The linear theory of dual-porosity and dual-permeability poro-chemo-electro-elasticity is presented. The theory outlines the dual-continuum formulation of multiple coupled processes involving solid deformation, pore fluid flow, and electrically charged species transport, within and in between two coexisting porosity systems of a fluid-saturated, poro-elastic medium. The described formulation is used to derive the analytical solutions to the inclined wellbore problem and axisymmetric Mandel-Type problem of dual-porosity, dual-permeability poro-chemo-electro-elasticity. The effects of chemical and electrical potentials on the distributions of stress and pore pressure are demonstrated by numerical examples pertaining to the considered problems. It is shown that the fully coupled nature of the solutions rigorously captures the seemingly anomalous time variations of the effective stress as driven by the pore fluid pressure disturbances, as well as the distribution and movement of anions/cations within the dual-porosity porous medium. The existing subset of published solutions on the subject is successfully reproduced as special cases of the solutions presented in this paper.
Issue Section:
Research Papers
References
1.
Yeung
, A.
, and Mitchell
, J.
, 1993
, “Coupled Fluid, Electrical and Chemical Flows in Soil
,” Geotechnique
, 43
(1
), pp. 121
–134
.2.
Huyghe
, J.
, and Janssen
, J.
, 1999
, “Thermo-Chemo- Eletro-Mechanical Formulation of Saturated Charged Porous Solids
,” Transp. Porous Media
, 34
(2
), pp. 129
–141
.3.
Heidug
, W.
, and Wong
, S.
, 1996
, “Hydration Swelling of Water-Absorbing Rocks: A Constitutive Model
,” Int. J. Numer. Anal. Methods Geomech.
, 20
(6
), pp. 403
–430
.4.
Huyghe
, J.
, 2007
, “Analytical Solution of a Pressure Transmission Experiment on Shale Using Electrochemomechanical Theory
,” J. Eng. Mech.
, 133
(9
), pp. 994
–1002
.5.
Ewy
, R. T.
, and Stankovic
, R. J.
, 2010
, “Shale Swelling, Osmosis, and Acoustic Changes Measured Under Simulated Downhole Conditions
,” SPE Drill. Completion
, 25
(2
), pp. 177
–186
.6.
Tran
, M.
, and Abousleiman
, Y.
, 2013
, “Anisotropic Porochemoelectroelastic Mandel's Problem Solutions for Applications in Reservoir Modeling and Laboratory Characterization
,” Mech. Res. Commun.
, 47
, pp. 89
–96
.7.
Lang
, G.
, Stewart
, P.
, Vella
, D.
, Waters
, S.
, and Goriely
, A.
, 2014
, “Is the Donnan Effect Sufficient to Explain Swelling in Brain Tissue Slices?
,” J. R. Soc. Interface
, 11
(96
), p. 20140123
.8.
Medved
, I.
, and Černý
, R.
, 2013
, “Osmosis in Porous Media: A Review of Recent Studies
,” Microporous Mesoporous Mater.
, 170
, pp. 299
–317
.9.
Ewy
, R. T.
, 2014
, “Shale Swelling/Shrinkage and Water Content Change Due to Imposed Suction and Due to Direct Brine Contact
,” Acta Geotechnica
, 9
(5
), pp. 869
–886
.10.
Biot
, M.
, 1941
, “General Theory of Three Dimensional Consolidation
,” J. Appl. Phys.
, 12
, pp. 155
–164
.11.
Bowen
, R.
, 1982
, “Compressible Porous Media Models by Use of the Theory of Mixtures
,” Int. J. Eng. Sci.
, 20
(6
), pp. 697
–735
.12.
Coussy
, O.
, Dormieux
, L.
, and Detournay
, E.
, 1998
, “From Mixture Theory to Biot's Approach for Porous Media
,” Int. J. Solids Struct.
, 35
(34–35
), pp. 4619
–4635
.13.
Dormieux
, L.
, Kondo
, D.
, and Ulm
, F.-J.
, 2006
, Microporomechanics
, Wiley
, Chichester, UK.14.
Cheng
, A.
, 2016
, Poroelasticity
, Springer International Publishing
, Basel, Switzerland
.15.
Anand
, L.
, 2015
, “2014 Drucker Medal Paper: A Derivation of the Theory of Linear Poroelasticity From Chemoelasticity
,” ASME J. Appl. Mech.
, 82
(11
), p. 111005
.16.
Nguyen
, V.
, and Abousleiman
, Y.
, 2010
, “Incorporating Electrokinetic Effects in the Porochemoelastic Inclined Wellbore Formulation and Solution
,” An. Acad. Bras. Ciênc.
, 8
, pp. 195
–222
.17.
Bunger
, A.
, Sarout
, J.
, Kear
, J.
, Piane
, C.
, Detournay
, E.
, Josh
, M.
, and Dewhurst
, D.
, 2014
, “Experimental Chemoporoelastic Characterization of Shale Using Millimeter-Scale Specimens
,” J. Petro. Sci. Eng.
, 118
(8
), pp. 40
–51
.18.
Abousleiman
, Y.
, Liu
, C.
, and Hoang
, S.
, 2013
, “Poromechanics Axisymmetric Mandel-Type Solutions and Pore Pressure Intricate Behaviors in Dual-Porosity Dual-Permeability Shale
,” Fifth Biot Conference on Poromechanics
, Vienna, Austria, July 10–12, pp. 2451
–2460
.19.
Liu
, C.
, Hoang
, S.
, Tran
, M.
, Abousleiman
, Y.
, and Ewy
, R.
, 2017
, “Poroelastic Dual-Porosity Dual-Permeability Simulation of Pressure Transmission Test on Chemically Active Shale
,” J. Eng. Mech.
, 143
(6
), p. 04017016
.20.
Liu
, C.
, and Abousleiman
, Y.
, 2017
, “Shale Dual-Porosity Dual-Permeability Poromechanical and Chemical Properties Extracted From Experimental Pressure Transmission Test
,” J. Eng. Mech.
, 143
(6
), p. 04017107
.21.
Tran
, M.
, and Abousleiman
, Y.
, 2013
, “Anisotropic Porochemoelectroelastic Solution for an Inclined Wellbore Drilled in Shale
,” ASME J. Appl. Mech.
, 80
(2
), p. 020912
.22.
Cowin
, S.
, Gailani
, G.
, and Benalla
, M.
, 2009
, “Hierarchical Poroelasticity: Movement of Interstitial Fluid Between Porosity Levels in Bones
,” Phil. Trans. R. Soc.
, 367
(67, pp. 3401
–3444
.23.
Barenblatt
, G.
, Zheltov
, I.
, and Kochina
, I.
, 1960
, “Basic Concepts in the Theory of Seepage of Homogeneous Liquids in Fissured Rocks [Strata]
,” J. Appl. Math. Mech.
, 24
(5
), pp. 1286
–1303
.24.
Beskos
, D.
, and Aifantis
, E.
, 1986
, “On the Theory of Consolidation With Double Porosity-II
,” Int. J. Eng. Sci.
, 24
(11
), pp. 1697
–1716
.25.
Wilson
, R.
, and Aifantis
, E.
, 1982
, “On the Theory of Consolidation With Double Porosity
,” Int. J. Eng. Sci.
, 20
, pp. 1009
–1035
.26.
Mehrabian
, A.
, and Abousleiman
, Y.
, 2014
, “Generalized Biot's Theory and Mandel's Problem of Multiple-Porosity and Multiple-Permeability Poroelasticity
,” J. Geophys. Res.: Solid Earth
, 119
(4
), pp. 2745
–2763
.27.
Mehrabian
, A.
, and Abousleiman
, Y.
, 2015
, “Gassmann Equations and the Constitutive Relations for Multiple-Porosity and Multiple-Permeability Poroelasticity With Applications to Oil and Gas Shale
,” Int. J. Numer. Anal. Meth. Geomech.
, 39
(14), pp. 1547
–1569
.28.
Mehrabian
, A.
, and Abousleiman
, Y.
, 2018
, “Theory and Analytical Solution to Cryer's Problem of N-Porosity and N-Permeability Poroelasticity
,” J. Mech. Phys. Solids
, 118
(18), pp. 218
–227
.29.
Liu
, C.
, and Abousleiman
, Y.
, 2018
, “Multiporosity/Multipermeability Inclined-Wellbore Solutions With Mudcake Effects
,” SPE J.
(preprint).30.
Carter
, P.
, and Booker
, R.
, 1982
, “Elastic Consolidation Around a Deep Circular Tunnel
,” Int. J. Solids Struct.
, 18
(12
), pp. 1059
–1074
.31.
Detournay
, E.
, and Cheng
, A. H.-D.
, 1988
, “Poroelastic Response of a Borehole in a Non-Hydrostatic Stress Field
,” Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
, 2
(3
), pp. 171
–182
.32.
Cui
, L.
, Cheng
, A.
, and Abousleiman
, Y.
, 1997
, “Poroelastic Solution for an Inclined Borehole
,” ASME J. Appl. Mech.
, 64
(1
), pp. 32
–38
.33.
Abousleiman
, Y.
, and Cui
, L.
, 1998
, “Poroelastic Solutions in Transversely Isotropic Media for Wellbore and Cylinder
,” Int. J. Solids Struct.
, 35
(34–35
), pp. 4905
–4929
.34.
Ekbote
, S.
, Abousleiman
, Y.
, and Zaman
, M.
, 2004
, “Analyses of Inclined Boreholes in Poroelastic Media
,” Int. J. Geomech.
, 4
(3
), pp. 178
–190
.35.
Mehrabian
, A.
, and Abousleiman
, Y.
, 2013
, “Generalized Poroelastic Wellbore Problem
,” Int. J. Numer. Anal. Methods Geomech.
, 37
(16
), pp. 2727
–2754
.36.
Sherwood
, J.
, and Bailey
, L.
, 1994
, “Swelling Shale Around a Cylindrical Wellbore
,” Proc. R. Soc. London A
, 44
(44), pp. 161
–184
.37.
Ekbote
, S.
, and Abousleiman
, Y.
, 2005
, “Porochemothermoelastic Solution for an Inclined Borehole in a Transversely Isotropic Formation
,” J. Eng. Mech.
, 131
(5
), pp. 522
–533
.38.
Ekbote
, S.
, and Abousleiman
, Y.
, 2006
, “Porochemoelastic Solution for an Inclined Borehole in a Transversely Isotropic Formation
,” J. Eng. Mech.
, 132
(7
), pp. 754
–763
.39.
Li
, X.
, 2003
, “Consolidation Around a Borehole Embedded in Media With Double Porosity Under Release of Geostatic Stresses
,” Mech. Res. Commun.
, 30
, pp. 95
–100
.40.
Abousleiman
, Y.
, and Nguyen
, V.
, 2005
, “Poromechanics Response of Inclined Wellbore Geometry in Fractured Porous Media
,” J. Eng. Mech.
, 131
(11
), pp. 1170
–1183
.41.
Nguyen
, V.
, and Abousleiman
, Y.
, 2009
, “Poromechanics Response of Inclined Wellbore Geometry in Chemically Active Fractured Porous Media
,” J. Eng. Mech.
, 135
(11
), pp. 1281
–1294
.42.
Armstrong
, C.
, Lar
, W.
, and Mow
, V.
, 1984
, “An Analysis of the Unconfined Compression of Articular Cartilage
,” ASME J. Biomech. Eng.
, 106
(2
), pp. 165
–173
.43.
Abousleiman
, Y.
, Cheng
, A.
, Cui
, L.
, Detournay
, E.
, and Roegiers
, J.-C.
, 1996
, “Mandel's Problem Revisited
,” Geotechnique
, 46
(2
), pp. 187
–195
.44.
Cui
, L.
, and Abousleiman
, Y.
, 2001
, “Time-Dependent Poromechanical Responses of Saturated Cylinders
,” J. Eng. Mech.
, 127
(4
), pp. 391
–398
.45.
Sawaguchi
, H.
, and Kurashige
, M.
, 2005
, “Constant Strain-Rate Compression Test of a Fluid-Saturated Poroelastic Sample With Positive or Negative Poisson's Ratio
,” Acta Mech.
, 179
(3–4
), pp. 145
–156
.46.
Nguyen
, V.
, and Abousleiman
, Y.
, 2010
, “Poromechanics Solutions to Plane Strain and Axisymmetric Mandel-Type Problems in Dual-Porosity and Dual-Permeability Medium
,” ASME J. Appl. Mech.
, 77
(1
), p. 011002
.47.
Bunger
, A.
, 2010
, “The Mandel-Cryer Effect in Chemoporoelasticity
,” Int. J. Numer. Anal. Methods Geomech.
, 34
(14
), pp. 1479
–1511
.48.
Aifantis
, E.
, 1977
, “Introducing a Multi-Porous Medium
,” Dev. Mech.
, 8
, pp. 209
–211
. 49.
Katchalsky
, A.
, and Curran
, P.
, 1967
, Nonequilibrium Thermodynamics in Biophysics
, Harvard University Press
, Cambridge, MA
. 50.
Onsager
, L.
, 1931
, “Reciprocal Relations in Irreversible Processes—I
,” Phys. Rev.
, 37
(4
), pp. 405
–426
.51.
Coussy
, O.
, 2004
, Poromechanics
, Wiley
, Chichester, UK. 52.
Sachs
, J.
, and Grodinsky
, A.
, 1987
, “An Electromechanically Coupled Poroelastic Medium Driven by an Applied Electrical Current: Surface Detection of Bulk Material Parameters
,” Phys. Chem. Hydrodyn.
, 11
(4
), pp. 585
–614
.53.
Corapcioglu
, Y.
, 1991
, “Formulation of Electro-Chemico-Osmotic Processes in Soils
,” Transp. Porous Media
, 6
(4
), pp. 435
–444
.54.
Mitchell
, J.
, 1993
, Fundamentals of Soil Behavior
, Wiley
, New York
. 55.
Gonçalvès
, J.
, Rousseau-Gueutin
, P.
, de Marsily
, G.
, Cosenza
, P.
, and Violette
, S.
, 2010
, “What is the Significance of Pore Pressure in a Saturated Shale Layer?
,” Water Resour. Res.
, 46
(4), p. W04514
.56.
Overbeek
, J.
, 1956
, “The Donnan Equilibrium
,” Prog. Biophys.
, 6
, pp. 57
–84
.57.
Carroll
, D.
, 1959
, “Ion Exchange in Clays and Other Minerals
,” Bull. Geol. Soc. Am.
, 7
, pp. 749
–780
.58.
Hang
, P.
, and Brindley
, G.
, 1970
, “Methylene Blue Absorption by Clay Minerals. Determination of Surface Areas and Cation Exchange Capacities
,” Clays Clay Miner.
, 18
, pp. 203
–212
.59.
Hiramatsu
, Y.
, and Oka
, Y.
, 1962
, “Stress Around a Shaft or Level Excavated in Ground With a Three-Dimensional Stress State
,” Mem. Frac. Eng. Kyotu Univ.
, 24
, pp. 56
–76
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