self-affine over a larger scale so that an incremental fracture wall offset likely leads to an increase in fracture aperture. X-ray microtomography of the fractures indicates that the contact area ratio of the tensile fractures after the confining pressure cycle inversely correlates with the fracture wall offset yielding values in the range of about 3–25%, depending, first, on the respective surface roughness and, second, on the strength of the asperities in contact. Moreover, the contact asperities mainly occur isolated and tend to be preferentially oriented in the direction perpendicular to the fracture wall displacement which, in turn, may induce flow anisotropy. This, overall, implies that relatively harder sedimentary rocks have a higher self-propping potential for sustainable fluid flow through fractures in comparison to relatively soft rocks when specific conditions regarding surface roughness and fracture wall offset are met.

scholarly journals Effect of Lower Surface Roughness on Nonlinear Hydraulic Properties of Fractures

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jinglong Li ◽  
Xianghui Li ◽  
Bo Zhang ◽  
Bin Sui ◽  
Pengcheng Wang ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Flow Rate ◽  
Stokes Equations ◽  
Flow Regimes ◽  
Lower Surface ◽  
Nonlinear Flow ◽  
Hydraulic Pressure

This study investigates the effect of fracture lower surface roughness on the nonlinear flow behaviors of fluids through fractures when the aperture fields are fixed. The flow is modeled with hydraulic pressure drop = 10 − 4 ~ 10 5   Pa / m by solving the Navier-Stokes equations based on rough fracture models with lower surface roughness varying from JRC = 1 to JRC = 19 . Here, JRC represents joint roughness coefficient. The results show that the proposed numerical method is valid by comparisons between numerically calculated results with theoretical values of three parallel-plate models. With the increment of hydraulic pressure drop from 10-4 to 105 Pa/m spanning ten orders of magnitude, the flow rate increases with an increasing rate. The nonlinear relationships between flow rate and hydraulic pressure drop follow Forchheimer’s law. With increasing the JRC of lower surfaces from 1 to 19, the linear Forchheimer coefficient decreases, whereas the nonlinear Forchheimer coefficient increases, both following exponential functions. However, the nonlinear Forchheimer coefficient is approximately three orders of magnitude larger than the linear Forchheimer coefficient. With the increase in Reynolds number, the normalized transmissivity changes from constant values to decreasing values, indicating that fluid flow transits from linear flow regimes to nonlinear flow regimes. The critical Reynolds number that quantifies the onset of nonlinear fluid flow ranges from 21.79 to 185.19.

scholarly journals Numerical Simulation of the Nonlinear Flow Properties in Self-Affine Aperture-Based Fractures

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Xin Zhou ◽  
Jianlong Sheng ◽  
Ruili Lu ◽  
Zuyang Ye ◽  
Wang Luo
Keyword(s):  
Fractal Dimension ◽  
Standard Deviation ◽  
Flow Rate ◽  
Empirical Relationship ◽  
Nonlinear Coefficient ◽  
Nonlinear Flow ◽  
Flow Properties ◽  
Navier Stokes Equation ◽  
Linear Coefficient ◽  
Hydraulic Aperture

In order to study the effect of fracture geometry on the nonlinear flow properties in aperture-based fractures, a fractal model based on the self-affinity is proposed to characterize the three-dimensional geometry of rough-walled fractures. By solving the N–S (Navier–Stokes) equation directly, the relationships between the Forchheimer-flow characteristics, fractal dimension, and standard deviation of the aperture have been obtained. The Forchheimer equation is validated to describe the nonlinear relationship between flow rate and pressure gradient. For lower flow rate, the influence of the fractal dimension almost can be ignored, but the linear coefficient increases and the hydraulic aperture decreases with increasing standard deviation of the aperture, respectively. For larger flow rate, the nonlinear coefficient increases with the growth of the standard deviation of the aperture and fractal dimension. Thus, an empirical relationship between the nonlinear coefficient, fractal dimension, and standard deviation of aperture is proposed. In addition, the critical Reynolds number decreases with the increase of the standard deviation of the aperture and the fractal dimension, and the numerical results are generally consistent with the experimental data.

Numerical simulations of wet snow avalanches: interplay between cohesion and friction

2021 ◽  
Author(s):  
Guillaume Chambon ◽  
Thierry Faug ◽  
Mohamed Naaim
Keyword(s):  
Numerical Simulations ◽  
Flow Regimes ◽  
Liquid Water Content ◽  
Snow Avalanches ◽  
Shallow Flow ◽  
Distinctive Features ◽  
Wide Range ◽  
Wet Snow ◽  
Sensitivity Studies ◽  
Avalanche Flow

<p>Wet snow avalanches present distinctive features such as unusual trajectories, peculiar deposit shapes, and a rheological behavior displaying a combination of granular and pasty features depending on the actual snow liquid water content. Complex transitions between dry (cold) and wet (hot) flow regimes can also occur during a single avalanche flow. In an attempt to account for this complexity, we report on numerical simulations of avalanches using a frictional-cohesive rheology implemented in a depth-averaged shallow-flow model. Through extensive sensitivity studies on synthetic and real topographies, we show that cohesion plays a key role to enrich the physics of the simulated flows, and to represent realistic avalanche behaviors. First, when coupled to a proper treatment of the yielding criterion, cohesion provides a way to define objective stopping criteria for the flow, independently of the issues incurred by artificial diffusion of the numerical scheme. Second, and more importantly, the interplay between cohesion and friction gives raise to a variety of nontrivial physical effects affecting the dynamics of the avalanches and the morphology of the deposits. The relative weights of frictional and cohesive contributions to the overall stress are investigated as a function of space and time during the propagation, and related to the formation of specific features such as lateral levées, hydraulic jumps, etc. This study represents a first step towards robust avalanches simulations, spanning the wide range of possible flow regimes, through shallow-flow approaches. Future improvements involving more refined cohesion parameterizations will be discussed.</p>

A new proposed method for observing fluid in rock fractures using the enhanced X-ray image of digital radiography

2021 ◽  
Author(s):  
Huan Sun ◽  
Qijian Long ◽  
Xiaoli Liu ◽  
Zhenni Ye ◽  
Enzhi Wang ◽  
...  
Keyword(s):  
Digital Radiography ◽  
Carbonate Rocks ◽  
Interaction Mechanism ◽  
Mechanical Tests ◽  
Initial Permeability ◽  
Nonlinear Flow ◽  
Rock Fractures ◽  
Diffusion Flow ◽  
X Ray ◽  
Transition Mechanism

Abstract Fluid in rock fractures always continually induces geo-catastrophe in water-rock system engineering. Intuitively observing fluid in fractures is the key method to reveal interaction mechanism of the water-rock under different engineering background, and provide some insights for solving engineering issues. This study proposes the visual method of fluid in rock fractures using enhanced X-ray image digital radiography (EXIDR), and carries out the coupled hydro-mechanical tests on the basis of the material scale of carbonate rocks, red bed mudstone (RBM) and coals. The experimental results show the transition mechanism of pipe flow (PF) to fissure flow (FF) during carbonate rock failures. The flow regime has undergone an evolution process from laminar flow to turbulent flow, also of this change with the fractal characteristics of PF-FF in carbonate rocks under multilevel stress loading. Also, the damage coefficient of RBM under coupled hydrodynamics and multilevel stress loading is non-linearly increasing. Therefore, the initial permeability of RBM under hydrodynamics is significant for geo-hazards prevention in the engineering, which are induced by the seepage and diffusion effects. Besides, the mean square flow (MSF) describes the flow rate varies as the fracture growth and extension, i.e. the fractional exponential evolution law that has a transition changes from super-diffusion flow to sub-diffusion flow. This indicates that fluid in fractures show the double behaviors of anomalous diffusion and nonlinear flow during coal and rock failures.

A numerical investigation of fluid flows induced by the oscillations of thin plates and evaluation of the associated hydrodynamic forces

2019 ◽  
Vol 874 ◽  
pp. 1057-1095 ◽  
Author(s):  
Artem N. Nuriev ◽  
Airat M. Kamalutdinov ◽  
Andrey G. Egorov
Keyword(s):  
Stokes Equations ◽  
Experimental Studies ◽  
Flow Regimes ◽  
Hydrodynamic Forces ◽  
Thin Plates ◽  
Oscillatory Process ◽  
Dimensionless Frequency ◽  
Two Dimensional ◽  
Wide Range ◽  
Hydrodynamic Influence

The paper is devoted to the problem of harmonic oscillations of thin plates in a viscous incompressible fluid. The two-dimensional flows caused by the plate oscillations and their hydrodynamic influence on the plates are studied. The fluid motion is described by the non-stationary Navier–Stokes equations, which are solved numerically on the basis of the finite volume method. The simulation is carried out for plates with different thicknesses and shapes of edges in a wide range of control parameters of the oscillatory process: dimensionless frequency and amplitude of oscillations. For the first time in the framework of one model all two-dimensional flow regimes, which were found earlier in experimental studies, are described. Two new flow regimes emerging along the stability boundaries of symmetric flow regimes are localized. The map of flow regimes in the frequency–amplitude plane is constructed. The analysis of the hydrodynamic influence of flows on the plates allow us to establish new effects associated with the influence of the shape of the plates on the drag and inertia forces. Due to these effects, the values of hydrodynamic forces can differ by 90 % at the same parameters of the oscillation. The lower and upper estimates of hydrodynamic forces obtained in the work have a good agreement with the experimental data presented in the literature.

scholarly journals Snow Avalanche Impact Measurements at the Seehore Test Site in Aosta Valley (NW Italian Alps)

Geosciences ◽  
2019 ◽  
Vol 9 (11) ◽  
pp. 471
Author(s):  
Margherita Maggioni ◽  
Monica Barbero ◽  
Fabrizio Barpi ◽  
Mauro Borri-Brunetto ◽  
Valerio De Biagi ◽  
...  
Keyword(s):  
Flow Regimes ◽  
Test Site ◽  
Snow Avalanche ◽  
Hazard Mapping ◽  
Force Measurements ◽  
Italian Alps ◽  
Scientific Discussion ◽  
Impact Forces ◽  
Wide Range ◽  
Avalanche Flow

In full-scale snow avalanche test sites, structures such as pylons, plates, or dams have been used to measure impact forces and pressures from avalanches. Impact pressures are of extreme importance when dealing with issues such as hazard mapping and the design of buildings exposed to avalanches. In this paper, we present the force measurements recorded for five selected avalanches that occurred at the Seehore test site in Aosta Valley (NW Italian Alps). The five avalanches were small to medium-sized and cover a wide range in terms of snow characteristics and flow dynamics. Our aim was to analyze the force and pressure measurements with respect to the avalanche characteristics. We measured pressures in the range of 2 to 30 kPa. Though without exhaustive measurements of the avalanche flows, we found indications of different flow regimes. For example, we could appreciate some differences in the vertical profile of the pressures recorded for wet dense avalanches and powder ones. Being aware of the fact that more complete measurements are necessary to fully describe the avalanche flows, we think that the data of the five avalanches triggered at the Seehore test site might add some useful information to the ongoing scientific discussion on avalanche flow regimes and impact pressure.

A Model for the Conductivity and Compliance of Unpropped and Natural Fractures

SPE Journal ◽  
2017 ◽  
Vol 22 (06) ◽  
pp. 1893-1914 ◽  
Author(s):  
Weiwei Wu ◽  
Mukul M. Sharma
Keyword(s):  
Plastic Deformation ◽  
Yield Stress ◽  
Young’S Modulus ◽  
Correlation Length ◽  
Young's Modulus ◽  
Heterogeneous Surfaces ◽  
Natural Fractures ◽  
Wide Range ◽  
Fracture Closure ◽  
Deformation Interaction

Summary Fluid flow in unpropped and natural fractures is critical in many geophysical processes and engineering applications. The flow conductivity in these fractures depends on their closure under stress, which is a complicated mechanical process that is challenging to model. The challenges come from the deformation interaction and the close coupling among the fracture geometry, pressure, and deformation, making the closure computationally expensive to describe. Hence, most of the previous models either use a small grid system or disregard deformation interaction or plastic deformation. In this study, a numerical model is developed to simulate the stress-driven closure and the conductivity for fractures with rough surfaces. The model integrates elastoplastic deformation and deformation interaction, and can handle contact between heterogeneous surfaces. Computation is optimized and accelerated by use of an algorithm that combines the conjugate-gradient (CG) method and the fast-Fourier-transform (FFT) technique. Computation time is significantly reduced compared with traditional methods. For example, a speedup of five orders of magnitude is obtained for a grid size of 512 × 512. The model is validated against analytical problems and experiments, for both elastic-only and elastoplastic scenarios. It is shown that interaction between asperities and plastic deformation cannot be ignored when modeling fracture closure. By applying our model, roughness and yield stress are found to have a larger effect on fracture closure and compliance than Young's modulus. Plastic deformation is a dominant contributor to closure and can make up more than 70% of the total closure in some shales. The plastic deformation also significantly alters the relationship between fracture stiffness and conductivity. Surfaces with reduced correlation length produce greater conductivity because of their larger apertures, despite more fracture closure. They have a similar fraction of area in contact as compared with surfaces with longer fracture length, but the pattern of area in contact is more scattered. Contact between heterogeneous surfaces with more soft minerals leads to increased plastic deformation and fracture closure, and results in lower fracture conductivity. Fracture compliance appears not to be as sensitive to the distribution pattern of hard and soft minerals. Our model compares well with experimental data for fracture closure, and can be applied to unpropped or natural fractures. These results are obtained for a wide range of conditions: surface profile following Gaussian distribution with correlation length of 50 µm and roughness of 4 to 50 µm, yield stress of 100 to 1500 MPa, and Young's modulus of 20 to 60 GPa. The results may be different for situations outside this range of parameters.

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