Skip to main content
  • Submit
  • About
    • Editorial Board
    • PNAS Staff
    • FAQ
    • Rights and Permissions
    • Site Map
  • Contact
  • Journal Club
  • Subscribe
    • Subscription Rates
    • Subscriptions FAQ
    • Open Access
    • Recommend PNAS to Your Librarian
  • Log in
  • My Cart

Main menu

  • Home
  • Articles
    • Current
    • Latest Articles
    • Special Features
    • Colloquia
    • Collected Articles
    • PNAS Classics
    • Archive
  • Front Matter
  • News
    • For the Press
    • Highlights from Latest Articles
    • PNAS in the News
  • Podcasts
  • Authors
    • Information for Authors
    • Purpose and Scope
    • Editorial and Journal Policies
    • Submission Procedures
    • For Reviewers
    • Author FAQ
  • Submit
  • About
    • Editorial Board
    • PNAS Staff
    • FAQ
    • Rights and Permissions
    • Site Map
  • Contact
  • Journal Club
  • Subscribe
    • Subscription Rates
    • Subscriptions FAQ
    • Open Access
    • Recommend PNAS to Your Librarian

User menu

  • Log in
  • My Cart

Search

  • Advanced search
Home
Home

Advanced Search

  • Home
  • Articles
    • Current
    • Latest Articles
    • Special Features
    • Colloquia
    • Collected Articles
    • PNAS Classics
    • Archive
  • Front Matter
  • News
    • For the Press
    • Highlights from Latest Articles
    • PNAS in the News
  • Podcasts
  • Authors
    • Information for Authors
    • Purpose and Scope
    • Editorial and Journal Policies
    • Submission Procedures
    • For Reviewers
    • Author FAQ

New Research In

Physical Sciences

Featured Portals

  • Physics
  • Chemistry
  • Sustainability Science

Articles by Topic

  • Applied Mathematics
  • Applied Physical Sciences
  • Astronomy
  • Computer Sciences
  • Earth, Atmospheric, and Planetary Sciences
  • Engineering
  • Environmental Sciences
  • Mathematics
  • Statistics

Social Sciences

Featured Portals

  • Anthropology
  • Sustainability Science

Articles by Topic

  • Economic Sciences
  • Environmental Sciences
  • Political Sciences
  • Psychological and Cognitive Sciences
  • Social Sciences

Biological Sciences

Featured Portals

  • Sustainability Science

Articles by Topic

  • Agricultural Sciences
  • Anthropology
  • Applied Biological Sciences
  • Biochemistry
  • Biophysics and Computational Biology
  • Cell Biology
  • Developmental Biology
  • Ecology
  • Environmental Sciences
  • Evolution
  • Genetics
  • Immunology and Inflammation
  • Medical Sciences
  • Microbiology
  • Neuroscience
  • Pharmacology
  • Physiology
  • Plant Biology
  • Population Biology
  • Psychological and Cognitive Sciences
  • Sustainability Science
  • Systems Biology

Branching of hydraulic cracks enabling permeability of gas or oil shale with closed natural fractures

Saeed Rahimi-Aghdam, Viet-Tuan Chau, Hyunjin Lee, Hoang Nguyen, Weixin Li, Satish Karra, Esteban Rougier, Hari Viswanathan, Gowri Srinivasan, and Zdeněk P. Bažant
PNAS January 29, 2019 116 (5) 1532-1537; published ahead of print January 29, 2019 https://doi.org/10.1073/pnas.1818529116
Saeed Rahimi-Aghdam
aDepartment of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Viet-Tuan Chau
bEarth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Hyunjin Lee
aDepartment of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Hoang Nguyen
aDepartment of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Weixin Li
aDepartment of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Satish Karra
bEarth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Esteban Rougier
bEarth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Hari Viswanathan
bEarth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Gowri Srinivasan
cX Computational Physics Division, Los Alamos National Laboratory, Los Alamos, NM 87545;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Zdeněk P. Bažant
aDepartment of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208;dDepartment of Mechanical Engineering, Northwestern University, Evanston, IL 60208;eDepartment of Materials Science, Northwestern University, Evanston, IL 60208
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • For correspondence: z-bazant@northwestern.edu
  1. Contributed by Zdeněk P. Bažant, November 21, 2018 (sent for review October 29, 2018; reviewed by Huajian Gao and John Hutchinson)

  • Article
  • Figures & SI
  • Info & Metrics
  • PDF
Loading

This article requires a subscription to view the full text. If you have a subscription you may use the login form below to view the article. Access to this article can also be purchased.

Significance

Development of a realistic model of fracking would allow better control. It should make it possible to optimize various parameters such as the history of pumping, its rate or cycles, changes of viscosity, etc. This could lead to an increase of the percentage of gas extraction from the deep shale strata, which currently stands at about 5% and rarely exceeds 15%.

Abstract

While hydraulic fracturing technology, aka fracking (or fraccing, frac), has become highly developed and astonishingly successful, a consistent formulation of the associated fracture mechanics that would not conflict with some observations is still unavailable. It is attempted here. Classical fracture mechanics, as well as current commercial software, predict vertical cracks to propagate without branching from the perforations of the horizontal well casing, which are typically spaced at 10 m or more. However, to explain the gas production rate at the wellhead, the crack spacing would have to be only about 0.1 m, which would increase the overall gas permeability of shale mass about 10,000×. This permeability increase has generally been attributed to a preexisting system of orthogonal natural cracks, whose spacing is about 0.1 m. However, their average age is about 100 million years, and a recent analysis indicated that these cracks must have been completely closed by secondary creep of shale in less than a million years. Here it is considered that the tectonic events that produced the natural cracks in shale must have also created weak layers with nanocracking or microcracking damage. It is numerically demonstrated that seepage forces and a greatly enhanced permeability along the weak layers, with a greatly increased transverse Biot coefficient, must cause the fracking to engender lateral branching and the opening of hydraulic cracks along the weak layers, even if these cracks are initially almost closed. A finite element crack band model, based on a recently developed anisotropic spherocylindrical microplane constitutive law, demonstrates these findings [Rahimi-Aghdam S, et al. (2018) arXiv:1212.11023].

  • fracking
  • poromechanics
  • Biot coefficient
  • seepage forces
  • damage

Footnotes

  • ↵1To whom correspondence should be addressed. Email: z-bazant{at}northwestern.edu.
  • Author contributions: S.R.-A. and Z.P.B. designed research and conceived the mathematical model; S.R.-A., V.-T.C., H.L., H.N., W.L., S.K., E.R., H.V., G.S., and Z.P.B. performed research; S.R.-A. analyzed data; and S.R.-A. and Z.P.B. directed the research and wrote the paper.

  • Reviewers: H.G., Brown University; and J.H., Harvard University.

  • The authors declare no conflict of interest.

Published under the PNAS license.

View Full Text

Log in using your username and password

Forgot your user name or password?

Purchase access

You may purchase access to this article. This will require you to create an account if you don't already have one.

Subscribers, for more details, please visit our Subscriptions FAQ.

Please click here to log into the PNAS submission website.

PreviousNext
Back to top
Article Alerts
Email Article

Thank you for your interest in spreading the word on PNAS.

NOTE: We only request your email address so that the person you are recommending the page to knows that you wanted them to see it, and that it is not junk mail. We do not capture any email address.

Enter multiple addresses on separate lines or separate them with commas.
Branching of hydraulic cracks enabling permeability of gas or oil shale with closed natural fractures
(Your Name) has sent you a message from PNAS
(Your Name) thought you would like to see the PNAS web site.
Citation Tools
Branching of hydraulic cracks enabling permeability of gas or oil shale with closed natural fractures
Saeed Rahimi-Aghdam, Viet-Tuan Chau, Hyunjin Lee, Hoang Nguyen, Weixin Li, Satish Karra, Esteban Rougier, Hari Viswanathan, Gowri Srinivasan, Zdeněk P. Bažant
Proceedings of the National Academy of Sciences Jan 2019, 116 (5) 1532-1537; DOI: 10.1073/pnas.1818529116

Citation Manager Formats

  • BibTeX
  • Bookends
  • EasyBib
  • EndNote (tagged)
  • EndNote 8 (xml)
  • Medlars
  • Mendeley
  • Papers
  • RefWorks Tagged
  • Ref Manager
  • RIS
  • Zotero
Request Permissions
Share
Branching of hydraulic cracks enabling permeability of gas or oil shale with closed natural fractures
Saeed Rahimi-Aghdam, Viet-Tuan Chau, Hyunjin Lee, Hoang Nguyen, Weixin Li, Satish Karra, Esteban Rougier, Hari Viswanathan, Gowri Srinivasan, Zdeněk P. Bažant
Proceedings of the National Academy of Sciences Jan 2019, 116 (5) 1532-1537; DOI: 10.1073/pnas.1818529116
del.icio.us logo Digg logo Reddit logo Twitter logo CiteULike logo Facebook logo Google logo Mendeley logo
  • Tweet Widget
  • Facebook Like
  • Mendeley logo Mendeley
Proceedings of the National Academy of Sciences: 116 (7)
Current Issue

Submit

Sign up for Article Alerts

Jump to section

  • Article
    • Abstract
    • Fluid Flow in Porous Solid, Without or With Cracking Damage
    • Equilibrium in Two-Phase Solid and Biot Coefficient
    • Two-Phase FE Simulations for a Single Damage Band
    • Do the Seepage Forces Suffice to Induce Crack Branching?
    • Hydraulic Crack Branching in Two-Phase Porous Solid with Closed Natural Fractures
    • Conclusions
    • Acknowledgments
    • Footnotes
    • References
  • Figures & SI
  • Info & Metrics
  • PDF

You May Also be Interested in

Several aspects of the proposal, which aims to expand open access, require serious discussion and, in some cases, a rethink.
Opinion: “Plan S” falls short for society publishers—and for the researchers they serve
Several aspects of the proposal, which aims to expand open access, require serious discussion and, in some cases, a rethink.
Image credit: Dave Cutler (artist).
Several large or long-lived animals seem strangely resistant to developing cancer. Elucidating the reasons why could lead to promising cancer-fighting strategies in humans.
Core Concept: Solving Peto’s Paradox to better understand cancer
Several large or long-lived animals seem strangely resistant to developing cancer. Elucidating the reasons why could lead to promising cancer-fighting strategies in humans.
Image credit: Shutterstock.com/ronnybas frimages.
Featured Profile
PNAS Profile of NAS member and biochemist Hao Wu
 Nonmonogamous strawberry poison frog (Oophaga pumilio).  Image courtesy of Yusan Yang (University of Pittsburgh, Pittsburgh).
Putative signature of monogamy
A study suggests a putative gene-expression hallmark common to monogamous male vertebrates of some species, namely cichlid fishes, dendrobatid frogs, passeroid songbirds, common voles, and deer mice, and identifies 24 candidate genes potentially associated with monogamy.
Image courtesy of Yusan Yang (University of Pittsburgh, Pittsburgh).
Active lifestyles. Image courtesy of Pixabay/MabelAmber.
Meaningful life tied to healthy aging
Physical and social well-being in old age are linked to self-assessments of life worth, and a spectrum of behavioral, economic, health, and social variables may influence whether aging individuals believe they are leading meaningful lives.
Image courtesy of Pixabay/MabelAmber.

More Articles of This Classification

Physical Sciences

  • Deep elastic strain engineering of bandgap through machine learning
  • Single-molecule excitation–emission spectroscopy
  • Microscopic description of acid–base equilibrium
Show more

Engineering

  • Deep elastic strain engineering of bandgap through machine learning
  • Realizing the potential of dielectric elastomer artificial muscles
  • Directional pumping of water and oil microdroplets on slippery surface
Show more

Related Content

  • No related articles found.
  • Scopus
  • PubMed
  • Google Scholar

Cited by...

  • No citing articles found.
  • Google Scholar

Similar Articles

Site Logo
Powered by HighWire
  • Submit Manuscript
  • Twitter
  • Facebook
  • RSS Feeds
  • Email Alerts

Articles

  • Current Issue
  • Latest Articles
  • Archive

PNAS Portals

  • Classics
  • Front Matter
  • Teaching Resources
  • Anthropology
  • Chemistry
  • Physics
  • Sustainability Science

Information

  • Authors
  • Editorial Board
  • Reviewers
  • Press
  • Site Map

Feedback    Privacy/Legal

Copyright © 2019 National Academy of Sciences. Online ISSN 1091-6490