Skip to main content

Integrated Experimental and Computational Characterization of Shale at Multiple Length Scales

  • Chapter
  • First Online:
New Frontiers in Oil and Gas Exploration

Abstract

Shale is known as a hydrocarbon source rock and is emerging as a potentially key component of the worldwide energy landscape via the recent development of hydraulic fracturing technique. A fundamental understanding of the fracturing behaviors of intact shale is the basis of any technological innovation aiming at increasing extraction efficiency. Considering the highly heterogeneous and fine-grained nature of shale, investigation and characterization should be conducted at multiple length scales. Through a brief overview of the experimental and computational studies for mechanical characterization of shale at different scales, this study investigates the possibility of integrating experimental and computational characterization research into a unified multiscale framework. Such multiscale framework is needed to predict macroscale shale fracturing behavior from the microscopic events. As preliminary results, an experimental characterization campaign of Marcellus shale at the macroscopic level and a micromechanical discrete model for predicting the mechanical behaviors of anisotropic shale are also presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Dormieux, L., & Ulm, F.-J. (2005). Applied micromechanics of porous materials. Vienna: Springer.

    Book  MATH  Google Scholar 

  2. Gale, J. F. W., Laubach, S. E., Olson, J. E., Eichhubl, P., & Fall, A. (2014). Natural fractures in shale: A review and new observations. AAPG Bulletin, 98, 2165–2216. doi:10.1306/08121413151.

    Article  Google Scholar 

  3. Koesoemadinata, A., El-Kaseeh, G., Banik, N., Dai, J., Egan, M., & Gonzalez, A., et al. (2011). Seismic reservoir characterization in Marcellus shale. 2011 SEG Annual Meeting. Society of Exploration Geophysicists.

    Google Scholar 

  4. Zhu, Y., Liu, E., Martinez, A., Payne, M. A., & Harris, C. E. (2011). Understanding geophysical responses of shale-gas plays. The Leading Edge, 30, 332–338. doi:10.1190/1.3567265.

    Article  Google Scholar 

  5. Goodway, B., Perez, M., Varsek, J., & Abaco, C. (2010). Seismic petrophysics and isotropic-anisotropic AVO methods for unconventional gas exploration. The Leading Edge, 29, 1500–1508. doi:10.1190/1.3525367.

    Article  Google Scholar 

  6. Treadgold, G., Campbell, B., McLain, B., Sinclair, S., & Nicklin, D. (2011). Eagle Ford shale prospecting with 3D seismic data within a tectonic and depositional system framework. The Leading Edge, 30, 48–53. doi:10.1190/1.3535432.

    Article  Google Scholar 

  7. Fertl, W. H. (1976). Evaluation of oil shales using geophysical well-logging techniques. In G. V. Chilingarian & T. F. Yen (Eds.), Developments in petroleum science (pp. 199–213). Amsterdam: Elsevier.

    Google Scholar 

  8. Sondergeld, C. H., Newsham, K. E., Comisky, J. T., Rice, M. C., & Rai, C. S. (2010). Petrophysical considerations in evaluating and producing shale gas resources. SPE Unconventional Gas Conference, Society of Petroleum Engineers. doi:10.2118/131768-MS.

  9. Abousleiman, Y., Tran, M. H., Hoang, S., Ortega, A., & Ulm, F.-J. (2009). GeoMechanics field characterization of the two prolific U.S. Mid-west gas plays with advanced wire-line logging tools. SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers. doi:10.2118/124428-MS.

  10. Abousleiman, Y., Tran, M., Hoang, S., Ortega, J. A., & Ulm, F.-J. (2010). Geomechanics field characterization of Woodford shale and Barnett shale with advanced logging tools and nano-indentation on drill cuttings. The Leading Edge, 29, 730–736. doi:10.1190/1.3447787.

    Article  Google Scholar 

  11. Brevik, I., Ahmadi, G. R., Hatteland, T., & Rojas, M. A. (2007). Documentation and quantification of velocity anisotropy in shales using wireline log measurements. The Leading Edge, 26, 272–277. doi:10.1190/1.2715048.

    Article  Google Scholar 

  12. Kebaili, A., & Schmitt, D. (1996). Velocity anisotropy observed in wellbore seismic arrivals: Combined effects of intrinsic properties and layering. Geophysics, 61, 12–20. doi:10.1190/1.1443932.

    Article  Google Scholar 

  13. Wong, R. C. K., Schmitt, D. R., Collis, D., & Gautam, R. (2008). Inherent transversely isotropic elastic parameters of over-consolidated shale measured by ultrasonic waves and their comparison with static and acoustic in situ log measurements. Journal of Geophysics and Engineering, 5, 103. doi:10.1088/1742-2132/5/1/011.

    Article  Google Scholar 

  14. Horsrud, P. (2001). Estimating mechanical properties of shale from empirical correlations. SPE Drilling and Completion, 16, 68–73. doi:10.2118/56017-PA.

    Article  Google Scholar 

  15. Lashkaripour, G. R. (1993). A statistical study on shale properties: Relationship among principal shale properties. PMGE Aust. Probabilistic Method Geotech. Eng.

    Google Scholar 

  16. McNally, G. H. (1987). Estimation of coal measures rock strength using sonic and neutron logs. Geoexploration, 24, 381–395. doi:10.1016/0016-7142(87)90008-1.

    Article  Google Scholar 

  17. Onyia, E. C. (1988). Relationships between formation strength. Drilling Strength, and Electric Log Properties. doi:10.2118/18166-MS.

    Google Scholar 

  18. Chang, C., Zoback, M. D., & Khaksar, A. (2006). Empirical relations between rock strength and physical properties in sedimentary rocks. Journal of Petroleum Science and Engineering, 51, 223–237. doi:10.1016/j.petrol.2006.01.003.

    Article  Google Scholar 

  19. Abousleiman, Y. N., Tran, M. H., Hoang, S., Bobko C. P., Ortega, A., & Ulm, F.-J. (2007). Geomechanics field and laboratory characterization of the woodford shale: The next gas play. SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers. doi:10.2118/110120-MS.

    Google Scholar 

  20. Kim, H., Cho, J.-W., Song, I., & Min, K.-B. (2012). Anisotropy of elastic moduli, P-wave velocities, and thermal conductivities of Asan Gneiss, Boryeong Shale, and Yeoncheon Schist in Korea. Engineering Geology, 147–148, 68–77. doi:10.1016/j.enggeo.2012.07.015.

    Article  Google Scholar 

  21. Nes, O.-M., Sonstebo, E. F., Horsrud, P., & Holt, R. M. (1998). Dynamic and static measurements on mm-size shale samples. SPE/ISRM Rock Mechanics in Petroleum Engineering, Society of Petroleum Engineers. doi:10.2118/47200-MS.

  22. Slatt, R., & Abousleiman, Y. (2011). Merging sequence stratigraphy and geomechanics for unconventional gas shales. The Leading Edge, 30, 274–282. doi:10.1190/1.3567258.

    Article  Google Scholar 

  23. Sondergeld, C. H., & Rai, C. S. (2011). Elastic anisotropy of shales. The Leading Edge, 30, 324–331. doi:10.1190/1.3567264.

    Article  Google Scholar 

  24. Sone, H., & Zoback, M. D. (2013). Mechanical properties of shale-gas reservoir rocks—Part 1: Static and dynamic elastic properties and anisotropy. Geophysics, 78, D381–D392. doi:10.1190/geo2013-0050.1.

    Article  Google Scholar 

  25. Sone, H., & Zoback, M. D. (2013). Mechanical properties of shale-gas reservoir rocks—Part 2: Ductile creep, brittle strength, and their relation to the elastic modulus. Geophysics, 78, D393–D402. doi:10.1190/geo2013-0051.1.

    Article  Google Scholar 

  26. Fjær, E., & Nes, O.-M. (2014). The impact of heterogeneity on the anisotropic strength of an outcrop shale. Rock Mechanics and Rock Engineering, 47, 1603–1611. doi:10.1007/s00603-014-0598-5.

    Article  Google Scholar 

  27. Simpson, N. D. J., Stroisz, A., Bauer, A., Vervoort, A., & Holt, R. M. (2014). Failure mechanics of anisotropic shale during Brazilian tests. 48th U.S. Rock Mechanics/Geomechanics Symposium.

    Google Scholar 

  28. Sierra, R., Tran, M. H., Abousleiman, Y. N., & Slatt, R. M., et al. (2010). Woodford Shale mechanical properties and the impacts of lithofacies. 44th US Rock Mech. Symp. 5th US-Can. Rock Mech. Symp.

    Google Scholar 

  29. Niandou, H., Shao, J. F., Henry, J. P., & Fourmaintraux, D. (1997). Laboratory investigation of the mechanical behaviour of Tournemire shale. International Journal of Rock Mechanics and Mining Sciences, 34, 3–16. doi:10.1016/S1365-1609(97)80029-9.

    Article  Google Scholar 

  30. Britt, L. K., & Schoeffler, J. (2009). The geomechanics of a shale play: What makes a shale prospective. SPE Eastern Regional Meeting, Society of Petroleum Engineers. doi:10.2118/125525-MS.

  31. Higgins, S. M., Goodwin, S. A., Donald, A., Bratton, T. R., & Tracy G. W. (2008) Anisotropic stress models improve completion design in the Baxter shale. SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers. doi:10.2118/115736-MS.

  32. Khan, S., Williams, R. E., Ansari, S., & Khosravi, N. (2012). Impact of mechanical anisotropy on design of hydraulic fracturing in shales. Abu Dhabi International Petroleum Conference and Exhibition, Society of Petroleum Engineers. doi:10.2118/162138-MS.

  33. Suarez-Rivera, R., Green, S. J., McLennan, J., & Bai, M. (2006). Effect of layered heterogeneity on fracture initiation in tight gas shales. SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers. doi:10.2118/103327-MS.

  34. Chandler, M., Meredith, P., & Crawford, B. (2013). Experimental determination of the fracture toughness and brittleness of the mancos shale, Utah. p EGU2013.

    Google Scholar 

  35. Jarvie, D. M., Hill, R. J., Ruble, T. E., & Pollastro, R. M. (2015). Unconventional shale-gas systems: The Mississippian Barnett Shale of north-central Texas as one model for thermogenic shale-gas assessment. AAPG Bulletin, 91(4), 475–499.

    Article  Google Scholar 

  36. Li, Q., Chen, M., Zhou, Y., Jin, Y., Wang, F. P., & Zhang, R. (2013). Rock mechanical properties of shale gas reservoir and their influences on hydraulic fracture. IPTC 2013: International Petroleum Technology Conference. doi:10.2523/16580-MS.

  37. Rickman, R., Mullen, M. J., Petre, J. E., Grieser, W. V., & Kundert, D. (2008). A practical use of shale petrophysics for stimulation design optimization: All shale plays are not clones of the Barnett shale. SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers. doi:10.2118/115258-MS.

  38. Wang, F. P., & Gale, J. F. W. (2009). Screening criteria for shale-Gas systems. Gulf Coast Association of Geological Societies Trans, 59, 779–793.

    Google Scholar 

  39. Holt, R. M., Fjaer, E., Nes, O. M., & Alassi, H. T. (2011). A shaly look at brittleness. 45th U.S. Rock Mechanics/Geomechanics Symposium.

    Google Scholar 

  40. Holt, R. M., Fjær, E., Stenebråten, J. F., & Nes, O.-M. (2015). Brittleness of shales: Relevance to borehole collapse and hydraulic fracturing. Journal of Petroleum Science and Engineering, 131, 200–209. doi:10.1016/j.petrol.2015.04.006.

    Article  Google Scholar 

  41. Hucka, V., & Das, B. (1974). Brittleness determination of rocks by different methods. International Journal of Rock Mechanics and Mining Science and Geomechanics Abstracts, 11, 389–392. doi:10.1016/0148-9062(74)91109-7.

    Article  Google Scholar 

  42. Yang, Y., Sone, H., Hows, A., & Zoback, M. D. (2013). Comparison of brittleness indices in organic-rich shale formations. 47th U.S. Rock Mechanics/Geomechanics Symposium.

    Google Scholar 

  43. Jin, X., Shah, S. N., Roegiers, J.-C., & Zhang, B. (2014). Fracability evaluation in shale reservoirs—an integrated petrophysics and geomechanics approach. SPE Hydraulic Fracturing Technology Conference, Society of Petroleum Engineers. doi:10.2118/168589-MS.

  44. Schmidt, R. A. (1977). Fracture mechanics of oil shale—unconfined fracture toughness, stress corrosion cracking, and tension test results. The 18th U.S. Symposium on Rock Mechanics (USRMS).

    Google Scholar 

  45. Akono, A.-T. (2013). Assessment of fracture properties and rate effects on fracture of materials by micro scratching: Application to gas shale. Thesis, Massachusetts Institute of Technology.

    Google Scholar 

  46. Haddad, M., & Sepehrnoori, K. (2015). Simulation of hydraulic fracturing in quasi-brittle shale formations using characterized cohesive layer: Stimulation controlling factors. Journal of Unconventional Oil and Gas Resources, 9, 65–83. doi:10.1016/j.juogr.2014.10.001.

    Article  Google Scholar 

  47. Parisio, F., Samat, S., & Laloui, L. (2014). An elasto-plastic-damage model for quasi-brittle shales. Proceedings of 48th US Rock Mechanics Symposium.

    Google Scholar 

  48. Yao, Y. (2011). Linear elastic and cohesive fracture analysis to model hydraulic fracture in brittle and ductile rocks. Rock Mechanics and Rock Engineering, 45, 375–387. doi:10.1007/s00603-011-0211-0.

    Article  Google Scholar 

  49. Eseme, E., Urai, J. L., Krooss, B. M., & Littke, R. (2007). Review of the mechanical properties of oil shales: Implications for exploitation and basin modelling. Oil Shale, 24(2), 159–175.

    Google Scholar 

  50. Sayers, C. M. (2013). The effect of anisotropy on the Young’s moduli and Poisson’s ratios of shales. Geophysical Prospecting, 61, 416–426. doi:10.1111/j.1365-2478.2012.01130.x.

    Article  Google Scholar 

  51. Vernik, L., & Nur, A. (1992). Ultrasonic velocity and anisotropy of hydrocarbon source rocks. Geophysics, 57, 727–735. doi:10.1190/1.1443286.

    Article  Google Scholar 

  52. Mokhtari M (2015). Characterization of anisotropy in organic-rich shales: Shear and tensile failure, wave velocity, matrix and fracture permeability. Thesis Colorado School of Mines.

    Google Scholar 

  53. Mokhtari, M., Bui, B. T., & Tutuncu, A. N. (2014). Tensile failure of shales: Impacts of layering and natural fractures. SPE Western North American and Rocky Mountain Joint Meeting, Society of Petroleum Engineers. doi:10.2118/169520-MS.

    Google Scholar 

  54. Eseme, E., Littke, R., & Krooss, B. M. (2006). Factors controlling the thermo-mechanical deformation of oil shales: Implications for compaction of mudstones and exploitation. Marine and Petroleum Geology, 23, 715–734. doi:10.1016/j.marpetgeo.2006.02.007.

    Article  Google Scholar 

  55. Josh, M., Esteban, L., Delle Piane, C., Sarout, J., Dewhurst, D. N., & Clennell, M. B. (2012). Laboratory characterisation of shale properties. Journal of Petroleum Science and Engineering, 88–89, 107–124. doi:10.1016/j.petrol.2012.01.023.

    Article  Google Scholar 

  56. Abousleiman, Y. N., Hoang, S. K., & Tran, M. H. (2010). Mechanical characterization of small shale samples subjected to fluid exposure using the inclined direct shear testing device. International Journal of Rock Mechanics and Mining Sciences, 47, 355–367. doi:10.1016/j.ijrmms.2009.12.014.

    Article  Google Scholar 

  57. Duveau, G., Shao, J. F., & Henry, J. P. (1998). Assessment of some failure criteria for strongly anisotropic geomaterials. Mech Cohesive-Frict Mater, 3, 1–26.

    Article  Google Scholar 

  58. Aoki, T., Tan, C. P., & Bamford, W. E. (1993). Effects of deformation and strength anisotropy on borehole failures in saturated shales. International Journal of Rock Mechanics and Mining Science and Geomechanics Abstracts, 30, 1031–1034. doi:10.1016/0148-9062(93)90067-N.

    Article  Google Scholar 

  59. Jaeger, J. C. (1960). Shear failure of anisotropic rocks. Geological Magazine, 97, 65–72. doi:10.1017/S0016756800061100.

    Article  Google Scholar 

  60. CHEN, P., HAN, Q., Ma, T., & Lin, D. (2015). The mechanical properties of shale based on micro-indentation test. Petroleum Exploration and Development, 42, 723–732. doi:10.1016/S1876-3804(15)30069-0.

    Article  Google Scholar 

  61. Ringstad, C., Lofthus, E. B., Sonstebo, E. F., Fjaer, E., Zausa, F., & Fuh, G.-F. (1998). Prediction of rock parameters from micro-indentation measurements: The effect of sample size. SPE/ISRM Rock Mechanics in Petroleum Engineering, Society of Petroleum Engineers. doi:10.2118/47313-MS.

    Google Scholar 

  62. Ulm, F.-J., & Abousleiman, Y. (2006). The nanogranular nature of shale. Acta Geotechnica, 1, 77–88. doi:10.1007/s11440-006-0009-5.

    Article  Google Scholar 

  63. Akono, A.-T., & Ulm, F.-J. (2011). Scratch test model for the determination of fracture toughness. Engineering Fracture Mechanics, 78, 334–342. doi:10.1016/j.engfracmech.2010.09.017.

    Article  Google Scholar 

  64. Sondergeld, C. H., Ambrose, R. J., Rai, C. S., & Moncrieff, J. (2010). Micro-structural studies of gas shales. SPE Unconventional Gas Conference, Society of Petroleum Engineers. doi:10.2118/131771-MS.

  65. Rybacki, E., Reinicke, A., Meier, T., Makasi, M., & Dresen, G. (2015). What controls the mechanical properties of shale rocks?—Part I: Strength and Young’s modulus. Journal of Petroleum Science and Engineering, 135, 702–722. doi:10.1016/j.petrol.2015.10.028.

    Article  Google Scholar 

  66. Sayers, C. M. (2013). The effect of kerogen on the elastic anisotropy of organic-rich shales. Geophysics, 78, D65–D74. doi:10.1190/geo2012-0309.1.

    Article  Google Scholar 

  67. Curtis, M. E., Ambrose, R. J., & Sondergeld, C. H. (2010). Structural characterization of gas shales on the micro- and nano-scales. Canadian unconventional resources and international petroleum conference, Society of Petroleum Engineers. doi:10.2118/137693-MS.

  68. Curtis, M. E., Sondergeld, C. H., Ambrose, R. J., & Rai, C. S. (2012). Microstructural investigation of gas shales in two and three dimensions using nanometer-scale resolution imaging. AAPG Bulletin, 96, 665–677. doi:10.1306/08151110188.

    Article  Google Scholar 

  69. Eliyahu, M., Emmanuel, S., Day-Stirrat, R. J., & Macaulay, C. I. (2015). Mechanical properties of organic matter in shales mapped at the nanometer scale. Marine and Petroleum Geology, 59, 294–304. doi:10.1016/j.marpetgeo.2014.09.007.

    Article  Google Scholar 

  70. Bobko, C., & Ulm, F.-J. (2008). The nano-mechanical morphology of shale. Mechanics of Materials, 40, 318–337. doi:10.1016/j.mechmat.2007.09.006.

    Article  Google Scholar 

  71. Ortega, J. A., Ulm, F.-J., & Abousleiman, Y. (2009). The nanogranular acoustic signature of shale. Geophysics, 74, D65–D84. doi:10.1190/1.3097887.

    Article  Google Scholar 

  72. Kumar, V., Sondergeld, C. H., & Rai, C. S. (2012). Nano to macro mechanical characterization of shale. SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers. doi:10.2118/159804-MS.

  73. Bennett, K. C., Berla, L. A., Nix, W. D., & Borja, R. I. (2015). Instrumented nanoindentation and 3D mechanistic modeling of a shale at multiple scales. Acta Geotechnica, 10, 1–14. doi:10.1007/s11440-014-0363-7.

    Article  Google Scholar 

  74. Oliver, W. C., & Pharr, G. M. (2004). Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. Journal of Materials Research, 19, 3–20.

    Article  Google Scholar 

  75. Tavallali, A., & Vervoort, A. (2010). Failure of layered sandstone under Brazilian test conditions: Effect of micro-scale parameters on macro-scale behaviour. Rock Mechanics and Rock Engineering, 43, 641–653. doi:10.1007/s00603-010-0084-7.

    Article  Google Scholar 

  76. Geertsma, J., & De Klerk, F. (1969). A rapid method of predicting width and extent of hydraulically induced fractures. Journal of Petroleum Technology, 21, 1571–1581. doi:10.2118/2458-PA.

    Article  Google Scholar 

  77. Khristianovic, S., & Zheltov, Y. (1955). Formation of vertical fractures by means of highly viscous fluids. In Proceedings 4th World Pet Congress Rome. pp 579–586.

    Google Scholar 

  78. Nordgren, R. P. (1972). Propagation of a vertical hydraulic fracture. Society of Petroleum Engineers Journal, 12, 306–314. doi:10.2118/3009-PA.

    Article  Google Scholar 

  79. Perkins, T. K., & Kern, L. R. (1961). Widths of hydraulic fractures. Journal of Petroleum Technology, 13, 937–949. doi:10.2118/89-PA.

    Article  Google Scholar 

  80. Morales, R. H., & Abou-Sayed, A. S. (1989). Microcomputer analysis of hydraulic fracture behavior with a pseudo-three-dimensional simulator. SPE Production Engineering, 4, 69–74. doi:10.2118/15305-PA.

    Article  Google Scholar 

  81. Settari, A., & Cleary, M. P. (1986). Development and testing of a pseudo-three-dimensional model of hydraulic fracture geometry. SPE Production Engineering, 1, 449–466. doi:10.2118/10505-PA.

    Article  Google Scholar 

  82. Advani, S. H., Lee, T. S., & Lee, J. K. (1990). Three-dimensional modeling of hydraulic fractures in layered media: Part I—finite element formulations. Journal of Energy Resources Technology, 112, 1–9. doi:10.1115/1.2905706.

    Article  Google Scholar 

  83. Gu, H., & Leung, K. H. (1993). 3D numerical simulation of hydraulic fracture closure with application to minifracture analysis. Journal of Petroleum Technology, 45, 206–255. doi:10.2118/20657-PA.

    Article  Google Scholar 

  84. Morita, N., Whitfill, D. L., & Wahl, H. A. (1988). Stress-intensity factor and fracture cross-sectional shape predictions from a three-dimensional model for hydraulically induced fractures. Journal of Petroleum Technology, 40, 1329–1342. doi:10.2118/14262-PA.

    Article  Google Scholar 

  85. Carter, B., Desroches, J., Ingraffea, A., & Wawrzynek, P. (2000). Simulating fully 3D hydraulic fracturing. Model Geomechanics, 200, 525–557.

    Google Scholar 

  86. Li, L. C., Tang, C. A., Li, G., Wang, S. Y., Liang, Z. Z., & Zhang, Y. B. (2012). Numerical simulation of 3D hydraulic fracturing based on an improved flow-stress-damage model and a parallel FEM technique. Rock Mechanics and Rock Engineering, 45, 801–818. doi:10.1007/s00603-012-0252-z.

    Google Scholar 

  87. Dahi-Taleghani, A., & Olson, J. E. (2011). Numerical modeling of multistranded-hydraulic-fracture propagation: Accounting for the interaction between induced and natural fractures. SPE Journal, 16, 575–581. doi:10.2118/124884-PA.

    Article  Google Scholar 

  88. Lecampion, B. (2009). An extended finite element method for hydraulic fracture problems. Communications in Numerical Methods in Engineering, 25, 121–133. doi:10.1002/cnm.1111.

    Article  MathSciNet  MATH  Google Scholar 

  89. Carrier, B., & Granet, S. (2012). Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model. Engineering Fracture Mechanics, 79, 312–328. doi:10.1016/j.engfracmech.2011.11.012.

    Article  Google Scholar 

  90. Chen, Z., Bunger, A. P., Zhang, X., & Jeffrey, R. G. (2009). Cohesive zone finite element-based modeling of hydraulic fractures. Acta Mechanica Solida Sinica, 22, 443–452. doi:10.1016/S0894-9166(09)60295-0.

    Article  Google Scholar 

  91. Sarris, E., & Papanastasiou, P. (2011). Modeling of hydraulic fracturing in a poroelastic cohesive formation. International Journal of Geomechanics, 12, 160–167. doi:10.1061/(ASCE)GM.1943-5622.0000121.

    Article  MATH  Google Scholar 

  92. Yuan, S. C., & Harrison, J. P. (2006). A review of the state of the art in modelling progressive mechanical breakdown and associated fluid flow in intact heterogeneous rocks. International Journal of Rock Mechanics and Mining Sciences, 43, 1001–1022. doi:10.1016/j.ijrmms.2006.03.004.

    Article  Google Scholar 

  93. Sammis, C. G., & Ashby, M. F. (1986). The failure of brittle porous solids under compressive stress states. Acta Metallurgica, 34, 511–526. doi:10.1016/0001-6160(86)90087-8.

    Article  Google Scholar 

  94. Zhang, J., Wong, T.-F., & Davis, D. M. (1990). Micromechanics of pressure-induced grain crushing in porous rocks. Journal of Geophysical Research - Solid Earth, 95, 341–352. doi:10.1029/JB095iB01p00341.

    Article  Google Scholar 

  95. Ashby, M. F., & Hallam (Née Cooksley), S. D. (1986). The failure of brittle solids containing small cracks under compressive stress states. Acta Metallurgica, 34, 497–510. doi:10.1016/0001-6160(86)90086-6.

    Article  Google Scholar 

  96. Brace, W. F., & Bombolakis, E. G. (1963). A note on brittle crack growth in compression. Journal of Geophysical Research, 68, 3709–3713. doi:10.1029/JZ068i012p03709.

    Article  Google Scholar 

  97. Horii, H., & Nemat-Nasser, S. (1985). Compression-induced microcrack growth in brittle solids: Axial splitting and shear failure. Journal of Geophysical Research - Solid Earth, 90, 3105–3125. doi:10.1029/JB090iB04p03105.

    Article  Google Scholar 

  98. Jing, L. (2003). A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering. International Journal of Rock Mechanics and Mining Sciences, 40, 283–353. doi:10.1016/S1365-1609(03)00013-3.

    Article  Google Scholar 

  99. Borst, R. D., Crisfield, M. A., Remmers, J. J. C., & Verhoosel, C. V. (2012). Nonlinear finite element analysis of solids and structures. Hoboken: John Wiley & Sons.

    Book  MATH  Google Scholar 

  100. Bobet, A., Fakhimi, A., Johnson, S., Morris, J., Tonon, F., & Yeung, M. (2009). Numerical models in discontinuous media: Review of advances for rock mechanics applications. Journal of Geotechnical and Geoenvironmental Engineering, 135, 1547–1561. doi:10.1061/(ASCE)GT.1943-5606.0000133.

    Article  Google Scholar 

  101. Lisjak, A., & Grasselli, G. (2014). A review of discrete modeling techniques for fracturing processes in discontinuous rock masses. Journal of Rock Mechanics and Geotechnical Engineering, 6, 301–314. doi:10.1016/j.jrmge.2013.12.007.

    Article  Google Scholar 

  102. Bažant, Z. P., & Oh, B. H. (1983). Crack band theory for fracture of concrete. Materiales de Construcción, 16, 155–177. doi:10.1007/BF02486267.

    Google Scholar 

  103. Hillerborg, A., Modéer, M., & Petersson, P.-E. (1976). Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research, 6, 773–781. doi:10.1016/0008-8846(76)90007-7.

    Article  Google Scholar 

  104. Collin, F., Chambon, R., & Charlier, R. (2006). A finite element method for poro mechanical modelling of geotechnical problems using local second gradient models. International Journal for Numerical Methods in Engineering, 65, 1749–1772. doi:10.1002/nme.1515.

    Article  MathSciNet  MATH  Google Scholar 

  105. Mühlhaus, H.-B., & Alfantis, E. C. (1991). A variational principle for gradient plasticity. International Journal of Solids and Structures, 28, 845–857. doi:10.1016/0020-7683(91)90004-Y.

    Article  MathSciNet  MATH  Google Scholar 

  106. Bažant, Z. P., & Pijaudier-Cabot, G. (1988). Nonlocal continuum damage, localization instability and convergence. Journal of Applied Mechanics, 55, 287–293. doi:10.1115/1.3173674.

    Article  MATH  Google Scholar 

  107. Adhikary, D. P., & Dyskin, A. V. (1997). A Cosserat continuum model for layered materials. Computers and Geotechnics, 20, 15–45. doi:10.1016/S0266-352X(96)00011-0.

    Article  Google Scholar 

  108. Riahi, A., & Curran, J. H. (2009). Full 3D finite element Cosserat formulation with application in layered structures. Applied Mathematical Modelling, 33, 3450–3464. doi:10.1016/j.apm.2008.11.022.

    Article  MathSciNet  MATH  Google Scholar 

  109. Fang, Z., & Harrison, J. P. (2002). Application of a local degradation model to the analysis of brittle fracture of laboratory scale rock specimens under triaxial conditions. International Journal of Rock Mechanics and Mining Sciences, 39, 459–476. doi:10.1016/S1365-1609(02)00036-9.

    Article  Google Scholar 

  110. Fang, Z., & Harrison, J. P. (2002). Development of a local degradation approach to the modelling of brittle fracture in heterogeneous rocks. International Journal of Rock Mechanics and Mining Sciences, 39, 443–457. doi:10.1016/S1365-1609(02)00035-7.

    Article  Google Scholar 

  111. Tang, C. A., Liu, H., Lee, P. K. K., Tsui, Y., & Tham, L. G. (2000). Numerical studies of the influence of microstructure on rock failure in uniaxial compression—Part I: Effect of heterogeneity. International Journal of Rock Mechanics and Mining Sciences, 37, 555–569. doi:10.1016/S1365-1609(99)00121-5.

    Article  Google Scholar 

  112. Cundall, P. A. (1971). A computer model for simulating progressive large scale movements in blocky rock systems. Proceedings symposium on rock fracture. ISRM Nancy 1

    Google Scholar 

  113. Cundall, P. A., & Strack, O. D. (1979). A discrete numerical model for granular assemblies. Geotechnique, 29, 47–65.

    Article  Google Scholar 

  114. Jing, L., & Stephansson, O. (2007). Fundamentals of discrete element methods for rock engineering: Theory and applications: Theory and applications. Amsterdam: Elsevier.

    Google Scholar 

  115. Cundall, D. P. A. (1989). Numerical experiments on localization in frictional materials. Ing-Arch, 59, 148–159. doi:10.1007/BF00538368.

    Article  Google Scholar 

  116. Itasca Consulting Group Inc. (2011). Universal Distinct Element Code (UDEC), Version 5.0. Minneapolis: Itasca Consulting Group, Inc.

    Google Scholar 

  117. Itasca Consulting Group Inc. (1999). PFC2D/3D (Particle Flow Code in 2/3 Dimensions), Version 2.0. Minneapolis, MN: Itasca Consulting Group, Inc.

    Google Scholar 

  118. Potyondy, D. O., & Cundall, P. A. (2004). A bonded-particle model for rock. International Journal of Rock Mechanics and Mining Sciences, 41, 1329–1364. doi:10.1016/j.ijrmms.2004.09.011.

    Article  Google Scholar 

  119. Schlangen, E., & Mier, J. G. M. V. (1992). Micromechanical analysis of fracture of concrete. International Journal of Damage Mechanics, 1, 435–454. doi:10.1177/105678959200100404.

    Article  Google Scholar 

  120. Schlangen, E., & Mier, J. G. M. V. (1995). Crack propagation in sandstone: Combined experimental and numerical approach. Rock Mechanics and Rock Engineering, 28, 93–110. doi:10.1007/BF01020063.

    Article  Google Scholar 

  121. Schlangen, E., & van Mier, J. G. M. (1992). Experimental and numerical analysis of micromechanisms of fracture of cement-based composites. Cement and Concrete Composites, 14, 105–118. doi:10.1016/0958-9465(92)90004-F.

    Article  Google Scholar 

  122. Schlangen, E., & van Mier, J. G. M. (1992). Simple lattice model for numerical simulation of fracture of concrete materials and structures. Materials and Structures, 25, 534–542. doi:10.1007/BF02472449.

    Article  Google Scholar 

  123. Schlangen, E., & Van Mier, J. (1994). Fracture simulations in concrete and rock using a random lattice. Computer Methods Advance Geomechanics, 2, 1641–1646.

    Google Scholar 

  124. Schlangen, E., & Garboczi, E. J. (1997). Fracture simulations of concrete using lattice models: Computational aspects. Engineering Fracture Mechanics, 57, 319–332. doi:10.1016/S0013-7944(97)00010-6.

    Article  Google Scholar 

  125. Schlangen, E., & Qian, Z. (2009). 3d modeling of fracture in cement-based materials. Journal of Multiscale Modeling, 01, 245–261. doi:10.1142/S1756973709000116.

    Article  Google Scholar 

  126. Bazant, Z. P., Tabbara, M., Kazemi, M., & Pijaudier‐Cabot, G. (1990). Random particle model for fracture of aggregate or fiber composites. Journal of Engineering Mechanics, 116, 1686–1705. doi:10.1061/(ASCE)0733-9399(1990)116:8(1686).

    Article  Google Scholar 

  127. Song, J. S., & Kim, K. S. (1995). Blasting induced fracturing and stress field evolution at fracture tips. The 35th U.S. Symposium on Rock Mechanics (USRMS).

    Google Scholar 

  128. Place, D., & Mora, P. (2000). Numerical simulation of localisation phenomena in a fault zone. In P. Mora, M. Matsu’ura R. Madariaga, J.-B. Minster (Eds.), Microsc. Macrosc. Simul. Predict. Model. Earthq. Process. (pp. 1821–1845) Birkhäuser Basel.

    Google Scholar 

  129. Bolander, J. E., & Saito, S. (1998). Fracture analyses using spring networks with random geometry. Engineering Fracture Mechanics, 61, 569–591.

    Article  Google Scholar 

  130. Bolander, J. E., & Sukumar, N. (2005). Irregular lattice model for quasistatic crack propagation. Physical Review B, 71, 094106. doi:10.1103/PhysRevB.71.094106.

    Article  Google Scholar 

  131. Katsman, R., Aharonov, E., & Scher, H. (2005). Numerical simulation of compaction bands in high-porosity sedimentary rock. Mechanics of Materials, 37, 143–162. doi:10.1016/j.mechmat.2004.01.004.

    Article  Google Scholar 

  132. Jirásek, M., & Bažant, Z. P. (1994). Macroscopic fracture characteristics of random particle systems. International Journal of Fracture, 69, 201–228. doi:10.1007/BF00034763.

    Article  Google Scholar 

  133. Cusatis, G., Bažant, Z. P., & Luigi, C. (2003). Confinement-shear lattice model for concrete damage in tension and compression: I. Theory. The Journal of Engineering, 129, 1439–1448. doi:10.1061/(ASCE)0733-9399(2003)129:12(1439).

    Google Scholar 

  134. Lilliu, G., & van Mier, J. G. M. (2003). 3D lattice type fracture model for concrete. Engineering Fracture Mechanics, 70, 927–941. doi:10.1016/S0013-7944(02)00158-3.

    Article  Google Scholar 

  135. Yip, M., Mohle, J., & Bolander, J. E. (2005). Automated modeling of three-dimensional structural components using irregular lattices. Computer-Aided Civil and Infrastructure Engineering, 20, 393–407. doi:10.1111/j.1467-8667.2005.00407.x.

    Article  Google Scholar 

  136. Munjiza, A. A. (2004). The combined finite-discrete element method. Hoboken: John Wiley & Sons.

    Book  MATH  Google Scholar 

  137. Munjiza, A., Owen, D. R. J., & Bicanic, N. (1995). A combined finite‐discrete element method in transient dynamics of fracturing solids. Engineering Computations, 12, 145–174. doi:10.1108/02644409510799532.

    Article  MATH  Google Scholar 

  138. Fabian, D., Peter, C., Daniel, B., & Torsten, G. (2007). Evaluation of damage-induced permeability using a three-dimensional Adaptive Continuum/Discontinuum Code (AC/DC). Physics and Chemistry of the Earth, Parts ABC, 32, 681–690. doi:10.1016/j.pce.2006.01.006.

    Article  Google Scholar 

  139. Deb, D., & Das, K. C. (2010). Extended finite element method for the analysis of discontinuities in rock masses. Geotechnical and Geological Engineering, 28, 643–659. doi:10.1007/s10706-010-9323-7.

    Article  Google Scholar 

  140. Fries, T.-P., & Belytschko, T. (2006). The intrinsic XFEM: A method for arbitrary discontinuities without additional unknowns. International Journal for Numerical Methods in Engineering, 68, 1358–1385. doi:10.1002/nme.1761.

    Article  MATH  Google Scholar 

  141. Ma, G. W., Wang, X. J., & Ren, F. (2011). Numerical simulation of compressive failure of heterogeneous rock-like materials using SPH method. International Journal of Rock Mechanics and Mining Sciences, 48, 353–363. doi:10.1016/j.ijrmms.2011.02.001.

    Article  Google Scholar 

  142. Ha, Y. D., & Bobaru, F. (2010). Studies of dynamic crack propagation and crack branching with peridynamics. International Journal of Fracture, 162, 229–244. doi:10.1007/s10704-010-9442-4.

    Article  MATH  Google Scholar 

  143. Lisjak, A., Grasselli, G., & Vietor, T. (2014). Continuum–discontinuum analysis of failure mechanisms around unsupported circular excavations in anisotropic clay shales. International Journal of Rock Mechanics and Mining Sciences, 65, 96–115. doi:10.1016/j.ijrmms.2013.10.006.

    Article  Google Scholar 

  144. Goodman, R. E. (1989). Introduction to rock mechanics (2nd ed.). New York: Wiley.

    Google Scholar 

  145. Mahjoub, M., Rouabhi, A., Tijani, M., & Granet, S. (2015). An approach to model the mechanical behavior of transversely isotropic materials. International Journal for Numerical and Analytical Methods in Geomechanics n/a–n/a. doi:10.1002/nag.2469.

    Google Scholar 

  146. Rouabhi, A., Tijani, M., & Rejeb, A. (2007). Triaxial behaviour of transversely isotropic materials: Application to sedimentary rocks. International Journal for Numerical and Analytical Methods in Geomechanics, 31, 1517–1535. doi:10.1002/nag.605.

    Article  MATH  Google Scholar 

  147. Tien, Y. M., & Kuo, M. C. (2001). A failure criterion for transversely isotropic rocks. International Journal of Rock Mechanics and Mining Sciences, 38, 399–412.

    Article  Google Scholar 

  148. Adhikary, D. P., & Guo, H. (2014). An orthotropic Cosserat elasto-plastic model for layered rocks. Rock Mechanics and Rock Engineering, 35, 161–170. doi:10.1007/s00603-001-0020-y.

    Article  Google Scholar 

  149. Pietruszczak, S., Lydzba, D., & Shao, J. F. (2002). Modelling of inherent anisotropy in sedimentary rocks. International Journal of Solids and Structures, 39, 637–648. doi:10.1016/S0020-7683(01)00110-X.

    Article  MATH  Google Scholar 

  150. Salager, S., François, B., Nuth, M., & Laloui, L. (2012). Constitutive analysis of the mechanical anisotropy of Opalinus Clay. Acta Geotechnica, 8, 137–154. doi:10.1007/s11440-012-0187-2.

    Article  Google Scholar 

  151. Mas Ivars, D., Pierce, M. E., Darcel, C., Reyes-Montes, J., Potyondy, D. O., Paul Young, R., et al. (2011). The synthetic rock mass approach for jointed rock mass modelling. International Journal of Rock Mechanics and Mining Sciences, 48, 219–244. doi:10.1016/j.ijrmms.2010.11.014.

    Article  Google Scholar 

  152. Park, B., & Min, K.-B. (2015). Bonded-particle discrete element modeling of mechanical behavior of transversely isotropic rock. International Journal of Rock Mechanics and Mining Sciences, 76, 243–255. doi:10.1016/j.ijrmms.2015.03.014.

    Article  Google Scholar 

  153. Lisjak, A., Tatone, B. S. A., Grasselli, G., & Vietor, T. (2014). Numerical modelling of the anisotropic mechanical behaviour of Opalinus clay at the laboratory-scale using FEM/DEM. Rock Mechanics and Rock Engineering, 47, 187–206. doi:10.1007/s00603-012-0354-7.

    Article  Google Scholar 

  154. Debecker, B., & Vervoort, A. (2013). Two-dimensional discrete element simulations of the fracture behaviour of slate. International Journal of Rock Mechanics and Mining Sciences, 61, 161–170. doi:10.1016/j.ijrmms.2013.02.004.

    Article  Google Scholar 

  155. Duan, K., & Kwok, C. Y. (2015). Discrete element modeling of anisotropic rock under Brazilian test conditions. International Journal of Rock Mechanics and Mining Sciences, 78, 46–56. doi:10.1016/j.ijrmms.2015.04.023.

    Article  Google Scholar 

  156. Park, B., & Min, K.-B. (2013). Discrete element modeling of transversely isotropic rock. 47th U.S. Rock Mechanics/Geomechanics Symposium.

    Google Scholar 

  157. Park, B., Park, B., & Min, K.-B. (2012). Discrete element modelling of shale as a transversely isotropic rock. ISRM Regional Symposium—7th Asian Rock Mechanics Symposium.

    Google Scholar 

  158. Brochard, L., Hantal, G., Laubie, H., Ulm, F., & Pellenq, R. (2013). Fracture mechanisms in organic-rich shales: Role of Kerogen. Fifth Biot Conference on Poromechanics (pp. 2471–2480).

    Google Scholar 

  159. Katti, D. R., Katti, K. S., & Alstadt, K. An insight into molecular scale interactions and in-situ nanomechanical properties of kerogen in green river oil shale. In V. S. Poromechanics (ed.), Proceedings Fifth Biot Conf. Poromechanics. ASCE, pp 2510–2516.

    Google Scholar 

  160. Zhang, Z., & Jamili, A. (2015). Modeling the Kerogen 3D molecular structure. doi:10.2118/175991-MS

  161. Cosenza, P., Prêt, D., Giraud, A., & Hedan, S. (2015). Effect of the local clay distribution on the effective elastic properties of shales. Mechanics of Materials, 84, 55–74. doi:10.1016/j.mechmat.2015.01.016.

    Article  Google Scholar 

  162. Hantal, G., Brochard, L., Laubie, H., Ebrahimi, D., Pellenq, R. J.-M., Ulm, F.-J., et al. (2014). Atomic-scale modelling of elastic and failure properties of clays. Molecular Physics, 112, 1294–1305. doi:10.1080/00268976.2014.897393.

    Article  Google Scholar 

  163. Bobko, C. P., Gathier, B., Ortega, J. A., Ulm, F.-J., Borges, L., & Abousleiman, Y. N. (2011). The nanogranular origin of friction and cohesion in shale-A strength homogenization approach to interpretation of nanoindentation results. International Journal for Numerical and Analytical Methods in Geomechanics, 35, 1854–1876. doi:10.1002/nag.984.

    Article  Google Scholar 

  164. Hassani, B., & Hinton, E. (1998). A review of homogenization and topology optimization II—analytical and numerical solution of homogenization equations. Computers and Structures, 69, 719–738. doi:10.1016/S0045-7949(98)00132-1.

    Article  MATH  Google Scholar 

  165. Chung, P. W., Tamma, K. K., & Namburu, R. R. (2001). Asymptotic expansion homogenization for heterogeneous media: Computational issues and applications. Composites Part Applied Science and Manufacturing, 32, 1291–1301. doi:10.1016/S1359-835X(01)00100-2.

    Article  Google Scholar 

  166. Fish, J., Shek, K., Pandheeradi, M., & Shephard, M. S. (1997). Computational plasticity for composite structures based on mathematical homogenization: Theory and practice. Computer Methods in Applied Mechanics and Engineering, 148, 53–73. doi:10.1016/S0045-7825(97)00030-3.

    Article  MathSciNet  MATH  Google Scholar 

  167. Ghosh, S., Lee, K., & Moorthy, S. (1995). Multiple scale analysis of heterogeneous elastic structures using homogenization theory and Voronoi cell finite element method. International Journal of Solids and Structures, 32, 27–62. doi:10.1016/0020-7683(94)00097-G.

    Article  MathSciNet  MATH  Google Scholar 

  168. Ghosh, S., Lee, K., & Moorthy, S. (1996). Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model. Computer Methods in Applied Mechanics and Engineering, 132, 63–116. doi:10.1016/0045-7825(95)00974-4.

    Article  MATH  Google Scholar 

  169. Fish, J., Chen, W., & Li, R. (2007). Generalized mathematical homogenization of atomistic media at finite temperatures in three dimensions. Computer Methods in Applied Mechanics and Engineering, 196, 908–922. doi:10.1016/j.cma.2006.08.001.

    Article  MathSciNet  MATH  Google Scholar 

  170. Feyel, F. (2003). A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua. Computer Methods in Applied Mechanics and Engineering, 192, 3233–3244. doi:10.1016/S0045-7825(03)00348-7.

    Article  MATH  Google Scholar 

  171. Forest, S., Pradel, F., & Sab, K. (2001). Asymptotic analysis of heterogeneous Cosserat media. International Journal of Solids and Structures, 38, 4585–4608. doi:10.1016/S0020-7683(00)00295-X.

    Article  MathSciNet  MATH  Google Scholar 

  172. Rezakhani, R., & Cusatis, G. (2015). Asymptotic expansion homogenization of discrete fine-scale models with rotational degrees of freedom for the simulation of quasi-brittle materials. Journal of the Mechanics and Physics of Solids, 88, 320–345.

    Article  MathSciNet  Google Scholar 

  173. Cusatis, G., Rezakhani, R., Alnaggar, M., Zhou, X., & Pelessone, D. (2014). Multiscale computational models for the simulation of concrete materials and structures. In N. Bícanić, H. Mang, G. Meschke, & R. de Borst (Eds.), Computer modeling concrete structures (pp. 23–38). Boca Raton: CRC Press.

    Chapter  Google Scholar 

  174. Li, W., Jin, C., Salviato, M., & Cusatis, G. (2015). Modeling of failure behavior of anisotropic shale using lattice discrete particle model. 49th U.S. Rock Mechanics/Geomechanics Symposium.

    Google Scholar 

  175. Cusatis, G., Mencarelli, A., Pelessone, D., & Baylot, J. (2011). Lattice Discrete Particle Model (LDPM) for failure behavior of concrete. II: Calibration and validation. Cement and Concrete Composites, 33, 891–905. doi:10.1016/j.cemconcomp.2011.02.010.

    Article  Google Scholar 

  176. Cusatis, G., Pelessone, D., & Mencarelli, A. (2011). Lattice Discrete Particle Model (LDPM) for failure behavior of concrete. I: Theory. Cement and Concrete Composites, 33, 881–890. doi:10.1016/j.cemconcomp.2011.02.011.

    Article  Google Scholar 

  177. Bramlette, M. N. (1946). The Monterey Formation of California and the origin of its siliceous rocks. (Vol. 212). US Government Printing Office.

    Google Scholar 

  178. Pelessone, D. (2006). MARS, modeling and analysis of the response of structures. User’s Man. ES3 Inc

    Google Scholar 

  179. Cho, J.-W., Kim, H., Jeon, S., & Min, K.-B. (2012). Deformation and strength anisotropy of Asan gneiss, Boryeong shale, and Yeoncheon schist. International Journal of Rock Mechanics and Mining Sciences, 50, 158–169. doi:10.1016/j.ijrmms.2011.12.004.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gianluca Cusatis .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Li, W., Jin, C., Cusatis, G. (2016). Integrated Experimental and Computational Characterization of Shale at Multiple Length Scales. In: Jin, C., Cusatis, G. (eds) New Frontiers in Oil and Gas Exploration. Springer, Cham. https://doi.org/10.1007/978-3-319-40124-9_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-40124-9_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40122-5

  • Online ISBN: 978-3-319-40124-9

  • eBook Packages: EnergyEnergy (R0)

Publish with us

Policies and ethics