Abstract：It is practically important for geomechanical modeling and wellbore stability analysis to obtain Biot coefficient of transverse isotropic shale accurately and efficiently. The dynamic and static Biot coefficient and elastic stiffness coefficient of marine-facies Longmaxi black shale in the South Sichuan Basin are investigated by using acoustic measurement and conventional triaxial compression in this study. The main results are as follows：The dynamic and static elastic stiffness coefficients，Young?s modulus both increase with confining pressure，and the dynamic value is higher than the corresponding static value. The value of Young?s modulus parallel to bedding is higher than that of perpendicular to bedding. However，the dynamic and static Poisson?s ratio has no significant rule with the increase of confining pressure and the change of bedding. In addition，the dynamic and static Biot coefficients decrease with confining pressure. And the Biot coefficients perpendicular to bedding are higher than those parallel to bedding. On the other hand，the static Biot coefficients are higher than the dynamic results. Finally the fitting analysis shows that there is a linear conversion relationship between dynamic and static Biot coefficients and Young?s modulus，respectively. The obtained anisotropic characteristics of Biot coefficient and the dynamic to static conversion relationship play an indispensable role in the geomechanical analysis in drilling and completion of shale.
[1] MAVKO G，MUKERJI T，DVORKIN J. The rock physics handbook: Tools for seismic analysis of porous media[M]. New York，USA：Cambridge University Press，2009：56–58.
[2] 葛洪魁，韩德华，陈 颙. 砂岩孔隙弹性特性的试验研究[J]. 岩石力学与工程学报，2001，20(3)：332–337.(GE Hongkui，HAN Dehua，CHEN Yong. Experimental investigation on poroelasticity of sandstones[J]. Chinese Journal of Rock Mechanics and Engineering，2001，20(3)：332–337.(in Chinese))
[3] 高 涛，郭 肖，孟文辉，等. 特低渗透砂岩有效应力系数测定[J]. 西安石油大学学报：自然科学版，2014，29(4)：46–49.(GAO Tao，GUO Xiao，MENG Wenhui，et al. Measurement of effective stress coefficient of ultra-low permeability sandstone[J]. Journal of Xi'an Shiyou University：Natural Science，2014，29(4)：46–49.(in Chinese))
[4] MORTEZA A，ABDOLRAHIM J，MOHAMMAD R S，et al. Rock physics model-based investigation on the relationship between static and dynamic Biot?s coefficients in carbonate rocks[J]. Journal of Petroleum Science and Engineering，2022，211(4)：110243.
[5] PARTHA P M，JOEL S，REZA R. Geomechanical appraisal and prospectivity analysis of the Goldwyer shale accounting for stress variation and formation anisotropy[J]. International Journal of Rock Mechanics and Mining Sciences，2020，135(11)：104513.
[6] 李忠平，周 文，谢润成，等. Biot系数非线性解释初探及其在井壁稳定性分析中的应用[J]. 石油钻采工艺，2012，34(1)：39–42.(LI Zhongping，ZHOU Wen，XIE Runcheng，et al. Preliminary study on non-liner interpretation of Biot coefficient of rock and its application on the analysis of wellbore stability[J]. Oil Drilling and Production Technology，2012，34(1)：39–42.(in Chinese))
[7] 程远方，程林林，黎 慧，等. 不同渗透性储层Biot系数测试方法研究及其影响因素分析[J]. 岩石力学与工程学报，2015，34(增2)： 3 998–4 004.(CHENG Yuanfang，CHENG Linlin，LI Hui，et al. Research on testing methods of Biot coefficient in reservoir with different permeability and its influencing factors[J]. Chinese Journal of Rock Mechanics and Engineering，2015，34(Supp.2)：3 998– 4 004.(in Chinese))
[8] 张保平，申卫兵，单文文. 岩石弹性模量与毕奥特(Biot)系数在压裂设计中的应用[J]. 石油钻采工艺，1996，18(3)：60–65.(ZHANG Baoping，SHEN Weibing，SHAN Wenwen. Applications of elastic modulus and Biot coefficient of rock in fracturing design[J]. Oil Drilling and Production Technology，1996，18(3)：60–65.(in Chinese))
[9] 王 斌，赵建国，李 伟，等. 异常高压对砂砾岩弹性性质影响的实验机理研究与压力预测新模型——以准噶尔盆地玛湖凹陷北斜坡三叠系为例[J]. 地球物理学报，2022，65(8)：3 157–3 171.(WANG Bin，ZHAO Jianguo，LI Wei，et al. Experimental study on the effect of abnormal high pressure on the elastic properties of glutenite and a novel pressure prediction model：a case study from Triassic Formation in north slope of Mahu Sag，Junggar Basin[J]. Chinese Journal of Geophysics，2022，65(8)：3 157–3 171.(in Chinese))
[10] 印兴耀，刘欣欣，曹丹平. 基于Biot相洽理论的致密砂岩弹性参数计算方法[J]. 石油物探，2013，52(5)：445–451.(YIN Xingyao，LIU Xinxin，CAO Danping. Elastic parameters calculation for tight sand reservoir based on Biot-consistent theory[J]. Geophysical Prospecting for Petroleum，2013，52(5)：445–451.(in Chinese))
[11] 马中高. Biot系数和岩石弹性模量的实验研究[J]. 石油与天然气地质，2008，29(1)：135–140.(MA Zhonggao. Experimental investigation into Biot?s coefficient and rock elastic moduli[J]. Oil and Gas Geology，2008，29(1)：135–140.(in Chinese))
[12] 王鸿升. 根据纵波速度估算多岩性有效应力系数[C]// 中国石油学会2021年物探技术研讨会论文集. 北京：《中国学术期刊(光盘版)》电子杂志社有限公司，2021：1 158–1 161.(WANG Hongsheng Estimation of effective stress coefficient of multiple lithology based on longitudinal wave velocity[C]// Proceedings of 2021 Geophysical Prospecting Technology Seminar of Chinese Petroleum Society. Beijing：China Academic Journals(CD Edition)Electronic Publishing House，2021：1 158–1 161.(in Chinese))
[13] ZHOU X J，VACHAPARAMPIL A，GHASSEMI A. A combined method to measure Biot?s coefficient for Rock[C]// 47th US Rock Mechanics/Geomechanics Symposium. San Francisco，USA：American Rock Mechanics Association，2015：1–9.
[14] MOHAMMAD M A，HELLE F C，IDA L F. Effective stress coefficient and Biot's coefficient of Chalk from the Valhall Field，North Sea[C]// 2009 SPE EUROPEC/EAGE Annual Conference and Exhibition. Amsterdam，Netherlands：Society of Petroleum Engineers，2009：1–8.
[15] 徐 欣，王 伟，胡明毅，等. 中孔中渗砂岩储层Biot系数测试方法对比研究[J]. 石油钻探技术，2018，46(2)：109–114.(XU Xin，WANG Wei，HU Mingyi，et al. Comparison and study over the Biot coefficients test methods in medium porosity and medium permeability sandstone reservoirs[J]. Petroleum Drilling Techniques，2018，46(2)：109–114.(in Chinese))
[16] ASADOLLAHPOUR E，EZAZI M，MOSTAFAVI I，et al. Biot?s coefficient determination of carbonate reservoir rocks by using static and dynamic experimental tests at ambient and reservoir temperatures -A case study from Iran carbonate field[J]. Journal of Petroleum Science and Engineering，2021，196(1)：108061.
[17] MOHAMMAD M A，MAI K B，IDA L F，et al. Biot's coefficient as an indicator of strength and porosity reduction：Calcareous sediments from Kerguelen Plateau[J]. Journal of Petroleum Science and Engineering，2010，70(3)：282–297.
[18] STEFFEN N，REINHARD F，BERNHARD M K，et al. Simultaneous determination of the effective stress coefficients for permeability and volumetric strain on a tight sandstone[J]. Journal of Natural Gas Science and Engineering，2021，95(11)：104186.
[19] CHEN Z W，PAN Z J，LIU J S，et al. Effect of the effective stress coefficient and sorption-induced strain on the evolution of coal permeability：experimental observations[J]. International Journal of Greenhouse Gas Control，2011，5(5)：1 284–1 293.
[20] HAN J，WU C F，JIANG X M，et al. Investigation on effective stress coefficients and stress sensitivity of different water-saturated coals using the response surface method[J]. Fuel，2022，316(5)：123238.
[21] 乔丽苹，王者超，李术才. 基于Tight gas致密砂岩储层渗透率的有效应力特性研究[J]. 岩石力学与工程学报，2011，30(7)：1 422– 1 427.(QIAO Liping，WANG Zhechao，LI Shucai. Effective stress law for permeability of tight gas reservoir sandstone[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(7)：1 422–1 427.(in Chinese))
[22] 丁艳艳，李 闽，肖文联. 围压对低渗砂岩渗透率有效应力系数的影响[J]. 地球物理学进展，2012，27(2)：696–701.(DING Yanyan，LI Min，XIAO Wenlian. The effect of confining pressure on effective pressure coefficient for permeability in low-permeability sandstones[J]. Progress in Geophysical，2012，27(2)：696–701.(in Chinese))
[23] 孟范宝. 特低渗透岩石孔隙弹塑性变形与有效应力系数的实验研究[博士学位论文][D]. 北京：中国石油大学(北京)，2018.(MENG Fanbao. Experimental research on pore elasto-plastic deformation and effective stress coefficient of ultra-low permeability rock[Ph. D. Thesis][D]. Beijing：China University of Petroleum(Beijing)，2018.(in Chinese))
[24] 尹 帅，丁文龙，王濡岳，等. 海陆过渡相致密砂岩储层Biot系数自适应预测方法研究[J]. 石油物探，2016，55(6)：861–868.(YIN Shuai，DING Wenlong，WANG Ruyue，et al. A new prediction method of Biot coefficient for marine-land transition phase tight sandstone reservoir based on the self-adapt method[J]. Geophysical Prospecting for Petroleum，2016，55(6)：861–868.(in Chinese))
[25] SALEMI H，YURIKOV A，LEBEDEV M，et al. A novel approach to determine the Biot?s coefficient using X?ray computed tomography[J]. Bulletin of Engineering Geology and the Environment，2021，80(10)： 7 865–7 877.
[26] AMIRI M，LASHKARIPOUR G R，GHABEZLOO S，et al. 3D spatial model of Biot?s effective stress coefficient using well logs，laboratory experiments，and geostatistical method in the Gachsaran oil field，southwest of Iran[J]. Bulletin of Engineering Geology and the Environment，2019，78(9)：4 633–4 646.
[27] DASSANAYAKE A B N，FUJII Y，FUKUDA D，et al. A new approach to evaluate effective stress coefficient for strength in Kimachi sandstone[J]. Journal of Petroleum Science and Engineering，2015，131(7)：70–79.
[28] HE J，RUI Z H，LING K G. A new method to determine Biot?s coefficients of Bakken samples[J]. Journal of Natural Gas Science and Engineering，2016，35(9)：259–264.
[29] LUO X，WERE P，LIU J F，et al. Estimation of Biot?s effective stress coefficient from well logs[J]. Environmental earth sciences，2015，73(11)：7 019–7 028.
[30] OLSEN C，HEDEGAARD K，FABRICIUS I L，et al. Prediction of Biot?s coefficient from rock-physical modeling of North Sea chalk[J]. Geophysics，2008，73(2)：89–96.
[31] LV A，AGHIGHI M A，MASOUMI H，et al. The effective stress coefficient of coal：a theoretical and experimental investigation[J]. Rock Mechanics and Rock Engineering，2021，54(8)：3 891–3 907.
[32] VOROBIEV S，VOROBYEV V，LUKIN S，et al. Evaluation of Biot?s coefficient using sonic logs and elastic moduli minimization[C]// International Petroleum Technology Conference. Riyadh，Saudi Arabia：Society of Petroleum Engineers，2022：1–11.
[33] CIVAN F. Effective-stress coefficients of porous rocks involving shocks and loading/unloading hysteresis[J]. SPE Journal，2021，26(1)：44–67.
[34] 唐 杰. 各向异性岩石的静态模量与动态模量实验研究[J]. 岩石力学与工程学报，2014，33(增1)：3 185–3 191.(TANG Jie. Experimental study of static and dynamic moduli for anisotropic rock[J]. Chinese Journal of Rock Mechanics and Engineering，2014，33(Supp.1)：3 185–3 191.(in Chinese))
[35] LING K G，HE J，PEI P，et al. Comparisons of Biot?s coefficients of Bakken core samples measured by three methods[C]// 50th US Rock Mechanics/Geomechanics Symposium. Houston，USA：American Rock Mechanics Association，2016：1–13.
[36] SAURABH S，HARPALANI S. The effective stress law for stress-sensitive transversely isotropic rocks[J]. International Journal of Rock Mechanics and Mining Sciences，2018，101(1)：69–77.
[37] 朱维耀，马东旭. 页岩储层有效应力特征及其对产能的影响[J]. 天然气地球科学，2018，29(6)：845–852.(ZHU Weiyao，MA Dongxu. Effective stress characteristics in shale and its effect on productivity[J]. Natural Gas Geoscience，2018，29(6)：845–852.(in Chinese))
[38] 夏宏泉，彭 梦，宋二超. 岩石各向异性Biot系数的获取方法及应用[J]. 测井技术，2019，43(5)：478–483.(XIA Hongquan，PENG Meng，SONG Erchao. Calculating method and application of rock anisotropic Biot coefficient[J]. Well Logging Technology，2019，43(5)：478–483. (in Chinese))
[39] ZHOU X J，GHASSEMI A. Biot?s effective stress coefficient tensor measurements on Mancos shale[C]// 53rd US Rock Mechanics/ Geomechanics Symposium. New York，USA：American Rock Mechanics Association，2019：1–14.
[40] 邹贤军，陈亚琳. 四川盆地涪陵地区龙马溪组页岩横向各向同性地应力测井评价方法[J]. 天然气地球科学，2018，29(12)：1 775– 1 780.(ZOU Xianjun，CHEN Yalin. Geostress logging evaluation method of Longmaxi Formation shale in Fuling area based on transversely isotropic model，Sichuan Basin[J]. Natural Gas Geoscience，2018，29(12)：1 775–1 780.(in Chinese))
[41] 宋连腾，刘忠华，李潮流，等. 基于横向各向同性模型的致密砂岩地应力测井评价方法[J]. 石油学报，2015，36(6)：707–714.(SONG Lianteng，LIU Zhonghua，LI Chaoliu，et al. Geostress logging evaluation method of tight sandstone based on transversely isotropic model[J]. Acta Petrolei Sinica，2015，36(6)：707–714.(in Chinese))
[42] 时 贤，程远方，常 鑫，等. 缺失声波条件下的页岩储层地应力测井解释方法[J]. 天然气工业，2014，34(12)：55–62.(SHI Xian，CHENG Yuanfang，CHANG Xin，et al. Calculation of the anisotropic in-situ stress for shale gas reservoirs with the absence of sonic log data[J]. Natural Gas Industry，2014，34(12)：55–62.(in Chinese))
[43] CRAWFORD B，LIANG Y M，GAILLOT P，et al. Determining static elastic anisotropy in shales from sidewall cores: impact on stress prediction and hydraulic fracture modeling[C]// Unconventional Resources Technology Conference. Austin，USA：Society of Petroleum Engineers，2020：1–18.
[44] ADERIBIGBE A，VALDES C C，HEIDARI Z. Integrated rock classification in the Wolfcamp Shale based on reservoir quality and anisotropic stress profile estimated from well logs[J]. Interpretation，2016，4(2)：SF1–SF18.
[45] MASSARO A S，ESPINOZA D N，FRYDMAN M，et al. Analyzing a suitable elastic geomechanical model for Vaca Muerta Formation[J]. Journal of South American Earth Sciences，2017，79(12)：472–488.
2023, Vol. 42 
