1887
  1. Home
  2. Conferences
  3. Conference Proceedings
  4. ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery
  5. Conference paper

Abstract

Summary

Recently, the accurate coupling between subsurface flow and reservoir geomechanics received more attention and importance in both academia and industry. This stems from the fact that incorporating a geomechanics model into upstream flow simulation is critical for obtaining accurate pore-predictions, predicting wellbore instabilities, and modeling hydraulic fracturing. One of the recently introduced iterative coupling algorithms to couple flow with geomechanics is the undrained split iterative coupling algorithm [1,2]. The convergence of this scheme is established in [1] for the single rate iterative coupling algorithm, and in [2] 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 poro-elastic media. In this work, following the approach in [4], we will extend these results to the case of heterogeneous poro-elastic 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 [3], we will establish a priori error estimates for the single rate case of the scheme in homogeneous poro-elastic media. In subsequent work, we will supplement our mathematical analysis with numerical results, highlighting the efficiency of the multirate undrained split iterative scheme over the single rate scheme in heterogeneous poro-elastic 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 poro-elastic media.

[1] Mikelic, A. and Wheeler, M. F. “Convergence of iterative coupling for coupled flow and geomechanics.” Computational Geosciences, 17:455–461, 2013.

[2] Kumar, K., Almani, T., Singh, G., and Wheeler, Mary F. “Multirate Undrained Splitting for Coupled Flow and Geomechanics in Porous Media,” Springer International Publishing, 43–440, 2016.

[3] Almani, T., Kumar, K., and Wheeler, M. F., “Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics.” Computational Geosciences, 21: 1157–1172, 2017.

[4] Almani, T., Kumar, K., and Wheeler, M. F., “Convergence Analysis of Single Rate and Multirate Fixed Stress Split Iterative Coupling Schemes in Heterogeneous Poroelastic Media,” ICES REPORT 17–23, The University of Texas at Austin, Sep. 2017.

© EAGE Publications BV
Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.201802261
2018-09-03
2024-04-23

  • From This Site

    /content/papers/10.3997/2214-4609.201802261
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Almani, T.
    [2016] Efficient algorithms for flow models coupled with geomechanics for porous media applications. Ph.D. thesis, The University of Texas at Austin, Austin, Texas.
     [Google Scholar]
  2. Almani, T., Dogru, A.H., Kumar, K., Singh, G. and Wheeler, M.F.
    [2016a] Convergence of Multirate Iterative Coupling of Geomechanics with Flow in a Poroelastic Medium.Saudi Aramco Journal of Technology, Spring2016.
     [Google Scholar]
  3. Almani, T., Kumar, K., Dogru, A., Singh, G. and Wheeler, M.
    [2016b] Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics.Computer Methods in Applied Mechanics and Engineering, 311, 180–207.
     [Google Scholar]
  4. Almani, T., Kumar, K. and Wheeler, M.F.
    [2016c] Multirate Undrained Splitting for Coupled Flow and Geomechanics in Porous Media. Ices report 16-13, Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas.
     [Google Scholar]
  5. [2017a] Convergence Analysis of Single Rate and Multirate Fixed Stress Split Iterative Coupling Schemes in Heterogeneous Poroelastic Media. Ices report 17–23, Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas.
     [Google Scholar]
  6. [2017b] Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics.Computational Geosciences, 21, 1157–1172.
     [Google Scholar]
  7. Almani, T., Lee, S., Wick, T. and Wheeler, M.F.
    [2017c] Multirate coupling for flow and geomechanics applied to hydraulic fracturing using an adaptive phase-field technique. In: The SPE Reservoir Simulation Conference.
     [Google Scholar]
  8. Bause, M., Radu, F.A. and Köcher, U.
    [2017] Space-time finite element approximation of the Biotporoe-lasticity system with iterative coupling.Computer Methods in Applied Mechanics and Engineering, 320, 745–768.
     [Google Scholar]
  9. Biot, M.A.
    [1941] General Theory of Three-Dimensional Consolidation.J. Appl. Phys., 12(2), 155–164.
     [Google Scholar]
  10. Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C. and Gaspar, F.J.
    [2018a] A parallel-in-time fixed-stress splitting method for Biot’s consolidation model.arXiv preprint arXiv:1802.00949.
     [Google Scholar]
  11. Borregales, M., Radu, F.A., Kumar, K. and Nordbotten, J.M.
    [2018b] Robust iterative schemes for non-linear poromechanics.Computational Geosciences.
     [Google Scholar]
  12. Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K. and Radu, F.A.
    [2017] Robust fixed stress splitting for BiotŠs equations in heterogeneous media.Applied Mathematics Letters, 68, 101–108.
     [Google Scholar]
  13. Castelletto, N., White, J.A. and Tchelepi, H.A.
    [2015] Accuracy and convergence properties of the fixed-stress iterative solution of two-way coupled poromechanics.International Journal for Numerical and Analytical Methods in Geomechanics.
     [Google Scholar]
  14. Dana, S., Ganis, B. and Wheeler, M.F.
    [2018] A multiscale fixed stress split iterative scheme for coupled flow and poromechanics in deep subsurface reservoirs.Journal of Computational Physics, 352, 1–22.
     [Google Scholar]
  15. Girault, V., Wheeler, M.F., Ganis, B. andMear, M.
    [2013] A Lubrication Fracture Model in a Poro-Elastic Medium. Tech. rep., The Institute for Computational Engineering and Sciences, The University of Texas at Austin.
     [Google Scholar]
  16. Kim, J., Tchelepi, H.A. and Juanes, R.
    [2009] Stability, Accuracy, and Efficiency of Sequential Methods for Coupled Flow and Geomechanics. In: The SPE Reservoir Simulation Symposium, Houston, Texas. SPE119084.
     [Google Scholar]
  17. [2011] Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits.Comput. Methods Appl. Mech. Engrg., 200(13–16), 1591–1606.
     [Google Scholar]
  18. Kumar, K., Almani, T., Singh, G. and Wheeler, M.F.
    [2016] Multirate Undrained Splitting for Coupled Flow and Geomechanics in Porous Media.Springer International Publishing, Cham, 431–440.
     [Google Scholar]
  19. Mikelic, A., Wang, B. and Wheeler, M.F.
    [2014] Numerical convergence study of iterative coupling for coupled flow and geomechanics.Computational Geosciences, 18, 325–341.
     [Google Scholar]
  20. Mikelic, A. and Wheeler, M.F.
    [2013] Convergence of iterative coupling for coupled flow and geomechanics.Computational Geosciences, 17,455–461.
     [Google Scholar]
  21. Phillips, P.J. and Wheeler, M.F.
    [2007a] A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case.Computational Geosciences, 11(2), 131–144.
     [Google Scholar]
  22. [2007b] A coupling of mixed and continuous Galerkin finite element methods for poroelasticity II: the discrete-in-time case.Computational Geosciences, 11(2), 145–158.
     [Google Scholar]
  23. Rodrigo, C., Gaspar, F.J., Hu, X. and Zikatanov, L.T.
    [2016] Stability and monotonicity for some discretizations of the BiotSs consolidation model.Computer Methods in Applied Mechanics and Engineering, 298, 183–204.
     [Google Scholar]
  24. Wheeler, M.F. and Yotov, I.
    [2006] A Multipoint Flux Mixed Finite Element Method.SIAM Journal of Numerical Analysis, 44, 2082–2106.
     [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.201802261
Loading
Convergence And Error Analysis Of The Undrained-Split Iterative Coupling Scheme In Heterogeneous Poro-Elastic Media
Conference Proceedings 2018, 1 (2018); https://doi.org/10.3997/2214-4609.201802261
/content/papers/10.3997/2214-4609.201802261
/content/papers/10.3997/2214-4609.201802261
Loading

Data & Media loading...

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error