Skip to main content

Advertisement

Log in

A parallel framework for a multipoint flux mixed finite element equation of state compositional flow simulator

  • Original Paper
  • Published:
Computational Geosciences Aims and scope Submit manuscript

Abstract

Mathematical models of physical problems are becoming increasingly complex and computationally intensive. At the same time, computing hardware is becoming more parallelized with an increasing number of cores promoting simultaneous tasks. In this work, we present a parallel, equation of state (EOS), compositional flow simulator for evaluating CO2 sequestration, enhanced oil recovery techniques such as gas flooding, and other subsurface porous media applications. Using the multipoint flux mixed finite element (MFMFE) method for spatial discretization, it can handle complex reservoir geometries using general distorted hexahedral grid elements, as well as satisfy local mass conservation and compute accurate phase fluxes. A parallel framework for the MFMFE is presented that has been extended to the highly non-linear, EOS, compositional flow model. Much of the non-linearity is due to the local flash and stability calculations associated with interphase mass transfer and phase behavior. Parallel multigrid linear solver libraries such as HYPRE are utilized to solve the algebraic problems on each Newton step. We perform a variety of strong and weak parallel scaling studies up to 10 million elements and 1024 processors, and discuss possible load balancing issues.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aavatsmark, I., Barkve, T., Bøe, O., Mannseth, T.: Discretization On unstructured grids for inhomogeneous, anisotropic media. Part I: Derivation of the methods. SIAM J. Sci. Comput. 19(5), 1700–1716 (1998)

    Article  Google Scholar 

  2. Acs, G., Doleschall, S., Farkas, E., et al.: General purpose compositional model. Soc. Pet. Eng. J. 25(04), 543–553 (1985)

    Article  Google Scholar 

  3. Coats, K.H., et al.: An equation of state compositional model. Soc. Pet. Eng. J. 20(05), 363–376 (1980)

    Article  Google Scholar 

  4. Dogru, A.H., Fung, L.S.K., Middya, U., Al-Shaalan, T.M., Pita, J.A., HemanthKumar, K., Su, H.J., Tan, J.C.T., Hoy, H., Dreiman, W.T., et al.: A next-generation parallel reservoir simulator for giant reservoirs. In: SPE/EAGE Reservoir Characterization Andamp; Simulation Conference (2009)

  5. Dogru, A.H., Sunaidi, H.A., Fung, L.S., Habiballah, W.A., Al-Zamel, N., Li, K.G., et al.: A parallel reservoir simulator for large-scale reservoir simulation. SPE Reserv. Eval. Eng. 5(01), 11–23 (2002)

    Article  Google Scholar 

  6. Douglas, J. Jr.: The numerical solution of a compositional model in petroleum reservoir engineering. SIAM-AMS Proc. 2, 54–59 (1970)

    Google Scholar 

  7. Edwards, M.G., Rogers, C.F.: Finite volume discretization with imposed flux continuity for the general tensor pressure equation. Comput. Geosci. 2(4), 259–290 (1998)

    Article  Google Scholar 

  8. Falgout, R., Ulrike, Y.: HYPRE:A Library of high performance preconditioners. Comput. Sci., ICCS 2002, 632–641 (2002)

    Google Scholar 

  9. Ganis, B., Kumar, K., Pencheva, G., Wheeler, M.F., Yotov, I., et al.: A multiscale mortar method and two-stage preconditioner for multiphase flow using a global jacobian approach. In: SPE Large Scale Computing and Big Data Challenges in Reservoir Simulation Conference and Exhibition. Society of Petroleum Engineers. SPE-172990-MS (2014)

  10. Gries, S., Stüben, K., Brown, G.L., Chen, D., Collins, D.A., et al.: Preconditioning for efficiently applying algebraic multigrid in fully implicit reservoir simulations. SPE J. 19(04), 726–736 (2014)

    Article  Google Scholar 

  11. Hajibeygi, H., Tchelepi, H.A., et al.: Compositional multiscale finite-volume formulation. SPE J. 19(02), 316–326 (2014)

    Article  Google Scholar 

  12. Ingram, R., Wheeler, M.F., Yotov, I.: A Multipoint Flux Mixed Finite Element Method on Hexahedra. SIAM J. Numer. Anal. 48(4), 1281–1312 (2010)

    Article  Google Scholar 

  13. Jenny, P., Tchelepi, H.A., Lee, S.H.: Unconditionally convergent nonlinear solver for hyperbolic conservation laws with s-shaped flux functions. J. Comput. Phys. 228(20), 7497–7512 (2009)

    Article  Google Scholar 

  14. Killough, J.E., Bhogeswara, R., et al.: Simulation of compositional reservoir phenomena on a distributed-memory parallel computer. J. Petrol. Tech. 43(11), 1–368 (1991)

    Google Scholar 

  15. Naumov, M., Arsaev, M., Castonguay, P., Cohen, J., Demouth, J., Eaton, J., Layton, S., Markovskiy, N., Reguly, I., Sakharnykh, N., et al.: Amgx: A library for gpu accelerated algebraic multigrid and preconditioned iterative methods. SIAM J. Sci. Comput. 37(5), S602–S626 (2015)

    Article  Google Scholar 

  16. Parashar, M., Wheeler, J.A., Pope, G., Wang, K., Wang, P., et al.: A new generation eos compositional reservoir simulator: Part ii-framework and multiprocessing. SPE Reservoir Simulation Symposium (1997)

  17. Peng, D.-Y., Robinson, D.B.: A new two-constant equation of state. Ind. Eng. Chem. Fundam. 15(1), 59–64 (1976)

    Article  Google Scholar 

  18. Rachford, H.H., Rice, J.D.: Procedure for use of electronic digital computers in calculating flash vaporization hydrocarbon equilibrium. Trans. Am. Inst. Min. Metall. Eng. 195, 327–328 (1952)

    Google Scholar 

  19. Reme, H., Øye, G.Å., Espedal, M.S., Fladmark, G.E.: Parallelization of a compositional reservoir simulator. In: Numerical Treatment of Multiphase Flows in Porous Media, pp. 244–266. Springer (2000)

  20. Russell, T.F., Wheeler, M.F.: Finite element and finite difference methods for continuous flows in porous media. Math. Reservoir Simul. 1, 35–106 (1983)

    Article  Google Scholar 

  21. Singh, G., Wheeler, M.F.: Compositional flow modeling using a multipoint flux mixed finite element method. Comput. Geosci. 20, 421–435 (2015)

    Article  Google Scholar 

  22. Wang, P., Yotov, I., Wheeler, M.F., Arbogast, T., Dawson, C., Parashar, M., Sepehrnoori, K.: A new generation EOS compositional reservoir simulator: Part I-formulation and discretization. In: SPE Reservoir Simulation Symposium. Society of Petroleum Engineers (1997)

  23. Watts, J.W., et al.: A compositional formulation of the pressure and saturation equations. SPE Reserv. Eng. 1(03), 243–252 (1986)

    Article  Google Scholar 

  24. Wheeler, M., Xue, G., Yotov, I.: A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra. Numer. Math. 121(1), 165–204 (2011)

    Article  Google Scholar 

  25. Wheeler, M.F., Xue, G., Yotov, I.: Accurate cell-centered discretizations for modeling multiphase flow in porous media on general hexahedral and simplicial grids. SPE J. 17(03), 779–793 (2012)

    Article  Google Scholar 

  26. Wheeler, M.F., Yotov, I.: A multipoint flux mixed finite element method. SIAM J. Numer. Anal. 44(5), 2082–2106 (2006)

    Article  Google Scholar 

  27. Zhang, D., Lu, Z.: An efficient, high-order perturbation approach for flow in random porous media via Karhunen–Loève and polynomial expansions. J. Comput. Phys. 194(2), 773–794 (2004)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by DOE grant FG02-04ER25617, DOE NETL grant DE-FE0023314, NSF grant 1546553, Statoil grant UTA13-000884, Saudi Aramco grant UTA11-000320, and the CSM industrial affiliates program. The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Benjamin Ganis.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ganis, B., Singh, G. & Wheeler, M.F. A parallel framework for a multipoint flux mixed finite element equation of state compositional flow simulator. Comput Geosci 21, 1189–1202 (2017). https://doi.org/10.1007/s10596-017-9683-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-017-9683-7

Keywords

Navigation