Skip to main content
SpringerLink
Log in

A DG Method for the Simulation of CO2 Storage in Saline Aquifer

  • Conference paper
  • First Online:
Advances in the Mathematical Sciences (AWMRS 2017)

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 15))

Included in the following conference series:

Abstract

To simulate the process of CO2 injection into deep saline aquifers, we use the isothermal two-phase two-component model, which takes mass transfer into account. We develop a new discontinuous Galerkin method called the “partial upwind” method for space discretization, incorporated with the backward Euler scheme for time discretization and the Newton–Raphson method for linearization. Numerical simulations show that the new method is a promising candidate for the CO2 storage problem in both homogenous and heterogenous porous media and is more robust to the standard discontinuous Galerkin method for some subsurface fluid flow problems.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

References

  1. P. Bastian, A fully coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure. Comput. Geosci. 18(5), 779–796 (2014)

    Article  MathSciNet  Google Scholar 

  2. P. Bastian, B. Riviere, Discontinuous Galerkin methods for two-phase flow in porous media. Technical Reports of the IWR (SFB 359) of the Universität Heidelberg, 2004

    Google Scholar 

  3. R.H. Brooks, A.T. Corey, Hydraulic Properties of Porous Media. Colorado State University Hydrology Papers, vol. 3 (Colorado State University, Fort Collins, 1964)

    Google Scholar 

  4. H. Class, A. Ebigbo, R. Helmig, H.K. Dahle, J.M. Nordbotten, M.A. Celia, P. Audigane, M. Darcis, J. Ennis-King, Y. Fan, et al., A benchmark study on problems related to CO2 storage in geologic formations. Comput. Geosci. 13(4), 409–434 (2009)

    Article  Google Scholar 

  5. Y. Epshteyn, B. Riviere, Fully implicit discontinuous finite element methods for two-phase flow. Appl. Numer. Math. 57(4), 383–401 (2007)

    Article  MathSciNet  Google Scholar 

  6. Y. Epshteyn, B. Riviere, Convergence of high order methods for miscible displacement. Int. J. Numer. Anal. Model. 5, 4763 (2008)

    MathSciNet  MATH  Google Scholar 

  7. A. Ern, I. Mozolevski, Discontinuous Galerkin method for two-component liquid–gas porous media flows. Comput. Geosci. 16(3), 677–690 (2012)

    Article  MathSciNet  Google Scholar 

  8. A. Ern, I. Mozolevski, L. Schuh, Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures. Comput. Methods Appl. Mech. Eng. 199(23), 1491–1501 (2010)

    Article  MathSciNet  Google Scholar 

  9. O. Eslinger, Discontinuous Galerkin finite element methods applied to two-phase, air-water flow problems, PhD thesis, The University of Texas at Austin, 2005

    Google Scholar 

  10. V. Girault, J. Li, B. Riviere, Strong convergence of the discontinuous Galerkin scheme for the low regularity miscible displacement equations. Numer. Methods Partial Differential Equations 33(2), 489513 (2017)

    Article  MathSciNet  Google Scholar 

  11. H. Huang, G. Scovazzi, A high-order, fully coupled, upwind, compact discontinuous Galerkin method for modeling of viscous fingering in compressible porous media. Comput. Methods Appl. Mech. Eng. 263, 169–187 (2013)

    Article  MathSciNet  Google Scholar 

  12. W. Klieber, B. Rivière, Adaptive simulations of two-phase flow by discontinuous Galerkin methods. Comput. Methods Appl. Mech. Eng. 196(1), 404–419 (2006)

    Article  MathSciNet  Google Scholar 

  13. J. Li, B. Riviere, High order discontinuous Galerkin method for simulating miscible flooding in porous media. Comput. Geosci. 19(6), 12511268 (2015)

    Article  MathSciNet  Google Scholar 

  14. J. Li, B. Riviere, Numerical modeling of miscible viscous fingering instabilities by high-order methods. Transp. Porous Media 113(3), 607628 (2016)

    Article  MathSciNet  Google Scholar 

  15. G. Scovazzi, A. Gerstenberger, S.S. Collis, A discontinuous Galerkin method for gravity-driven viscous fingering instabilities in porous media. J. Comput. Phys. 233, 373–399 (2013)

    Article  MathSciNet  Google Scholar 

  16. G. Scovazzi, H. Huang, S.S. Collis, J. Yin, A fully-coupled upwind discontinuous Galerkin method for incompressible porous media flows: high-order computations of viscous fingering instabilities in complex geometry. J. Comput. Phys. 252, 86–108 (2013)

    Article  MathSciNet  Google Scholar 

  17. G. Scovazzi, M.F. Wheeler, A. Mikelić, S. Lee, Analytical and variational numerical methods for unstable miscible displacement flows in porous media. J. Comput. Phy. 335, 444–496 (2017)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of computational and applied mathematics, Rice University, Houston, TX, USA

    Beatrice Riviere & Xin Yang

Authors
  1. Beatrice Riviere
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xin Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Beatrice Riviere .

Editor information

Editors and Affiliations

  1. Center for Communications Res, San Diego, CA, USA

    Alyson Deines

  2. Department of Mathematics, Texas State University, San Marcos, TX, USA

    Daniela Ferrero

  3. Bryn Mawr College, Ardmore, PA, USA

    Erica Graham

  4. United States Military Academy, New York, NY, USA

    Mee Seong Im

  5. Los Alamos National Laboratory, Los Alamos, NM, USA

    Carrie Manore

  6. Department of Mathematics, University of San Diego, San Diego, CA, USA

    Candice Price

Rights and permissions

Reprints and permissions

Copyright information

© 2018 The Author(s) and the Association for Women in Mathematics

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Riviere, B., Yang, X. (2018). A DG Method for the Simulation of CO2 Storage in Saline Aquifer. In: Deines, A., Ferrero, D., Graham, E., Im, M., Manore, C., Price, C. (eds) Advances in the Mathematical Sciences. AWMRS 2017. Association for Women in Mathematics Series, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-98684-5_12

Download citation

Publish with us

Policies and ethics

Search

Navigation