Volume 32 Issue 1
Feb.  2026
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ZHANG C X,TANG H Y,TANG Y X,et al.,2026. Study on the influence of in-situ stress changes on shale fracture propagation considering the effect of effective stress coefficients[J]. Journal of Geomechanics,32(1):197−212 doi: 10.12090/j.issn.1006-6616.2025145
Citation: ZHANG C X,TANG H Y,TANG Y X,et al.,2026. Study on the influence of in-situ stress changes on shale fracture propagation considering the effect of effective stress coefficients[J]. Journal of Geomechanics,32(1):197−212 doi: 10.12090/j.issn.1006-6616.2025145

Study on the influence of in-situ stress changes on shale fracture propagation considering the effect of effective stress coefficients

doi: 10.12090/j.issn.1006-6616.2025145
Funds:  This research was financially supported by the General Program of the National Natural Science Foundation of China (Grant No.52374043) and the Sichuan Provincial Natural Science Foundation Program (Grant No. 2026NSFSCZY0097).
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  • Received: 2025-09-30
  • Revised: 2025-11-30
  • Accepted: 2026-01-19
  • Available Online: 2026-01-19
  • Published: 2026-02-27
  •   Objective  The geometry of multi-stage hydraulic fractures in shale gas horizontal wells is influenced by the three-dimensional in-situ stress distribution. The single-well stress profile serves as a crucial basis for predicting fracture height, and both the effective stress coefficient (Biot's coefficient) and the vertical grid resolution significantly impact the interpreted stress profile, consequently affecting the accuracy of fracture height prediction.   Methods  This study employs different Biot's coefficients (constant values and functions varying with logs) and vertical grid resolutions to compute stress profiles. It simulates and analyzes the differences in planar 3D fracture geometries under various stress profiles, systematically investigating the influence of Biot's coefficient on the stress profile and fracture geometry, and subsequently optimizing the vertical grid resolution and the method for interpreting Biot's coefficient.   Results  The results indicate that as Biot's coefficient decreases, the variation amplitude of the vertical in-situ stress profile increases, thereby restricting the vertical propagation capability of hydraulic fractures. Increasing the vertical grid resolution in the fracturing model helps to reduce the influence range of stress extremes; a 1 m vertical grid resolution achieves a favorable balance between simulation efficiency and accuracy. The Biot's coefficients calculated using empirical formulas and the poroelastic model yield similar results, with errors relative to laboratory measurements ranging from 3.68% to 3.93%. These methods provide a better match to stress test results from different formations. Furthermore, the simulated fracture heights using these variable coefficients align more closely with actual downhole fracture height monitoring results compared to using a constant Biot's value, showing errors of 8.64% to 9.94% compared to microseismic monitoring results from a vertical-to-horizontal well at the same site.   Conclusions  Through the analysis of initial in-situ stress fitting accuracy and the subsequent correspondence between simulated fracture height and monitoring data, it can be concluded that selecting an appropriate Biot's coefficient enables more realistic predictions of in-situ stress distribution and fracture propagation geometry. [Significance] This study provides valuable insights for future stress distribution calculations and fracture height predictions in shale gas wells through an in-depth discussion on the effects of Biot's coefficient and vertical grid resolution.

     

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  • [1]
    ALAMEER M, ALMANI T, KHAN K, et al. , 2025. Computational framework to assess the influence of the Biot coefficient on formation breakdown pressures in tight gas formations[C]//Paper presented at the 59th U. S. rock mechanics/geomechanics symposium. Santa Fe: ARMA: ARMA-2025-0314.
    [2]
    ASEM P, TAROKH A, TUROS M, et al. , 2022. Measuring the Biot coefficient for a fluid-saturated crystalline rock[C]//Paper presented at the 56th U. S. rock mechanics/geomechanics symposium. Santa Fe: ARMA: ARMA-2022-0502.
    [3]
    AZADPOUR M, JAVAHERIAN A, SABERI M R, et al., 2022. 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, 211: 110243. doi: 10.1016/j.petrol.2022.110243
    [4]
    BERRYMAN J G, 1992. Effective stress for transport properties of inhomogeneous porous rock[J]. Journal of Geophysical Research: Solid Earth, 97(B12): 17409-17424. doi: 10.1029/92JB01593
    [5]
    BIOT M A, WILLIS D G, 1957. The elastic coefficients of the theory of consolidation[J]. Journal of Applied Mechanics, 24(4): 594-601. doi: 10.1115/1.4011606
    [6]
    BODAGHABADI S, MOOSAVI S J, 2008. A simple practical method to determine the Biot coefficient for hydromechanical analyses[C]//Paper presented at the ISRM international symposium - 5th Asian rock mechanics symposium. Tehran, Iran: ISRM: ISRM-ARMS5-2008-020.
    [7]
    CHENG Y F, CHENG L L, LI H, et al., 2015. Research on testing methods of Biot coefficient in reservoir with different permeability and its influencing factors[J]. Chinese Journal of Rock Mechanics and Engineering, 34(S2): 3998-4004. (in Chinese with English abstract)
    [8]
    COSTA A, CUSINI M, JIN T, et al., 2022. A multi-resolution approach to hydraulic fracture simulation[J]. International Journal of Fracture, 237(1): 165-188. doi: 10.1007/s10704-022-00662-y
    [9]
    DONG Z, TANG S B, RANJITH P G, et al., 2018. A theoretical model for hydraulic fracturing through a single radial perforation emanating from a borehole[J]. Engineering Fracture Mechanics, 196: 28-42. doi: 10.1016/j.engfracmech.2018.04.029
    [10]
    DONTSOV E V, PEIRCE A P, 2015. A non-singular integral equation formulation to analyse multiscale behaviour in semi-infinite hydraulic fractures[J]. Journal of Fluid Mechanics, 781: R1. doi: 10.1017/jfm.2015.451
    [11]
    FILIPPOV D, VASEKIN B, MAKSIMOV D, et al. , 2020. High-resolution hydraulic fracture network modeling on adaptive PEBI grids[C]//Proceedings of the ECMOR XVII. European Association of Geoscientists & Engineers, physical event cancelled: 1-11.
    [12]
    GOKARAJU D, ALDIN M, THOMBARE A, et al. , 2018. A novel method for experimental characterization of the poroelastic constants in unconventional formations[C]//Paper presented at the SPE/AAPG/SEG unconventional resources technology conference. Houston: SPE: URTEC-2902907-MS.
    [13]
    HALL J, ALVAREZ E, 2010. Overcoming the limitations of rock physics modelling in porous rock with complex mineralogy[C]//Paper presented at the SPWLA 51st annual logging symposium. Perth: SPWLA: SPWLA-2010-69661.
    [14]
    HE J, RUI Z H, LING K G, 2016. A new method to determine Biot's coefficients of Bakken samples[J]. Journal of Natural Gas Science and Engineering, 35: 259-264. doi: 10.1016/j.jngse.2016.08.061
    [15]
    JIA L C, 2023. Experimental investigation on dynamic and static Biot coefficients of transversely isotropic shale[J]. Chinese Journal of Rock Mechanics and Engineering, 42(S2): 4130-4139. (in Chinese with English abstract)
    [16]
    KASANI H A, SELVADURAI A P S, 2023. A review of techniques for measuring the Biot coefficient and other effective stress parameters for fluid-saturated rocks[J]. Applied Mechanics Reviews, 75(2): 020801. doi: 10.1115/1.4055888
    [17]
    KIM K, ESPINOZA D N, 2023. Determination of Biot coefficient for low-permeability rocks accounting for undrained loading[C]//Paper presented at the 57th U. S. rock mechanics/geomechanics symposium. Atlanta: ARMA: ARMA-2023-0694.
    [18]
    LI N, CHEN H, ZHANG X M, et al. , 2019. Simultaneous prediction of rock matrix modulus and critical porosity[J]. Applied Geophysics, 16(1): 14-24, 137.
    [19]
    LI Z, LIU H X, LI L, et al. , 2019. Prediction of abnormal pressure in Lingshui deep-water high temperature formation based on improved bowers method[J]. Journal of Xi'an Shiyou University (Natural Science Edition), 34(6): 60-66, 73. (in Chinese with English abstract)
    [20]
    LIU J, HUI C, FAN J M, et al., 2021. Distribution characteristics of the present-day in-situ stress in the Chang 6 tight sandstone reservoirs of the Yanchang Formation in the Heshui Area, Ordos Basin, China and suggestions for development[J]. Journal of Geomechanics, 27(1): 31-39. (in Chinese with English abstract)
    [21]
    MA X D, ZOBACK M D, 2017. Laboratory experiments simulating poroelastic stress changes associated with depletion and injection in low‐porosity sedimentary rocks[J]. Journal of Geophysical Research: Solid Earth, 122(4): 2478-2503. doi: 10.1002/2016JB013668
    [22]
    MAKHNENKO R M, LABUZ J F, 2013. Unjacketed bulk compressibility of sandstone in laboratory experiments[C]//Proceedings of the 5th Biot conference on poromechanics. Vienna: ASCE: 481-488.
    [23]
    MENG W, TIAN T, SUN D S, et al., 2022. Research on stress state in deep shale reservoirs based on in-situ stress measurement and rheological model[J]. Journal of Geomechanics, 28(4): 537-549. (in Chinese with English abstract)
    [24]
    MORSCHBACHER M J, VASQUEZ G F, FIGUEIREDO M P, et al. , 2024. Biot coefficient from sonic logs with laboratory data calibration: a Brazillian pre-salt field case study[C]//Paper presented at the SPWLA 65th annual logging symposium. Rio de Janeiro: SPWLA: SPWLA-2024-0003.
    [25]
    NARASIMHAN S, SHAIKH H, GRAY J K, et al. , 2016. Effect of horizontal stress models and Biot poro-elasticity on predicted fracture geometry[C]//Paper presented at the SPE hydraulic fracturing technology conference. The Woodlands: SPE: SPE-179162-MS.
    [26]
    NERMOEN A, KORSNES R, CHRISTENSEN H F, et al. , 2013. Measuring the Biot stress coefficient and is implications on the effective stress estimate[C]//Paper presented at the 47th U. S. rock mechanics/geomechanics symposium. San Francisco, California: ARMA: ARMA-2013-282.
    [27]
    OKADA Y, 1985. Surface deformation due to shear and tensile faults in a half-space[J]. Bulletin of the Seismological Society of America, 75(4): 1135-1154. doi: 10.1785/BSSA0750041135
    [28]
    QIAO L P, WONG R C K, AGUILERA R, et al., 2012. Determination of Biot's effective-stress coefficient for permeability of Nikanassin sandstone[J]. Journal of Canadian Petroleum Technology, 51(3): SPE-150820-PA.
    [29]
    SALEMI H, NOURIFARD N, IGLAUER S, et al. , 2020. Acoustic approach to determine Biot effective stress coefficient of sandstone using true triaxial cell (TTSC)[C]//Paper presented at the 54th U. S. rock mechanics/geomechanics symposium. ARMA, physical event cancelled: ARMA-2020-1048.
    [30]
    SUN D S, PANG F, LI A W, et al., 2020. In-situ stress profile prediction based on the rheological model: a case study of Well AY-1 in the Qianbei area of Guizhou Province[J]. Natural Gas Industry, 40(3): 58-64. (in Chinese with English abstract)
    [31]
    TANG H Y, WINTERFELD P H, WU Y S, et al., 2016. Integrated simulation of multi-stage hydraulic fracturing in unconventional reservoirs[J]. Journal of Natural Gas Science and Engineering, 36: 875-892. doi: 10.1016/j.jngse.2016.11.018
    [32]
    TERZAGHI K V, 1966. The shearing resistance of saturated soils and the angle between the planes of shear[C]//Proceedings of the 1st international conference on soil mechanics and foundation engineering. Harvard: ISRM: ISRM-1CONGRESS-1966-061.
    [33]
    VASQUEZ G F, MORSCHBACHER M J, JUSTEN J C R, et al. , 2025. Biot Coefficient from well logs with lab calibration: a Brazilian pre-salt case study[C]//Paper presented at the 59th U. S. rock mechanics/geomechanics symposium. Santa Fe: ARMA: ARMA-2025-0762.
    [34]
    XIA H Q, PENG M, SONG E C, 2019. Calculating method and application of rock anisotropic Biot coefficient[J]. Well Logging Technology, 43(5): 478-483. (in Chinese with English abstract)
    [35]
    YANG Q, LI J C, LI L, et al. , 2023. Deep coal seam in-situ stress evaluation through the integration of sonic logging and micro-indentation methods[C]//Paper presented at the 57th U. S. rock mechanics/geomechanics symposium. Atlanta: ARMA: ARMA-2023-0250.
    [36]
    ZENG Q D, YAO J, SHAO J F, 2019. Study of hydraulic fracturing in an anisotropic poroelastic medium via a hybrid EDFM-XFEM approach[J]. Computers and Geotechnics, 105: 51-68. doi: 10.1016/j.compgeo.2018.09.010
    [37]
    ZHENG J, HE Y S, WANG Y, et al., 2024. Propagation and optimization of complex fractures of shale gas wells based on FEM-DFN: taking horizontal well group X1 in Changning shale gas reservoir as an example[J]. Fault-Block Oil & Gas Field, 31(3): 415-423. (in Chinese with English abstract)
    [38]
    ZHOU X J, VACHAPARAMPIL A, GHASSEMI A, 2015. A combined method to measure Biot’s coefficient for rock[C]//Paper presented at the 49th U. S. rock mechanics/geomechanics symposium. San Francisco: ARMA: ARMA-2015-584.
    [39]
    ZHU W Y, MA D X, 2018. Effective stress characteristics in shale and its effect on productivity[J]. Natural Gas Geoscience, 29(6): 845-852. (in Chinese with English abstract) doi: 10.1016/j.jnggs.2018.12.001
    [40]
    ZOBACK M D, 2010. Reservoir geomechanics[M]. Cambridge: Cambridge University Press.
    [41]
    ZOU X J, CHEN Y L, 2018. Geostress logging evaluation method of Longmaxi Formation shale in Fuling area based on transversely isotropic model, Sichuan Basin[J]. Natural Gas Geoscience, 29(12): 1775-1780, 1808. (in Chinese with English abstract)
    [42]
    程远方, 程林林, 黎慧, 等, 2015. 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, 34(S2): 3998-4004. doi: 10.13722/j.cnki.jrme.2014.1212
    [43]
    贾利春, 2023. 横观各向同性页岩动、静态有效应力系数试验研究[J]. 岩石力学与工程学报, 42(S2): 4130-4139. doi: 10.13722/j.cnki.jrme.2022.1143
    [44]
    李中, 刘和兴, 李磊, 等, 2019. 基于改进的Bowers法预测南海陵水深水高温地层异常压力[J]. 西安石油大学学报(自然科学版), 34(6): 60-66, 73.
    [45]
    刘建, 惠晨, 樊建明, 等, 2021. 鄂尔多斯盆地合水地区长6致密砂岩储层现今地应力分布特征及其开发建议[J]. 地质力学学报, 27(1): 31-39.
    [46]
    孟文, 田涛, 孙东生, 等, 2022. 基于原位地应力测试及流变模型的深部泥页岩储层地应力状态研究[J]. 地质力学学报, 28(4): 537-549.
    [47]
    孙东生, 庞飞, 李阿伟, 等, 2020. 基于流变模型的地应力剖面预测: 以贵州黔北地区安页1井为例[J]. 天然气工业, 40(3): 58-64. doi: 10.3787/j.issn.1000-0976.2020.03.007
    [48]
    夏宏泉, 彭梦, 宋二超, 2019. 岩石各向异性Biot系数的获取方法及应用[J]. 测井技术, 43(5): 478-483. doi: 10.16489/j.issn.1004-1338.2019.05.007
    [49]
    郑健, 何永生, 汪勇, 等, 2024. 基于FEM-DFN的页岩气井复杂裂缝扩展与优化: 以长宁页岩气藏X1水平井组为例[J]. 断块油气田, 31(3): 415-423. doi: 10.6056/dkyqt202403007
    [50]
    朱维耀, 马东旭, 2018. 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, 29(6): 845-852. doi: 10.11764/j.issn.1672-1926.2018.05.018
    [51]
    邹贤军, 陈亚琳, 2018. 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, 29(12): 1775-1780, 1808. doi: 10.11764/j.issn.1672-1926.2018.10.017
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