Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media
Saudi Arabian Oil Company (Aramco), Saudi Arabia.
Saudi Arabian Oil Company (Aramco), Saudi Arabia.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). University of Bergen, Norway.
Saudi Arabian Oil Company (Aramco), Saudi Arabia; MIT, USA.
2019 (English)In: Computational Geosciences, ISSN 1420-0597, E-ISSN 1573-1499Article in journal (Refereed) In press
Abstract [en]

Recently, an accurate coupling between subsurface flow and reservoir geomechanics has received more attention in both academia and industry. This stems from the fact that incorporating a geomechanics model into upstream flow simulation is critical for accurately predicting wellbore instabilities and hydraulic fracturing processes. One of the recently introduced iterative coupling algorithms to couple flow with geomechanics is the undrained split iterative coupling algorithm as reported by Kumar et al. (2016) and Mikelic and Wheeler (Comput. Geosci. 17: 455–461 2013). The convergence of this scheme is established in Mikelic and Wheeler (Comput. Geosci. 17:455–461 2013) for the single rate iterative coupling algorithm and in Kumar et al. (2016) for the multirate iterative coupling algorithm, in which the flow takes multiple finer time steps within one coarse mechanics time step. All previously established results study the convergence of the scheme in homogeneous poroelastic media. In this work, following the approach in Almani et al. (2017), we extend these results to the case of heterogeneous poroelastic media, in which each grid cell is associated with its own set of flow and mechanics parameters for both the single rate and multirate schemes. Second, following the approach in Almani et al. (Comput. Geosci. 21:1157–1172 2017), we establish a priori error estimates for the single rate case of the scheme in homogeneous poroelastic media. To the best of our knowledge, this is the first rigorous and complete mathematical analysis of the undrained split iterative coupling scheme in heterogeneous poroelastic media.

Place, publisher, year, edition, pages
Springer, 2019.
Keywords [en]
A priori error estimates, Biot system, Contraction mapping, Heterogeneous poroelastic media, Poroelasticity, Undrained split iterative coupling
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-75698DOI: 10.1007/s10596-019-09860-5Scopus ID: 2-s2.0-85070293897OAI: oai:DiVA.org:kau-75698DiVA, id: diva2:1369665
Funder
The Research Council of Norway, Lab2FieldAvailable from: 2019-11-12 Created: 2019-11-12 Last updated: 2019-11-14Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records BETA

Kumar, Kundan

Search in DiVA

By author/editor
Kumar, Kundan
By organisation
Department of Mathematics and Computer Science (from 2013)
In the same journal
Computational Geosciences
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 1 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf