夏彬伟,廖传斌,罗亚飞,冀凯楠
XIA Binwei,LIAO Chuanbin,LUO Yafei,JI Kainan

• 1:重庆大学煤矿灾害动力学与控制国家重点实验室
• 2:重庆大学复杂煤气层瓦斯抽采国家地方联合工程实验室

摘要(Abstract)：

煤储层裂隙是煤层气渗流的主要通道，决定了煤储层的渗透性及煤层气产能，研究裂隙结构特征与煤储层渗透性的关系对准确预测煤层气产能具有重要理论及实践意义。基于经典立方定律渗透率模型，同时考虑分形理论、裂隙网络结构特征及有效应力，构建包含复杂弯曲裂隙特征的分形渗透率模型，将分形渗透率模型与S&D(Shi-Durucan)模型相结合，建立真三轴应力作用下的裂隙煤渗透率模型。开展真三轴应力条件下的气体渗流实验，将构建的渗透率模型与试验结果及S&D模型拟合数据对比，该渗透率模型与实验结果具有良好的一致性，能够体现出三向应力加载条件下应力对渗透率变化的影响趋势，与S&D模型相比更能反映煤岩渗透率的各向异性特征。基于该渗透率模型，定量分析了煤岩裂隙结构参数对其渗透率的影响。结果表明，煤岩渗透率与孔隙率φ(0.05～0.41)、分形维数D_f(2.37～2.81)、最大裂隙长度l_(max_(3.5～8.0 cm)、比例系数β(0.010～0.065)呈正幂律关系；与迂曲度分形维数D_(Tf)(2.005～2.275)，裂隙倾角θ(10°～80°)呈负幂律关系。研究成果对准确预测煤岩储层渗透率，揭示煤储层中煤层气的流动机理具有重要作用。
Fractures in coal reservoirs, which act as the major seepage pathways for coalbed methane(CBM), determine the permeability and CBM productivity of coal reservoirs. Research on the relationships between fracture structures and reservoir permeability is of great theoretical and practical significance for the accurate prediction of CBM productivity.Based on the classical cubic law-based permeability model, as well as the fractal theory, fracture network structures, and effective stress, this study built a permeability model containing complex bending fractures, which was then combined with the S & D(Shi-Durucan) model to build the permeability model of fractured coals under the action of true triaxial stresses. Then, gas seepage experiments under true triaxial stresses were conducted, followed by the comparison of the results of the final permeability model with the experimental results and the fitting data of the S & D model. As shown by the comparison results, the results of the permeability model agreed well with the experimental results and thus can reflect the trend of the influence of stress on permeability under the loading of triaxial stresses. The comparison results also indicate that the permeability model built in this study can reflect the anisotropy of coal permeability more effectively than the S & D model. Using this permeability model, this study quantitatively analyzed the effects of fracture structures of coals on coal permeability. The results indicate that the coal permeability exhibited positive power-law relationships with porosity φ(0.05-0.41), fractal dimension D_f(2.37-2.81), maximum fracture length l_(max)(3.5-8.0 cm), and proportionality coefficient β(0.010-0.065) and negative power-law relationships with tortuosity fractal dimension D_(Tf)(2.005-2.275) and fracture dip angle θ(10°-80°). The results of this study will play an important role in accurately predicting the permeability of coal reservoirs and revealing the flow mechanisms of CBM in coal reservoirs.

关键词(KeyWords)： 煤层气;渗透率;迂曲度;分形维数;真三轴应力
coalbed methane;permeability;tortuosity;fractal dimension;true triaxial stress

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金重点项目(U19B2009);国家自然科学基金面上项目(51974042);; 山西省科技厅重点研发项目(20191101015)

作者(Author): 夏彬伟,廖传斌,罗亚飞,冀凯楠
XIA Binwei,LIAO Chuanbin,LUO Yafei,JI Kainan

参考文献(References)：

• [1]CAI Yidong,LIU Dameng,PAN Zhejun,et al.Partial coal pyrolysis and its implication to enhance coalbed methane recovery:Asimulation study[J].Energy&Fuels,2017,31(5):4895-4903.
• [2]LI Zhenglan,DUAN Yonggang,FANG Quantang,et al.A study of relative permeability for transient two-phase flow in a low permeability fractal porous medium[J].Advances in Geo-Energy Research,2018,2(4):369-379.
• [3]ZENG Jie,LIU Jishan,LI Wai,et al.Evolution of shale permeability under the influence of gas diffusion from the fracture wall into the matrix[J].Energy&Fuels,2020,34(4):4393-4406.
• [4]LUO Yafei,XIA Binwei,LI Honglian,et al.Fractal permeability model for dual-porosity media embedded with natural tortuous fractures[J].Fuel,2021,295:120610.
• [5]叶建平，侯淞译，张守仁.“十三五”期间我国煤层气勘探开发进展及下一步勘探方向[J].煤田地质与勘探，2022,50(3):15-22.YE Jianping,HOU Songyi,ZHANG Shouren.Progress of coalbed methane exploration and development in China during the13th Five-Year Plan period and the next exploration direction[J].Coal Geology&Exploration,2022,50(3):15-22.
• [6]XU Jianchun,SUN Baojiang,CHEN Bailian.A hybrid embedded discrete fracture model for simulating tight porous media with complex fracture systems[J].Journal of Petroleum Science and Engineering,2019,174:131-143.
• [7]MANDELBROT B B,WHEELER J A.The fractal geometry of nature[J].American Journal of Physics,1983,51(3):286-287.
• [8]YU Boming,CHENG Ping.A fractal permeability model for bi-dispersed porous media[J].International Journal of Heat and Mass Transfer,2002,45(14):2983-2993.
• [9]XIAO Boqi,ZHANG Xian,WANG Wei,et al.A fractal model for water flow through unsaturated porous rocks[J].Fractals,2018,26(2):1840015.
• [10]DU Pengbin,ZHAO Chuntian,PENG Peng,et al.Fractal characterization of permeability prediction model in hydrate-bearing porous media[J].Chemical Engineering Science,2020,218:115576.
• [11]刘冠男，叶大羽，高峰，等.幂率型裂隙分布煤层渗流场与变形应力场耦合模型及数值模拟[J].岩石力学与工程学报，2022,41(3):492-502.LIU Guannan,YE Dayu,GAO Feng,et al.Coupled model of seepage and deformation fields in power-law fracture-distributed coal seam[J].Chinese Journal of Rock Mechanics and Engineering,2022,41(3):492-502.
• [12]MEI Lan,ZHANG Heng,WANG Lei,et al.Fractal analysis of shape factor for matrix-fracture transfer function in fractured reservoirs[J].Oil&Gas Science and Technology,2020,75:47.
• [13]MIAO Tongjun,YU Boming,DUAN Yonggang,et al.A fractal analysis of permeability for fractured rocks[J].International Journal of Heat and Mass Transfer,2015,81:75-80.
• [14]王刚，黄娜，蒋宇静，等.考虑分形特征的节理面渗流计算模型[J].岩石力学与工程学报，2014,33(增刊2):3397-3405.WANG Gang,HUANG Na,JIANG Yujing,et al.Seepage calculation model for rough joint surface considering fractal characteristics[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(Sup.2):3397-3405.
• [15]LIU Richeng,JIANG Yujing,LI Bo,et al.A fractal model for characterizing fluid flow in fractured rock masses based on randomly distributed rock fracture networks[J].Computers and Geotechnics,2015,65:45-55.
• [16]ZHENG Qian,YU Boming.A fractal permeability model for gas flow through dual-porosity media[J].Journal of Applied Physics,2012,111(2):024316.
• [17]WANG Fuyong,CHENG Hui.A fractal permeability model for2D complex tortuous fractured porous media[J].Journal of Petroleum Science and Engineering,2020,188:106938.
• [18]徐超，王凯，郭琳，等.采动覆岩裂隙与渗流分形演化规律及工程应用[J].岩石力学与工程学报，2022,41(12):2389-2403.XU Chao,WANG Kai,GUO Lin,et al.Fractal evolution law of overlying rock fracture and seepage caused by mining and its engineering application[J].Chinese Journal of Rock Mechanics and Engineering,2022,41(12):2389-2403.
• [19]MIAO Tongjun,YANG Shanshan,LONG Zhangcai,et al.Fractal analysis of permeability of dual-porosity media embedded with random fractures[J].International Journal of Heat and Mass Transfer,2015,88:814-821.
• [20]XIA Binwei,LUO Yafei,HU Huarui,et al.Fractal permeability model for a complex tortuous fracture network[J].Physics of Fluids,2021,33(9):096605.
• [21]WITHERSPOON P A,WANG J S Y,IWAI K,et al.Validity of cubic law for fluid flow in a deformable rock fracture[J].Water Resources Research,1980,16(6):1016-1024.
• [22]ZHU Jianting,CHENG Yanyan.Effective permeability of fractal fracture rocks:Significance of turbulent flow and fractal scaling[J].International Journal of Heat and Mass Transfer,2018,116:549-556.
• [23]KLIMCZAK C,SCHULTZ R A,PARASHAR R,et al.Cubic law with aperture-length correlation:Implications for network scale fluid flow[J].Hydrogeology Journal,2010,18(4):851-862.
• [24]LIU Richeng,LI Bo,JIANG Yujing.Critical hydraulic gradient for nonlinear flow through rock fracture networks:The roles of aperture,surface roughness,and number of intersections[J].Advances in Water Resources,2016,88:53-65.
• [25]李波波，王斌，杨康，等.煤岩孔裂隙结构分形特征及渗透率模型研究[J].煤炭科学技术，2021,49(2):226-231.LI Bobo,WANG Bin,YANG Kang,et al.Study on fractal characteristics of coal pore fissure structure and permeability model[J].Coal Science and Technology,2021,49(2):226-231.
• [26]LU Shouqing,CHENG Yuanping,LI Wei.Model development and analysis of the evolution of coal permeability under different boundary conditions[J].Journal of Natural Gas Science and Engineering,2016,31:129-138.
• [27]CONNELL L D,MAZUMDER S,SANDER R,et al.Laboratory characterisation of coal matrix shrinkage,cleat compressibility and the geomechanical properties determining reservoir permeability[J].Fuel,2016,165:499-512.
• [28]CUI Xiaojun,BUSTIN R M,CHIKATAMARLA L.Adsorption-induced coal swelling and stress:Implications for methane production and acid gas sequestration into coal seams[J].Journal of Geophysical Research,2007,112:B10202.
• [29]SHI Jiquan,DURUCAN S.A model for changes in coalbed permeability during primary and enhanced methane recovery[J].SPE Reservoir Evaluation&Engineering,2005,8(4):291-299.
• [30]MCKEE C R,BUMB A C,KOENIG R A.Stress-dependent permeability and porosity of coal and other geologic formations[J].SPE Formation Evaluation,1988,3(1):81-91.
• [31]李铭辉.真三轴应力条件下储层岩石的多物理场耦合响应特性研究[D].重庆：重庆大学，2016.LI Minghui.Research on multi-physics coupling behaviors of reservoir rocks under true triaxial stress conditions[D].Chongqing:Chongqing University,2016.
• [32]杜锋，王凯，董香栾，等.基于CT三维重构的煤岩组合体损伤破坏数值模拟研究[J].煤炭学报，2021,46(增刊1):253-262.DU Feng,WANG Kai,DONG Xiangluan,et al.Numerical simulation of damage and failure of coal-rock combination based on CT three-dimensional reconstruction[J].Journal of China Coal Society,2021,46(Sup.1):253-262.
• [33]王凯，郭阳阳，王刚，等.真三轴路径下含瓦斯复合煤岩体渗流及力学破坏特性[J].煤炭学报，2023,48(1):226-237.WANG Kai,GUO Yangyang,WANG Gang,et al.Seepage and mechanical failure characteristics of gas-bearing composite coal-rock under true triaxial path[J].Journal of China Coal Society,2023,48(1):226-237.
• [34]张培森，赵成业，侯季群，等.温度-应力-渗流耦合条件下红砂岩渗流特性试验研究[J].岩石力学与工程学报，2020,39(10):1957-1974.ZHANG Peisen,ZHAO Chengye,HOU Jiqun,et al.Experimental study on seepage characteristics of deep sandstone under temperature-stress-seepage coupling conditions[J].Chinese Journal of Rock Mechanics and Engineering,2020,39(10):1957-1974.
• [35]ANOOSHEH Y,HOSSEIN H,MUHAMMAD S.Permeability,porosity,and percolation properties of two-dimensional disordered fracture networks[J].Physical Review E,Statistical,Nonlinear,and Soft Matter Physics,2011,84(4 Pt 2):046317.
• [36]ZHANG Bo,LI Yong,FANTUZZI N,et al.Investigation of the flow properties of CBM based on stochastic fracture network modeling[J].Materials,2019,12(15):2387.

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