Abstract
A better understanding of the stress–strain behaviors of shale samples after shale-CO2 or shale-water–CO2 interactions is of great importance to CO2 enhanced shale gas exploitation and CO2 sequestrating in shale reservoirs. In this study, a constitutive model that combines with the modified Duncan–Chang model and Weibull distribution-based model is applied to investigate the stress–strain characteristics of low-clay shale samples treated by sub-/super-critical CO2 and sub-/super-critical CO2 + water for different times (10 days, 20 days, and 30 days). The results show that the model could describe well the crack closure stage, the elastic stage, and the inelastic stage of shale samples. The axial strain at the connection point between the two models varies from 28.51 to 43.36% of the axial strain at the failure point. Shale-CO2 or shale-water–CO2 interactions make shale samples more ductile at the crack closure stage, which can be depicted as the increase of initial elastic modulus during the imbibition process. The brittleness index values (BI) which are calculated based on the combined constitutive model increase with increasing soaking time for shale samples treated by sub-/super-critical CO2, and decrease with increasing soaking time for shale samples treated by sub-/super-critical CO2 + water.
Similar content being viewed by others
References
Carroll SA, McNab WW, Dai Z, Torres SC (2012) Reactivity of Mount Simon sandstone and the Eau Claire shale under CO2 storage conditions. Environ Sci Technol 47:252–261
Duncan JM (1970) Nonlinear analysis of stress and strain in soils. Jour Smf Div 96:1629–1653
Fan C-K, Sun Y-K, Li Q, Lu H-F, Niu Z-Y, Li X-Y (2017) Testing technology of fiber Bragg grating in the shale damage experiments under uniaxial compression conditions. Rock Soil Mechanics 38:2456–2464. https://doi.org/10.16285/j.rsm.2017.08.036
Fan C, Li Q, Li X, Niu Z, Xu L (2018) Dynamic optical fiber monitoring of water-saturated sandstone during supercritical CO2 injection at different sequestration pressures. In: Zhan L, Chen Y, Bouazza A (eds) Proceedings of the 8th international congress on environmental geotechnics volume 1: towards a sustainable geoenvironment. Environmental engineering. Springer Singapore, Berlin
Fei W, Li Q, Wei X, Song R, Jing M, Li X (2015) Interaction analysis for CO2 geological storage and underground coal mining in ordos basin. China Eng Geol 196:194–209. https://doi.org/10.1016/j.enggeo.2015.07.017
Gunter W, Wiwehar B, Perkins E (1997) Aquifer disposal of CO2-rich greenhouse gases: extension of the time scale of experiment for CO2-sequestering reactions by geochemical modelling. Mineral Petrol 59:121–140
Hucka V, Das B Brittleness determination of rocks by different methods. In: International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1974. vol 10. Elsevier, pp 389–392
Jarvie DM, Hill RJ, Ruble TE, Pollastro RM (2007) Unconventional shale-gas systems: the Mississippian Barnett Shale of north-central Texas as one model for thermogenic shale-gas assessment. Aapg Bull 91:475–499
Jiang YD, Xian XF, Jian SU (2005) Research on distortion of singlerock and constitutive relation. Rock Soil Mechanics 26:941–945
Jiang Y, Luo Y, Lu Y, Qin C, Liu H (2016) Effects of supercritical CO2 treatment time, pressure, and temperature on microstructure. of shale Energy 97:173–181. https://doi.org/10.1016/j.energy.2015.12.124
Kivi IR, Ameri M, Molladavoodi H (2018) Shale brittleness evaluation based on energy balance analysis of stress-strain curves Journal of Petroleum Science & Engineering
Kolle JJ, Coiled-Tubing Drilling with Supercritical Carbon Dioxide. In: CIM International Conference on Horizontal Well Technology, Calgary, Alberta, Canada, 2000/1/1/ 2000. Society of Petroleum Engineers, SPE. https://doi.org/10.2118/65534-MS
Li C, Caner FC, Chau VT, Bažant ZP (2017a) Spherocylindrical microplane constitutive model for shale and other anisotropic rocks. J Mech Phys Solids 103:155–178. https://doi.org/10.1016/j.jmps.2017.03.006
Li H, Lu Y, Zhou L, Han S, Gou Y (2017b) A new constitutive model for calculating the loading-path dependent proppant deformation and damage analysis of fracture conductivity. J Nat Gas Sci Eng 46:365–374. https://doi.org/10.1016/j.jngse.2017.08.005
Li X, Lei X, Li Q, Li X (2017c) Experimental investigation of Sinian shale rock under triaxial stress monitored by ultrasonic transmission and acoustic emission. J Nat Gas Sci Eng 43:110–123. https://doi.org/10.1016/j.jngse.2017.03.035
Li Y, Jia D, Rui Z, Peng J, Fu C, Zhang J (2017d) Evaluation method of rock brittleness based on statistical constitutive relations for rock damage J Pet Sci Eng 153:123–132
Likhtman VI, Shchukin ED, Rebinder PA (1964) Physicochemical mechanics of metals: adsorbtion phenomena in the process of deformation and failure of metals
Lu Y, Ao X, Tang J, Jia Y, Zhang X, Chen Y (2016) Swelling of shale in supercritical carbon dioxide. J Nat Gas Sci Eng 30:268–275. https://doi.org/10.1016/j.jngse.2016.02.011
Lyu Q, Long X, Ranjith PG, Kang Y (2016a) Unconventional gas: experimental study of the influence of subcritical carbon dioxide on the mechanical properties of black shale. Energies 9:516
Lyu Q, Ranjith P, Long X, Ji B (2016b) Experimental investigation of mechanical properties of black shales after CO2-water. Rock Inter Mater 9:663
Lyu Q, Long X, PG R, Tan J, Zhou J, Wang Z, Luo W (2018a) A laboratory study of geomechanical characteristics of black shales after sub-critical/super-critical CO2 + brine saturation. Geomech Geophys Geo-Energy Geo-Resour. https://doi.org/10.1007/s40948-018-0079-5
Lyu Q, Long X, Ranjith PG, Tan J, Kang Y (2018b) Experimental investigation on the mechanical behaviours of a low-clay shale under water-based fluids. Eng Geol 233:124–138. https://doi.org/10.1016/j.enggeo.2017.12.002
Lyu Q, Long X, Ranjith PG, Tan J, Kang Y, Wang Z (2018c) Experimental investigation on the mechanical properties of a low-clay shale with different adsorption times in sub-/super-critical CO. 2 Energy 147:1288–1298. https://doi.org/10.1016/j.energy.2018.01.084
Ma T, Yang C, Chen P, Wang X, Guo Y (2016) On the damage constitutive model for hydrated shale using CT scanning technology. J Nat Gas Sci Eng 28:204–214. https://doi.org/10.1016/j.jngse.2015.11.025
Meng F, Zhou H, Zhang C, Xu R, Lu J (2015) Evaluation methodology of brittleness of rock based on post-peak stress–strain curves. Rock Mech Rock Eng 48:1787–1805
Middleton RS et al (2015) Shale gas and non-aqueous fracturing fluids: opportunities and challenges for supercritical CO2. Appl Energy 147:500–509
Miyazaki K, Tenma N, Aoki K, Yamaguchi T (2012) A Nonlinear elastic model for triaxial compressive properties of artificial methane-hydrate-bearing. Sediment Samples Energies 5:4057–4075
Munoz H, Taheri A, Chanda EK (2016) Fracture energy-based brittleness index development and brittleness quantification by pre-peak strength parameters in rock uniaxial compression. Rock Mech Rock Eng 49:4587–4606
Parisio F, Laloui L (2017) Plastic-damage modeling of saturated quasi-brittle shales. Int J Rock Mech Min 93:295–306. https://doi.org/10.1016/j.ijrmms.2017.01.016
Parisio F, Samat S, Laloui L (2015a) Constitutive analysis of shale: a coupled damage plasticity approach. Int J Solids Struct 75–76:88–98
Parisio F, Samat S, Laloui L (2015b) Constitutive analysis of shale: a coupled damage plasticity approach. Int J Solids Struct 75–76:88–98. https://doi.org/10.1016/j.ijsolstr.2015.08.003
Profit M, Dutko M, Yu J, Cole S, Angus D, Baird A (2016) Complementary hydro-mechanical coupled finite/discrete element and microseismic modelling to predict hydraulic fracture propagation in tight shale reservoirs. Comput Part Mech 3:229–248. https://doi.org/10.1007/s40571-015-0081-4
Ren W, Li G, Tian S, Sheng M, Geng L (2016) Analytical modelling of hysteretic constitutive relations governing spontaneous imbibition of fracturing fluid in shale. J Nat Gas Sci Eng 34:925–933. https://doi.org/10.1016/j.jngse.2016.07.050
Rickman R, Mullen MJ, Petre JE, Grieser WV, Kundert DA (2008) Practical use of shale petrophysics for stimulation design optimization: all shale plays are not clones of the barnett shale. In: Spe Technical Conference and Exhibition
Rogala A, Krzysiek J, Bernaciak M, Hupka J (2013) Non-aqueous fracturing technologies for shale gas recovery Physicochemical Problems of Mineral Processing 49
Wang Z-l, Li Y-c, Wang JG (2007) A damage-softening statistical constitutive model considering rock residual strength. Comput Geosci-Uk 33:1–9. https://doi.org/10.1016/j.cageo.2006.02.011
Wang H, Li G, Shen Z (2012) A feasibility analysis on shale gas exploitation with supercritical carbon dioxide. Energy Source Part A 34:1426–1435. https://doi.org/10.1080/15567036.2010.529570
Wang H, Li G, Shen Z, Tian S, Sun B, He Z, Lu P (2015) Experiment on rock breaking with supercritical carbon dioxide jet. J Petrol Sci Eng 127:305–310. https://doi.org/10.1016/j.petrol.2015.01.006
White JA, Burnham AK, Camp DW (2017) A thermoplasticity model for oil shale. Rock Mech Rock Eng 50:677–688. https://doi.org/10.1007/s00603-016-0947-7
Xingang Z, Jiaoli K, Bei L (2013) Focus on the development of shale gas in China—Based on SWOT analysis. Renew Sustain Energy Rev 21:603–613. https://doi.org/10.1016/j.rser.2012.12.044
Yang Y, Wang L, Fang Y, Mou C (2017) Integrated value of shale gas development: a comparative analysis in the United States and China. Renew Sustain Energy Rev 76:1465–1478. https://doi.org/10.1016/j.rser.2016.11.174
Yin H, Zhou J, Xian X, Jiang Y, Lu Z, Tan J, Liu G (2017) Experimental study of the effects of sub- and super-critical CO2 saturation on the mechanical characteristics of organic-rich shales. Energy 132:84–95
Zhang D, Ranjith P, Perera M (2016) The brittleness indices used in rock mechanics and their application in shale hydraulic fracturing: a review. J Petrol Sci Eng 143:158–170
Zhang S, Wang X, Wang C, Song R, Huo H (2017) Compressive behavior and constitutive model for roller compacted concrete under impact loading: considering vertical stratification. Constr Build Mater 151:428–440. https://doi.org/10.1016/j.conbuildmat.2017.06.113
Zhou J, Liu G, Jiang Y, Xian X, Liu Q, Zhang D, Tan J (2016) Supercritical carbon dioxide fracturing in shale and the coupled effects on the permeability of fractured shale: an experimental study. J Nat Gas Sci Eng 36:369–377. https://doi.org/10.1016/j.jngse.2016.10.005
Acknowledgements
The authors would like to thank all the technical staffs of the Geo-lab at Monash University for their help with the experimental work, the help of Prof. Jeffrey M. Dick and Dr. Asim Shahzad for the writing revision, and the financial support from the Innovation-Driven Project of Central South University (Grant no.: 502501005), the National Natural Science Foundation of China (Grant No. 41872151), and the China Postdoctoral Science Foundation (Grant no.: 2018M630913).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Lyu, Q., Tan, J., Dick, J.M. et al. Stress–Strain Modeling and Brittleness Variations of Low-Clay Shales with CO2/CO2-Water Imbibition. Rock Mech Rock Eng 52, 2039–2052 (2019). https://doi.org/10.1007/s00603-018-1687-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00603-018-1687-7