Abstract
The economic production of gas and oil from shales requires repeated hydraulic fracturing operations to stimulate these tight reservoir rocks. Besides simple depletion, the often observed decay of production rate with time may arise from creep-induced fracture closure. We examined experimentally the creep behavior of an immature carbonate-rich Posidonia shale, subjected to constant stress conditions at temperatures between 50 and 200 °C and confining pressures of 50–200 MPa, simulating elevated in situ depth conditions. Samples showed transient creep in the semibrittle regime with high deformation rates at high differential stress, high temperature and low confinement. Strain was mainly accommodated by deformation of the weak organic matter and phyllosilicates and by pore space reduction. The primary decelerating creep phase observed at relatively low stress can be described by an empirical power law relation between strain and time, where the fitted parameters vary with temperature, pressure and stress. Our results suggest that healing of hydraulic fractures at low stresses by creep-induced proppant embedment is unlikely within a creep period of several years. At higher differential stress, as may be expected in situ at contact areas due to stress concentrations, the shale showed secondary creep, followed by tertiary creep until failure. In this regime, microcrack propagation and coalescence may be assisted by stress corrosion. Secondary creep rates were also described by a power law, predicting faster fracture closure rates than for primary creep, likely contributing to production rate decline. Comparison of our data with published primary creep data on other shales suggests that the long-term creep behavior of shales can be correlated with their brittleness estimated from composition. Low creep strain is supported by a high fraction of strong minerals that can build up a load-bearing framework.
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Abbreviations
- A, B, c 1,2, m, t 0, s, k :
-
Creep constants
- B r :
-
Brittleness
- d :
-
Indenter diameter
- F :
-
Volume fraction
- \(h,\dot{h}\) :
-
Indentation depth, rate
- n :
-
Stress exponent
- P :
-
Confining pressure
- Q :
-
Activation energy
- T :
-
Temperature
- t :
-
Time
- V :
-
Activation volume
- \(\varepsilon ,\dot{\varepsilon }\) :
-
Axial strain, strain rate
- ϕ :
-
Porosity
- σ :
-
Differential stress
- σ net :
-
Indenter stress
References
Akrad OM, Miskimins JL, Prasad M (2011) The effects of fracturing fluids on shale rock mechanical properties and proppant embedment. In: SPE annual technical conference and exhibition. Society of Petroleum Engineers, Denver
Almasoodi MM, Abousleiman YN, Hoang SK (2014) Viscoelastic creep of Eagle Ford shale: investigating fluid–shale interaction. In: SPE/CSUR Unconventional Resources Conference. Society of Petroleum Engineers, Calgary
Alramahi B, Sundberg MI (2012) Proppant embedment and conductivity of hydraulic fractures in shales. In: 46th U.S. Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association, Chicago
Atkinson BK, Meredith PG (1987) The theory of subcritical crack growth with applications to minerals and rocks. In: Atkinson BK (ed) Fracture mechanics of rock. Academic Press, London, pp 111–166
Baihly JD, Altman RM, Malpani R, Luo F (2010) Shale gas production decline trend comparison over time and basins. In: SPE annual technical conference and exhibition. Society of Petroleum Engineers, Florence
Bikong C, Hoxha D, Shao JF (2015) A micro-macro model for time-dependent behavior of clayey rocks due to anisotropic propagation of microcracks. Int J Plast 69:73–88
Bonini M, Debernardi D, Barla M, Barla G (2007) The mechanical behaviour of clay shales and implications on the design of tunnels. Rock Mech Rock Eng 42:361
Brantut N, Baud P, Heap MJ, Meredith PG (2012) Micromechanics of brittle creep in rocks. J Geophys Res 117:B08412
Brantut N, Heap MJ, Meredith PG, Baud P (2013) Time-dependent cracking and brittle creep in crustal rocks: a review. J Struct Geol 52:17–43
Brantut N, Heap MJ, Baud P, Meredith PG (2014) Rate- and strain-dependent brittle deformation of rocks. J Geophys Res Solid Earth 119:1818–1836
Bürgmann R, Dresen G (2008) Rheology of the lower crust and upper mantle: evidence from rock mechanics, geodesy, and field observations. Annu Rev Earth Planet Sci 36:531–567
Chang C, Zoback MD (2009) Viscous creep in room-dried unconsolidated Gulf of Mexico shale (I): experimental results. J Pet Sci Eng 69:239–246
Chang C, Zoback MD (2010) Viscous creep in room-dried unconsolidated Gulf of Mexico shale (II): development of a viscoplasticity model. J Pet Sci Eng 72:50–55
Chen D, Ye Z, Pan Z, Zhou Y, Zhang J (2017) A permeability model for the hydraulic fracture filled with proppant packs under combined effect of compaction and embedment. J Pet Sci Eng 149:428–435
Chong KP, Smith JW, Khaliki BA (1978) Creep and relaxation of oil shale. In: 19th U.S. Symposium on Rock Mechanics (USRMS). American Rock Mechanics Association, Reno
Ciccotti M (2009) Stress-corrosion mechanisms in silicate glasse. J Phys D Appl Phys 42:214006. doi:10.1088/0022-3727/42/21/214006
Cogan J (1976) Triaxial creep tests of Opohonga limestone and Ophir shale. Int J Rock Mech Min Sci Geomech Abstr 13:1–10
de Waal JA, Smits RMM (1988) Prediction of reservoir compaction and surface subsidence: field application of a new model. SPE Form Eval 3:347–356
Dorner D, Röller K, Stöckhert B (2014) High temperature indentation creep tests on anhydrite—a promising first look. Solid Earth 5:805–819
Dudley JW II, Myers MT, Shew RD, Arasteh MM (1998) Measuring compaction and compressibilities in unconsolidated reservoir materials by time-scaling creep. SPE Reservoir Eval Eng 1:430–437
Fabre G, Pellet F (2006) Creep and time-dependent damage in argillaceous rocks. Int J Rock Mech Min Sci 43:950–960
Findley WN, Lai JS, Onaran K (1976) Creep and relaxation of nonlinear viscoelastic materials with an introduction to linear viscoelasticity. Dover Publications, New York
Fischer Q, Kets F, Crook A (2013) Self-sealing of faults and fractures in argillaceous formations: evidence from the petroleum industry. Nagra Arbeitsber. NAB 13-06
Fjær E, Larsen I, Holt RM, Bauer A (2014) A creepy model for creep. In: 48th U.S. Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association, Minneapolis
Frost H, Ashby M (1982) Deformation-mechanism maps. The plasticity and creep of metals and ceramics. Pergamon Press, Oxford
Gasc-Barbier M, Chanchole S, Bérest P (2004) Creep behavior of Bure clayey rock. Appl Clay Sci 26:449–458
Guo J, Liu Y (2012) Modeling of proppant embedment: elastic deformation and creep deformation. In: SPE international production and operations conference & exhibition. Society of Petroleum Engineers, Doha
Gupta VB (1975) The creep behavior of standard linear solid. J Appl Polym Sci 19:2917
Hagin P, Zoback M (2004) Viscous deformation of unconsolidated reservoir sands—Part 2: linear viscoelastic models. Geophysics 69:742–751
Hart E (1970) A phenomenological theory for plastic deformation of polycrystalline metals. Acta Metall 18:599–610
Heap MJ, Baud P, Meredith PG, Bell AF, Main IG (2009a) Time-dependent brittle creep in Darley Dale sandstone. J Geophys Res Solid Earth 114:B07203
Heap MJ, Baud P, Meredith PG (2009b) Influence of temperature on brittle creep in sandstones. Geophys Res Lett 36:L19305. doi:10.1029/2009GL039373
Heller RJ, Zoback MD (2011) Adsorption, swelling and viscous creep of synthetic clay samples. In: 45th U.S. Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association, San Francisco
Hol S, Zoback MD (2013) Creep behavior of coal and shale related to adsorption of reservoir fluids. In: 47th U.S. Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association, San Francisco
Howarth RW, Ingraffea A, Engelder T (2011) Natural gas: should fracking stop? Nature 477:271–275
Hughes JD (2013) Energy: a reality check on the shale revolution. Nature 494:307–308
Ibanez WD, Kronenberg AK (1993) Experimental deformation of shale: mechanical properties and microstructural indicators of mechanisms. Int J Rock Mech Min Sci Geomech Abstr 30:723–734
Jiang Q, Qi Y, Wang Z, Zhou C (2013) An extended Nishihara model for the description of three stages of sandstone creep. Geophys J Int 193:841–854
Karato S (2008) Deformation of earth materials. Cambridge University Press, New York
Kassis SM, Sondergeld CH (2010) Gas shale permeability: effects of roughness, proppant, fracture offset, and confining pressure. In: International oil and gas conference and exhibition in China. Society of Petroleum Engineers, Beijing
Kranz RL (1980) The effects of confining pressure and stress difference on static fatigue of granite. J Geophys Res 85(B4):1854–1866
Kranz RL, Harries WJ, Carter NL (1982) Static fatigue of granite at 200°C. Geophys Res Lett 9:1–4
LaFollette RF, Carman PS (2010) Proppant diagenesis: results so far. In: SPE Unconventional Gas Conference. Society of Petroleum Engineers, Pittsburgh
Li Y, Ghassemi A (2012) Creep behavior of Barnett, Haynesville, and Marcellus shale. In: 46th U.S. Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association, Chicago
Li X, Shao Z (2016) Investigation of macroscopic brittle creep failure caused by microcrack growth under step loading and unloading in rocks. Rock Mech Rock Eng 49:2581–2593
Liu Y, Sharma MM (2005) Effect of fracture width and fluid rheology on proppant settling and retardation: an experimental study. In: SPE annual technical conference and exhibition. Society of Petroleum Engineers, Dallas
Lockner DA (1995) Rock Failure. In: Ahrens TJ (ed) Rock physics and phase relations: a handbook of physical constants. Ref. Shelf. AGU, Washington, pp 127–147
Main IG (2000) A damage mechanics model for power-law creep and earthquake aftershock and foreshock sequences. Geophys J Int 142:151–161
Masuti S, Barbot SD, Karato S-I, Feng L, Banerjee P (2016) Upper-mantle water stratification inferred from observations of the 2012 Indian Ocean earthquake. Nature 538:373–377
McGlade C, Speirs J, Sorrell S (2013) Unconventional gas—a review of regional and global resource estimates. Energy 55:571–584
Mighani S, Taneja S, Sondergeld CH, Rai CS (2015) Nanoindentation creep measurements on shale. In: 49th U.S. Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association, San Francisco
Morales RH, Suarez-Rivera R, Edelman E (2011) Experimental evaluation of hydraulic fracture impairment in shale reservoirs. In: 45th U.S. Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association, San Francisco
Mouazen M, Poulesquen A, Vergnes B (2011) Correlation between thermal and rheological studies to characterize the behavior of bitumen. Rheol Acta 50:169–178
Nara Y, Morimoto K, Yoneda T, Hiroyoshi N, Kaneko K (2011) Effects of humidity and temperature on subcritical crack growth in sandstone. Int J Solids Struct 48:1130–1140
Naumann M, Hunsche U, Schulze O (2007) Experimental investigations on anisotropy in dilatancy, failure and creep of Opalinus Clay. Phys Chem Earth Parts A/B/C 32:889–895
Norris JQ, Turcotte DL, Moores EM, Brodsky EE, Rundle JB (2016) Fracking in Tight Shales: what is it, what does it accomplish, and what are its consequences? Annu Rev Earth Planet Sci 44:321–351
Paterson MS (1970) A high-pressure, high-temperature apparatus for rock deformation. Int J Rock Mech Min Sci 7:517–526
Paterson M (2013) Materials science for structural geology. Springer, London
Paterson MS, Wong TF (2005) Experimental rock deformation—the brittle field, 2nd edn. Springer, Berlin
Patzek T, Male F, Marder M (2014) A simple model of gas production from hydrofractured horizontal wells in shales. AAPG Bull 98:2507–2529
Pedlow J, Sharma M (2014) Changes in shale fracture conductivity due to interactions with water-based fluids. In: SPE hydraulic fracturing technology conference. Society of Petroleum Engineers, The Woodlands
Ranalli G (1987) Rheology of the earth: deformation and flow processes in geophysics and geodynamics. Allen & Unwin, Boston
Rassouli FS, Zoback MD (2015) Long-term creep experiments on Haynesville shale rocks. In: 49th U.S. Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association, San Francisco
Reinicke A, Rybacki E, Stanchits S, Huenges E, Dresen G (2010) Hydraulic fracturing stimulation techniques and formation damage mechanisms—implications from laboratory testing of tight sandstone–proppant systems. Chemie der Erde - Geochemistry 70(Supplement 3):107–117
Rybacki E, Paterson MS, Wirth R, Dresen G (2003) Rheology of calcite–quartz aggregates deformed to large strain in torsion. J Geophys Res 108:2089. doi:10.1029/2002JB001833
Rybacki E, Reinicke A, Meier T, Makasi M, Dresen G (2015) What controls the mechanical properties of shale rocks?—Part I: strength and Young’s modulus. J Pet Sci Eng 135:702–722
Rybacki E, Meier T, Dresen G (2016) What controls the mechanical properties of shale rocks?—Part II: brittleness. J Pet Sci Eng 144:39–58
Schmitt L, Forsans T, Santarelli FJ (1994) Shale testing and capillary phenomena. Int J Rock Mech Min Sci 31:441–447
Sone H, Zoback MD (2010) Strength, creep and frictional properties of gas shale reservoir rocks. In: 44th U.S. Rock Mechanics Symposium and 5th U.S.-Canada Rock Mechanics Symposium. American Rock Mechanics Association, Salt Lake City
Sone H, Zoback MD (2011) Visco-plastic properties of shale gas reservoir rocks. In: 45th U.S. Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association, San Francisco
Sone H, Zoback MD (2013) Mechanical properties of shale-gas reservoir rocks—Part 2: ductile creep, brittle strength, and their relation to the elastic modulus. Geophysics 78:D393–D402
Sone H, Zoback MD (2014) Time-dependent deformation of shale gas reservoir rocks and its long-term effect on the in situ state of stress. Int J Rock Mech Min Sci 69:120–132
Stegent NA, Wagner AL, Mullen J, Borstmayer RE (2010) Engineering a successful fracture-stimulation treatment in the Eagle Ford shale. In: Tight Gas Completions Conference. Society of Petroleum Engineers, San Antonio
Stouffer DC, Dame LT (1996) Inelastic deformation of metals. Wiley, New York
van Oort E (2003) On the physical and chemical stability of shales. J Pet Sci Eng 38:213–235
Volk LJ, Raible CJ, Carroll HB, Spears JS (1981) Embedment of high strength proppant into low-permeability reservoir rock. In: SPE/DOE low permeability gas reservoirs symposium. Society of Petroleum Engineers, Denver
Wang H (2016) What factors control shale gas production decline trend: a comprehensive analysis and investigation. In: SPE/IAEE hydrocarbon economics and evaluation symposium. Society of Petroleum Engineers, Houston
Wilshire B, Burt H (2008) Damage evolution during creep of steels. Int J Press Vessels Pip 85:47–54
Yang Y, Zoback M (2016) Viscoplastic deformation of the Bakken and adjacent formations and its relation to hydraulic fracture growth. Rock Mech Rock Eng 49:689–698
Yu HD, Chen WZ, Gong Z, Tan XJ, Ma YS, Li XL, Sillen X (2015) Creep behavior of boom clay. Int J Rock Mech Min Sci 76:256–264
Zhang C, Rothfuchs T (2004) Experimental study of the hydro-mechanical behaviour of the Callovo-Oxfordian argillite. Appl Clay Sci 26:325–336
Zhang J, Kamenov A, Zhu D, Hill D (2013) Laboratory measurement of hydraulic fracture conductivities in the Barnett Shale. In: International Petroleum Technology Conference. International Petroleum Technology Conference, Beijing
Zhang J, Ouyang L, Zhu D, Hill AD (2015) Experimental and numerical studies of reduced fracture conductivity due to proppant embedment in the shale reservoir. J Pet Sci Eng 130:37–45
Zhang D, Ranjith PG, Perera MSA (2016a) The brittleness indices used in rock mechanics and their application in shale hydraulic fracturing: a review. J Pet Sci Eng 143:158–170
Zhang J, Zhu D, Hill AD (2016b) Water-induced damage to propped-fracture conductivity in shale formations. SPE Prod Oper 31:147–156
Acknowledgements
This work was supported by the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 640979 (SXT). We thank Masline Makasi for sample handling, Stefan Gehrmann for sample and thin section preparation, Anja Schreiber for TEM foil preparation, Tobias Meier for providing porosity data and Michael Naumann for assistance with deformation experiments. Insightful comments of two anonymous reviewers improved the manuscript.
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Rybacki, E., Herrmann, J., Wirth, R. et al. Creep of Posidonia Shale at Elevated Pressure and Temperature. Rock Mech Rock Eng 50, 3121–3140 (2017). https://doi.org/10.1007/s00603-017-1295-y
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DOI: https://doi.org/10.1007/s00603-017-1295-y