Abstract
This paper experimentally investigates the role of high temperature treatment on pore characteristics, permeability, critical Reynolds number, and flow nonlinearity of granite exposed to temperatures of 100~800 °C. First, variations in pore characteristics, porosity, and pore fractal dimension of granite were analyzed using the mercury intrusion method. Then, a number of water flow tests were conducted on the samples with confining pressures varying from 10 to 30 MPa. The results show that (i) the cumulative pore volume of granite shows an increase with temperatures, which first increases gradually in the range of 100~400 °C, and increases significantly in the range of 400~800 °C. The pore structure becomes developed gradually; (ii) as the temperature increases from 100 to 800 °C, the pore fractal dimension decreases by 12.09%, indicating gradually weaken complexity of pore distributions. An exponential function is used to evaluate the increasing porosity of rock based on the temperature levels; (iii) the relations between volume flow rate and pressure gradient can be well described using the Forchheimer’s law. Both linear and nonlinear coefficients increase with the confining pressure. The equivalent permeability experiences an exponential increase with the temperature due to thermally induced defects; (iv) by defining a critical nonlinear effect factor of 10%, the critical pressure gradient was calculated, which increases with the confining pressure. The critical Reynolds number shows a decrease of 25.49%~67.74% with confining pressure due to more isolated contact areas and tortuous flow paths but increases by a factor of 5.97~17.24 with the temperature. A three-order polynomial function is used to analyze the decrease in transmissivity versus the pressure gradient. The Forchheimer’s law results are evaluated by plotting the normalized transmissivity against the pressure gradient, and an increase in the temperature generally shifts the fitted curves downward.
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References
Andrade JSJ, Costa UMS, Almeida MP, Makse HA, Stanley HE (1999) Inertial effects on fluid flow through disordered porous media. Physical Review Letters 82(26):5249–5252
Anovitz LM, Cole DR (2015) Characterization and analysis of porosity and pore structures. Reviews in Mineralogy & Geochemistry 88:61–164
Brown D (1995) The US Hot Dry Rock program - 20 years of experience in reservoir testing. Proceedings of World Geothermal Congress, Firenze, In, pp 2607–2611
Brush DJ, Thomson NR (2003) Fluid flow in synthetic rough-walled fractures: Navier-Stokes, stokes, and local cubic law simulations. Water Resources Research 39(4):1037–1041
Chen SW, Yang CH, Wang GB (2017) Evolution of thermal damage and permeability of Beishan granite. Applied Thermal Engineering 110:1533–1542
Chen YF, Zhou JQ, Hu SH, Hu R, Zhou CB (2015) Evaluation of Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures. Journal of Hydrology 529:993–1006
Cherubini C, Giasi CI, Pastore N (2012) Bench scale laboratory tests to analyze non-linear flow in fractured media. Hydrology & Earth System Sciences Discussions 9(4):2511–2522
Fisher LR, Lark PD (1979) An experimental study of the Washburn equation for liquid flow in very fine capillaries. Journal of Colloid & Interface Science 69(3):486–492
Gallot T, Malcolm A, Szabo TL, Brown S, Burns D, Fehler M (2015) Characterizing the nonlinear interaction of S- and P-waves in a rock sample. Journal of Applied Physics 117(3):034902
Giménez D, Perfect E, Rawls WJ, Pachepsky Y (1997) Fractal models for predicting soil hydraulic properties: a review. Engineering Geology 48(3–4):161–183
Hassanzadegan A, Blöcher G, Milsch H, Urpi L, Zimmermann G (2014) The effects of temperature and pressure on the porosity evolution of Flechtinger sandstone. Rock Mechanics and Rock Engineering 47(2):421–434
Huang N, Liu RC, Jiang YJ, Cheng YF, Li B (2019) Shear-flow coupling characteristics of a three-dimensional discrete fracture network-fault model considering stress-induced aperture variations. Journal of Hydrology. 571:416–424
Javadi M, Sharifzadeh M, Shahriar K, Mitani Y (2014) Critical Reynolds number for nonlinear flow through rough-walled fractures: the role of shear processes. Water Resources Research 50(2):1789–1804
Katz AJ, Thompson AH (1985) Fractal sandstone pores: implications for conductivity and pore formation. Physical Review Letters 54(12):1325–1328
Kong B, Wang E, Li Z, Wang X, Niu Y, Kong X (2017) Acoustic emission signals frequency-amplitude characteristics of sandstone after thermal treated under uniaxial compression. Journal of Applied Geophysics 136:190–197
Kristinsdóttir LH, Flóvenz ÓG, Árnason K, Bruhn D, Milsch H, Spangenberg E, Kulenkampff J (2010) Electrical conductivity and P-wave velocity in rock samples from high-temperature Icelandic geothermal fields. Geothermics 39(1):94–105
Krohn CE, Thompson AH (1986) Fractal sandstone pores: automated measurements using scanning-electron-microscope images. Physical Review B. 33(9):6366–6374
Liu Q, Qian Z, Wu Z (2019) Micro/macro physical and mechanical variation of red sandstone subjected to cyclic heating and cooling: an experimental study. Bulletin of Engineering Geology and the Environment 78(3):1485-1499
Liu RC, Li B, Jiang YJ (2016a) Critical hydraulic gradient for nonlinear flow through rock fracture networks: the roles of aperture, surface roughness, and number of interactions. Advances in Water Resources 88:53–65
Liu RC, Yu L, Jiang YJ (2016b) Quantitative estimates of normalized transmissivity and the onset of nonlinear fluid flow through rough rock fractures. Rock Mechanics & Rock Engineering 50(4):1–9
Mahanta B, Singh TN, Ranjith PG (2016) Influence of thermal treatment on mode I fracture toughness of certain Indian rocks. Engineering Geology 210:103–114
Mandelbrot BB (1983) The fractal geometry of nature. WH Freeman, New York
Masri M, Sibai M, Shao JF, Mainguy M (2014) Experimental investigation of the effect of temperature on the mechanical behavior of Tournemire shale. International Journal of Rock Mechanics & Mining Sciences 70(9):185–191
Nasseri MHB, Schubnel A, Young RP (2007) Coupled evolutions of fracture toughness and elastic wave velocities at high crack density in thermally treated westerly granite. International Journal of Rock Mechanics & Mining Sciences 44(4):601–616
Peng RD, Yang YC, Ju Y, Mao LT, Yang YM (2011) Computation of fractal dimension of rock pores based on gray CT images. Chinese Science Bulletin 56(31):3346–3357
Penumadu D, Dean J (2000) Compressibility effect in evaluating the pore-size distribution of kaolin clay using mercury intrusion porosimetry. Canadian Geotechnical Journal 37:393–405
Perfect E, Kay BD (1995) Applications of fractals in soil and tillage research: a review. Soil & Tillage Research 36(1–2):1–20
Pini R, Krevor S, Krause M, Benson S (2013) Capillary heterogeneity in sandstone rocks during CO2 water core-flooding experiments. Energy Procedia 37:5473–5479
Qian JZ, Chen Z, Zhan HB, Guan HC (2011) Experimental study of the effect of roughness and Reynolds number on fluid flow in rough-walled single fractures: a check of local cubic law. Hydrological Processes 25(4):614–622
Quinn PM, Parker BL, Cherry JA (2011) Using constant head step tests to determine hydraulic apertures in fractured rock. Journal of Contaminant Hydrology 126(1):85–99
Radilla G, Nowamooz A, Fourar M (2013) Modeling non-Darcian single- and two-phase flow in transparent replicas of rough-walled rock fractures. Transport in Porous Media 98(2):401–426
Ranjith PG, Viete DR, Chen BJ, Perera MSA (2012) Transformation plasticity and the effect of temperature on the mechanical behavior of Hawkesbury sandstone at atmospheric pressure. Engineering Geology 151:120–127
Rong G, Peng J, Yao M, Jiang Q, Wong LNY (2018) Effects of specimen size and thermal-damage on physical and mechanical behavior of a fine-grained marble. Engineering Geology 232:46–55
Rong G, Yang J, Cheng L, Zhou CB (2016) Laboratory investigation of nonlinear flow characteristics in rough fractures during shear process. Journal of Hydrology 541:1385–1394
Salimzadeh S, Nick HM, Zimmerman RW (2018) Thermoporoelastic effects during heat extraction from low-permeability reservoirs. Energy 142:546–558
Schmitt M, Fernandes CP, Wolf FG, da Cunha Neto JAB, Rahner CP, dos Santos VSS (2015) Characterization of Brazilian tight gas sandstones relating permeability and Angstrom-to micron-scale pore structures. Journal of Natural Gas Science and Engineering 27(2):785–807
Schmittbuhl J, Steyer A, Jouniaux L, Toussaint R (2008) Fracture morphology and viscous transport. International Journal of Rock Mechanics & Mining Sciences 45(3):422–430
Shafirovich E, Varma A (2009) Underground coal gasification: a brief review of current status. Industrial & Engineering Chemistry Research 48(17):7865–7875
Souley M, Homand F, Pepa S, Hoxha D (2001) Damage-induced permeability changes in granite: a case example at the URL in Canada. International Journal of Rock Mechanics & Mining Sciences 38(2):297–310
Su HJ, Jing HW, Yin Q, Yu L, Wang YC, Wu XJ (2017) Strength and deformation behaviors of veined marble specimens after vacuum heat treatment under conventional triaxial compression. Acta Mechanica Sinica 33(5):886–898
Sun Q, Zhang W, Xue L, Zhang Z, Su T (2015) Thermal damage pattern and thresholds of granite. Environmental Earth Sciences 74(3):2341–2349
Takarli M, Prince W, Siddique R (2008) Damage in granite under heating/cooling cycles and water freeze-thaw condition. International Journal of Rock Mechanics & Mining Sciences 45:1164–1175
Tanaka K, Kurumisawa K (2002) Development of technique for observing pores in hardened cement paste. Cement & Concrete Research 32(9):1435–1441
Wang M, Chen YF, Ma GW, Zhou JQ, Zhou CB (2016) Influence of surface roughness on nonlinear flow behaviors in 3D self-affine rough fractures: Lattice Boltzmann simulations. Advances in Water Resources 96:373–388
Witherspoon PA, Wang JSY, Iwai K, Gale JE (1980) Validity of Cubic Law for fluid flow in a deformable rock fracture. Water Resources Research 16(6):1016–1024
Xia CC, Qian X, Lin P, Xiao WM, Gui Y (2017) Experimental investigation of nonlinear flow characteristics of real rock joints under different contact conditions. Journal of Hydraulic Engineering 143(3):04016090
Xie HP, Gao F, Ju Y (2015) Research and development of rock mechanics in deep ground engineering. Chinese Journal of Rock Mechanics & Engineering 34(11):2161–2178 (in Chinese)
Xiong F, Jiang QH, Ye ZY, Zhang XB (2018) Nonlinear flow behavior through rough-walled rock fractures: the effect of contact area. Computers and Geotechnics 102:179–195
Xu P, Yang SQ (2019) Influence of stress and high-temperature treatment on the permeability evolution behavior of sandstone. Acta Mechanica Sinica, https://doi.org/10.1007/s10409-018-0824-6.
Xu TF, Zhang YJ, Zeng ZF, Bao XH (2012) Technology progress in an enhanced geothermal system (Hot Dry Rock). Science & Technology Review 30(32):42–45 (in Chinese)
Yao M, Rong G, Zhou C, Peng J (2016) Effects of thermal damage and confining pressure on the mechanical properties of coarse marble. Rock Mechanics & Rock Engineering 49(6):2043–2054
Yasuhara H, Kinoshita N, Ohfuji H, Takahashi M, Ito K, Kishida K (2015) Long-term observation of permeability in sedimentary rocks under high-temperature and stress conditions and its interpretation mediated by microstructural investigations. Water Resources Research 51(7):5425–5449
Yin Q, He L, Jing H, Zhu D (2018a) Quantitative estimates of nonlinear flow characteristics of deformable rough-walled rock fractures with various lithologies. Processes 6(9):149–163
Yin Q, Jing H, Liu R, Ma G, Yu L, Su H (2018c) Experimental study on stress-dependent nonlinear flow behavior and normalized transmissivity of real rock fracture networks. Geofluids, https://doi.org/10.1155/2018/8217921.
Yin Q, Jing H, Ma G, Su H, Liu R (2018b) Investigating the roles of included angle and loading condition on the critical hydraulic gradient of real rock fracture networks. Rock Mechanics & Rock Engineering 51(10):3167–3177
Yin Q, Ma GW, Jing HW, Wang HD, Su HJ, Liu RC (2017) Hydraulic properties of 3D rough-walled fractures during shearing: an experimental study. Journal of Hydrology 555:169–184
Yin T, Li X, Cao W, Xia K (2015) Effects of thermal treatment on tensile strength of Laurentian granite using Brazilian test. Rock Mechanics & Rock Engineering 48(6):2213–2223
Zeng Z, Grigg R (2006) A criterion for non-Darcy flow in porous media. Transport in Porous Media 63(1):57–69
Zhang N, He M, Zhang B, Qiao F, Sheng H, Hu Q (2016a) Pore structure characteristics and permeability of deep sedimentary rocks determined by mercury intrusion porosimetry. Journal of Earth Science 27(4):670–676
Zhang W, Sun Q, Zhang Y, Xue L, Kong F (2018) Porosity and wave velocity evolution of granite after high-temperature treatment: a review. Environmental Earth Sciences. https://doi.org/10.1007/s12665-018-7514-3
Zhang Y, Sun Q, He H, Cao L, Zhang W, Wang B (2017) Pore characteristics and mechanical properties of sandstone under the influence of temperature. Applied Thermal Engineering 113:537–543
Zhang ZY, Nemcik J (2013) Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures. Journal of Hydrology 447(1):139–151
Zhang ZZ, Gao F, Gao YN, Xu XL, Hou P, Teng T, Shang XJ (2016b) Fractal structure and model of pore size distribution of granite under high temperatures. Chinese Journal of Rock Mechanics and Engineering 35(12):2426–2438 (in Chinese)
Zhao Y, Feng Z, Zhao Y, Wan Z (2017) Experimental investigation on thermal cracking, permeability under HTHP and application for geothermal mining of HDR. Energy 132:305–314
Zharikov AV, Vitovtova VM, Shmonov VM, Grafchikov AA (2003) Permeability of the rocks from the Kola superdeep borehole at high temperature and pressure: implication to fluid dynamics in the continental crust. Tectonophysics 370(1):177–191
Zhou JQ, Hu SH, Fang S, Chen YF, Zhou CB (2015) Nonlinear flow behaviour at low Reynolds numbers through rough-walled fractures subjected to normal compressive loading. International Journal of Rock Mechanics & Mining Sciences 80:202–218
Zhu T, Jing H, Su H, Yin Q, Du M, Han G (2016) Physical and mechanical properties of sandstone containing a single fissure after exposure to high temperatures. International Journal of Mining Science and Technology 26(2):319–325
Zimmerman RW, Al Yaarubi A, Pain CC, Grattoni CA (2004) Non-linear regimes of fluid flow in rock fractures. International Journal of Rock Mechanics & Mining Sciences 41(3):163–169
Zimmerman RW, Bodvarsson GS (1996) Hydraulic conductivity of rock fractures. Transport in Porous Media 23(1):1–30
Zunino F, Castro J, Lopez M (2015) Thermo-mechanical assessment of concrete microcracking damage due to early-age temperature rise. Construction & Building Materials 81(6):140–153
Zuo JP, Wang JT, Sun YJ, Chen Y, Jiang GH, Li YH (2017) Effects of thermal treatment on fracture characteristics of granite from Beishan, a possible high-level radioactive waste disposal site in China. Engineering Fracture Mechanics 182:425–437
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This study received financial support from the Fundamental Research Funds for the Central Universities, China (No. 2018QNA32).
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Yin, Q., Jing, H., Liu, R. et al. Pore characteristics and nonlinear flow behaviors of granite exposed to high temperature. Bull Eng Geol Environ 79, 1239–1257 (2020). https://doi.org/10.1007/s10064-019-01628-6
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DOI: https://doi.org/10.1007/s10064-019-01628-6