Abstract
In this study, a numerical methodology has been developed and discussed to investigate the influence of in situ stresses, including normal and tractional stresses, on the permeability of a heterogeneous intact rock. Flow properties of a representative rock sample composed of three different rock types, randomly located in a rock block, is studied under different stress regimes. Porosity and permeability within each rock type is distributed using statistical distributions. Different stress regimes corresponding to the rock sample located at surface, and at subsurface with horizontal stresses applied in two different orientations are investigated. The stress distribution in the rock sample under different stress scenarios is calculated and is used to update the permeability and porosity at different locations within the rock sample. The ensemble permeability tensors are calculated by running flow simulations in three perpendicular directions and upscaling the permeability from the element level (5 mm) to the sample scale (5 m). It is demonstrated that the flow properties of the studied heterogeneous rock sample reduce considerably when the sample is taken from the surface to a depth of 1 km. More importantly, it is shown that when the horizontal stresses are not perpendicular to the sidewalls of the rock sample, they create shear stresses which further reduce the permeability.
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Abbreviations
- C :
-
Fourth-order stiffness tensor
- E :
-
Young’s modulus (GPa)
- f :
-
Vector of body forces (N)
- G :
-
Shear modulus (GPa)
- I :
-
Identity matrix
- K 0 :
-
Median initial permeability (m2)
- k :
-
Permeability tensor
- p :
-
Pore fluid pressure (MPa)
- P 0 :
-
Initial pressure (MPa)
- P eff :
-
Effective pressure (MPa)
- S V :
-
Overburden stress (MPa)
- S H :
-
Maximum horizontal stress (MPa)
- S h :
-
Minimum horizontal stress (MPa)
- u :
-
Velocity vector
- u, v, w :
-
Displacements in x, y, and z directions (m)
- V:
-
Volume (m3)
- δ v :
-
Virtual velocity field
- t :
-
Shear stress vector
- α:
-
Porosity sensitivity exponent
- γ:
-
Pressure sensitivity coefficient (MPa−1)
- ε :
-
Strain
- μ :
-
Pore fluid viscosity (m2/s)
- υ :
-
Poisson’s ratio
- ρ :
-
Rock density (kg/m3)
- σ :
-
Cauchy stress tensor
- σ′:
-
Cauchy effective stress tensor
- Φ :
-
Porosity (%)
- Φ 0 :
-
Average initial porosity (%)
References
Abaqus Theory Guide (2016) Dassault Systèmes, Providence, RI, USA
Agheshlui H, Sedaghat MH, Matthai S (2018) Stress influence on fracture aperture and permeability of fragmented rocks. J Geophys Res Solid Earth. https://doi.org/10.1029/2017jb015365
Agheshlui H, Sedaghat MH, Azizmohammadi S (2019) A comparative study of stress influence on fracture apertures in fragmented rocks. J Rock Mech Geotech Eng 11(1):38–45. https://doi.org/10.1016/j.jrmge.2018.05.003
Azizmohammadi S, Matthäi SK (2017) Is the permeability of naturally fractured rocks scale dependent? Water Resour Res. https://doi.org/10.1002/2016wr019764
Baghbanan A, Jing L (2008) Stress effects on permeability in a fractured rock mass with correlated fracture length and aperture. Int J Rock Mech Min Sci 45(8):1320–1334. https://doi.org/10.1016/j.ijrmms.2008.01.015
Bhandari AR, Flemings PB, Polito PJ, Cronin MB, Bryant SL (2015) Anisotropy and stress dependence of permeability in the barnett shale. Transp Porous Media 108(2):393–411. https://doi.org/10.1007/s11242-015-0482-0
David C, Wong T-F, Zhu W, Zhang J (1994) Laboratory measurement of compaction-induced permeability change in porous rocks: implications for the generation and maintenance of pore pressure excess in the crust. Pure Appl Geophys 143(1):425–456. https://doi.org/10.1007/bf00874337
Dong J-J, Hsu J-Y, Wu W-J, Shimamoto T, Hung J-H, Yeh E-C, Sone H (2010) Stress-dependence of the permeability and porosity of sandstone and shale from TCDP Hole-A. Int J Rock Mech Min Sci 47(7):1141–1157. https://doi.org/10.1016/j.ijrmms.2010.06.019
Fernandez G, Moon J (2010) Excavation-induced hydraulic conductivity reduction around a tunnel—Part 1: guideline for estimate of ground water inflow rate. Tunn Undergr Space Technol 25(5):560–566. https://doi.org/10.1016/j.tust.2010.03.006
Gan Q, Elsworth D (2016) A continuum model for coupled stress and fluid flow in discrete fracture networks. Geomech Geophys Geo-Energy Geo-Resour 2(1):43–61. https://doi.org/10.1007/s40948-015-0020-0
Guo H, Yuan L, Shen B, Qu Q, Xue J (2012) Mining-induced strata stress changes, fractures and gas flow dynamics in multi-seam longwall mining. Int J Rock Mech Min Sci 54:129–139. https://doi.org/10.1016/j.ijrmms.2012.05.023
Kazemi H, Gilman JR (1993) Multiphase flow in fractured petroleum reservoirs. In: Bear J, Tsang CF, d. Marsily G (eds) Flow and contaminant transport in fractured rocks. Academic Press, San Diego, pp 267–323
Latham J-P, Xiang J, Belayneh M, Nick HM, Tsang C-F, Blunt MJ (2013) Modelling stress-dependent permeability in fractured rock including effects of propagating and bending fractures. Int J Rock Mech Min Sci 57:100–112. https://doi.org/10.1016/j.ijrmms.2012.08.002
Lei Q, Wang X, Xiang J, Latham JP (2017) Polyaxial stress-dependent permeability of a three-dimensional fractured rock layer. Hydrogeol J 25(8), 2251–2262. https://doi.org/10.1007/s10040-017-1624-y
Liu HH, Ranjith PG, Georgi DT, Lai BT (2016) Some key technical issues in modelling of gas transport process in shales: a review. Geomech Geophys Geo-Energy Geo-Resour 2(4):231–243. https://doi.org/10.1007/s40948-016-0031-5
Min K-B, Rutqvist J, Tsang C-F, Jing L (2004) Stress-dependent permeability of fractured rock masses: a numerical study. Int J Rock Mech Min Sci 41(7):1191–1210. https://doi.org/10.1016/j.ijrmms.2004.05.005
Neretnieks I (1993) Solute transport in fractured rock: application to radionuclide waste repositories. In: Bear J, Tsang C-F, d. Marsily G (eds) Flow and contaminant transport in fractured rock. Academic Press, San Diego, pp 39–127
Ranathunga AS, Perera MSA, Ranjith PG, De Silva GPD (2017) A macro-scale view of the influence of effective stress on carbon dioxide flow behaviour in coal: an experimental study. Geomechan Geophys Geo-Energy Geo-Resour 3(1):13–28. https://doi.org/10.1007/s40948-016-0042-2
Zheng J, Zheng L, Liu H-H, Ju Y (2015) Relationships between permeability, porosity and effective stress for low-permeability sedimentary rock. Int J Rock Mech Min Sci 78:304–318. https://doi.org/10.1016/j.ijrmms.2015.04.025
Acknowledgement
Caroline Milliotte (FEI Inc., Canberra, Australia) is thanked for the generation of the complex geometry of rock types. Also, Dr. Mohammad Sedaghat is thanked for his advice on the flow simulation processes.
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Agheshlui, H. Stress influence on the permeability of a sample heterogeneous rock. Geomech. Geophys. Geo-energ. Geo-resour. 5, 159–170 (2019). https://doi.org/10.1007/s40948-019-00111-6
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DOI: https://doi.org/10.1007/s40948-019-00111-6