Research Papers

Why Fracking Works

[+] Author and Article Information
Zdeněk P. Bažant

McCormick Institute Professor and
W.P. Murphy Professor of Civil and Mechanical
Engineering and Materials Science,
Northwestern University,
2145 Sheridan Road,
CEE/A135, Evanston, IL 60208
e-mail: z-bazant@northwestern.edu

Marco Salviato, Viet T. Chau

Department of Civil
and Environmental Engineering,
Northwestern University,
2145 Sheridan Road,
Evanston, IL 60208

Hari Viswanathan

Subsurface Flow and Transport Team Leader
Computational Earth Science,
EES-16, Sch. A,
Los Alamos National Laboratory,
Los Alamos, NM 87545

Aleksander Zubelewicz

Los Alamos National Laboratory,
Los Alamos, NM 87545

Although this term is often used pejoratively, it is adopted here because of its brevity. If used in science, it will cease to be disparaging.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States government purposes.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 6, 2014; final manuscript received August 4, 2014; accepted manuscript posted August 7, 2014; published online August 27, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(10), 101010 (Aug 27, 2014) (10 pages) Paper No: JAM-14-1295; doi: 10.1115/1.4028192 History: Received July 06, 2014; Revised August 04, 2014; Accepted August 07, 2014

Although spectacular advances in hydraulic fracturing, also known as fracking, have taken place and many aspects are well understood by now, the topology, geometry, and evolution of the crack system remain an enigma and mechanicians wonder: Why fracking works? Fracture mechanics of individual fluid-pressurized cracks has been clarified but the vital problem of stability of interacting hydraulic cracks escaped attention. First, based on the known shale permeability, on the known percentage of gas extraction from shale stratum, and on two key features of the measured gas outflow which are (1) the time to peak flux and (2) the halftime of flux decay, it is shown that the crack spacing must be only about 0.1 m. Attainment of such a small crack spacing requires preventing localization in parallel crack systems. Therefore, attention is subsequently focused on the classical solutions of the critical states of localization instability in a system of cooling or shrinkage cracks. Formulated is a hydrothermal analogy which makes it possible to transfer these solutions to a system of hydraulic cracks. It is concluded that if the hydraulic pressure profile along the cracks can be made almost uniform, with a steep enough pressure drop at the front, the localization instability can be avoided. To achieve this kind of profile, which is essential for obtaining crack systems dense enough to allow gas escape from a significant portion of kerogen-filled nanopores, the pumping rate (corrected for the leak rate) must not be too high and must not be increased too fast. Furthermore, numerical solutions are presented to show that an idealized system of circular equidistant vertical cracks propagating from a horizontal borehole behaves similarly. It is pointed out that one useful role of the proppants, as well as the acids that promote creation of debris in the new cracks, is to partially help to limit crack closings and thus localization. To attain the crack spacing of only 0.1 m, one must imagine formation of hierarchical progressively refined crack systems. Compared to new cracks, the system of pre-existing uncemented natural cracks or joints is shown to be slightly more prone to localization and thus of little help in producing the fine crack spacing required. So, from fracture mechanics viewpoint, what makes fracking work?–the mitigation of fracture localization instabilities. This can also improve efficiency by fracturing more shale. Besides, it is environmentally beneficial, by reducing flowback per m3 of gas. So is the reduction of seismicity caused by dynamic fracture instabilities (which are more severe in underground CO2 sequestration).

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Beckwith, R., 2010, “Hydraulic Fracturing: The Fuss, the Facts, the Future,” J. Pet. Technol., 62(12), pp. 34–41.
Montgomery, C. T., and Smith, M. B., 2010, “Hydraulic Fracturing: History of an Enduring Technology,” J. Pet. Technol., 62(12), pp. 26–32.
Society of Petroleum Engineers, 2010, Legends of Hydraulic Fracturing, (CDROM), Society of Petroleum Engineers, Richardson, TX.
Adachi, J. I., and Detournay, E., 2008, “Plane Strain Propagation of a Hydraulic Fracture in a Permeable Rock,” Eng. Fract. Mech., 75(16), pp. 4666–4694. [CrossRef]
Gale, J. F. W., Reed, R. M., and Holder, J., 2007, “Natural Fractures in the Barnett Shale and Their Importance for Fracture Treatments,” AAPG Bull., 91(4), pp. 603–622. [CrossRef]
Bažant, Z. P., Salviato, M., and Chau, V. T., 2014, “Why Fracking Works and How to Optimize It,” Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL, Report No. 14-06/008w.
Cipolla, C. L., Mayerhofer, M. J., and Warpinski, N. R., 2009, “Fracture Design Considerations in Horizontal Wells Drilled in Unconventional Gas Reservoirs,” SPE Hydraulic Fracturing Technology Conference, Woodlands, TX, January 19–21.
Rijken, P., and Cooke, M. L., 2001, “Role of Shale Thickness on Vertical Connectivity of Fractures: Application of Crack-Bridging Theory to the Austin Chalk,” Tectonophysics, 337(1–2), pp. 117–133. [CrossRef]
Haifeng, Z., Hang, L., Guohua, C., Yawei, L., Jun, S., and Peng, R., 2013, “New Insight Into Mechanisms of Fracture Network Generation in Shale Gas Reservoir,” J. Pet. Sci. Eng., 110, pp. 193–198. [CrossRef]
Ajayi, B., Aso, I. I., Terry, I. J., Walker, K., Wutherich, K., Caplan, J., Gerdorn, D. W., Clark, B. D., Gunguly, U., Li, X., Xu, Y., Yang, H., Liu, H., Luo, Y., and Waters, G., 2013, “Stimulation Design for Unconventional Resurces,” Oilfield Rev., 25(2), pp. 34–46.
Gale, J. F. W., 2002, “Specifying Lengths of Horizontal Wells in Fractured Reservoirs,” SPE Reservoir Eval. Eng., 5(3), pp. 266–272. [CrossRef]
Olson, J. E., 2004, “Predicting Fracture Swarms—The Influence of Subcritical Crack Growth and the Crack-Tip Process Zone on Joint Spacing in Rock,” J. Geol. Soc. London, 231, pp. 73–87. [CrossRef]
Louck, R. G., Reed, R. M., Ruppel, S. C., and Jarvie, D. M., 2009, “Morphology, Genesis, and Distribution of Nanometer-Scale Pores in Siliceous Mudstones of the Mississippian Barnett Shale,” J. Sediment. Res., 79(12), pp. 848–861. [CrossRef]
Javadpour, F., Fisher, D., and Unsworth, M., 2007, “Nanoscale Gas Flow in Shale Gas Sediments,” J. Can. Pet. Technol., 46(10), pp. 55–61. [CrossRef]
Javadpour, F., 2009, “Nanopores and Apparent Permeability of Gas Flow in Mudrocks (Shales and Siltstones),” J. Can. Pet. Technol., 48(8), pp. 16–21. [CrossRef]
Maurel, O., Reess, T., Matallah, M., de Ferron, A., Chen, W., La Borderie, C., Pijaudier-Cabot, G., Jacques, A., and Rey-Bethbeder, F., 2010, “Electrohydraulic Shock Wave Generation as a Means to Increase Intrinsic Permeability of Mortar,” Cem. Concr. Res., 40(12), pp. 1631–1638. [CrossRef]
Soeder, D. J., 1988, “Porosity and Permeability of Eastern Devonian Gas Shale,” SPE Form. Eval., 3(1), pp. 116–124. [CrossRef]
Cui, X., Bustin, A. M. M., and Bustin, R. M., 2009, “Measurements of Gas Permeability and Diffusivity of Tight Reservoir Rocks: Different Approaches and Their Applications,” Geofluids, 9(3), pp. 208–223. [CrossRef]
Metwally, Y. M., and Sondergeld, C. H., 2010, “Measuring Low Permeabilities of Gas-Sands and Shales Using a Pressure Transmission Technique,” Int. J. Rock Mech. Min. Sci., 48(7), pp. 1135–1144. [CrossRef]
Guidry, K., Luffel, D., and Curtis, J., 1996, “Development of Laboratory and Petrophysical Techniques for Evaluating Shale Reservoirs: Final Technical Report, October 1986–September 1993,” Gas Shale Project Area, ResTech, Inc., Houston, TX, GRI Contract No. 5086-213-1390, Report No. GRI-95/0496.
API, 1998, Recommended Practices for Core Analysis, 2nd ed., American Petroleum Institute, Washington, DC, Recommended Practice 40.
Adachi, J., Siebrits, E., and Peirce, A., 2007, “Computer Simulation of Hydraulics Fractures,” Int. J. Rock Mech. Min. Sci., 44(5), pp. 739–757. [CrossRef]
Bear, J., 1988, Dynamics of Fluids in Porous Media, American Dover Publications, Mineola, NY.
Stevenson, A. C., 1945, “Complex Potentials in Two-Dimensional Elasticity,” Proc. R. Soc. London, Ser. A, 184(997), pp. 129–179. [CrossRef]
Mason, J. E., 2011, “Well Production Profiles Assess Fayetteville Shale Gas Potential,” Oil Gas J., 109(14), pp. 76–81. [CrossRef]
Bažant, Z. P., and Ohtsubo, R., 1978, “Geothermal Heat Extraction by Water Circulation Through a Large Crack in Dry Hot Rock Mass,” Int. J. Numer. Anal. Methods Geomech., 2(4), pp. 317–327. [CrossRef]
Bažant, Z. P., and Ohtsubo, H., 1977, “Stability Conditions for Propagation of a System of Cracks in a Brittle Solid,” Mech. Res. Commun., 4(5), pp. 353–366. [CrossRef]
Bažant, Z. P., and Cedolin, L., 1991, Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories, Oxford University Press, New York.
Bažant, Z. P., and Cedolin, L., 2003, Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories, 2nd. ed., Dover Publications, Mineola, NY.
Bažant, Z. P., and Cedolin, L., 2010, Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories, 3rd ed., World Scientific, Singapore.
Bažant, Z. P., Ohtsubo, R., and Aoh, K., 1979, “Stability and Post-Critical Growth of a System of Cooling and Shrinkage Cracks,” Int. J. Fract., 15(5), pp. 443–456. [CrossRef]
Nemat-Nasser, S., Keer, L. M., and Parihar, K. S., 1976, “Unstable Growth of Thermally Induced Interacting Cracks in Brittle Solids,” Int. J. Solids Struct., 14(6), pp. 409–430. [CrossRef]
Bažant, Z. P., and Wahab, A. B., 1979, “Instability and Spacing of Cooling or Shrinkage Cracks,” J. Eng. Mech.-ASCE, 105(5), pp. 873–889.
Chen, W., Maurel, O., Reess, T., de Ferron, A., La Borderie, C., Pijaudier-Cabot, G., Rey-Bethbeder, F., and Jacques, A., 2012, “Experimental Study on an Alternative Oil Stimulation Technique for Tight Gas Reservoirs Based on Dynamic Shock Waves Generated by Pulsed Arc Electrohydraulic Discharges,” J. Pet. Sci. Eng., 88–89, pp. 67–74. [CrossRef]
Safari, R., Huang, J., Mutlu, U., and Glanville, J., 2014, “3D Analysis and Engineering Design of Pulsed Fracturing in Shale Gas Reservoirs,” 48th U.S. Rock Mechanics/Geomechanics Symposium, Minneapolis, MN, June 1-4.
Bažant, Z. P., and Caner, F. C., 2013, “Comminution of Solids Caused by Kinetic Energy of High Shear Strain Rate, With Implications for Impact, Shock and Shale Fracturing,” Proc. Natl. Acad. Sci. U.S.A., 110(48), pp. 19291–19294. [CrossRef] [PubMed]
Bažant, Z. P., and Caner, F. C., 2014, “Impact Comminution of Solids Due to Local Kinetic Energy of High Shear Strain Rate: I. Continuum Theory and Turbulence Analogy,” J. Mech. Phys. Solids, 64, pp. 223–235 (with Corrigendum, 2014, 67, p. 14). [CrossRef]
Timoshenko, S., and Goodier, J. N., 1970, Theory of Elasticity, 3rd ed., McGraw-Hill, New York, Secs. 62, 63.


Grahic Jump Location
Fig. 1

Overall scheme of hydraulic fracturing: (a) one of many segments, subdivided in 5–8 fracturing stages; (b) one fracturing stage composed of 5–8 pipe perforation cluster; (c) one perforation cluster with 5–8 perforations along the pipes (not to scale)

Grahic Jump Location
Fig. 2

Schematic of gas flow from shale to surface, showing a layer of shale between two open vertical hydraulic cracks of spacing s, with subsequent profiles of gas pressure p, and the passage of gas to the surface

Grahic Jump Location
Fig. 3

Schematic of (a) the volume of shale stratum to be fracked, considered for the purpose of analysis as elliptical cylinder, and a scaled-down cylinder representing the portion of shale volume that is actually fracked; (b) undeformed and (c) deformed cross sections of the scaled cylinder, reduced according to the known percentage of terminal gas extraction from the shale

Grahic Jump Location
Fig. 4

Histories of gas flux at the surface observed at five different sites of Fayetteville shale [25], in actual and logarithmic time scales. Top row: curves of optimum fits; middle row: curves when characteristic delay time τ is changed; bottom row: curves when the crack spacing s is changed

Grahic Jump Location
Fig. 5

Path of the lengths of thermal cooling cracks in the crack length space, adapted from Ref. [26]

Grahic Jump Location
Fig. 6

Schematic representation of fracturing behavior (a) with crack localization—undesirable, and (b) without crack localization—desirable (prevention of localization greatly increases the percentage of gas that can be reached from the shale stratum by hydraulic fracturing)

Grahic Jump Location
Fig. 7

Leading crack length as a function of the depth of penetration front, for different temperature profiles along the cracks, adapted from Ref. [26]

Grahic Jump Location
Fig. 8

Analogy of thermal and hydraulic cracks. The formation of the cooling cracks (a) can be decomposed into two steps: in the first step (b) the cracks are imagined to be glued so as to be kept closed. In the second step (c), the cracks are imagined to be unglued and allowed to open.

Grahic Jump Location
Fig. 9

(a) Idealized circular hydraulic cracks around a horizontal borehole considered for simple analysis of localization instability (not to scale) and (b) dimensionless critical crack lengths as a function of dimensionless applied pressure Π1=(p0-σh)/E for different hydraulic pressure profiles shown. The results show that nearly uniform pressure profiles prevent localization.

Grahic Jump Location
Fig. 10

Schematic horizontal section showing how a hierarchical refinement of hydraulic crack system may lead to crack spacing of about 0.1 m



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