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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access March 25, 2019

A Graph Theoretic Approach for Spatial Analysis of Induced Fracture Networks

Deborah Glosser and Jennifer R. Bauer

Abstract

Drilling induced fractures are generated when excessive stresses around a borehole cause tensile failure of the wellbore wall. If stress concentrations are great enough, compressive failures can form in the region surrounding the wellbore, leading to wellbore breakout, and the potential compromise of wellbore integrity. Another category of induced fracture networks are hydraulically induced fractures, which are generated by the injection of pressurized fluids into the subsurface. Overlapping induced fracture networks between collocated wellbores may increase pathways in the subsurface, and create the potential for unwanted fluid leakage. The generation of induced fractures is greatly dependent upon the structural and geological characteristics. Probabilistic-based simulations are often used to model fracture systems. Several methods for modeling local fracture networks have been proposed in the literature. These models often involve the generation of randomly located fractures, and may have limited capabilities for honoring engineered fractures such as induced fracture networks. We present a graph theoretic approach for identifying geospatial regions and wellbores at increased risk for subsurface connectivity based on wellbore proximity and local lithologic characteristics. The algorithm is coded in Matlab, and transforms 3 dimensional geospatial data to graph form for rapid computation of pairwise and topological relationships between wellbores (nodes), andthe spatial radius of induced fractures (edges). Induced fracture reaches are represented as cylinders with a radius r, based on literature derived ranges for fracture lengths for different lithologies (e.g. shale, sandstone).

The topological algorithm is compared to a standard graph-based k-nearest neighbor algorithm to demonstrate the value of incorporating lithologic attributes in graph-based fracture models. The algorithms are applied to two scenarios using Pennsylvania wellbore and lithologic data: a subset of data from the Bradford field, as well as a known leakage scenario in Armstrong County. The topological algorithm presented in this paper can be used to complement existing fracture models to better account for the reach of induced fractures, and to identify spatial extents at increased risk for unwanted subsurface connectivity. As a result, the method presented in this paper can be part of a cumulative strategy to reduce uncertainty inherent to combined geologic and engineered systems. The model output provides valuable information for industry to develop environmentally safe drilling and injection plans; and for regulators to identify specific wellbores at greater risk for leakage, and to develop targeted, science-based monitoring policies for higher risk regions.

References

1. D. Glosser, K. Rose, and J. Bauer, Spatio-temporal analysis to constrain uncertainty in wellbore datasets: an adaptable analytical approach in support of science-based decision making. Journal of Sustainable Energy Engineering, in press (2016).10.7569/JSEE.2016.629502Search in Google Scholar

2. State Oil and Gas Groundwater Investigations and Their Role in Advancing Regulatory Reforms a Two-State Review: Ohio and Texas, Groundwater Protection Council (2011).Search in Google Scholar

3. K.M Keranen, H.M. Savage, G.A. Abers, and E.S. Cochran, Potentially induced earthquakes in Oklahoma, USA: Links between wastewater injection and the 2011 Mw 5.7 earthquake sequence. Geology41(6), 699–702 (2013).10.1130/G34045.1Search in Google Scholar

4. D. Soeder, S. Sharma, N. Pekney, L. Hopkinson R. Dilmore, B. Kutchko, et al., An approach for assessing engineering risk from shale gas wells in the United States. In International Journal of Coal Geology, Special Issue: Unconventional Natural Gas and the Environment (2014) (in press).10.1016/j.coal.2014.01.004Search in Google Scholar

5. W. Ellsworth, Injection induced earthquakes. Science.341(6142), 1225942 (2013).10.1126/science.1225942Search in Google Scholar

6. J. A. Montague and G. F. Pinder, Potential of hydraulically induced fractures to communicate with existing wellbores. Water Resources Research51(10), 8303–8315 (2015).10.1002/2014WR016771Search in Google Scholar

7. M. TIngay, J. Reinicker, and B. Muller, Borehole breakout and drilling-induced fracture analysis from image logs. World Stress Map Project (2008).Search in Google Scholar

8. M. D. Zoback, D. Moos, and L. Mastin, Well Bore Breakouts and in Situ Stress, J. Geophys. Res., USGS Staff Published Paper, 90, B7, pp. 5523–5530 (1985).10.1029/JB090iB07p05523Search in Google Scholar

9. R.M Dilmore, J.I. Sams, D.B. Glosser, and K.M. Carter, Spatial and temporal characteristics of historical oil and gas wells in Pennsylvania: implications for new shale gas resources. Environmental Science and Technology49, 12015–12023 (2015).10.1021/acs.est.5b00820Search in Google Scholar

10. National Energy Technology Laboratory, FracGen and NNFlow software v. 14.9, https://edx.netl.doe.gov/dataset/fracgen-and-nfflow-version-14-9 accessed 4/11/2016.Search in Google Scholar

11. P. Valko and M.J. Economides, Propagation of Hydraulically Induced Fractures – A Continuum Damage Mechanics Approach. International Journal of Rock Mechanics, Mineral Science, and Geochemistry31(3) 221–229 (1994).10.1016/0148-9062(94)90466-9Search in Google Scholar

12. C. Zeeb, E. Gomez-Rivez, P. Bons, S. Virgo, and P. Blum, Fracture network evaluation program (FraNEP): A software for analyzing 2D fracture trace-line maps. Computers and Geoscience60, 11–22 (2013).10.1016/j.cageo.2013.04.027Search in Google Scholar

13. J. Pach, Geometric Graph Theory, Mathematical Institute of Hungarian Academy of Sciences,http://dcg.epfl.ch/page-117408-en.html accessed 4/11/2016.Search in Google Scholar

14. L. D. Cohen and R. Kimmel, Global minimum for active contour models: A minimal path approach. International Journal of Computer Vision24(1), 57–78 (1997).10.1023/A:1007922224810Search in Google Scholar

15. J. Pereira-Leal, A. Enright, and C. Ouzounis. Detection of functional modules from protein interaction networks. PROTEINS: Structure, Function and Bioinformatics54, 49–57 (2004).Search in Google Scholar

16. S. Yook, Z. Oltvai, and A. Barabasi, Functional and topological characterization of protein interaction networks. Proteomics4, 928–942 (2004).10.1002/pmic.200300636Search in Google Scholar

17. M. Alizadeh, Z. Movahed, R. Junin, R. Mohsin, M. Alizadeh, and M. Alizadeh, Finding the Drilling Induced Fractures and Borehole Breakouts Using Image Logs. Journal of Advanced Research10(1), 9–30 (2015).Search in Google Scholar

18. West Virginia Geologic and Environmental Survey, Interactive Mapping http://ims.wvgs.wvnet.edu/index.html (2015).Search in Google Scholar

19. N.-N.G. Intellingence Agency of EUA, World Geodetic System 1984, WGS-84. p. 3 (1984).Search in Google Scholar

20. W. Dong, C. Moses, and K. Li, Efficient k-nearest neighbor graph construction for generic similarity measures. WWW 577–586 (2011).10.1145/1963405.1963487Search in Google Scholar

21. V. Garcia, E. Debreuve, and M. Barlaud, Fast k nearest neighbor search using GPU. 2008 IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit. Work. 2, 1–6 (2008).Search in Google Scholar

22. Y. P. Mack and M. Rosenblatt, Multivariate k-nearest neighbor density estimates. J. Multivar. Anal. 9(1), 1–15 (1979).10.1016/0047-259X(79)90065-4Search in Google Scholar

23. R. Hammack, G. Veloski, and J. Sams, Rapid Methods for Locating Existing Well Penetrations in Unconventional Well Development Areas of Pennsylvania, Unconventional Resources Technology Conference, 20–22 July, San Antonio, SPE-178558-MS (2015).10.2118/178558-MSSearch in Google Scholar

24. PA DCNR. The Pennsylvania Internet Record Imaging System/Wells Information System (PA*IRIS/WIS): Gateway to Detailed Oil and Gas Well Information Data http://www.pairis.state.pa.us accessed during 2013.Search in Google Scholar

25. Pennsylvania Spatial Data Access Center, Oil and Gas Wells in Pennsylvania, http://www.pasda.psu.edu/ accessed during 2013.Search in Google Scholar

26. R. Arnold and W.J. Kemnitzer, Petroleum in the United States and possessions: a presentation and interpretation of the salient data of geology, technology, and economics of petroleum in each state and possession treated according to the conventional major field divisions; Harper & brothers (1931).Search in Google Scholar

27. US Geological Survey. Minerals Yearbook Digital Collection http://digital.library.wisc.edu/1711.dl/EcoNatRes.MineralsYearBk.Search in Google Scholar

28. Pennsylvania Spatial Data Access Center, Geology of Pennsylvania, http://www.pasda.psu.edu/ accessed during 2015.Search in Google Scholar

29. Department of Environmental Protection, Stray Natural Gas Migration Associated with Oil and Gas Wells http://www.dep.state.pa.us/dep/subject/advcoun/oil_gas/2009/Stray%20Gas%20Migration%20Cases.pdf Accessed during 2016.Search in Google Scholar

30. DEP Office of Oil and Gas Management Compliance Report, inspection ID 1692786 http://www.depreportingservices.state.pa.us/ReportServer/Pages/ReportViewer.aspx?/Oil_Gas/OG_Compliance accessed during 2016.Search in Google Scholar

31. M. Brudy and M.D. Zoback, Drilling induced tensile well fractures: implications for determination of in situ stress orientation and magnitude. International Journal of Rock Mechanics and Mining Sciences36, 191–215 (1999).10.1016/S0148-9062(98)00182-XSearch in Google Scholar

32. J.R. de Druezy, P. Davy, and O. Bour, Hydraulic properties of two dimensional random fracture networks following a power law length distribution. Water Resources Research37(8), 2065–2078 (2001).10.1029/2001WR900011Search in Google Scholar

33. N.E. Odling, Scaling and connectivity of joint systems in sandstones from western Norway. J. Struct. Geol.19, 1257–1271 (1997).10.1016/S0191-8141(97)00041-2Search in Google Scholar

34. O. Bour and P. Davy, Connectivity of random fault networks following a power law fault length distribution. Water Resour. Res. 33, 1567–1583 (1997).10.1029/96WR00433Search in Google Scholar

Received: 2016-05-27
Accepted: 2016-08-26
Published Online: 2019-03-25
Published in Print: 2016-12-01

© 2016 Deborah Glosser et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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