Advertisement

Multi-model hybrid compositional simulator with application to segregated flow

  • 7 Accesses

Abstract

In cases with significant density difference between the injection mixture and the reservoir fluids, segregation can take place on short temporal scales relative to the typical time-step lengths of the simulation. A fully resolved 3D description is computationally demanding and is often difficult to achieve with buoyancy segregated flow. Vertical equilibrium (VE) is one possible technique for effective upscaling in regions of gravity segregation and has been widely considered for CO2 storage applications. VE has connections to pseudo-relative permeability models for gas injection. In this work, we use a general pseudo-relative permeability model to couple conventional 3D and upscaled models, including VE formulations with support for compositional simulations. This gives a flexible framework where different choices of coarsening and pseudoization can be used locally throughout the domain, allowing for an optimal trade-off between runtime and accuracy. The new approach is demonstrated within the framework of a fully implicit compositional flow simulator with nonlinear equation-of-state, which provides a robust and stable base for inclusion of additional physical effects. Moreover, we discuss the limitations of different possible approximations for the phase equilibrium of the compositional VE regions, and which cases they may be useful for. Possible applications for this methodology include gas injection for enhanced oil recovery, CO2 storage in aquifers, or other gas-storage scenarios. We demonstrate the approach for gas injection and migration on both conceptual unstructured grids as well as corner-point models taken from real fields and saline aquifers from the Norwegian Continental Shelf.

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

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.

References

  1. 1.

    Barker, J., Fayers, F.: Transport coefficients for compositional simulation with coarse grids in heterogeneous media. SPE Adv. Technol. Ser. 2(02), 103–112 (1994)

  2. 2.

    Barker, J., Thibeau, S.: A critical review of the use of pseudorelative permeabilities for upscaling. SPE Reserv. Eng. 12(2), 138–143 (1997)

  3. 3.

    Becker, B., Guo, B., Bandilla, K., Celia, M.A., Flemisch, B., Helmig, R.: An adaptive multiphysics model coupling vertical equilibrium and full multidimensions for multiphase flow in porous media. Water Resour. Res. 54(7), 4347–4360 (2018)

  4. 4.

    Cavanagh, A.J., Haszeldine, R.S., Nazarian, B.: The Sleipner CO2 storage site: Using a basin model to understand reservoir simulations of plume dynamics. First Break 33, 61–68 (2015)

  5. 5.

    Coats, K.H.: An equation of state compositional model. SPE J. 20(05), 363–376 (1980)

  6. 6.

    Coats, K.H., Dempsey, J.R., Henderson, J.H.: The use of vertical equilibrium in two-dimensional simulation of three-dimensional reservoir preformance. Soc. Pet. Eng. J., 68–71 (1971)

  7. 7.

    Coats, K.H., Nielsen, R.L., Terune, M.H., Weber, G.A.: Simulation of three-dimensional, two-phase flow in oil and gas reservoirs. Soc. Pet. Eng. J., 377–388 (1967)

  8. 8.

    Digital, S.: The MATLAB Reservoir Simulation Toolbox 2018b. http://www.sintef.no/MRST/ (2018)

  9. 9.

    Eiken, O., Ringrose, P., Hermanrud, C., Nazarian, B., Torp, T.A., Høier, L.: Lessons learned from 14 years of CCS operations: Sleipner. In: Salah, Snøhvit (eds.) Energy Procedia. 10th International Conference on Greenhouse Gas Control Technologies, vol. 4, pp 5541–5548 (2011)

  10. 10.

    Espósito, R.O., Alijó, P. H.R., Scilipoti, J.A., Tavares, F.W.: Phase equilibrium thermodynamics. In: Compositional Grading in Oil and Gas Reservoirs, pp 35–80. Elsevier (2017)

  11. 11.

    Gasda, S.E., Nordbotten, J.M., Celia, M.A.: Vertically averaged approaches for CO2 migration with solubility trapping. Water Resour Res, 47(5) (2011)

  12. 12.

    Guo, B., Bandilla, K.W., Nordbotten, J.M., Celia, M.A., Keilegavlen, E., Doster, F.: A multiscale multilayer vertically integrated model with vertical dynamics for co2 sequestration in layered geological formations. Water Resour. Res. 52(8), 6490–6505 (2016)

  13. 13.

    Indrupskiy, I.M., Lobanova, O.A., Zubov, V.R.: Non-equilibrium phase behavior of hydrocarbons in compositional simulations and upscaling. Comput. Geosci. 21(5-6), 1173–1188 (2017)

  14. 14.

    Iranshahr, A., Chen, Y., Voskov, D.V.: A coarse-scale compositional model. Comput. Geosci. 18(5), 797–815 (2014)

  15. 15.

    Jacks, H.H., Smith, O.J.E., Mattax, C.C.: The modeling of a three-dimensional reservoir with a two-dimensional reservoir simulator – the use of dynamic pseudo functions. Soc. Pet. Eng. J. 13(3), 175–185 (1973)

  16. 16.

    Krogstad, S., Lie, K.A., Møyner, O, Nilsen, H.M., Raynaud, X., Skaflestad, B.: MRST-AD – an open-source framework for rapid prototyping and evaluation of reservoir simulation problems. In: SPE Reservoir Simulation Symposium, pp 23–25, Houston (2015)

  17. 17.

    Kyte, J.R., Berry, D.W.: New pseudo functions to control numerical dispersion. Soc. Pet. Eng. J. 15(4), 269–276 (1975)

  18. 18.

    Lie, K.-A.: An introduction to reservoir simulation using MATLAB/GNU Octave. Cambridge University Press (2019)

  19. 19.

    Lindeberg, E., Wessel-Berg, D.: Vertical convection in an aquifer column under a gas cap of co2. Energy Conversion Manag. 38, S229–S234 (1997). Proceedings of the Third International Conference on Carbon Dioxide Removal

  20. 20.

    Martin, J.C.: Some mathematical aspects of two phase flow with application to flooding and gravity segregation. Prod. Monthly 22(6), 22–35 (1958)

  21. 21.

    Martin, J.C.: Partial integration of equation of multiphase flow. Soc. Pet. Eng. J., 370–380 (1968)

  22. 22.

    Michelsen, M.L.: The isothermal flash problem. Part I. Stability. Fluid Phase Equilib. 9(1), 1–19 (1982)

  23. 23.

    Møyner, O., Nilsen, H.M.: Multiresolution coupled vertical equilibrium model for fast flexible simulation of co 2 storage. Comput. Geosci. 23(1), 1–20 (2019)

  24. 24.

    Møyner, O., Tchelepi, H.: A mass-conservative sequential implicit multiscale method for isothermal equation of state compositional problems. SPE Journal. To appear (2018)

  25. 25.

    Nilsen, H.M., Lie, K.A., Andersen, O.: Fully-implicit simulation of vertical-equilibrium models with hysteresis and capillary fringe. Comput. Geosci. 20(1), 49–67 (2015)

  26. 26.

    Nilsen, H.M., Lie, K.A., Andersen, O.: Fully-implicit simulation of vertical-equilibrium models with hysteresis and capillary fringe. Comput. Geosci. 20(1), 49–67 (2016)

  27. 27.

    Nilsen, H.M., Lie, K.A., Andersen, O.: Robust simulation of sharp-interface models for fast estimation of CO2 trapping capacity. Comput. Geosci. 20(1), 93–113 (2016)

  28. 28.

    Nordbotten, J.M., Celia, M.A.: Geological Storage of CO2: Modeling Approaches for Large-Scale Simulation. Wiley, Hoboken (2012)

  29. 29.

    Salehi, A.: Upscaling of compositional flow simulation based on a non-equilibrium formulation. Ph.D. thesis, Stanford University Stanford CA (2016)

  30. 30.

    Salehi, A., Voskov, D., Tchelepi, H.: Thermodynamically consistent transport coefficients for upscaling of compositional processes. In: SPE Reservoir Simulation Symposium. Society of Petroleum Engineers (2013)

  31. 31.

    Stone, H.L.: Rigorous black oil pseudo functions. In: SPE Symposium on Reservoir Simulation, pp 17–20. Society of Petroleum Engineers, Anaheim (1991)

  32. 32.

    Whitson, C.H., Belery, P.: Compositional gradients in petroleum reservoirs. In: University of Tulsa Centennial Petroleum Engineering Symposium. Society of Petroleum Engineers (1994)

Download references

Author information

Correspondence to Halvor M. Nilsen.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Møyner, O., Andersen, O. & Nilsen, H.M. Multi-model hybrid compositional simulator with application to segregated flow. Comput Geosci (2020). https://doi.org/10.1007/s10596-019-09910-y

Download citation

Keywords

  • Compositional simulation
  • Vertical equilibrium
  • CO2 storage
  • Multi-physics