Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks

2016 ◽  
Vol 24 (7) ◽  
pp. 1623-1649 ◽  
Author(s):  
Richeng Liu ◽  
Bo Li ◽  
Yujing Jiang ◽  
Na Huang
Keyword(s):  
Rock Fracture ◽  
Fracture Networks ◽  
Equivalent Permeability ◽  
Mathematical Expressions ◽  
Rock Fracture Networks

scholarly journals Estimating the Effect of Fractal Dimension on Representative Elementary Volume of Randomly Distributed Rock Fracture Networks

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Jing Zhang ◽  
Liyuan Yu ◽  
Hongwen Jing ◽  
Richeng Liu
Keyword(s):  
Fractal Dimension ◽  
Functional Relationship ◽  
Rock Fracture ◽  
Representative Elementary Volume ◽  
Width Ratio ◽  
Elementary Volume ◽  
Equivalent Permeability ◽  
Length Width ◽  
Rock Fracture Networks

The effect of fractal dimension (Df) on the determination of representative elementary volume (REV) was investigated through numerical experimentations, in which a new method was adopted to extract submodels that have different length-width ratios from original discrete facture networks (DFNs). Fluid flow in 1610 DFNs with different geometric characteristics of fractures and length-width ratios was simulated, and the equivalent permeability was calculated. The results show that the average equivalent permeability (KREV) at the REV size for DFNs increases with the increase in Df. The KREV shows a downward trend with increasing length-width ratio of the submodel. A strong exponent functional relationship is found between the REV size and Df. The REV size decreases with increasing Df. With the increment of the length-width ratio of submodels, the REV size shows a decreasing trend. The effects of length-width ratio and Df on the REV size can be negligible when Df≥1.5, but are significant when Df<1.5.

scholarly journals From invasion percolation to flow in rock fracture networks

2012 ◽  
Vol 391 (1-2) ◽  
pp. 264-277 ◽  
Author(s):  
Salomon J. Wettstein ◽  
Falk K. Wittel ◽  
Nuno A.M. Araújo ◽  
Bill Lanyon ◽  
Hans J. Herrmann
Keyword(s):  
Rock Fracture ◽  
Invasion Percolation ◽  
Fracture Networks ◽  
Rock Fracture Networks

scholarly journals Multi-scale approach to invasion percolation of rock fracture networks

2014 ◽  
Vol 519 ◽  
pp. 353-363 ◽  
Author(s):  
Ali N. Ebrahimi ◽  
Falk K. Wittel ◽  
Nuno A.M. Araújo ◽  
Hans J. Herrmann
Keyword(s):  
Rock Fracture ◽  
Invasion Percolation ◽  
Fracture Networks ◽  
Multi Scale ◽  
Rock Fracture Networks

The fractal description model of rock fracture networks characterization

2019 ◽  
Vol 129 ◽  
pp. 71-76
Author(s):  
Lili Sui ◽  
Jian Yu ◽  
Dingbang Cang ◽  
Wenjing Miao ◽  
Heyuan Wang ◽  
...  
Keyword(s):  
Rock Fracture ◽  
Fracture Networks ◽  
Rock Fracture Networks ◽  
Fractal Description

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

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Qian Yin ◽  
Hongwen Jing ◽  
Richeng Liu ◽  
Guowei Ma ◽  
Liyuan Yu ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Rock Fracture ◽  
Hydraulic Gradient ◽  
Nonlinear Flow ◽  
Fracture Networks ◽  
Critical Hydraulic Gradient ◽  
Boundary Load ◽  
Flow Through ◽  
Stress Dependent ◽  
Rock Fracture Networks

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 a and nonlinear coefficient b in Forchheimer’s law J=aQ+bQ2 generally decrease with the number of intersections but increase with the boundary load. The relationships between a and b can be well fitted with a power function. A nonlinear effect factor E=bQ2/(aQ+bQ2) was used to quantitatively characterize the nonlinear behaviors of fluid flow through fracture networks. By defining a critical value of E = 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 T/T0=1-exp⁡(-αJ-0.45) for decreased normalized transmissivity T/T0 against the hydraulic gradient J was established. When the hydraulic gradient is small, T/T0 holds a constant value of 1.0. With increasing hydraulic gradient, the reduction rate of T/T0 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.

The “small-world” topology of rock fracture networks

2007 ◽  
Vol 377 (1) ◽  
pp. 323-328 ◽  
Author(s):  
Luca Valentini ◽  
Diego Perugini ◽  
Giampiero Poli
Keyword(s):  
Rock Fracture ◽  
Small World ◽  
Fracture Networks ◽  
Rock Fracture Networks
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