Critical hydraulic gradient for nonlinear flow through rock fracture networks: The roles of aperture, surface roughness, and number of intersections

Liu, Richeng; Li, Bo; Jiang, Yujing

doi:10.1016/j.advwatres.2015.12.002

Cited by 169 publications

(94 citation statements)

References 74 publications

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“…The JRC values of all 2D profiles were estimated based on the values of 2 using (13) proposed by Tse and Cruden [39]. Here, JRC is a dimensionless index ranging from 1 to 20 [40], which has been widely accepted in the field of rock mechanics and rock engineering [22,41].…”

Section: Rock Fracture Specimen Preparationmentioning

confidence: 99%

“…In such case, the conductivity of the fractures calculated using the cubic law will be overestimated [15][16][17]. In addition, natural rock fractures are often characteristic of rough walls, intersections, and asperity contacts, which make the fluid flow process even more complex and difficult to accurately describe [18][19][20][21][22]. Therefore, a thorough understanding of Relationships between / 0 and Re (after [23]).…”

Section: Introductionmentioning

confidence: 99%

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Experimental Study on Stress-Dependent Nonlinear Flow Behavior and Normalized Transmissivity of Real Rock Fracture Networks

et al. 2018

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The mechanism and quantitative descriptions of nonlinear fluid flow through rock fractures are difficult issues of high concern in underground engineering fields. In order to study the effects of fracture geometry and loading conditions on nonlinear flow properties and normalized transmissivity through fracture networks, stress-dependent fluid flow tests were conducted on real rock fracture networks with different number of intersections (1, 4, 7, and 12) and subjected to various applied boundary loads (7, 14, 21, 28, and 35 kN). For all cases, the inlet hydraulic pressures ranged from 0 to 0.6 MPa. The test results show that Forchheimer's law provides an excellent description of the nonlinear fluid flow in fracture networks. The linear coefficient and nonlinear coefficient in Forchheimer's law = + 2 generally decrease with the number of intersections but increase with the boundary load. The relationships between and can be well fitted with a power function. A nonlinear effect factor = 2 /( + 2 ) was used to quantitatively characterize the nonlinear behaviors of fluid flow through fracture networks. By defining a critical value of = 10%, the critical hydraulic gradient was calculated. The critical hydraulic gradient decreases with the number of intersections due to richer flowing paths but increases with the boundary load due to fracture closure. The transmissivity of fracture networks decreases with the hydraulic gradient, and the variation process can be estimated using an exponential function. A mathematical expression / 0 = 1 − exp(− −0.45 ) for decreased normalized transmissivity / 0 against the hydraulic gradient was established. When the hydraulic gradient is small, / 0 holds a constant value of 1.0. With increasing hydraulic gradient, the reduction rate of / 0 first increases and then decreases. The equivalent permeability of fracture networks decreases with the applied boundary load, and permeability changes at low load levels are more sensitive.

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Section: Rock Fracture Specimen Preparationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Experimental Study on Stress-Dependent Nonlinear Flow Behavior and Normalized Transmissivity of Real Rock Fracture Networks

et al. 2018

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“…However, when the aperture heterogeneity of each fracture in complex fracture networks is considered, it is a timeconsuming and even unavailable task for calculations. The discrete fracture network model that neglects the influence of rock matrix permeability has been rapidly developed during the past 40 years (Min and Jing, 2003;Liu et al, 2016b). From Fig.…”

Section: Introductionmentioning

confidence: 99%

“…1. Schematic view of fractured porous media (Liu et al, 2016b). voirs. Section 2 introduces the relationships between geometric properties and permeability of fracture networks.…”

Section: Introductionmentioning

confidence: 99%

Geometrical, fractal and hydraulic properties of fractured reservoirs: A mini-review

Wei

Xia

2017

Adv. Geo-Energ. Res.

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Fractures and fracture networks play an important role in fluid flow and transport properties of oil and gas reservoirs. Accurate estimation of geometrical characteristics of fracture networks and their hydraulic properties are two key research directions in the fields of fluids flow in fractured porous media. Recent works focusing on the geometrical, fractal and hydraulic properties of fractured reservoirs are reviewed and summarized in this mini-review. The effects of several important parameters that significantly influences hydraulic properties are specifically discussed and analyzed, including fracture length distribution, aperture distribution, boundary stress and anisotropy. The methods for predicting fractal dimension of fractures and models for fracture networks and fractured porous media based on fractal-based approaches are addressed. Some comments and suggestions are also given on the future research directions and fractal fracture networks as well as fractured porous media.

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“…Generally speaking, the effect of Young's modulus is analyzed in two ways. One is the pressure-dependent Young's modulus model (PDM) [26][27], the progressive failure process may be more significant. However, the two models can hardly be solved with analytical method.…”

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confidence: 99%

Analytical Strain-softening Solutions of a spherical cavity

Zhang

Quan

et al. 2018

Lat. Am. j. solids struct.

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This paper deals with a spherical cavity excavated in infinite homogeneous and isotropic strain-softening rock mass subjected to a hydrostatic initial Displacements and stresses distributions are two of the most important information for underground engineering, for that it can provide a theoretical foundation for geotechnical engineering optimism design and stability evaluation. In past few years, many scholars have developed series of (semi-)analytical and numerical solutions for circular openings and spherical cavities. . However, most of those solutions are based on the common elasto-perfectly-plastic and elasto-brittle-plastic models, because those solutions can be easily obtained using simple mathematical methods. However, most of the geotechnical materials display strain-softening behavior in the post-failure region. Therefore, the normally used elasto-perfectly plastic model and elasto-brittleplastic model can't well represent the actual failure process. Brown et al. were the earliest ones to analyze the stresses and displacements of circular openings excavated in the strain-softening rock mass. But, the assumption of constant elastic strain in the plastic region, which should obey the generalized Hooke's law, leads to a poor accuracy of the results. And Wang points out that Brown et al.'s solution is difficult to predict the plastic radius [11]. Carranza-Torres and Fairhurst's solution for H-B rock mass, which is based on the so-called self-similarity of H-B criterion, is theoretically rigorous. But, it seems rather complicated for practical use and is applicable only to the As we see, all of the solutions for strain-softening rock mass are based on semi-analytical and numerical method, no analytical solutions are available. Additionally, most of the indoor and field tests show that material properties of rock mass change during the failure process, not only strength parameters but also elastic parameters, i.e. Yong's modulus and Poisson's ratio. This is the so-called elasto-plastic coupling effect. Generally speaking, the effect of Young's modulus is analyzed in two ways. One is the pressure-dependent Young's modulus model (PDM) [26][27], the progressive failure process may be more significant. However, the two models can hardly be solved with analytical method. Considering the different tensile and compressive Young's modulus, Luo et al. obtained the closed-form solutions of spherical cavities in elastobrittle-plastic rock mass [28]. The difficulty of analytical methods for strain-softening rock mass is the coupling effect between softening index and material properties. In view of this, the Multi-step Brittle-Plastic model (MBPM) is proposed to solve the stress, strain, and displacement in the post-failure region for the spherical cavity. Moreover, the deterioration process of elastic parameters and strength parameters are also considered.

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Critical hydraulic gradient for nonlinear flow through rock fracture networks: The roles of aperture, surface roughness, and number of intersections

Cited by 169 publications

References 74 publications

Experimental Study on Stress-Dependent Nonlinear Flow Behavior and Normalized Transmissivity of Real Rock Fracture Networks

Experimental Study on Stress-Dependent Nonlinear Flow Behavior and Normalized Transmissivity of Real Rock Fracture Networks

Geometrical, fractal and hydraulic properties of fractured reservoirs: A mini-review

Analytical Strain-softening Solutions of a spherical cavity

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