济阳拗陷页岩储层水平井裂缝扩展数值模拟
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摘要
由于物理实验受到实验条件、数量的限制,难以对裂缝扩展规律开展大规模的研究。因此,在有了一定的岩石力学测试、页岩压裂破裂方式测试以及页岩压裂裂缝扩展物模试验的基础上,开展了页岩压裂裂缝起裂及扩展规律数值模拟研究。基于流固耦合Biot固结理论、Darcy渗流定律,采用最大拉伸强度准则和Mohr Coulomb准则损伤阈值进行单元损伤判断,引入全新的材料分布算法,建立了水力压裂裂缝扩展的有限元计算模型。进行了岩石样本的参数标定试验。采用有限元计算方法研究了地应力、页岩脆性指数、压裂液黏度和层理特征等关键物理参数对页岩裂缝扩展的影响。结果表明,当脆性指数较小时,水力裂缝主要沿最大主应力方向在页岩基质中扩展,难以转向形成复杂缝网。层理胶结强度较高时,水力作用即便在局部压开天然层理,也难以持续以大角度偏离,而只能形成比较单一的裂缝。地应力比、压裂液黏度越低,层理密度等特性越高时,裂纹网络越复杂。
Physical experiments are limited by experimental conditions and the number of experimental samples available. Thus,it is difficult to conduct large-scale studies on fracture propagation patterns. Hence, a numerical simulation study on fracture initiation and propagation patterns during hydraulic fracturing of shales is conducted based on certain mechanical tests of rocks,rupture tests on hydraulic fracturing of shales, and physical model tests on fracture propagation during hydraulic fracturing of shales. Based on fluid-solid coupling through Biot′s consolidation theory and Darcy′s seepage law, the maximum tensile strength criterion, and the Mohr-Coulomb criterion as a damage threshold for damage determination of units, a new material distribution algorithm is introduced to construct a finite element calculation model of fracture propagation during hydraulic fracturing. Parameter calibration tests were performed on rock samples, and the influences of key physical parameters on fracture propagation in shales were investigated through the finite element calculation method. The key physical parameters are ground stresses, brittleness indices of shales, the viscosity of fracturing fluids, and bedding characteristics. The general view is that when brittleness indices are small, hydraulic fractures propagate in the shale matrix mostly along the direction of the maximum principal stress. The fractures hardly change direction to form a complex network of fractures. For highly cemented beds, hydraulic actions cannot deviate at a large angle continuously, even in partially open natural beds, and thus form only relatively uniform fractures. Fracture networks become more complex when ground stress ratios and the viscosity of fracturing fluids are lower, and bedding densities are higher.
Physical experiments are limited by experimental conditions and the number of experimental samples available. Thus,it is difficult to conduct large-scale studies on fracture propagation patterns. Hence, a numerical simulation study on fracture initiation and propagation patterns during hydraulic fracturing of shales is conducted based on certain mechanical tests of rocks,rupture tests on hydraulic fracturing of shales, and physical model tests on fracture propagation during hydraulic fracturing of shales. Based on fluid-solid coupling through Biot′s consolidation theory and Darcy′s seepage law, the maximum tensile strength criterion, and the Mohr-Coulomb criterion as a damage threshold for damage determination of units, a new material distribution algorithm is introduced to construct a finite element calculation model of fracture propagation during hydraulic fracturing. Parameter calibration tests were performed on rock samples, and the influences of key physical parameters on fracture propagation in shales were investigated through the finite element calculation method. The key physical parameters are ground stresses, brittleness indices of shales, the viscosity of fracturing fluids, and bedding characteristics. The general view is that when brittleness indices are small, hydraulic fractures propagate in the shale matrix mostly along the direction of the maximum principal stress. The fractures hardly change direction to form a complex network of fractures. For highly cemented beds, hydraulic actions cannot deviate at a large angle continuously, even in partially open natural beds, and thus form only relatively uniform fractures. Fracture networks become more complex when ground stress ratios and the viscosity of fracturing fluids are lower, and bedding densities are higher.
引文
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[15]张汝生,王强,张祖国,等.水力压裂裂缝三维扩展ABAQUS数值模拟研究[J].石油钻采工艺,2012(6):69-72. doi:10.13639/j.odpt.2012.06.024ZHANG Rusheng,WANG Qiang,ZHANG Zuguo, et al.Research of ABAQUS numerical simulation of 3D fracture propagation in hydraulic fracturing process[J]. Oil Drilling&Production Technology, 2012(6):69-72. doi:10.13639/j.odpt.2012.06.024
[16]曾青冬,姚军,孙致学.页岩气藏压裂缝网扩展数值模拟[J].力学学报,2015,47(5):994-999. doi:10.-6052/0459-1879-15-014ZENG Qingdong, YAO Jun, SUN Zhixue. Numerical modeling of fracture network propagation in shale reservoirs[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5):994-999. doi:10.6052/0459-1879--15-014
[17]曾青冬,姚军.基于扩展有限元的页岩水力压裂数值模拟[J].应用数学和力学,2014, 35(11):1239-1248.doi:10.3789/j.jssn.1000-0887.2014.11.007ZENG Qingdong, YAO Jun. Numerical simulation of shale hydraulic fracturing based on the extended finite element method[J]. Applied Mathematics and Mechanics,2014,35(11):1239-1248. doi:10.3789/j.jssn. 1000-0887.-2014.11.007
[18] GORDELIY E, PEIRCE A. Coupling schemes for modeling hydraulic fracture propagation using the XFEM[J].Computer Methods in Applied Mechanics&Engineering,2013, 253(1):305-322. doi:10.1016/j.cma.2102.08.017
[19] TALEGHANI A D. Analysis of hydraulic fracture propagation in fractured reservoirs:An improved model for the interaction between induced and natural fractures[D].Austin:University of Texas at Austin, 2009.
[20] REN Q W, DONG Y W, YU T T. Numerical modeling of concrete hydraulic fracturing with extended finite element method[J]. Science in China Series E:Technological Sciences, 2009, 52(3):559-565. doi:10.1007/s11431-009--0058-8
[21] LECAMPION B. An extended finite element method for hydraulic fracture problems[J]. Communications in Numerical Methods in Engineering, 2009, 25(2):121-133.doi:10.1002/cnm.1111
[22] OLSON J E, TALEGHANI A D. Modeling simultaneous growth of multiple hydraulic fractures and their interaction with natural fractures[C]. Society of Petroleum Engineers,2009. doi:10.2118/119739-MS
[23]曾青冬,姚军.水平井多裂缝同步扩展数值模拟[J].石油学报,2015,36(12):1571-1579.doi:10.-7623/syxb201512012ZENG Qingdong,YAO Jun. Numerical simulation of multiple fractures simultaneous propagation in horizontal wells[J]. Acta Petrolei Sinica, 2015, 36(12):1571-1579.doi:10.7623/syxb201512012
[2]刘玉章,杨立峰,王欣,等.页岩气水力压裂裂缝缝网完善程度概论[J].天然气工业,2017, 37(7):34-39.doi:10.3787/j.issn.1000-0976.2017.07.005 LIU Yuzhang,YANG Lifeng, WANG Xin, et al. Introduction to the completion degree of hydraulic fracture networks in shale gas reservoirs[J]. Natural Gas Industry, 2017, 37(7):34-39.doi:10.3787/j.issn.1000-0976.2017.07.005
[3]姚军,孙海,黄朝琴,等.页岩气藏开发中的关键力学问题[J].中国科学:物理学力学天文学,2013,43(12):1527-1547. doi:10.1360/132013-97YAO Jun, SUN Hai, HUANG Zhaoqin, et al. Key mechanical problems in the development of shale gas reservoirs[J]. Scientia Sinica Physica, Mechanica&Astronomica, 2013,43(12):1527-1547. doi:10.1360/132013-97
[4] MAYERHOFER M J,LOLON E,WARPINSKI N R,et al. What is stimulated reservoir volume?[J]. SPE Production&Operations, 2010, 25(1):89-98. doi:10.-2118/119890-PA
[5]郭建春,苟波,任山,等.川西页岩一砂岩交互水平井压裂参数优化设计[J].石油学报,2014, 35(3):511-518. doi:10.7623/syxb201403013GUO Jianchun,GOU Bo,REN Shan, et al. Fracturing parameters optimization design for horizontal well with shale and sandstone in terbeds in Western Sichuan[J].Acta Petrolei Sinica, 2014, 35(3):511-518. doi:10.-7623/syxb201403013
[6] GEERTSMA J, KLERK F D. A rapid method of predicting width and extent of hydraulically induced fractures[J]. Journal of Petroleum Technology, 1969, 21(12):1571-1581. doi:10.2118/2458-PA
[7] PERKINS T K, KERN L R. Widths of hydraulic fractures[C]. SPE 89-PA, 1961. doi:10.2118/89-PA
[8] NORDGREN R P. Propagation of a vertical hydraulic fracture[J]. Society of Petroleum Engineers Journal, 1972,12(4):306-314. doi:10.2118/3009-PA
[9] XU W,THIERCELIN M J,GANGULY U,et al.Wiremesh:A novel shale fracturing simulator[C]. International Oil and Gas Conference and Exhibition in China,2010. doi:10.2118/132218-MS
[10] WENG X,KRESSE O, COHEN C E,et al. Modeling of hydraulic fracture network propagation in a naturally fractured formation[J]. SPE Production&Operations, 2011,26(4):368-380. doi:10.2118/140253-MS
[11]时贤,程远方,蒋恕,等.页岩储层裂缝网络延伸模型及其应用[J].石油学报,2014, 35(6):1130-1137. doi:10.7623/syxb201406010SHI Xian, CHENG Yuanfang, JIANG Shu, et al. Simulation of complex fracture network propagation and its application for shale gas reservoir[J]. Acta Petrolei Sinica,2014,35(6):1130-1137. doi:10.7623/syxb201406010
[12] FU P, JOHNSON S M, CARRIGAN C R. An explicitly coupled hydro-geomechanical model for simulatinghydraulic fracturing in arbitrary discrete fracture networks[J]. International Journal for Numerical&Analytical Methods in Geomechanics, 2014,37(14):2278-2300.doi:10.1002/nag.2135
[13]连志龙,张劲,吴恒安,等.水力压裂扩展的流固耦合数值模拟研究[J].岩土力学,2008,29(11):3021-3026.doi:10.16285/j.rsm.2008.11.003LIAN Zhilong, ZHANG Jin, WU Heng'an, et al. A simulation study of hydraulic fracturing propagation with a solidfluid coupling model[J]. Rock and Soil Mechanics, 2008,29(11):3021-3026. doi:10.16285/j.rsm.2008.11.003
[14]薛炳,张广明,吴恒安,等.油井水力压裂的三维数值模拟[J].中国科学技术大学学报,2008, 38(11):1322-1325, 1347.XUE Bing, ZHANG Guangming, WU Heng'an, et al.Three-dimensional numerical simulation of hydraulic fracture in oil wells[J]. Journal of University of Science and Technology of China, 2008,38(11):1322-1325,1347.
[15]张汝生,王强,张祖国,等.水力压裂裂缝三维扩展ABAQUS数值模拟研究[J].石油钻采工艺,2012(6):69-72. doi:10.13639/j.odpt.2012.06.024ZHANG Rusheng,WANG Qiang,ZHANG Zuguo, et al.Research of ABAQUS numerical simulation of 3D fracture propagation in hydraulic fracturing process[J]. Oil Drilling&Production Technology, 2012(6):69-72. doi:10.13639/j.odpt.2012.06.024
[16]曾青冬,姚军,孙致学.页岩气藏压裂缝网扩展数值模拟[J].力学学报,2015,47(5):994-999. doi:10.-6052/0459-1879-15-014ZENG Qingdong, YAO Jun, SUN Zhixue. Numerical modeling of fracture network propagation in shale reservoirs[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5):994-999. doi:10.6052/0459-1879--15-014
[17]曾青冬,姚军.基于扩展有限元的页岩水力压裂数值模拟[J].应用数学和力学,2014, 35(11):1239-1248.doi:10.3789/j.jssn.1000-0887.2014.11.007ZENG Qingdong, YAO Jun. Numerical simulation of shale hydraulic fracturing based on the extended finite element method[J]. Applied Mathematics and Mechanics,2014,35(11):1239-1248. doi:10.3789/j.jssn. 1000-0887.-2014.11.007
[18] GORDELIY E, PEIRCE A. Coupling schemes for modeling hydraulic fracture propagation using the XFEM[J].Computer Methods in Applied Mechanics&Engineering,2013, 253(1):305-322. doi:10.1016/j.cma.2102.08.017
[19] TALEGHANI A D. Analysis of hydraulic fracture propagation in fractured reservoirs:An improved model for the interaction between induced and natural fractures[D].Austin:University of Texas at Austin, 2009.
[20] REN Q W, DONG Y W, YU T T. Numerical modeling of concrete hydraulic fracturing with extended finite element method[J]. Science in China Series E:Technological Sciences, 2009, 52(3):559-565. doi:10.1007/s11431-009--0058-8
[21] LECAMPION B. An extended finite element method for hydraulic fracture problems[J]. Communications in Numerical Methods in Engineering, 2009, 25(2):121-133.doi:10.1002/cnm.1111
[22] OLSON J E, TALEGHANI A D. Modeling simultaneous growth of multiple hydraulic fractures and their interaction with natural fractures[C]. Society of Petroleum Engineers,2009. doi:10.2118/119739-MS
[23]曾青冬,姚军.水平井多裂缝同步扩展数值模拟[J].石油学报,2015,36(12):1571-1579.doi:10.-7623/syxb201512012ZENG Qingdong,YAO Jun. Numerical simulation of multiple fractures simultaneous propagation in horizontal wells[J]. Acta Petrolei Sinica, 2015, 36(12):1571-1579.doi:10.7623/syxb201512012