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A note on reservoir simulation for heterogeneous porous media

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Abstract

We present a front-tracking method for solving two-phase reservoir simulation problems arising in reservoirs with varying geological properties. The method preserves exactly the characteristic features of saturation fronts crossing media discontinuities. Two test examples are presented.

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References

  1. Aziz, K. and Settari, A.,Petroleum Reservoir Simulation, Elsevier, London, New York, 1979.

    Google Scholar 

  2. Bratvedt, F., Bratvedt, K., Buchholz, C., Holden, H., Holden, L. and Risebro, N. H., A new front tracking method for reservoir simulation,SPE J. Reservoir Simulation (Feb. 1992), 107–116.

  3. Bratvedt, F., Bratvedt, K., Buchholz, C., Gimse, T., Holden, H., Holden, L. and Risebro, N. H., Front tracking for reservoir simulation,Proc. Conference Dedicated to the Memory of Raphael HØegh-Krohn, edited by H. Holden and T. LindstrØm, Cambridge Univ. Press, 1992, pp. 409–427.

  4. Chavent, G., Cohen, G. and Jaffre, J., A finite element simulator for incompressible two phase flow,Transport in Porous Media 2 (1987), 465–478.

    Google Scholar 

  5. Crandall, M. and Majda, A., The method of fractional steps for conservation laws,Numer. Math. 34 (1980), 285–314.

    Google Scholar 

  6. Dafermos, C. M., Polygonal approximation of solutions of the initial value problem for a conservation law,J. Math. Anal. Appl. 38 (1972), 33–41.

    Google Scholar 

  7. Gimse, T., A numerical method for a system of equations modelling one-dimensional three-phase flow in a porous medium,Notes on Num. Fluid Mech. 24 (1989), 159–168.

    Google Scholar 

  8. Gimse, T. and Risebro, N. H., Riemann problems with discontinuous flux functions,Proc. Third Internat. Conf. Hyperbolic Problems, Uppsala, 1990, pp. 488–502.

  9. Gimse, T. and Risebro, N. H., Solution of the Cauchy problem for a conservation law with a discontinuous flux function,SIAM J. Math. Anal. 23 (1992), 635–648.

    Google Scholar 

  10. Glimm, J., Lindquist, B., McBryan, O. A., Plohr, B. and Yaniv, S., Front tracking for petroleum reservoir simulation, SPE preprint 12238 (1981), pp. 41–49.

  11. Holden, H., Holden, L. and HØegh-Krohn, R., A numerical method for first order nonlinear scalar conservation laws in one-dimension,Comput. Math. Appl. 15 (1988), 595–602.

    Google Scholar 

  12. Holden, H. and Risebro, N. H., A fractional steps method for scalar conservation laws without the CFL-condition,Math. Comput. (to appear).

  13. Holden, L. and HØegh-Krohn, R., A class ofN nonlinear hyperbolic conservation laws,J. Differential Equations 84 (1990), 73–99.

    Google Scholar 

  14. KruŽkov, N., Quasi-linear equations of the first order,Mat. Sb. 2 (1970), 217–243.

    Google Scholar 

  15. Peaceman, D. W.,Fundamentals of Numerical Reservoir Simulation, Elsevier, Amsterdam, 1977.

    Google Scholar 

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Gimse, T., Risebro, N.H. A note on reservoir simulation for heterogeneous porous media. Transp Porous Med 10, 257–270 (1993). https://doi.org/10.1007/BF00616812

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  • DOI: https://doi.org/10.1007/BF00616812

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