Development of Proxy Model for Hydraulic Fracturing and Seismic Wave Propagation Processes

  • Manik SinghEmail author
  • Sanjay Srinivasan
Special Issue


Characterization of discrete fracture networks is necessary for unconventional reservoir development, as they control the flow of fluids toward the hydraulically fractured well. Interpretation of microseismic data provides information about the discrete fracture network in the vicinity of a well. While microseismic interpretation is currently based on plotting the swarm of microseismic events, the inference of fracture-related information from such data is likely to be non-unique. To address this non-uniqueness, the presented workflow involves applying a forward model that produces a synthetic seismogram corresponding to a suite of natural fractured reservoir models. The characteristics of the generated seismograms can be compared with the observed seismogram to determine the suite of fracture models that best reflect the observed seismic signature. The available full physics models are computationally expensive and cannot be applied within this framework. Hence, a proxy model is developed that is computationally inexpensive so that it can be applied on a large ensemble of models within the Bayesian model selection framework described above. Seismic wave propagation during a fracturing job involves many intermediate processes such as diffraction and reflection. As analytical solutions for most of these processes exist, a coupled analytical model is proposed. Firstly, a hydraulic fracture propagation model is coupled with a model for the interaction between a hydraulic fracture and a natural fracture. This interaction results in slip events along natural fractures that in turn can trigger a seismic event. With knowledge of the location of the slip event, a Green’s function solution is applied to model the propagation of the seismic wave. Using the results from the slip event and Green’s function, a synthetic seismogram is generated. Finally, the seismic signature from multiple slip events along several natural fractures is combined. Validation of individual elements of the coupled proxy model to experiments is shown. A comparison of the developed proxy model with more computationally expensive models is also performed.


Proxy modeling Microseismic Fracture propagation Seismic wave propagation 



Support from NSF in the form of Grant UP60D60 is gratefully acknowledged. Funding was provided by the Directorate for Computer and Information Science and Engineering.


  1. Adachi J, Siebrits E, Peirce A, Desroches J (2007) Computer simulation of hydraulic fractures. Int J Rock Mech Min Sci 44(5):739–757CrossRefGoogle Scholar
  2. Aki K, Richards PG (2002) Quantitative seismology. University Science Books, SausalitoGoogle Scholar
  3. Blanton TL (1982) An experimental study of interaction between hydraulically induced and pre-existing fractures. In: SPE unconventional gas recovery symposium, Society of Petroleum EngineersGoogle Scholar
  4. Bouchon M (2003) A review of the discrete wavenumber method. Pure Appl Geophys 160(3):445–465CrossRefGoogle Scholar
  5. Bunger AP, Detournay E, Garagash DI (2005) Toughness-dominated hydraulic fracture with leak-off. Int J Fract 134(2):175–190CrossRefGoogle Scholar
  6. Detournay E, Garagash D (2003) The near-tip region of a fluid-driven fracture propagating in a permeable elastic solid. J Fluid Mech 494:1–32CrossRefGoogle Scholar
  7. Detournay E, Peirce A, Bunger A (2007) Viscosity-dominated hydraulic fractures. In: 1st Canada-US rock mechanics symposium, American Rock Mechanics AssociationGoogle Scholar
  8. Economides MJ, Nolte KG (1989) Reservoir stimulation, vol 2. Prentice Hall, Englewood CliffsGoogle Scholar
  9. Garagash DI (2006) Propagation of a plane-strain hydraulic fracture with a fluid lag: early-time solution. Int J Solids Struct 43(18):5811–5835CrossRefGoogle Scholar
  10. Geertsma J, De Klerk F (1969) A rapid method of predicting width and extent of hydraulically induced fractures. J Pet Technol 21(12):1–571CrossRefGoogle Scholar
  11. Gu H, Weng X, Lund JB, Mack MG, Ganguly U, Suarez-Rivera R (2012) Hydraulic fracture crossing natural fracture at nonorthogonal angles: a criterion and its validation. SPE Prod Oper 27(01):20–26Google Scholar
  12. Gudmundsson A (2011) Rock fractures in geological processes. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  13. Guglielmi Y, Cappa F, Avouac JP, Henry P, Elsworth D (2015) Seismicity triggered by fluid injection-induced aseismic slip. Science 348(6240):1224–1226CrossRefGoogle Scholar
  14. Herrmann RB (2013) Computer programs in seismology: an evolving tool for instruction and research. Seismol Res Lett 84:1081–1088CrossRefGoogle Scholar
  15. Huang W, Wang R, Li H, Chen Y (2017) Unveiling the signals from extremely noisy microseismic data for high-resolution hydraulic fracturing monitoring. Sci Rep 7(1):11996CrossRefGoogle Scholar
  16. Khristianovic S, Zheltov Y (1955) Formation of vertical fractures by means of highly viscous liquid. In: 4th world petroleum congress, World Petroleum CongressGoogle Scholar
  17. Mangrove (2017) Petrel simulation suite. Schlumberger, HoustonGoogle Scholar
  18. Nordgren R (1972) Propagation of a vertical hydraulic fracture. Soc Pet Eng J 12(04):306–314CrossRefGoogle Scholar
  19. Perkins T, Kern L (1961) Widths of hydraulic fractures. J Pet Technol 13(09):937–949CrossRefGoogle Scholar
  20. Potluri N, Zhu D, Hill A D (2005) The effect of natural fractures on hydraulic fracture propagation. In: SPE European formation damage conference, society of petroleum engineersGoogle Scholar
  21. Renshaw C, Pollard D (1995) An experimentally verified criterion for propagation across unbounded frictional interfaces in brittle, linear elastic materials. Int J Rock Mech Min Sci Geomech Abstr 32:237–249CrossRefGoogle Scholar
  22. Sneddon IN (1946) The distribution of stress in the neighbourhood of a crack in an elastic solid. Proc R Soc Lond A 187(1009):229–260CrossRefGoogle Scholar
  23. Tanioka Y, Ruff LJ (1997) Source time functions. Seismol Res Lett 68(3):386–400CrossRefGoogle Scholar
  24. Warpinski N, Teufel L (1987) Influence of geologic discontinuities on hydraulic fracture propagation (includes associated papers 17011 and 17074). J Pet Technol 39(02):209–220CrossRefGoogle Scholar
  25. Warpinski N, Abou-Sayed I, Moschovidis Z, Parker C (1993) Hydraulic fracture model comparison study: complete results. Technical report, Sandia National Labs., Albuquerque, NM (United States); Gas Research Inst., Chicago, IL (United States)Google Scholar

Copyright information

© International Association for Mathematical Geosciences 2019

Authors and Affiliations

  1. 1.Department of Energy and Mineral EngineeringThe Pennsylvania State UniversityState CollegeUSA

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