1887

Abstract

Summary

We discuss the application of modern high-resolution schemes to a hyperbolic system that models polymer flooding. This system consists of a pair of non-strictly hyperbolic conservation laws. In general, high-resolution schemes are often used for model problems where high accuracy is required in the presence of shocks or discontinuities. Polymer flooding is a difficult process to model, especially since the dynamics of the flow lead to concentration fronts that are not self-sharpening. Because the water viscosity is strongly affected by the polymer concentration, it is crucial to capture polymer fronts accurately to resolve the nonlinear displacement mechanism correctly and its efficiency for enhanced recover.

The main objective of this work is to compare different first- and higher-order methods in terms of how the discontinuities are treated. The discussion will focus on the validity, convergence and robustness of the schemes. Especially, different initial conditions and the inclusion of adsorption and permeability reduction can change not only the solution, but also the behavior of the different numerical methods. We show that these effects also can influence the applicability of a solver and we investigate of how suitable different numerical methods are for different polymer flooding situations.

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/content/papers/10.3997/2214-4609.20141852
2014-09-08
2024-03-29
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References

  1. Adimurthi, Jaffré, J. and Veerappa Gowda, G.D.
    [2004] Godunov-type methods for conservation laws with a flux function discontinuous in space. SIAM Journal on Numerical Analysis, 42(1), 179–208.
    [Google Scholar]
  2. Adimurthi, Veerappa Gowda, G.D. and Jaffré, J.
    [2013] The DFLU flux for systems of conservation laws. Journal of Computational and Applied Mathematics, 247, 123–.
    [Google Scholar]
  3. Dang, C., Chen, Z., Nguyen, N., Bae, W. and Phung, T.
    [2011] Development of Isotherm Polymer/Surfactant Adsorption Models in Chemical Flooding. Paper SPE 147872 presented at the SPE Asia Pacific Oil and Gas Conference and Exhibition, Jakarta, Indonesia, 20-22 September.
    [Google Scholar]
  4. Hagen, T.R., Henriksen, M.O., Hjelmervik, J.M. and Lie, K.A.
    [2007] How to solve systems of conservation laws numerically using the graphics processor as a high-performance computational engine. In: Geometric Modelling, Numerical Simulation, and Optimization. Springer, 211–264.
    [Google Scholar]
  5. Harten, A.
    [1983] High resolution schemes for hyperbolic conservation laws. Journal of Computational Physics, 49(3), 357–393.
    [Google Scholar]
  6. Isaacson, E.L.
    [1981] Global solution of a riemann problem for a non-strictly hyperbolic system of conservation laws arising in enhanced oil recovery. Rockefeller University preprints.
    [Google Scholar]
  7. Johansen, T. and Winther, R.
    [1988] The solution of the Riemann problem for a hyperbolic system of conservation laws modeling polymer flooding. SIAM Journal on Mathematical Analysis, 19(3), 541–566.
    [Google Scholar]
  8. Kurganov, A., Noelle, S. and Petrova, G.
    [2001] Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. SIAM Journal on Scientific Computing, 23(3), 707–740.
    [Google Scholar]
  9. Lake, L.W.
    [1989] Enhanced oil recovery.
    [Google Scholar]
  10. LeVeque, R.J.
    [1992] Numerical methods for conservation laws. Birkhauser.
    [Google Scholar]
  11. Ogunberu, A. and Asghari, K.
    [2005] Water permeability reduction under flow-induced polymer adsorption. Journal of Canadian Petroleum Technology, 44(11).
    [Google Scholar]
  12. Pope, G.
    [1980] The application of fractional flow theory to enhanced oil recovery. Old SPE Journal, 20(3), 191–205.
    [Google Scholar]
  13. Roe, P.L.
    [1985] Some contributions to the modelling of discontinuous flows. Large-scale computations in fluid mechanics, vol. 1, 163–193.
    [Google Scholar]
  14. Schlumberger and Geoquest
    [2005] Eclipse technical description. Multi-Segment Wells.
    [Google Scholar]
  15. Shu, C.W.
    [1988] Total-variation-diminishing time discretizations. SIAM Journal on Scientific and Statistical Computing, 9(6), 1073–1084.
    [Google Scholar]
  16. Sudarshan Kumar, K., Praveen, C. and Veerappa Gowda, G.D.
    [2013] Multicomponent polymer flooding in two dimensional oil reservoir simulation. arXiv preprint arXiv:1303.5590.
    [Google Scholar]
  17. Temple, B.
    [1982] Global solution of the cauchy problem for a class of 2× 2 nonstrictly hyperbolic conservation laws. Advances in Applied Mathematics, 3(3), 335–375.
    [Google Scholar]
  18. Todd, M.R. and Longstaff, W.J.
    [1972] The development testing and application of a numerical simulator for predicting miscible flood performance. Journal of Petroleum Technology, 24(07), 874–882.
    [Google Scholar]
  19. Van Leer, B.
    [1974] Towards the ultimate conservative difference scheme. ii. monotonicity and conservation combined in a second-order scheme. Journal of Computational Physics, 14(4), 361–370.
    [Google Scholar]
  20. [1977] Towards the ultimate conservative difference scheme iii. upstream-centered finite-difference schemes for ideal compressible flow. Journal of Computational Physics, 23(3), 263–275.
    [Google Scholar]
  21. [1979] Towards the ultimate conservative difference scheme. v. a second-order sequel to godunov’s method. Journal of Computational Physics, 32(1), 101–136.
    [Google Scholar]
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