Abstract
Creep deformation in shale rocks is an important factor in many applications, such as the sustainability of geostructures, wellbore stability, evaluation of land subsidence, CO2 storage, toxic waste containment, and hydraulic fracturing. One mechanism leading to this time-dependent deformation under a constant load is the dissolution/formation processes accompanied by chemo-mechanical interactions with a reactive environment. When dissolution/formation processes occur within the material phases, the distribution of stress and strain within the material microstructure changes. In the case of the dissolution process, the stress carried by the dissolving phase is distributed into neighboring voxels, which leads to further deformation of the material. The aim of this study was to explore the relationship between the microstructural evolution and time-dependent creep behavior of rocks subjected to chemo-mechanical loading. This work uses the experimentally characterized microstructural and mechanical evolution of a shale rock induced by interactions with a reactive brine (CO2-rich brine) and a non-reactive brine (N2-rich brine) under high-pressure and high-temperature conditions to compute the resulting time-dependent deformation using a time-stepping finite-element-based modeling approach. Sample microstructure snapshots were obtained using segmented micro-CT images of the rock samples before and after the reactions. Coupled nanoindentation/EDS provided spatial alteration of the mechanical properties of individual material phases due to the dissolution and precipitation processes as a result of chemo-mechanical loading of the samples. The time-dependent mechanically informed microstructures were then incorporated into a mechanical model to calculate the creep behavior caused by the dissolution/precipitation processes independent of the inherent viscous properties of the mineral phases. The results indicate the substantial role of the dissolution/precipitation processes on the viscous behavior of rocks subjected to reactive environments.
Highlights
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A computational scheme incorporating experimental data calculated time-dependent creep strain in shale rock due to chemo-mechanical loading.
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A time-dependent microstructural model and time-stepping finite element model were coupled to build the computational framework.
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Micro-CT imaging and coupled nanoidentation/EDS techniques were utilized in the microstructural model to study the evolution of shale rock exposed to CO2- and N2-rich brine, at high-pressure and high-temperature conditions.
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Creep deformation distribution varied based on the extent and spatial variability of the reaction, with different behavior observed under CO2 and N2 conditions.
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The results highlight the important role of the interplay between the dissolution and precipitation processes on the VE/VP behavior of rocks in reactive environments.
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Data availability
The data that support the findings of this study are available from the corresponding author, Sara Abedi, upon reasonable request.
References
Abedi S, Slim M, Hofmann R, Bryndzia T, Ulm F-J (2016a) Nanochemo-mechanical signature of organic-rich shales: a coupled indentation–EDX analysis. Acta Geotech 11(3):559–572
Abedi S, Slim M, Ulm F-J (2016b) Nanomechanics of organic-rich shales: the role of thermal maturity and organic matter content on texture. Acta Geotech 11(4):775–787
Abel JF, Lee FT (1980) Subsidence potential in shale and crystalline rocks. US Geological Survey, Reston, pp 2331–1258
Atkinson BK (1984) Subcritical crack growth in geological materials. J Geophys Res Solid Earth 89(B6):4077–4114
Baud P, Vinciguerra S, David C, Cavallo A, Walker E, Reuschlé T (2009) Compaction and failure in high porosity carbonates: mechanical data and microstructural observations. Pure Appl Geophys 166(5–7):869–898
Buscarnera G, Das A (2016) Chemo-mechanics of cemented granular solids subjected to precipitation and dissolution of mineral species. Int J Numer Anal Meth Geomech 40(9):1295–1320
Castellanza R, Nova R (2004) Oedometric tests on artificially weathered carbonatic soft rocks. J Geotech Geoenviron Eng 130(7):728–739
Castellanza R, Gerolymatou E, Nova R (2008) An attempt to predict the failure time of abandoned mine pillars. Rock Mech Rock Eng 41(3):377–401
Chang C, Zoback M (2008) Creep in unconsolidated shale and its implication on rock physical properties. The 42nd US Rock Mechanics Symposium (USRMS)
Christensen R (2012) Theory of viscoelasticity: an introduction. Elsevier, Amsterdam
Ciantia MO, Castellanza R (2016) Modelling weathering effects on the mechanical behaviour of rocks. Eur J Environ Civ Eng 20(9):1054–1082
Ciantia MO, Castellanza R, Crosta GB, Hueckel T (2015) Effects of mineral suspension and dissolution on strength and compressibility of soft carbonate rocks. Eng Geol 184:1–18
Clark AC, Vanorio T (2016) The rock physics and geochemistry of carbonates exposed to reactive brines. J Geophys Res Solid Earth 121(3):1497–1513
Cook JE, Goodwin LB, Boutt DF (2011) Systematic diagenetic changes in the grain-scale morphology and permeability of a quartz-cemented quartz arenite. AAPG Bull 95(6):1067–1088
Coussy O (2004) Poromechanics. Wiley, New York
Dautriat J, Gland N, Dimanov A, Raphanel J (2011) Hydromechanical behavior of heterogeneous carbonate rock under proportional triaxial loadings. J Geophys Res 116(B01205). https://doi.org/10.1029/2009JB000830
Dewers T, Ortoleva P (1990) A coupled reaction/transport/mechanical model for intergranular pressure solution, stylolites, and differential compaction and cementation in clean sandstones. Geochim Cosmochim Acta 54(6):1609–1625
Emmanuel S, Ague JJ (2009) Modeling the impact of nano-pores on mineralization in sedimentary rocks. Water Resourc Res. https://doi.org/10.1029/2008WR007170
Fernandez-Merodo J, Castellanza R, Mabssout M, Pastor M, Nova R, Parma M (2007) Coupling transport of chemical species and damage of bonded geomaterials. Comput Geotech 34(4):200–215
Ferreira T, Rasb W (2012) ImageJ user guide: IJ 1.46 r
Fick A (1855) Ueber Diffusion (On Diffusion). Annalen der Physik und Chemie von J. C. Pogendorff 94:59–86
Fjaer E, Holt R, Horsrud P, Raaen A, Risnes R (2008) Petroleum related rock mechanics, 2nd edn. Elsevier BV, Radarweg, p 29 (1000)
Gajo A, Loret B, Hueckel T (2002) Electro-chemo-mechanical couplings in saturated porous media: elastic–plastic behaviour of heteroionic expansive clays. Int J Solids Struct 39(16):4327–4362
Gajo A, Cecinato F, Hueckel T (2015) A micro-scale inspired chemo-mechanical model of bonded geomaterials. Int J Rock Mech Min Sci 80:425–438
Garboczi EJ, Bentz DP, Martys NS (1999) 1. Digital images and computer modeling. Experimental methods in the physical sciences, vol 35. Elsevier, Amsterdam, pp 1–41
Garboczi EJ (1998) Finite element and finite difference programs for computing the linear electric and elastic properties of digital images of random materials
Ghoussoub J, Leroy YM (2001) Solid–fluid phase transformation within grain boundaries during compaction by pressure solution. J Mech Phys Solids 49(10):2385–2430
Grgic D (2011) Influence of CO2 on the long‐term chemomechanical behavior of an oolitic limestone. J Geophys Res Solid Earth 116(B7)
Haecker C-J, Garboczi E, Bullard J, Bohn R, Sun Z, Shah SP, Voigt T (2005) Modeling the linear elastic properties of Portland cement paste. Cem Concr Res 35(10):1948–1960
Haldar SK (2013) Introduction to mineralogy and petrology. Elsevier, Amsterdam
Hangx SJ, Spiers CJ (2009) Reaction of plagioclase feldspars with CO2 under hydrothermal conditions. Chem Geol 265(1–2):88–98
He W, Hajash A, Sparks D (2002) A model for porosity evolution during creep compaction of sandstones. Earth Planet Sci Lett 197(3–4):237–244
Heidug WK, Leroy YM (1994) Geometrical evolution of stressed and curved solid-fluid phase boundaries: 1. Transformation kinetics. J Geophys Res Solid Earth 99(B1):505–515
Horsrud P, Holt RM, Sonstebo EF, Svano G, Bostrom B (1994) Time dependent borehole stability: laboratory studies and numerical simulation of different mechanisms in shale. In: Rock Mechanics in Petroleum Engineering, Delft, Netherlands 29–31 August. https://doi.org/10.2118/28060-MS
Hu LB, Hueckel T (2007a) Coupled chemo-mechanics of intergranular contact: toward a three-scale model. Comput Geotech 34(4):306–327
Hu LB, Hueckel T (2007b) Creep of saturated materials as a chemically enhanced rate-dependent damage process. Int J Numer Anal Meth Geomech 31(14):1537–1565
Huang W, Keller W (1970) Dissolution of rock-forming silicate minerals in organic acids: simulated first-stage weathering of fresh mineral surfaces. Am Mineral J Earth Planet Mater 55(11–12):2076–2094
Huang W, Kiang W (1972) Laboratory dissolution of plagioclase feldspars in water and organic acids at room temperature. Am Mineral J Earth Planet Mater 57(11–12):1849–1859
Hueckel T, Hu L, Hu M (2016) Coupled chemo-mechanics: a comprehensive process modeling for Energy Geotechnics. In: Energy geotechnics: proceedings of the 1st international conference on energy geotechnics, ICEGT, Germany
Kannan K, Rajagopal K (2011) A thermodynamical framework for chemically reacting systems. Z Angew Math Phys 62(2):331–363
Karato S-I, Jung H (2003) Effects of pressure on high-temperature dislocation creep in olivine. Philos Mag 83(3):401–414
Kawano M, Tomita K (1996) Amorphous aluminum hydroxide formed at the earliest weathering stages of K-feldspar. Clays Clay Miner 44(5):672–676
Lehner FK (1990) Thermodynamics of rock deformation by pressure solution. Deformation processes in minerals, ceramics and rocks. Springer, New York, pp 296–333
Li X, Rahman S, Grasley ZC (2016) Computationally implemented modeling of creep of composite materials caused by phase dissolution. Comput Mater Sci 125:61–71
Li X, Grasley Z, Garboczi EJ, Bullard JW (2017) Simulation of the influence of intrinsic CSH aging on time-dependent relaxation of hydrating cement paste. Constr Build Mater 157:1024–1031
Lu P, Fu Q, Seyfried WE Jr, Hedges SW, Soong Y, Jones K, Zhu C (2013) Coupled alkali feldspar dissolution and secondary mineral precipitation in batch systems–2: New experiments with supercritical CO2 and implications for carbon sequestration. Appl Geochem 30:75–90
Nabika H, Itatani M, Lagzi I (2019) Pattern formation in precipitation reactions: the Liesegang phenomenon. Langmuir 36(2):481–497
Nermoen A, Korsnes RI, Aursjø O, Madland MV, Kjørslevik TA, Østensen G (2016) How stress and temperature conditions affect rock-fluid chemistry and mechanical deformation. Front Phys 4:2
Neveux L, Grgic D, Carpentier C, Pironon J, Truche L, Girard J (2014) Experimental simulation of chemomechanical processes during deep burial diagenesis of carbonate rocks. J Geophys Res Solid Earth 119(2):984–1007
Niemeijer A, Spiers C, Bos B (2002) Compaction creep of quartz sand at 400–600 C: experimental evidence for dissolution-controlled pressure solution. Earth Planet Sci Lett 195(3–4):261–275
Nova R, Castellanza R, Tamagnini C (2003) A constitutive model for bonded geomaterials subject to mechanical and/or chemical degradation. Int J Numer Anal Meth Geomech 27(9):705–732
Prakash R, Nguene PCK, Benoit D, Henkel K, Abedi S (2021) Assessment of local phase to mechanical response link: application to the chemo-mechanical identification of rock phases subjected to reactive environments. J Nat Gas Sci Eng 89:103857
Prakash R, Abedi S (2022) Computational modeling of creep behavior in shales induced by fluid-rock interaction. In: 56th US rock mechanics/geomechanics symposium
Prakash R, Ahmad S, Abedi S (2023) Chemo-mechanical alteration of Permian shale after exposure to CO2-rich brine at high-temperature and high-pressure conditions (under review)
Rajagopal KR, Srinivasa AR (2004) On the thermomechanics of materials that have multiple natural configurations Part I: viscoelasticity and classical plasticity. Zeitschrift Für Angewandte Mathematik Und Physik ZAMP 55:861–893
Reesman A, Keller W (1965) Calculation of apparent standard free energies of formation of six rock-forming silicate minerals from solubility data. Am Mineral J Earth Planet Mater 50(10):1729–1739
Reesman A, Keller W (1968) Aqueous solubility studies of high-alumina and clay minerals. Am Mineral J Earth Planet Mater 53(5–6):929–942
Rimstidt JD, Chermak JA, Schreiber ME (2017) Processes that control mineral and element abundances in shales. Earth Sci Rev 171:383–399
Rutter E (1976) A discussion on natural strain and geological structure-the kinetics of rock deformation by pressure solution. Philos Trans R Soc Lond Ser A Math Phys Sci 283(1312):203–219
Rutter E (1983) Pressure solution in nature, theory and experiment. J Geol Soc 140(5):725–740
Rybacki E, Herrmann J, Wirth R, Dresen G (2017) Creep of Posidonia shale at elevated pressure and temperature. Rock Mech Rock Eng 50(12):3121–3140
Schimmel M, Hangx S, Spiers C (2022) Effect of pore fluid chemistry on uniaxial compaction creep of Bentheim sandstone and implications for reservoir injection operations. Geomech Energy Environ 29:100272
Shimizu I (1995) Kinetics of pressure solution creep in quartz: theoretical considerations. Tectonophysics 245(3–4):121–134
Tada R, Siever R (1989) Pressure solution during diagenesis. Annu Rev Earth Planet Sci 17:89
Tengattini A, Das A, Nguyen GD, Viggiani G, Hall SA, Einav I (2014) A thermomechanical constitutive model for cemented granular materials with quantifiable internal variables. Part I—theory. J Mech Phys Solids 70:281–296
Ulm F-J, Coussy O (1995) Modeling of thermochemomechanical couplings of concrete at early ages. J Eng Mech 121(7):785–794
Ulm F-J, Coussy O (1996) Strength growth as chemo-plastic hardening in early age concrete. J Eng Mech 122(12):1123–1132
Ulm F-J, Torrenti J-M, Adenot F (1999) Chemoporoplasticity of calcium leaching in concrete. J Eng Mech 125(10):1200–1211
Vanorio T (2015) Recent advances in time-lapse, laboratory rock physics for the characterization and monitoring of fluid-rock interactions. Geophysics 80(2):WA49–WA59
Vanorio T (2018) Challenges and recent advances in rock physics. In: International geophysical conference, Beijing, China, 24–27 April 2018
Varzina A, Cizer Ö, Yu L, Liu S, Jacques D, Perko J (2020) A new concept for pore-scale precipitation-dissolution modelling in a lattice Boltzmann framework–application to portlandite carbonation. Appl Geochem 123:104786
Voorhees PW (1985) The theory of Ostwald ripening. J Stat Phys 38:231–252
Wawersik WR, Rudnicki JW, Dove P, Harris J, Logan JM, Pyrak-Nolte L, Orr FM Jr, Ortoleva PJ, Richter F, Warpinski NR (2001) Terrestrial sequestration of CO2: an assessment of research needs. Advances in geophysics, vol 43. Elsevier, Amsterdam, pp 97–IX
Weyl PK (1959) Pressure solution and the force of crystallization: a phenomenological theory. J Geophys Res 64(11):2001–2025
Wineman AS, Rajagopal KR (2000) Mechanical response of polymers: an introduction. Cambridge University Press, Cambridge
Yuan G, Cao Y, Schulz H-M, Hao F, Gluyas J, Liu K, Yang T, Wang Y, Xi K, Li F (2019) A review of feldspar alteration and its geological significance in sedimentary basins: from shallow aquifers to deep hydrocarbon reservoirs. Earth Sci Rev 191:114–140
Acknowledgements
Acknowledgment is made to the National Science Foundation (Grant CMMI-2045242) and to the donors of the American Chemical Society Petroleum Research Fund (PRF 60545-ND9) for supporting this work.
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Prakash, R., Abedi, S. Experimentally Informed Simulation of Creep Behavior in Shale Rocks Induced by Chemo-mechanical Loading. Rock Mech Rock Eng 56, 6631–6645 (2023). https://doi.org/10.1007/s00603-023-03413-0
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DOI: https://doi.org/10.1007/s00603-023-03413-0