地下空间逾渗与裂缝属性的关系分析
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摘要
裂缝连通性评价是地下空间研究的重要内容。逾渗分析是研究裂缝网络连通性的一种有效手段。裂缝网络逾渗临界值多使用裂缝间接表征参数(如分形维数)来确定,但存在裂缝网络连通性不同却有相同间接表征参数的情况,这降低了预测的可靠性。为避免此类问题并更加准确快速地表征裂缝网络的连通性,文章在构建逾渗临界值方程时,摒弃了间接参数简化的方式,使用裂缝直接表征参数(如裂缝数量、长度等)进行非线性拟合。通过二维数值模拟建立不同参数的离散裂缝网络模型,分析逾渗低、中、高概率临界条件与裂缝直接表征参数的关系,建立逾渗临界条件预测方程,并对方程在不同尺度研究区的应用进行了讨论和验证。结果表明:预测方程可有效地预测不同概率的逾渗临界值。同时文章在预测方程的基础上,建立了裂缝网络连通性评价标准,这对于裂缝发育地区的地下空间评价工作具有一定的指导和借鉴意义。
Evaluation of fracture network connectivity is an important part of studying the underground space while percolation analysis is an effective way to examine the connectivity of a fracture network.Percolation threshold of a fracture network is typically determined by indirect characterization parameters of fractures(eg.,fractal dimension).However,fracture networks with different connectivity may have the same indirect characterization parameters,leading to decreased prediction reliability.To avoid this problem and to more accurately and quickly characterize fracture network connectivity,we built percolation threshold equations using direct characterization parameters(e.g.,fracture length and number)by nonlinear fitting instead of using indirect characterization parameters in the simplified approach.The equations were drawn from the relationships between percolation thresholds and direct characterization parameters of different two-dimensional discrete fracture networks;application of these equations in different scaled fracture networks was discussed and validated.The results show that these equations can efficiently predict percolation thresholds of different scaled fracture networks.Based on this result,we developed criteria for estimating connectivity of fracture networks,which provide certain guidance and reference point for the evaluation of underground space in fractured areas.
Evaluation of fracture network connectivity is an important part of studying the underground space while percolation analysis is an effective way to examine the connectivity of a fracture network.Percolation threshold of a fracture network is typically determined by indirect characterization parameters of fractures(eg.,fractal dimension).However,fracture networks with different connectivity may have the same indirect characterization parameters,leading to decreased prediction reliability.To avoid this problem and to more accurately and quickly characterize fracture network connectivity,we built percolation threshold equations using direct characterization parameters(e.g.,fracture length and number)by nonlinear fitting instead of using indirect characterization parameters in the simplified approach.The equations were drawn from the relationships between percolation thresholds and direct characterization parameters of different two-dimensional discrete fracture networks;application of these equations in different scaled fracture networks was discussed and validated.The results show that these equations can efficiently predict percolation thresholds of different scaled fracture networks.Based on this result,we developed criteria for estimating connectivity of fracture networks,which provide certain guidance and reference point for the evaluation of underground space in fractured areas.
引文
[1]黄钟,陈珺,石晓冬.北京中心城重点地区地下空间开发利用研究[J].地下空间与工程学报,2006,2(增刊2):1281-1286.
[2]中国工程院课题组.中国城市地下空间开发利用研究[M].北京:中国建筑工业出版社,2001.
[3]童林旭.中国城市地下空间的发展道路[J].地下空间与工程学报,2005,1(1):1-6.
[4]钱七虎.迎接我国城市地下空间开发高潮[J].岩土工程学报,1998,20(1):112-113.
[5]曾联波.低渗透砂岩储层裂缝的形成与分布[M].北京:科学出版社,2008.
[6]冯增朝,赵阳升,吕兆兴.强随机分布裂隙介质的二维逾渗规律研究[J].岩石力学与工程学报,2006,25(增刊2):3904-3908.
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[8] SHOKRI A R,BABADAGLI T,JAFARI A.A critical analysis of the relationship between statistical-and fractalfracture-network characteristics and effective fracture-network permeability[J].SPE Reservoir Evaluation&Engineering,2016,19(3):494-510.
[9] THOVERT J F,MOURZENKO V V,ADLER P M.Percolation in three-dimensional fracture networks for arbitrary size and shape distributions[J].Physical Review E,2017,95(4):42112.
[10] KHAMFOROUSH M,SHAMS K,THOVERT J F,et al.Permeability and percolation of anisotropic three-dimensional fracture networks[J].Physical Review E,2008,77(5):56307.
[11] KHAMFOROUSH M,SHAMS K.Percolation thresholds of agroup of anisotropic three-dimensional fracture networks[J].Physica A:Statistical Mechanics and Its Applications,2007,385(2):407-420.
[12] ZHAO Y,FENG Z,ZHAO X L V,et al.Percolation laws of a fractal fracture-pore double medium[J].Fractals,2016,24(4):1650053.
[13]冯增朝,赵阳升,吕兆兴.二维孔隙裂隙双重介质逾渗规律研究[J].物理学报,2007,56(5):2796-2801.
[14]吕兆兴,冯增朝,赵阳升,等.孔隙裂隙双重介质的三维逾渗数值模拟研究[J].岩土力学,2007(增刊1):291-294.
[15]李乐,李克非.含随机裂纹网络孔隙材料渗透率的逾渗模型研究[J].物理学报,2015,64(13):316-326.
[16] ROBINSON P C.Connectivity of fracture systems:apercolation theory approach[J].Journal of Physics A:Mathematical and General,1983,16(3):605-614.
[17] BOUR O,DAVY P.Connectivity of random fault networks following apower law fault length distribution[J].Water Resources Research,1997,33(7):1567-1583.
[18] MANZOCCHI T.The connectivity of two-dimensional networks of spatially correlated fractures[J].Water Resources Research,2002,38(9):1162.
[19] BARKER J A.Intersection statistics and percolation criteria for fractures of mixed shapes and sizes[J].Computers&Geosciences,2018,112:47-53.
[20] XU C,DOWD P.A new computer code for discrete fracture network modelling[J].Computers&Geosciences,2010,36(3):292-301.
[21]董少群,曾联波,XU C,等.储层裂缝随机建模方法研究进展[J].石油地球物理勘探,2018,53(3):625-641.
[22]董少群,曾联波,曹菡,等.裂缝密度约束的离散裂缝网络建模方法与实现[J].地质论评,2018,64(5):1302-1314.
[23] MARDIA K V,NYIRONGO V B,WALDER A N,et al.Markov Chain Monte Carlo implementation of rock fracture modelling[J].Mathematical Geology,2007,39(4):355-381.
[24] DONG S,ZENG L,DOWD P,et al.A fast method for fracture intersection detection in discrete fracture networks[J].Computers and Geotechnics,2018,98:205-216.
[25] YI Y B,TAWERGHI E.Geometric percolation thresholds of interpenetrating plates in three-dimensional space[J].Physical Review E,2009,79(4):41134.
[2]中国工程院课题组.中国城市地下空间开发利用研究[M].北京:中国建筑工业出版社,2001.
[3]童林旭.中国城市地下空间的发展道路[J].地下空间与工程学报,2005,1(1):1-6.
[4]钱七虎.迎接我国城市地下空间开发高潮[J].岩土工程学报,1998,20(1):112-113.
[5]曾联波.低渗透砂岩储层裂缝的形成与分布[M].北京:科学出版社,2008.
[6]冯增朝,赵阳升,吕兆兴.强随机分布裂隙介质的二维逾渗规律研究[J].岩石力学与工程学报,2006,25(增刊2):3904-3908.
[7] HUNT A G,SAHIMI M.Flow,Transport,and reaction in porous media:percolation scaling,critical-path analysis,and effective medium approximation[J].Reviews of Geophysics,2017,55(4):993-1078.
[8] SHOKRI A R,BABADAGLI T,JAFARI A.A critical analysis of the relationship between statistical-and fractalfracture-network characteristics and effective fracture-network permeability[J].SPE Reservoir Evaluation&Engineering,2016,19(3):494-510.
[9] THOVERT J F,MOURZENKO V V,ADLER P M.Percolation in three-dimensional fracture networks for arbitrary size and shape distributions[J].Physical Review E,2017,95(4):42112.
[10] KHAMFOROUSH M,SHAMS K,THOVERT J F,et al.Permeability and percolation of anisotropic three-dimensional fracture networks[J].Physical Review E,2008,77(5):56307.
[11] KHAMFOROUSH M,SHAMS K.Percolation thresholds of agroup of anisotropic three-dimensional fracture networks[J].Physica A:Statistical Mechanics and Its Applications,2007,385(2):407-420.
[12] ZHAO Y,FENG Z,ZHAO X L V,et al.Percolation laws of a fractal fracture-pore double medium[J].Fractals,2016,24(4):1650053.
[13]冯增朝,赵阳升,吕兆兴.二维孔隙裂隙双重介质逾渗规律研究[J].物理学报,2007,56(5):2796-2801.
[14]吕兆兴,冯增朝,赵阳升,等.孔隙裂隙双重介质的三维逾渗数值模拟研究[J].岩土力学,2007(增刊1):291-294.
[15]李乐,李克非.含随机裂纹网络孔隙材料渗透率的逾渗模型研究[J].物理学报,2015,64(13):316-326.
[16] ROBINSON P C.Connectivity of fracture systems:apercolation theory approach[J].Journal of Physics A:Mathematical and General,1983,16(3):605-614.
[17] BOUR O,DAVY P.Connectivity of random fault networks following apower law fault length distribution[J].Water Resources Research,1997,33(7):1567-1583.
[18] MANZOCCHI T.The connectivity of two-dimensional networks of spatially correlated fractures[J].Water Resources Research,2002,38(9):1162.
[19] BARKER J A.Intersection statistics and percolation criteria for fractures of mixed shapes and sizes[J].Computers&Geosciences,2018,112:47-53.
[20] XU C,DOWD P.A new computer code for discrete fracture network modelling[J].Computers&Geosciences,2010,36(3):292-301.
[21]董少群,曾联波,XU C,等.储层裂缝随机建模方法研究进展[J].石油地球物理勘探,2018,53(3):625-641.
[22]董少群,曾联波,曹菡,等.裂缝密度约束的离散裂缝网络建模方法与实现[J].地质论评,2018,64(5):1302-1314.
[23] MARDIA K V,NYIRONGO V B,WALDER A N,et al.Markov Chain Monte Carlo implementation of rock fracture modelling[J].Mathematical Geology,2007,39(4):355-381.
[24] DONG S,ZENG L,DOWD P,et al.A fast method for fracture intersection detection in discrete fracture networks[J].Computers and Geotechnics,2018,98:205-216.
[25] YI Y B,TAWERGHI E.Geometric percolation thresholds of interpenetrating plates in three-dimensional space[J].Physical Review E,2009,79(4):41134.