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The Total Compressibility Condition and Resolution of Local Nonlinearities in an Implicit Black-Oil Model with Capillary Effects

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Abstract

An implicit black-oil model with capillary effects is studied. Various primary unknowns which include one of the phase pressures are considered, and qualitative and quantitative consequences of a choice are discussed. In particular, a total compressibility condition is defined and a local nonlinear problem is studied. A numerical method to solve the local problem is discussed.

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References

  • K. Aziz A. Settari (1979) Petroleum Reservoir Simulation Applied Science Publishers Ltd London

    Google Scholar 

  • J. Bear (1972) Dynamics of Fluids in Porous Media Elsevier New York

    Google Scholar 

  • G. Chavent J. Jaffre (1986) Mathematical Models and Finite Elements for Reservoir Simulation North-Holland Amsterdam

    Google Scholar 

  • Z. Chen (2000) ArticleTitle‘Formulations and numerical methods for the black oil model in porous media’ SIAM J. Numer. Anal. 38 IssueID2 489–514 Occurrence Handle10.1137/S0036142999304263

    Article  Google Scholar 

  • Z. Chen G. Huan B. Li (2004) ArticleTitle‘An improved IMPES method for two-phase flow in porous media Transport Porous Media 54 IssueID3 361–376 Occurrence Handle10.1023/B:TIPM.0000003667.86625.15

    Article  Google Scholar 

  • Coats, K.: 1999, ‘A note on Impes and some Impes-based simulation Models’. in: Fifteenth SPE Symposium on Reservoir Simulation, Houston, Texas, Society of Petroleum Engineers, SPE 49774, pp. 21–39.

  • Coats, K. H., Thomas, L. K. and Pierson, R. G.: 1995, Compositional and black oil reservoir simulator, in: The 13th SPE Symposium on Reservoir Simulation, San Antonio, Texas.

  • Eclipse-100, Reference Manual’ 1998. Schlumberger Technology Corporation.

  • R. Helmig (1997) Multiphase Flow and Transport Processes in the Subsurface Springer Berlin

    Google Scholar 

  • C. T. Kelley (1995) Iterative Methods for Linear and Nonlinear Equations SIAM Philadelphia

    Google Scholar 

  • Killough, J. E.: 1995, Ninth SPE comparative solution projection: a reexamination of black-oil simulation, in: the 13th Symposium on Reservoir Simulation, San Antonio, Texas, SPE 29110, pp. 135–147.

  • S. Lacroix Y. Vassilevski M. Wheeler J. Wheeler (2003) ArticleTitleIterative solution methods for modeling multiphase flow in porous media fully implicitly SIAM J. Sci. Comp. 25 IssueID3 905–926 Occurrence Handle10.1137/S106482750240443X

    Article  Google Scholar 

  • L. W. Lake (1989) Enhanced Oil Recovery Prentice-Hall NJ

    Google Scholar 

  • Q. Lu (2000) A parallel multi-block/multi-physics approach for multi-phase flow in porous media University of Texas at Austin Austin, Texas

    Google Scholar 

  • Q. Lu M. Peszynska X. Gai (2001) Implicit Black-oil Model in IPARS Framework University of Texas at Austin Austin, TX

    Google Scholar 

  • Q. Lu M. Peszyńska M. F. Wheeler (2002) ArticleTitleA parallel multi-block black-oil model in multi-model implementation SPE J 7 IssueID3 278–287

    Google Scholar 

  • W. D. J. McCain (1990) The Properties of Petroleum Fluids EditionNumber2 PennWell Books Tulsa Oklahoma

    Google Scholar 

  • S. Minkoff C. Stone S. Bryant M. Peszyńska (2004) ArticleTitleCoupled geomechanics and flow simulation for time-lapse seismic modeling Geophysics 69 IssueID1 200–211 Occurrence Handle10.1190/1.1649388

    Article  Google Scholar 

  • S. Minkoff C. M. Stone S. Bryant M. Peszyńska M. F. Wheeler (2003) ArticleTitleA loose coupling algorithm for fluid flow and geomechanical deformation modeling J. Petrol. Sci. Eng. 38 37–56 Occurrence Handle10.1016/S0920-4105(03)00021-4

    Article  Google Scholar 

  • D. W. Peaceman (1977) Fundamentals of Numerical Reservoir Simulation Elsevier Scientfic Amsterdam

    Google Scholar 

  • M. Peszyńska (2003) Multiphysics coupling of three-phase and two-phase models of flow in porous media W. Wendland M. Efendiev (Eds) Analysis and Simulation of Multifield Problems NumberInSeriesVol. 12. Springer-Verlag New York

    Google Scholar 

  • M. Peszyńska M. F. Wheeler I. Yotov (2002) ArticleTitleMortar upscaling for multiphase flow in porous media Comput. Geosci. 6 73–100

    Google Scholar 

  • W. H. Press S. A. Teukolsky W. T. Vetterling B. P. Flannery (1992) Numerical Recipes in C EditionNumber2 Cambridge University Press Cambridge

    Google Scholar 

  • Showalter, R. E.: 1997, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, Vol. 49 of Mathematical Surveys and Monographs, Amer. Math. Soc. Providence, RI.

  • J. A. Trangenstein J. B. Bell (1989) ArticleTitleMathematical structure of the black-oil model for petroleum reservoir simulation SIAM J. Appl. Math. 49 IssueID3 749–783 Occurrence Handle10.1137/0149044

    Article  Google Scholar 

  • Watts, J. W.: 1986, A compositional formulation of the pressure and saturation equations, SPERE 243–252.

  • Wheeler, J. A.: 1998–2000, ‘IPARS User’s Manual’. Technical report, Center for Subsurface Modeling, Texas Institute for Computational and Applied Mathematics, University of Texas at Austin.

  • M. F. Wheeler M. Peszyńska (2002) ArticleTitleComputational engineering and science methodologies for modeling and simulation of subsurface applications Adv. Water Resour. 25 IssueID8–12 1147–1173

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Oregon State University, Corvallis, OR, 97331-4605, U.S.A.

    Małgorzata Peszyńska

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  1. Małgorzata Peszyńska
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Correspondence to Małgorzata Peszyńska.

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Dedicated to the memory of John J. Wheeler

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Peszyńska, M. The Total Compressibility Condition and Resolution of Local Nonlinearities in an Implicit Black-Oil Model with Capillary Effects. Transp Porous Med 63, 201–222 (2006). https://doi.org/10.1007/s11242-005-4427-x

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  • DOI: https://doi.org/10.1007/s11242-005-4427-x

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