Browse > Article
http://dx.doi.org/10.12989/gae.2022.28.5.437

Geomechanical and hydrogeological validation of hydro-mechanical two-way sequential coupling in TOUGH2-FLAC3D linking algorithm with insights into the Mandel, Noordbergum, and Rhade effects  

Lee, Sungho (School of Earth and Environmental Sciences, Seoul National University)
Park, Jai-Yong (Geology Division, Korea Institute of Geoscience and Mineral Resources)
Kihm, Jung-Hwi (Department of Fire and Disaster Prevention, Jungwon University)
Kim, Jun-Mo (School of Earth and Environmental Sciences, Seoul National University)
Publication Information
Geomechanics and Engineering / v.28, no.5, 2022 , pp. 437-454 More about this Journal
Abstract
The hydro-mechanical (HM) two-way sequential coupling in the TOUGH2-FLAC3D linking algorithm is validated completely and successfully in both M to H and H to M directions, which are initiated by mechanical surface loading for geomechanical validation and hydrological groundwater pumping for hydrogeological validation, respectively. For such complete and successful validation, a TOUGH2-FLAC3D linked numerical model is developed first by adopting the TOUGH2-FLAC3D linking algorithm, which uses the two-way (fixed-stress split) sequential coupling scheme and the implicit backward time stepping method. Two geomechanical and two hydrogeological validation problems are then simulated using the linked numerical model together with basic validation strategies and prerequisites. The second geomechanical and second hydrogeological validation problems are also associated with the Mandel effect and the Noordbergum and Rhade effects, respectively, which are three phenomenally well-known but numerically challenging HM effects. Finally, sequentially coupled numerical solutions are compared with either analytical solutions (verification) or fully coupled numerical solutions (benchmarking). In all the four validation problems, they show almost perfect to extremely or very good agreement. In addition, the second geomechanical validation problem clearly displays the Mandel effect and suggests a proper or minimum geometrical ratio of the height to the width for the rectangular domain to maximize agreement between the numerical and analytical solutions. In the meantime, the second hydrogeological validation problem clearly displays the Noordbergum and Rhade effects and implies that the HM two-way sequential coupling scheme used in the linked numerical model is as rigorous as the HM two-way full coupling scheme used in a fully coupled numerical model.
Keywords
geomechanical validation; hydrogeological validation; hydro-mechanical two-way sequential coupling; Mandel effect; Noordbergum effect; Rhade effect; TOUGH2-FLAC3D linking algorithm;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Rutqvist, J., Borgesson, L., Chijimatsu, M., Kobayashi, A., Jing, L., Nguyen, T.S., Noorishad, J. and Tsang, C.F. (2001), "Thermohydromechanics of partially saturated geological media: Governing equations and formulation of four finite element models", Int. J. Rock Mech. Min. Sci., 38(1), 105-127. https://doi.org/10.1016/S1365-1609(00)00068-X.   DOI
2 Taron, J. (2009), "Geophysical and geochemical analyses of flow and deformation in fractured rock", Ph.D. Dissertation, Pennsylvania State University, University Park, Pennsylvania, USA, 183 pp.
3 Taron, J. and Elsworth, D. (2010), "Coupled mechanical and chemical processes in engineered geothermal reservoirs with dynamic permeability", Int. J. Rock Mech. Min. Sci., 47(8), 1339-1348. https://doi.org/10.1016/j.ijrmms.2010.08.021.   DOI
4 Taron, J., Min, K.B., Yasuhara, H., Trakoolngam, K. and Elsworth, D. (2006), "Numerical simulation of coupled thermo-hydrochemo-mechanical processes through the linking of hydrothermal and solid mechanics codes", Proceedings of the 41st US Rock Mechanics Symposium (Golden Rocks 2006), Colorado School of Mines, Golden, Colorado, USA, June, Volume 1, Paper No. ARMA/USRMS-06-1128, 268-276.
5 Hutnak, M., Hurwitz, S., Ingebritsen, S.E. and Hsieh, P.A. (2009), "Numerical models of caldera deformation: Effects of multiphase and multicomponent hydrothermal fluid flow", J. Geophys. Res. Solid Earth, 114(4), B04411. https://doi.org/10.1029/2008JB006151.   DOI
6 Itasca Consulting Group (2017), "FLAC3D: Fast Lagrangian analysis of continua in 3 dimensions, version 6.0", Manual, Itasca Consulting Group, Minneapolis, Minnesota, USA, 11 volumes (Volume 1: User's guide).
7 Itasca Consulting Group (1997), "FLAC3D: Fast Lagrangian analysis of continua in 3 dimensions, version 2.0", Manual, Itasca Consulting Group, Minneapolis, Minnesota, USA, 5 volumes (Volume 1: User's guide).
8 Terzaghi, K. (1925), Erdbaumechanik auf Bodenphysikalischer Grundlage, Franz Deuticke, Leipzig, Saxony, Germany, 399 pp (in German).
9 van Eyden, W.A.A., Kuper, H.W. and Santema, P. (1964), "Some methods used in the geo-hydrologic survey of the south-western deltaic area in the Netherlands", in IAHS Red Books, Volume 63, Proceeding of the Symposium on Surface Waters, 13th IUGG (International Union of Geodesy and Geophysics) General Assembly, University of California, Berkeley, California, USA, August, 1963, International Association of Hydrological Sciences, Ghent, East Flanders, Belgium, 528-557.
10 Itasca Consulting Group (2009), "FLAC3D: Fast Lagrangian analysis of continua in 3 dimensions, version 4.0", Manual, Itasca Consulting Group, Minneapolis, Minnesota, USA, 12 volumes (Volume 1: User's guide).
11 Kim, J. (2010), "Sequential methods for coupled geomechanics and multiphase flow", Ph.D. Dissertation, Stanford University, Stanford, California, USA, 248 pp.
12 Kim, J. and Moridis, G.J. (2013), "Development of the T+M coupled flow-geomechanical simulator to describe fracture propagation and coupled flow-thermal-geomechanical processes in tight/shale gas systems", Comput. Geosci., 60, 184-198. https://doi.org/10.1016/j.cageo.2013.04.023.   DOI
13 Kim, J., Sonnenthal, E. and Rutqvist, J. (2015), "A sequential implicit algorithm of chemo-thermo-poro-mechanics for fractured geothermal reservoirs", Comput. Geosci., 76, 59-71. https://doi.org/10.1016/j.cageo.2014.11.009.   DOI
14 Kim, J., Tchelepi, H.A. and Juanes, R. (2011a), "Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits", Comput. Meth. Appl. Mech. Eng., 200(13-16), 1591-1606. https://doi.org/10.1016/j.cma.2010.12.022.   DOI
15 Lee, J., Min, K.B. and Rutqvist, J. (2015a), "TOUGH-UDEC simulator for the coupled multiphase fluid flow, heat transfer, and deformation in fractured porous media", in Hassani, F.P., Hadjigeorgiou, J. and Archibald, J. (Editors), Innovations in Applied and Theoretical Rock Mechanics: Proceedings of the 13th ISRM (International Society for Rock Mechanics and Rock Engineering) International Congress of Rock Mechanics, Montreal Congress and Exhibition Centre (Palais des Congres), Montreal, Quebec, Canada, May, Paper No. ISRM-13CONGRESS-2015-231, 1-10.
16 Bear, J. and Corapcioglu, M.Y. (1981), "Mathematical model for regional land subsidence due to pumping, 2. Integrated aquifer subsidence equations for vertical and horizontal displacements", Water Resour. Res., 17(4), 947-958. https://doi.org/10.1029/WR017i004p00947.   DOI
17 Rodrigues, J.D. (1983), "The Noordbergum effect and characterization of aquitards at the Rio Maior mining project", Ground Water, 21(2), 200-207. https://doi.org/10.1111/j.1745-6584.1983.tb00714.x.   DOI
18 Aboustit, B.L., Advani, S.H., Lee, J.K. and Sandhu, R.S. (1982), "Finite element evaluations of thermo-elastic consolidation", in Goodman, R.E. and Hueze, F.E. (Editors), Issues in Rock Mechanics: Proceedings of the 23rd Symposium on Rock Mechanics, University of California, Berkeley, California, USA, August, Society of Mining Engineers, American Institute of Mining, Metallurgical and Petroleum Engineers, New York, New York, USA, 587-595.
19 Barksdale, H.C., Sundstrom, R.W. and Brunstein, M.S. (1936), "Supplementary report on the ground-water supplies of the Atlantic City region", Special Report No. 6, New Jersey State Water Policy Commission, Trenton, New Jersey, USA, 139 pp.
20 Biot, M.A. and Willis, D.G. (1957), "The elastic coefficients of the theory of consolidation", J. Appl. Mech., Trans. Am. Soc. Mech. Eng., 24(4), 594-601. https://doi.org/10.1115/1.4011606.   DOI
21 Bishop, A.W. and Blight, G.E. (1963), "Some aspects of effective stress in saturated and partly saturated soils", Geotechnique, 13(3), 177-197 (in English with French synopsis). https://doi.org/10.1680/geot.1963.13.3.177.   DOI
22 Kwon, S. and Lee, C. (2018), "THM analysis for an in situ experiment using FLAC3D-TOUGH2 and an artificial neural network", Geomech. Eng., 16(4), 363-373. https://doi.org/10.12989/gae.2018.16.4.363.   DOI
23 Carslaw, H.S. and Jaeger, J.C. (1959), Conduction of Heat in Solids, 2nd Edition, Oxford University Press, London, UK, 510 pp.
24 COMSOL (2021), "COMSOL Multiphysics: A general-purpose simulation software for finite element analysis, version 6.0", Manual, COMSOL, Burlington, Massachusetts, USA, 14 volumes (Volume 1: Installation guide).
25 Cryer, C.W. (1963), "A comparison of the three-dimensional theories of Biot and Terzaghi", Q. J. Mech. Appl. Math., 16(4), 401-412. https://doi.org/10.1093/qjmam/16.4.401.   DOI
26 Kim, J.M. and Parizek, R.R. (1999), "Three-dimensional finite element modelling for consolidation due to groundwater withdrawal in a desaturating anisotropic aquifer system", Int. J. Numer. Anal. Meth. Geomech., 23(6), 549-571. https://doi.org/10.1002/(SICI)1096-9853(199905)23:6<549::AID-NAG983>3.0.CO;2-Y.   DOI
27 Kolditz, O., Gorke, U.J., Shao, H. and Wang, W. (Editors) (2012), Thermo-Hydro-Mechanical-Chemical Processes in Fractured Porous Media: Benchmarks and Examples, Lecture Notes in Computational Science and Engineering, Volume 86, Springer-Verlag, Berlin, Germany, 399 pp.
28 Lee, S., Park, J.Y., Kihm, J.H. and Kim, J.M. (2015b), "TOUGH2-FLAC3D THM: An integrated numerical model for coupled multi-phase thermo-hydro-mechanical processes in porous, fractured, and fractured porous geologic media by one-way and two-way sequential coupling of TOUGH2 and FLAC3D, version 1.0", Technical Report No. GGEL-2015-9, Geological and Groundwater Engineering Laboratory, School of Earth and Environmental Sciences, Seoul National University, Seoul, Korea, 59 pp.
29 Love, A.E.H. (1944), A Treatise on the Mathematical Theory of Elasticity, 4th Edition (republication), Dover Publications, New York, New York, USA, 643 pp.
30 Hu, L., Winterfeld, P.H., Fakcharoenphol, P. and Wu, Y.S. (2013), "A novel fully-coupled flow and geomechanics model in enhanced geothermal reservoirs", J. Petrol. Sci. Eng., 107, 1-11. https://doi.org/10.1016/j.petrol.2013.04.005.   DOI
31 Kim, J., Sonnenthal, E. and Rutqvist, J. (2012a), "A sequential implicit algorithm of chemo-thermo-poro-mechanics for fractured geothermal reservoirs", Proceedings of the TOUGH Symposium 2012, Lawrence Berkeley National Laboratory, University of California, Berkeley, California, USA, September, 275-282.
32 Verruijt, A. (1969), "Elastic storage of aquifers", in De Wiest, R.J.M. (Editor), Flow through Porous Media, Academic Press, New York, New York, USA, 331-376.
33 Mandel, J. (1953), "Consolidation des sols (etude mathematique)", Geotechnique, 3(7), 287-299 (in French with English synopsis). https://doi.org/10.1680/geot.1953.3.7.287.   DOI
34 Noorishad, J., Tsang, C.F. and Witherspoon, P.A. (1984), "Coupled thermal-hydraulic-mechanical phenomena in saturated fractured porous rocks: Numerical approach", J. Geophys. Res. Solid Earth, 89(B12), 10365-10373. https://doi.org/10.1029/JB089iB12p10365.   DOI
35 Nur, A. and Byerlee, J.D. (1971), "An exact effective stress law for elastic deformation of rock with fluids", J. Geophys. Res., 76(26), 6414-6419. https://doi.org/10.1029/JB076i026p06414.   DOI
36 Winterfeld, P.H. and Wu, Y.S. (2015), "Simulation of coupled thermal-hydrological-mechanical phenomena in porous and fractured media", Proceedings of the 2015 SPE (Society of Petroleum Engineers) Reservoir Simulation Symposium, Royal Sonesta Hotel-Houston Galleria, Houston, Texas, USA, February, Paper No. SPE-173210-MS, 1-15.
37 Kim, J., Tchelepi, H.A. and Juanes, R. (2011b), "Stability and convergence of sequential methods for coupled flow and geomechanics: Drained and undrained splits", Comput. Meth. Appl. Mech. Eng., 200(23-24), 2094-2116. https://doi.org/10.1016/j.cma.2011.02.011.   DOI
38 Kim, J.M. (2002), "COWADE123D: A finite element model for fully coupled saturated-unsaturated water flow in deforming one-, two-, and three-dimensional porous and fractured media, version 2.11", Technical Report No. GGEL-2002-9, Geological and Groundwater Engineering Laboratory, School of Earth and Environmental Sciences, Seoul National University, Seoul, Korea, 304 pp.
39 Kim, J.M. (2004), "Fully coupled poroelastic governing equations for groundwater flow and solid skeleton deformation in variably saturated true anisotropic porous geologic media", Geosci. J., 8(3), 291-300. https://doi.org/10.1007/BF02910248.   DOI
40 Kim, J.M. and Parizek, R.R. (1997), "Numerical simulation of the Noordbergum effect resulting from groundwater pumping in a layered aquifer system", J. Hydrol., 202(1-4), 231-243. https://doi.org/10.1016/S0022-1694(97)00067-X.   DOI
41 Lei, H., Xu, T. and Jin, G. (2015), "TOUGH2Biot - A simulator for coupled thermal-hydrodynamic-mechanical processes in subsurface flow systems: Application to CO2 geological storage and geothermal development", Comput. Geosci., 77, 8-19. https://doi.org/10.1016/j.cageo.2015.01.003.   DOI
42 Kim, J.M. (2000), "Generalized poroelastic analytical solutions for pore water pressure change and land subsidence due to surface loading", Geosci. J., 4(2), 95-104. https://doi.org/10.1007/BF02910130.   DOI
43 Kim, J.M. (2006), "COWADE123D: A finite element model for fully coupled saturated-unsaturated water flow in deforming one-, two-, and three-dimensional true anisotropic porous, fractured, and fractured porous geologic media, version 2.17", Technical Report No. GGEL-2006-11, Geological and Groundwater Engineering Laboratory, School of Earth and Environmental Sciences, Seoul National University, Seoul, Korea, 298 pp.
44 Kim, J.M. and Parizek, R.R. (2005), "Numerical simulation of the Rhade effect in layered aquifer systems due to groundwater pumping shutoff", Adv. Water Resour., 28(6), 627-642. https://doi.org/10.1016/j.advwatres.2004.12.005.   DOI
45 McTigue, D.F. (1986), "Thermoelastic response of fluid-saturated porous rock", J. Geophys. Res. Solid Earth, 91(9), 9533-9542. https://doi.org/10.1029/JB091iB09p09533.   DOI
46 Olivella, S., Gens, A., Carrera, J. and Alonso, E.E. (1996), "Numerical formulation for a simulator (CODE_BRIGHT) for the coupled analysis of saline media", Eng. Comput., 13(7), 87-112. https://doi.org/10.1108/02644409610151575.   DOI
47 Pruess, K., Oldenburg, C. and Moridis, G. (2012), "TOUGH2 user's guide, version 2.0 (revised version)", Technical Report No. LBNL-43134, Lawrence Berkeley National Laboratory, University of California, Berkeley, California, USA, 197 pp.
48 Wolff, R.G. (1970b), "Relationship between horizontal strain near a well and reverse water level fluctuation", Water Resour. Res., 6(6), 1721-1728. https://doi.org/10.1029/WR006i006p01721.   DOI
49 Winterfeld, P.H. and Wu, Y.S. (2016), "Simulation of coupled thermal/hydrological/mechanical phenomena in porous media", SPE J., 21(3), 1041-1049. https://doi.org/10.2118/173210-PA.   DOI
50 Wolff, R.G. (1970a), "Field and laboratory determination of the hydraulic diffusivity of a confining bed", Water Resour. Res., 6(1), 194-203. https://doi.org/10.1029/WR006i001p00194.   DOI
51 Xu, T., Sonnenthal, E., Spycher, N. and Pruess, K. (2006), "TOUGHREACT user's guide: A simulation program for non-isothermal multiphase reactive geochemical transport in variably saturated geologic media, version 1.2", Technical Report No. LBNL-55460, Lawrence Berkeley National Laboratory, University of California, Berkeley, California, USA, 200 pp.
52 Xu, T., Sonnenthal, E., Spycher, N. and Zheng, L. (2014), "TOUGHREACT V3.0-OMP reference manual: A parallel simulation program for non-isothermal multiphase geochemical reactive transport", Technical Report No. LBNL-DRAFT, Lawrence Berkeley National Laboratory, University of California, Berkeley, California, USA, 141 pp.
53 Pruess, K. (1991), "TOUGH2 - A general-purpose numerical simulator for multiphase fluid and heat flow", Technical Report No. LBL-29400, Lawrence Berkeley Laboratory, University of California, Berkeley, California, USA, 102 pp.
54 Rutqvist, J. and Tsang, C.F. (2003), "TOUGH-FLAC: A numerical simulator for analysis of coupled thermal-hydrologic-mechanical processes in fractured and porous geological media under multi-phase flow conditions", Proceedings of the TOUGH Symposium 2003, Lawrence Berkeley National Laboratory, University of California, Berkeley, California, USA, May, 1-9.
55 Kim, J.M. (1995), "COWADE123D: A finite element model for fully coupled saturated-unsaturated water flow in deforming one-, two-, and three-dimensional porous and fractured media, version 1.0", Technical Report No. HGL-1995-9, Hydrogeology Laboratory, Department of Geosciences, Pennsylvania State University, University Park, Pennsylvania, USA, 254 pp.
56 Kim, J.M. (1996), "A fully coupled model for saturated-unsaturated fluid flow in deformable porous and fractured media", Ph.D. Dissertation, Pennsylvania State University, University Park, Pennsylvania, USA, 201 pp.
57 Pan, P.Z., Rutqvist, J., Feng, X.T. and Yan, F. (2013), "Modeling of caprock discontinuous fracturing during CO2 injection into a deep brine aquifer", Int. J. Greenh. Gas Control, 19, 559-575. https://doi.org/10.1016/j.ijggc.2013.10.016.   DOI
58 Pan, P.Z., Rutqvist, J., Feng, X.T. and Yan, F. (2014a), "An approach for modeling rock discontinuous mechanical behavior under multiphase fluid flow conditions", Rock Mech. Rock Eng., 47(2), 589-603. https://doi.org/10.1007/s00603-013-0428-1.   DOI
59 Rutqvist, J. (2017), "An overview of TOUGH-based geomechanics models", Comput. Geosci., 108, 56-63. https://doi.org/10.1016/j.cageo.2016.09.007.   DOI
60 Pruess, K., Oldenburg, C. and Moridis, G. (1999), "TOUGH2 user's guide, version 2.0", Technical Report No. LBNL-43134, Lawrence Berkeley National Laboratory, University of California, Berkeley, California, USA, 197 pp.
61 Winterfeld, P.H., Wu, Y.S., Pruess, K. and Oldenburg, C. (2012), "Development of an advanced thermal-hydrological-mechanical model for CO2 storage in porous and fractured saline aquifers", Proceedings of the TOUGH Symposium 2012, Lawrence Berkeley National Laboratory, University of California, Berkeley, California, USA, September, 806-813.
62 Taron, J., Elsworth, D. and Min, K.B. (2009), "Numerical simulation of thermal-hydrologic-mechanical-chemical processes in deformable, fractured porous media", Int. J. Rock Mech. Min. Sci., 46(5), 842-854. https://doi.org/10.1016/j.ijrmms.2009.01.008.   DOI
63 Thompson, M. and Willis, J.R. (1991), "A reformation of the equations of anisotropic poroelasticity", J. Appl. Mech., Trans. Am. Soc. Mech. Eng., 58(3), 612-616. https://doi.org/10.1115/1.2897239.   DOI
64 Winterfeld, P.H. and Wu, Y.S. (2013), "User's guide for TOUGH2-CSM (TOUGH2-Carbon Sequestration Model): Massively parallel simulation of fully-coupled flow with geomechanics", Technical Report No. CSM-DE-FC26-09FE0000988, Colorado School of Mines, Golden, Colorado, USA, 151 pp.
65 Xu, T., Sonnenthal, E., Spycher, N. and Pruess, K. (2004), "TOUGHREACT user's guide: A simulation program for nonisothermal multiphase reactive geochemical transport in variably saturated geologic media", Technical Report No. LBNL-55460, Lawrence Berkeley National Laboratory, University of California, Berkeley, California, USA, 197 pp.
66 Das, B.M. (1994), Principles of Geotechnical Engineering, 3rd Edition, PWS Publishing Company, Boston, Massachusetts, USA, 672 pp.
67 Andreasen, G.E. and Brookhart, J.W. (1963), "Reverse water-level fluctuations", in Bentall, R. (Editor), "Methods of collecting and interpreting ground-water data", Water-Supply Paper No. 1544-H, United States Geological Survey, Denver, Colorado, USA, 30-35.
68 Biot, M.A. (1941), "General theory of three-dimensional consolidation", J. Appl. Phys., 12(2), 155-164. https://doi.org/10.1063/1.1712886.   DOI
69 Cheng, A.H.D. (1997), "Material coefficients of anisotropic poroelasticity", Int. J. Rock Mech. Min. Sci., 34(2), 199-205. https://doi.org/10.1016/S0148-9062(96)00055-1.   DOI
70 Rutqvist, J., Wu, Y.S., Tsang, C.F. and Bodvarsson, G. (2002), "A modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock", Int. J. Rock Mech. Min. Sci., 39(4), 429-442. https://doi.org/10.1016/S1365-1609(02)00022-9.   DOI
71 Broska, J.C. and Barnette, H.L. (1999), "Hydrogeology and analysis of aquifer characteristics in west-central Pinellas County, Florida", Open-File Report No. 99-185, United States Geological Survey, Denver, Colorado, USA, 23 pp.
72 Dassault Systemes Simulia (2014), "Abaqus: A software suite for finite element analysis, version 6.14", Manual, Dassault Systemes Simulia, Providence, Rhode Island, USA, 19 volumes (Volume 1: Abaqus/CAE user's guide).
73 Domenico, P.A. and Schwartz, F.W. (1990), Physical and Chemical Hydrogeology, John Wiley and Sons, New York, New York, USA, 824 pp.
74 Fakcharoenphol, P., Xiong, Y., Hu, L., Winterfeld, P.H., Xu, T. and Wu, Y.S. (2013), "User's guide of TOUGH2-EGS (TOUGH2-Enhanced Geothermal Systems): A coupled geomechanical and reactive geochemical simulator for fluid and heat flow in enhanced geothermal systems, version 1.0", Technical Report No. CSM-DE-EE0002762, Colorado School of Mines, Golden, Colorado, USA, 172 pp.
75 Xu, T., Spycher, N., Sonnenthal, E., Zheng, L. and Pruess, K. (2012), "TOUGHREACT user's guide: A simulation program for non-isothermal multiphase reactive transport in variably saturated geologic media, version 2.0", Technical Report No. LBNL-DRAFT, Lawrence Berkeley National Laboratory, University of California, Berkeley, California, USA, 240 pp.
76 Carroll, M.M. (1979), "An effective stress law for anisotropic elastic deformation", J. Geophys. Res. Solid Earth, 84(13), 7510-7512. https://doi.org/10.1029/JB084iB13p07510.   DOI
77 Jaeger, J.C., Cook, N.G.W. and Zimmerman, R.W. (2007), Fundamentals of Rock Mechanics. 4th Edition, Blackwell Publishing, Malden, Massachusetts, USA, 475 pp.
78 Langguth, H.R. and Treskatis, C. (1989), "Reverse water level fluctuations in semiconfined aquifer systems - "Rhade effect"", J. Hydrol., 109(1-2), 79-93. https://doi.org/10.1016/0022-1694(89)90008-5.   DOI
79 Geertsma, J. (1957), "A remark on the analogy between thermoelasticity and the elasticity of saturated porous media", J. Mech. Phys. Solids, 6(1), 13-16. https://doi.org/10.1016/0022-5096(57)90042-X.   DOI
80 Ferris, J.G., Knowles, D.B., Brown, R.H. and Stallman, R.W. (1962), "Theory of aquifer tests", Water-Supply Paper No. 1536-E, United States Geological Survey, Denver, Colorado, USA, 174 pp.
81 Hurwitz, S., Christiansen, L.B. and Hsieh, P.A. (2007), "Hydrothermal fluid flow and deformation in large calderas: Inferences from numerical simulations", J. Geophys. Res. Solid Earth, 112(2), B02206. https://doi.org/10.1029/2006JB004689.   DOI
82 Huang, Z.Q., Winterfeld, P.H., Xiong, Y., Wu, Y.S. and Yao, J. (2015), "Parallel simulation of fully-coupled thermal-hydromechanical processes in CO2 leakage through fluid-driven fracture zones", Int. J. Greenh. Gas Control, 34, 39-51. https://doi.org/10.1016/j.ijggc.2014.12.012.   DOI
83 Pan, P.Z., Rutqvist, J., Feng, X.T. and Yan, F. (2014b), "TOUGH-RDCA modeling of multiple fracture interactions in caprock during CO2 injection into a deep brine aquifer", Comput. Geosci., 65, 24-36. https://doi.org/10.1016/j.cageo.2013.09.005.   DOI
84 Fakcharoenphol, P., Hu, L. and Wu, Y.S. (2012), "A fully-coupled fully-implicit flow and geomechanics model: Application for enhanced geothermal reservoir simulations", Proceedings of the 37th Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, USA, January-February, Technical Report No. SGP-TR-194, Stanford Geothermal Program, Stanford University, Stanford, California, USA, Paper No. Fakcharoenphol, 1-10.
85 Freeze, R.A. and Cherry, J.A. (1979), Groundwater, Prentice-Hall, Englewood Cliffs, New Jersey, USA, 604 pp.
86 Kim, J. and Moridis, G.J. (2014), "Gas flow tightly coupled to elastoplastic geomechanics for tight- and shale-gas reservoirs: Material failure and enhanced permeability", SPE J., 19(6), 1110-1125. https://doi.org/10.2118/155640-PA.   DOI
87 Kim, J., Sonnenthal, E.L. and Rutqvist, J. (2012b), "Formulation and sequential numerical algorithms of coupled fluid/heat flow and geomechanics for multiple porosity materials", Int. J. Numer. Meth. Eng., 92(5), 425-456. https://doi.org/10.1002/nme.4340.   DOI
88 Rutqvist, J. (2011), "Status of the TOUGH-FLAC simulator and recent applications related to coupled fluid flow and crustal deformations", Comput. Geosci., 37(6), 739-750. https://doi.org/10.1016/j.cageo.2010.08.006.   DOI
89 Kim, J., Moridis, G.J., Yang, D. and Rutqvist, J. (2012c), "Numerical studies on two-way coupled fluid flow and geomechanics in hydrate deposits", SPE J., 17(2), 485-501. https://doi.org/10.2118/141304-PA.   DOI
90 Abousleiman, Y., Cheng, A.H.D., Cui, L., Detournay, E. and Roegiers, J.C. (1996), "Mandel's problem revisited", Geotechnique, 46(2), 187-195 (in English with French synopsis). https://doi.org/10.1680/geot.1996.46.2.187.   DOI