Investigations of Water Flow Behaviors Induced by Local Temperature Variations through a Single Rough Fracture for the Enhanced Geothermal Systems

  • LI Jiawei ,
  • YE Lin
Expand
  • 1. Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China
    2. School of Power and Energy, Northwestern Polytechnical University, Xi’an 710072, China

Online published: 2024-04-30

Supported by

The authors would like to acknowledge the National Key R&D Program of China (Grant No. 2021YFB1507405), the Youth Fund of the National Natural Science Foundation of China (Grant No. 52204040), General Program of China Postdoctoral Science Foundation (Grant No. 2021M701929) and the Fundamental Research Funds for the Central Universities.

Copyright

Science Press, Institute of Engineering Thermophysics, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2024

Abstract

In recent years, Enhanced Geothermal System (EGS) technologies have been applied to the geothermal resources production in the Hot Dry Rock (HDR). The core of EGS technologies is to adopt hydraulic fracturing in the reservoir to create a connected network of discrete fractures with the consideration of water as a working fluid for hydraulic fracturing and heat production. This paper investigates the characteristics of water flow behaviors through a single rough fracture under different temperature and pressure conditions. A single fracture model with rough fracture surfaces is constructed and then characterized, and influences of the anisotropic factor on the average tortuosity and frictional resistance coefficient of water flow through a single fracture with rough surfaces have been compared and analyzed. With consideration of other impacting factors (temperature, pressure, fracture roughness), the impact of mass flow rate has also been presented. Numerical simulation results present that changes of average tortuosity for water flow through a single rough facture are mainly affected by temperature. It can be observed that higher temperature leads to larger average tortuosity but the frictional resistance coefficient shows an opposite trend. As for pressure conditions, it is found that effects of pressure on average tortuosity and frictional resistance coefficient is very small, which can be neglected under high pressure conditions. Furthermore, the average tortuosity shows a progressively linear relationship with the mass flow rate. On the contrary, the frictional resistance coefficient has a negative relationship with the mass flow rate. It is revealed that when the mass flow rate reaches a critical point, the influences of temperature on the frictional resistance coefficient will be negligible. Comparisons of single rough fractures with different anisotropic factors show that values of average tortuosity and frictional resistance coefficient have positive relationships with the increase of anisotropic factors.

Cite this article

LI Jiawei , YE Lin . Investigations of Water Flow Behaviors Induced by Local Temperature Variations through a Single Rough Fracture for the Enhanced Geothermal Systems[J]. Journal of Thermal Science, 2024 , 33(3) : 1055 -1064 . DOI: 10.1007/s11630-024-1945-9

References

[1] William E.G., Geothermal energy: Renewable energy and the environment. CRC Press, 2010.
[2] Johnston I.W., Narsillo G.A., Colls S., Emerging geothermal energy technologies. KSCE Journal of Civil Engineering, 2011, 15(4): 643–653.
[3] Omar E., Haitham A.R., Frede B., Renewable energy resources: Current status, future prospects and their enabling technology. Renewable and Sustainable Energy Reviews, 2014, 39: 748–764.
[4] BP plc. BP 2017 Statistical Review of World Energy. June 2018.
[5] Geothermal Energy Association, 2016 annual U.S. & global geothermal power production report. Washington D.C., 2016.
[6] Brown D.W., Duchane D.V., Heiken G., et al., Mining the Earth’s heat: Hot Dry Rock geothermal energy. Springer Science & Business Media, 2012.
[7] Tester J.W., Anderson B.J., Batchelor A.S., et al., The future of geothermal energy, impact of enhanced geothermal systems on the United States in the 21st century. MIT Report, 2006.
[8] Xu R.N., Zhang L., Zhang F.Z., et al., A review on heat transfer and energy conversion in the enhanced geothermal systems with water/CO2 as working fluid. International Journal of Energy Research, 2015, 39(13): 1722–1741.
[9] Pruess K., Enhanced geothermal systems (EGS) using CO2 as working fluid – A novel approach for generating renewable energy with simultaneous sequestration of carbon. Geothermics, 2006, 35: 351–367.
[10] Zhu J.L., Hu K.Y., Lu X.L., et al., A review of geothermal energy resources, development, and applications in  China: Current status and prospects. Energy, 2015, 93: 466–483.
[11] Olasolo P., Jua´rez M.C., Morales M.P., et al., Enhanced geothermal systems (EGS): A review. Renewable & Sustainable Energy Reviews, 2016, 56: 133–144.
[12] Moeck I.S., Catalog of geothermal play types based on geologic controls. Renewable and Sustainable Energy Reviews, 2014, 37: 867–882.
[13] Lomize G.M., Flow in fractured rocks (in Russian). Gesemergoizdat, Moscow, Russia, 1951.
[14] Gangi A.F., Variation of whole and fractured porous rock permeability with confining pressure. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1978, 15(5): 249–257.
[15] Berkowitz B., Braester C., Solute transport in fracture channel and parallel plate models. Geophysical Research Letters, 1991, 18(2): 227–230.
[16] Liu Z.Y., Chen M., Zhang G.Q., Analysis of the influence of a natural fracture network on hydraulic fracture propagation in carbonate formations. Rock Mechanics and Rock Engineering, 2014, 47(2): 575–587.
[17] Lanaro F., A random field model for surface roughness and aperture of rock fractures. International Journal of Rock Mechanics and Mining Sciences, 2000, 37(8): 1195–1210.
[18] Gouze P., Noiriel C., Bruderer C., et al., X-ray tomography characterization of fracture surfaces during dissolution. Geophysical Research Letters, 2003, 30(5): 1267.
[19] Muralidharan V., Chakravarthy D., Putra E., et al., Investigating fracture aperture distributions under various stress conditions using X-Ray CT scanner. Canadian International Petroleum Conference, June 8-10, 2004, Calgary, Alberta, Canada. PETSOC-2004-230.
[20] Qian J., Zhan H., Zhao W., et al., Experimental study of turbulent unconfined groundwater flow in a single fracture. Journal of Hydrology, 2005, 311(1–4): 134–142.
[21] Qian J., Chen Z., Zhan H., et al., 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, 2011, 25(4): 614–622.
[22] Su G.W., Geller J.T., Pruess K., et al., Experimental studies of water seepage and intermittent flow in unsaturated, rough-walled fractures. Water Resources Research, 1999, 35(4): 1019–1037.
[23] Noiriel C., Gouze P., Made B., 3D analysis of geometry and flow changes in a limestone fracture during dissolution. Journal of Hydrology, 2013, 486: 211–223.
[24] Tsang C.F., Neretnieks I., Flow channeling in heterogeneous fractured rocks. Reviews of Geophysics, 1998, 36(2): 275–298.
[25] Co C.K.D., Pollard D.D., Horne R.N., Towards a better understanding of the impact of fracture roughness on permeability-stress relationships using first principles. 2017, 42nd Stanford Geothermal Workshop Proceedings.
[26] Hakami E., Larsson E., Aperture measurements and flow experiments on a single natural fracture. International Journal of Rock Mechanics and Mining Science, 1996, 33(4): 395–404.
[27] Abelin H., Birgersson L., Widen H., et al., Channelling experiment. Technical report, Swedish Nuclear Fuel and Waste Management Company, 1990.
[28] Watanabe N., Hirano N., Tsuchiya N., Determination of aperture structure and fluid flow in a rock fracture by high-resolution numerical modelling on the basis of a flow-through experiment under confining pressure. Water Resources Research, 2008, 44(6): W06412.
[29] Brown S.R., Fluid flow through rock joints the effect of surface roughness. Journal of Geophysical Research, 1987, 92(B2): 1337–1347.
[30] Zimmerman R.W., Kumar S., Bodvarsson G.S., Lubrication theory analysis of the permeability of rough-walled fractures. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1991, 28(4): 325–331.
[31] Brush D.J., Thomson N.R., Fluid flow in synthetic rough-walled fractures: Navier-Stokes, Stokes, and local cubic law simulations. Water Resource Research, 2003, 39(4): 1085.
[32] Yeo I.W., Ge S., Applicable range of the Reynolds equation for fluid flow in a rock Fracture. Geosciences Journal, 2005, 9(4): 347–352.
[33] Ishibashi T., Watanabe N., Hirano N., et al., Upgrading of aperture model based on surface geometry of natural fracture for evaluating channeling flow. GRC Transactions, 2012, 36: 481–486.
[34] Wang M., Chen Y., Ma G., et al., Influence of surface roughness on nonlinear flow behaviors in 3D self-affine rough fractures: Lattice Boltzmann simulations. Advances in Water Resources, 2016, 96: 373–388.
[35] Dou Z., Zhou Z., Sleep B.E., Influence of wettability on interfacial area during immiscible liquid invasion into a 3D self-affine rough fracture: Lattice Boltzmann simulations. Advances in Water Resources, 2013, 61: 1–11.
[36] Zou L.C., Jing L.R., Cvetkovic V., Modeling of flow and mixing in 3D rough-walled rock fracture intersections. Advances in Water Resources, 2017, 107: 1–9.
[37] Dreuzy J.R., Meheust Y., Pichot G., Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks (DFN). Journal of Geophysical Research, 2012, 117: B11207.
[38] Zhang L., Jiang P.X., Wang Z., et al., Convective heat transfer of supercritical CO2 in a rock fracture for enhanced geothermal systems. Applied Thermal Engineering, 2017, 115: 923–936.
[39] Stoffel P., Kuempel A., Mueller D., Cloud-based optimal control of individual borehole heat exchangers in a geothermal field. Journal of Thermal Science, 2022, 31(5): 1253–1265.
[40] Schifflechner C., Wieland C., Spliethoff H., CO2 Plume Geothermal (CPG) systems for combined heat and power production: an evaluation of various plant configurations. Journal of Thermal Science, 2022, 31(5): 1266–1278.
[41] Küempel A., Stoffel P., Mueller D., Development of a long-term operational optimization model for a building energy system supplied by a geothermal field. Journal of Thermal Science, 2022, 31(5): 1293–1301. 
[42] Huang S.L., Oelfke S.M., et al., Applicability of fractal characterization and modelling to rock joint profiles. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1992, 29(2): 89–98.
[43] Odling N.E., Natural fracture profiles, fractal dimension and joint roughness coefficients. Rock Mechanics and Rock Engineering, 1994, 27(3): 135–153.
[44] Schmittbuhl J., Steyer A., Jouniaux L., et al., Fracture morphology and viscous transport. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(3): 422–430.
[45] Mandelbrot B.B., The fractal geometry of nature. Freeman 1982, San Francisco.
[46] Molz F., Liu H., Szulga J., Fractional Brownian motion and fractional Gaussian noise in subsurface hydrology: a review, presentation of fundamental properties, and extensions. Water Resource Research, 1997, 33(10): 2273–2286.
[47] Brown S.R., Simple mathematical model of a rough fracture. Journal of Geophysical Research, 1995, 100: 5941–5952.
[48] Duda A., Koza Z., Matyka M., Hydraulic tortuosity in arbitrary porous media flow. Physical Review E, 2011, 84: 036319.
[49] Sheikh B., Pak A., Numerical investigation of the effects of porosity and tortuosity on soil permeability using coupled three-dimensional discrete-element method and lattice Boltzmann method. Physical Review E, 2015, 91: 053301.
[50] Javadi M., Sharifzadeh M., Shahriar K., et al., Critical Reynolds number for nonlinear flow through rough-walled fractures: The role of shear processes. Water Resources Research, 2014, 50: 1789–1804.
[51] Zhang Z., Nemcik J., Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures. Journal of Hydrology, 2013, 477: 139–151.
[52] Brown G.O., The history of the Darcy-Weisbach equation for pipe flow resistance. Environmental History of Water Resources, 2002, 38: 34–43.
[53] Chen Z., Qian, J., Zhan, H., et al., Effect of roughness on water flow through a synthetic single rough fracture. Environmental Earth Science, 2017, 76: 186.

Outlines

/