DOI: https://doi.org/10.26089/NumMet.v18r318

Accelerated explicit-implicit algorithms for the simulation of two-phase Flow toward a horizontal multistage hydraulically fractured well

Authors

  • A.B. Mazo
  • M.R. Khamidullin

Keywords:

two-phase filtration
hydraulic fracturing
IMPES method
FIM method

Abstract

Explicit-implicit approximation schemes for the numerical simulation of 3D two-phase flows toward a horizontal multistage hydraulically fractured well are proposed. This approach is based on the division of the computational domain into local subdomains and on using either an explicit or implicit scheme for the saturation transport equation with consideration of a local Courant number.

New computational technologies

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Published

2017-05-31

Issue

Vol. 18 (2017): Issue 3.

Section

Section 1. Numerical methods and applications

Author Biographies

A.B. Mazo

Kazan Federal University
• Professor

M.R. Khamidullin

Kazan Federal University
• Professor

References

  1. K. S. Basniev, I. N. Kochina, and V. M. Maksimov, Underground Hydrodynamics (Nedra, Moscow, 1993) [in Russian].
  2. K. Aziz and A. Settari, Petroleum Reservoir Simulation (Appl. Sci. Publ., London, 1979; Nedra, Moscow, 1982).
  3. K. H. Coats, “Reservoir simulation,” in Petroleum Engineering Handbook (SPE Press, Richardson, 1987), Chap. 48.
  4. R. Shen and S. Gao, “Numerical Simulation of Production Performance of Fractured Horizontal Wells Considered Conductivity Variation,” in Proc. 3rd Int. Conf. on Computer and Electrical Engineering (IACSIT Press, Singapore, 2012), Vol. 53, No. 2.36.
  5. A. I. Shangaraeva and D. V. Shevchenko, “Speed up of the Oil Saturation Numerical Algorithm for the Plane-Parallel Filtration,” Appl. Math. Sci. 9, 7467-7474 (2015).
  6. J. R. Appleyard, I. M. Cheshire, and R. K. Pollard, “Special Techniques for Fully-Implicit Simulators,” in Proc. European Symp. on Enhanced Oil Recovery, Bournemouth, U.K., September 21-23, 1981 (Elsevier, New York, 1981), pp. 395-408.
  7. G. W. Thomas and D. H. Thurnau, “Reservoir Simulation Using an Adaptive Implicit Method,” SPE J. 23 (5), 759-768 (1983).
  8. L. S.-K. Fung, D. A. Collins, and L. X. Nghiem, “An Adaptive-Implicit Switching Criterion Based on Numerical Stability Analysis,” SPE Reserv. Eng. 4 (1), 45-51 (1989).
  9. J. W. Watts and  J. S. Shaw, “A New Method for Solving the Implicit Reservoir Simulation Matrix Equation,” in Proc. SPE Reservoir Simulation Symposium, The Woodlands, USA, January 31-February 2, 2005.
    doi 10.2118/93068-MS
  10. N. A. Marchenko, A. Kh. Pergament, S. B. Popov, et al., Hierarchy of Explicit-Implicit Difference Schemes for Multiphase Filtration Problems , Preprint No. 97 (Keldysh Institute of Applied Mathematics, Moscow, 2008).
  11. B. Lu, T. Alshaalan, and M. F. Wheeler, “Iteratively Coupled Reservoir Simulation for Multiphase Flow,” in Proc. SPE Annual Technical Conference and Exhibition, Anaheim, USA, November 11-14, 2007.
    doi 10.2118/110114-MS
  12. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer, New York, 2002).
  13. W. Hackbusch, Multi-Grid Methods and Applications (Springer, Berlin, 1985).
  14. M. C. Christensen, K. L. Eskildsen, A. P. Engsig-Karup, and M. Wakefield, “Nonlinear Multigrid for Reservoir Simulation,” SPE J. 21 (3), 0888-0898 (2016).
  15. W. A. Mulder and R. H. J. Gmeling-Meyling, “Numerical Simulation of Two-Phase Flow Using Locally Refined Grids in Three Space Dimensions,” SPE Advanced Technology Series 1 (1) (1993).
    doi 10.2118/21230-PA
  16. G. S. Shiralkar, G. C. Fleming, J. W. Watts, et al., “Development and Field Application of a High Performance, Unstructured Simulator with Parallel Capability,” in Proc. SPE Reservoir Simulation Symposium, The Woodlands, USA, January 31-February 2, 2005.
    doi 10.2118/93080-MS
  17. P. A. Mazurov and A. V. Tsepaev, “Parallel Algorithms for Solving Two-Phase Flow Problems with Fine Grid Segments,” Vychisl. Metody Programm. 7, 251-258 (2006).
  18. A. V. Tsepaev, “Application of Heterogeneous Computing Systems for Solving the Problem of Fluid Flow by Domain Decomposition Methods,” Vychisl. Metody Programm. 13, 38-43 (2012).
  19. M. R. Khamidullin, “Numerical Simulation of One-Phase Flow to Multi-Stage Hydraulically Fractured Horizontal Well,” Uchen. Zap. Kazan. Gos. Univ. Fiz. Mat. 158 (2), 287-301 (2016).
  20. A. B. Mazo, K. A. Potashev, E. I. Kalinin, and D. V. Bulygin, “Oil Reservoir Simulation with the Superelement Method,” Mat. Model. 25 (8), 51-64 (2013).
  21. K. D. Nikitin, “Nonlinear Finite Volume Method for Two-Phase Flow in Porous Media,” Mat. Model. 22 (11), 131-147 (2010).
  22. A. Henk, Iterative Krylov Methods for Large Linear Systems (Cambridge Univ. Press, Cambridge, 2003).
  23. C. A. J. Fletcher, Computational Techniques for Fluid Dynamics (Springer, Heidelberg, 1988; Mir, Moscow, 1991).

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