(1. Faculty of Civil Engineering and Mechanics，Kunming University of Science and Technology，Kunming，Yunnan 650500，China；
2. State Key Laboratory of Geomechanics and Geotechnical Engineering，Institute of Rock and Soil Mechanics，
Chinese Academy of Sciences，Wuhan，Hubei 430071，China)
Abstract：To study the coupling mechanism of seepage and heat transfer in high-temperature rough rock fracture and to improve the efficiency of geothermal energy extraction，lattice Boltzmann method the double distribution functions were applied to deal with the evolution of seepage velocity field and heat transfer temperature field separately. Considering the effects of fluid temperature on its kinematic viscosity and thermal diffusion，a numerical model was proposed to simulate the coupled process of seepage and heat transfer in rough rock fracture. And the accuracy of the model was verified according to a classic example. Based on the proposed model，the effects of rough fracture surface and dynamic evolution of fluid physical parameters on the coupling mechanism of seepage and heat transfer were analyzed，and the relationship between the roughness of fracture surface and the performance indicators of geothermal extraction was discussed. The results show that the obstruction effect of the rough fracture surface increases the inertial pressure drop and reduces its seepage velocity，which makes the heat transfer between water and rock more sufficient，and the water temperature is higher at the outlet. Neglecting the influence of fluid temperature on its kinematic viscosity seriously overestimates the flow velocity，and significantly underestimates the thermal breakthrough time. As the roughness of the fracture surface intensifies，its thermal breakthrough time gradually increases，while the heat production power shows a decreasing trend. When the fractal dimension of fracture surface is 1.079 8，its thermal breakthrough time increases by 191.49% compared to the smooth fracture，and the heat production power is only 44.36% of that of smooth fracture. In addition，when the pressure drops are the same，the smoother the fracture surface is，the higher the heat recovery rate obtained within the same time. However，due to its shorter heat breakthrough time，the heat recovery rate is significantly reduced when the thermal breakthrough occurs.
申林方1，苏 威1，张家明1，王志良1，李邵军2，徐则民1. 考虑流体热物理性质动态演化的高温岩石粗糙裂隙渗流传热效应研究[J]. 岩石力学与工程学报, 2024, 43(6): 1359-1370.
SHEN Linfang1，SU Wei1，ZHANG Jiaming1，WANG Zhiliang1，LI Shaojun2，XU Zemin1. Study on the seepage and heat transfer effect of rough fractures in hot matrix considering dynamic thermophysical properties of fluid. , 2024, 43(6): 1359-1370.
[1] 国家发展和改革委员会，国家能源局，国土资源部. 地热能开发利用“十三五”规划[EB/OL]. https://www.ndrc.gov.cn/fggz/fzzlgh/gjjzxgh/ 201706/t20170605_1196776.html，2017.(National Development and Reform Commission，National Energy Administration，Ministry of Land and Resources. “13th Five Year Plan”for geothermal energy development and utilization[EB/OL]. https://www.ndrc.gov.cn/fggz/fzzlgh/gjjzxgh/ 201706/t20170605_1196776.html，2017.(in Chinese))
[2] 郭明晶，成金华，丁 洁，等. 中国地热资源开发利用的技术，经济与环境评价[M]. 武汉：中国地质大学出版社，2016：21–24.(GUO Mingjing，CHENG Jinhua，DING Jie，et al. Technical，economic and environmental evaluation of geothermal resources development and utilization in China[M]. Wuhan：China University of Geosciences Press，2016：21–24.(in Chinese))
[3] 董芋双，王志国，薛 孟，等. 基于REV的干热岩裂隙渗流传热耦合模拟研究[J]. 工程热物理学报，2023，44(9)：2 340–2 346. (DONG Yushuang，WANG Zhiguo，XUE Meng，et al. Coupled simulation of seepage and heat transfer in hot dry rock fractures based on REV[J]. Journal of Engineering Thermophysics，2023，44(9)：2 340–2 346.(in Chinese))
[4] SNOW D T. A parallel plate model of fractured permeable media[Ph. D. Thesis][D]. Berkeley：University of California of Berkeley，1965.
[5] LOMIZE G M. Flow in fractured rocks[R]. Moscow：Gosemergoizdat，1951.
[6] ZIMMERMAN R W，BODVARSSON G S. Hydraulic conductivity of rock fractures[J]. Transport in Porous Media，1996，23(1)：1–30.
[7] BROSH D J，THOMSON N R. Fluid flow in synthetic rough-walled fractures: Navier-Stokes，Stokes，and local cubic law simulations[J]. Water Resources Research，2003，39(4)：1 085–1 100.
[8] WILSON C R，WITHERSPOON P A. Steady state flow in rigid networks of fractures[J]. Water Resources Research，1974，10(2)：328–335.
[9] ZIMMERMAN R W，AI-YAARUBI A，PAIN C C，et al. Non-linear regimes of fluid flow in rock fractures[J]. International Journal of Rock Mechanics and Mining Sciences，2004，41(Supp.1)：163–169.
[10] ZHAO J，BROWN E T. Hydro-thermo-mechanical properties of joints in the Carnmenellis granite[J]. Quarterly Journal of Engineering Geology and Hydrogeology，1992，25(4)：279–290.
[11] WANG L，CARDENAS M B，SLOTTKE D T，et al. Modification of the local cubic law of fracture flow for weak inertia，tortuosity，and roughness[J]. Water Resources Research，2015，51(4)：2 064–2 080.
[12] 肖维民，夏才初，王 伟. 考虑三维形貌特征的粗糙节理渗流空腔模型研究[J]. 岩石力学与工程学报，2011，30(增2)：3 786–3 795. (XIAO Weimin，XIA Caichu，WANG Wei. Study of void model for fluid flow through joint by considering 3D topography characteristics[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(Supp.2)：3 786–3 795.(in Chinese))
[13] 朱红光，易 成，谢和平，等. 基于立方定律的岩体裂隙非线性流动几何模型[J]. 煤炭学报，2016，41(4)：822–828.(ZHU Hongguan，YI Cheng，XIE Heping，et al. A new geometric model for non-linear flow in rough-walled fractures based on the cubic law[J]. Journal of China Coal Society，2016，41(4)：822–828.(in Chinese))
[14] CHEN Y F，ZHOU J Q，HU S H，et al. Evaluation of Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures[J].Journal of Hydrology，2015，529：993–1 006.
[15] WANG M，CHEN Y F，MA G W，et al. Influence of surface roughness on nonlinear flow behaviors in 3D self-affine rough fractures：Lattice Boltzmann simulations[J]. Advances in Water Resources，2016，96：373–388.
[16] 周 新，盛建龙，叶祖洋，等. 岩体粗糙裂隙几何特征对其Forchheimer型渗流特性的影响[J]. 岩土工程学报，2021，43(11)：2 075–2 083.(ZHOU Xin，SHENG Jianlong，YE Zuyang，et al. Effects of geometrical feature on Forchheimer-flow behavior through rough-walled rock fractures[J]. Chinese Journal of Geotechnical Engineering，2021，43(11)：2 075–2 083.(in Chinese))
[17] 田 霄，叶祖洋，罗 旺. 岩体裂隙几何结构对其渗流传热特性的影响[J]. 岩土力学，2023，44(12)：3 512–3 521.(TIAN Xiao，YE Zuyang，LUO Wang. Effect of rock fracture geometry on its seepage and heat transfer characteristics[J]. Rock and Soil Mechanics，2023，44(12)：3 512–3 521.(in Chinese))
[18] 高雪峰，张延军，黄奕斌，等.花岗岩粗糙单裂隙对流换热特性的数值模拟[J]. 岩土力学，2020，41(5)：1 761–1 769.(GAO Xuefeng，ZHANG Yanjun，HUANG Yibin，et al. Numerical simulation of convective heat transfer characteristics of a rough single fracture in granite[J]. Rock and Soil Mechanics，2020，41(5)：1 761–1 769.(in Chinese))
[19] LUO S，ZHAO Z H，PENG H，et al. The role of fracture surface roughness in macroscopic fluid flow and heat transfer in fractured rocks[J]. International Journal of Rock Mechanics and Mining Sciences，2016，87：29–38.
[20] 王亚宁，陆 川，王贵玲. 岩石导热热阻对裂隙对流换热的影响机制[J]. 煤田地质与勘探，2023，51(3)：113–122.(WANG Yaning，LU Chuan，WANG Guiling. Influencing mechanism of rock thermal resistance on convective heat transfer of fracture[J]. Coal Geology and Exploration，2023，51(3)：113–122.(in Chinese))
[21] SHEN S，XU J L，ZHOU J J，et al. Flow and heat transfer in microchannels with rough wall surface[J]. Energy Conversion and Management，2006，47(11–12)：1 311–1 325.
[22] 姚 池，邵玉龙，杨建华，等. 非线性渗流对裂隙岩体渗流传热过程的影响[J]. 岩土工程学报，2020，42(6)：1 050–1 058.(YAO Chi，SHAO Yulong，YANG Jianhua，et al. Effect of nonlinear seepage on flow and heat transfer process of fractured rocks[J]. Chinese Journal of Geotechnical Engineering，2020，42(6)：1 050–1 058.(in Chinese))
[23] YAO C，SHAO Y，YANG J，et al. Effects of fracture density，roughness，and percolation of fracture network on heat-flow coupling in hot rock masses with embedded three-dimensional fracture network[J]. Geothermics，2020，87：101846.
[24] CHERKAOUI I，BETTAIBI S，BARKAOUI A，et al. Numerical study of pulsatile thermal magnetohydrodynamic blood flow in an artery with aneurysm using lattice Boltzmann method(LBM)[J]. Communications in Nonlinear Science and Numerical Simulation，2023，123：107281.
[25] 曾非同，关向雨，黄以政，等. 基于多尺度多物理场的油浸式变压器流动–传热数值研究[J]. 电工技术学报，2020，35(16)：3 436–3 444. (ZENG Feitong，GUAN Xiangyu，HUANG Yizheng，et al. Numerical study on flow-heat transfer of oil-immersed transformer based on multiple-scale and multiple-physical fields[J]. Transactions of China Electrotechnical Society，2020，35(16)：3 436–3 444.(in Chinese))
[26] KRUGGEL-EMDEN H，KRAVETS B，SURYANARAYANA M K，et al. Direct numerical simulation of coupled fluid flow and heat transfer for single particles and particle packings by a LBM-approach[J]. Powder Technology，2016，294：236–251.
[27] ZHAO X，LUO T F，JIN H，A predictive model for self-，Maxwell-Stefan，and Fick diffusion coefficients of binary supercritical water mixtures[J]. Journal of Molecular Liquids，2021，324：114735.
[28] SUN Z X，ZHANG X，XU Y，et al. Numerical simulation of the heat extraction in EGS with thermal-hydraulic-mechanical coupling method based on discrete fractures model[J]，Energy，2017，120：20–33.
[29] QIAN Y H，D'HUMIERES D，LALLEMAND P. Lattice BGK models for navier-stokes equation[J]. Europhysics Letters，1992，17(6)：479–484.
[30] GUO Z L，ZHENG C G，SHI B C. Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method[J]. Chinese Physics，2002，11(4)：366–374.
[31] TIMM K，KUSUMAATMAJA H，KUZMIN A，et al. The Lattice Boltzmann Method：Principles and practice[M]. Switzerland：Springer，2017：326–328.
[32] 申林方，王志良，曾 叶，等. 基于粗糙岩体裂隙表面反应的格子Boltzmann渗流–溶解耦合模型[J]. 岩石力学与工程学报，2019，38(8)：1 615–1 626.(SHEN Linfang，WANG Zhiliang，ZENG Ye，et al. A coupled seepage and dissolution model of rough rock fractures considering surface reaction based on lattice Boltzmann method[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(8)：1 615–1 626.(in Chinese))
[33] 黄 娜，蒋宇静，程远方，等. 基于3D打印技术的复杂三维粗糙裂隙网络渗流特性试验及数值模拟研究[J]. 岩土力学，2021，42(6)：1 659–1 668.(HUANG Na，JIANG Yujing，CHENG Fangyuan，et al. Experimental and numerical study of hydraulic properties of three-dimensional rough fracture networks based on 3D printing technology[J]. Rock and Soil Mechanics，2021，42(6)：1 659–1 668.(in Chinese))
[34] 金 辉，宋星星，郭烈锦. 多孔介质中超临界水渗流压降特性研究[J]. 工程热物理学报，2016，37(1)：99–103.(JIN Hui，SONG Xingxing，GUO Liejin. Investigation on pressure drop characteristics of supercritical water seepage in porous media[J]. Journal of Engineering Thermophysics，2016，37(1)：99–103.(in Chinese))
[35] 朱大龙. 深层地热水供热回灌井布置方式及取热层热突破机理研究[硕士学位论文][D]. 济南：山东建筑大学，2018.(ZHU Dalong. Research on irrigation wells arrangement and aquifer thermal breakthrough of deep geothermal water heating[M. S. Thesis][D]. Jinan：Shandong Jianzhu University，2018.(in Chinese))
2024, Vol. 43 
