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Rock Mechanics and Rock Engineering

, Volume 52, Issue 11, pp 4731–4746 | Cite as

Experimental and Numerical Studies of the Hydraulic Properties of Three-Dimensional Fracture Networks with Spatially Distributed Apertures

  • Na Huang
  • Yujing JiangEmail author
  • Richeng Liu
  • Bo Li
Original Paper
  • 286 Downloads

Abstract

Fluid flow tests on three-dimensional (3D) transparent fracture networks were performed to clarify the effect of aperture heterogeneity on the hydraulic properties of rough fractures. The five-axis machining combined with the 3D construction technique was applied to create the transparent sample, which ensures the direct visualization and quantification of flow behavior through the fractures. The effects of the anisotropic aperture on flow channeling and permeability of the fracture networks were evaluated using a developed numerical code, the validity of which has been verified by the flow test results. The numerical investigation was extended to complex 3D discrete fracture networks with large fracture densities. The results show that five-axis machining can reproduce a 3D fracture network sample with spatially distributed apertures by first machining the fracture blocks and subsequently assembling them. An obvious channeling flow in the sample was observed during the flow tests. With decreasing mean and/or increasing deviation of the aperture fields following a normal distribution, the localization of fluid flow is increasingly obvious; the main flow channels account for approximately 26–67% of the fracture planes. The ratio of permeability of the model with apertures following truncated lognormal distributions to those following complete lognormal distributions first showed remarkably increase and subsequently approached 1.0 with the increasing truncation threshold of the aperture distribution. A mathematical expression is proposed for predicting the critical truncation threshold, which is defined when the normalized permeability is equal to 0.9. The suitability of upscaling the proposed expression to complex 3D discrete fracture networks is verified, which can help to determine the proper truncation threshold when simulating a fracture aperture with lognormal distribution functions in fractured rock masses.

Keywords

Fracture network Flow test Aperture Channeling flow Truncation threshold 

List of Symbols

A

Coefficient in the Forchheimer’s law representing viscous effect

As

Cross-sectional area of the fracture

B

Coefficient in the Forchheimer’s law representing inertial effect

a

The power law exponent

b

Fracture aperture

em

Mean value of normal distribution of aperture

et

Truncation threshold of aperture

ec

Critical truncation threshold of aperture

fb

Body force

g

Gravitational acceleration

h

Hydraulic head

hk

The trace of the hydraulic head on Sk in fracture plane f

i

Hydraulic gradient

K

The equivalent permeability

K0

The equivalent permeability of the model with parallel plates

Kt

The equivalent permeability calculated with aperture following truncated lognormal distribution

Kc

The equivalent permeability calculated with aperture following complete lognormal distribution

KE

The equivalent permeability obtained by laboratorial experiment

KS

The equivalent permeability obtained by numerical simulation

l

Fracture length

n

Fracture number

P

Hydraulic pressure

Q

Flow rate

Rf

The ratios of the area of preferential flow paths to that of the total fracture planes

r1

The relative error of permeability between experimental and numerical results

Sk

Fracture intersection line

t

Time

u

The logarithm of the mean value of lognormal distribution of aperture

v

Flow velocity tensor

w

Fracture width

ρ

Fluid density

η

The ratio of permeability the complete lognormal distribution

μ

Dynamic viscosity

σ

The deviation of normal distribution of aperture

σf

The deviation of lognormal distribution of aperture

Notes

Acknowledgements

This study has been partially funded by National Natural Science Foundation of China, China (Grant nos. 51709260, 51609136), Natural Science Foundation of Jiangsu Province, China (no. BK20170276), Japan Society for the Promotion of Science (JSPS) (no. P17382), and JSPS Grant-in-Aid for Scientific Research (no. 17H03506). These supports are gratefully acknowledged.

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Petroleum EngineeringChina University of Petroleum (East China)QingdaoChina
  2. 2.School of EngineeringNagasaki UniversityNagasakiJapan
  3. 3.State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and TechnologyShandong University of Science and TechnologyQingdaoPeople’s Republic of China
  4. 4.State Key Laboratory for Geomechanics and Deep Underground EngineeringChina University of Mining and TechnologyXuzhouPeople’s Republic of China
  5. 5.Center of Rock Mechanics and GeohazardsShaoxing UniversityShaoxingChina

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