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An analysis of physical models and numerical schemes for polymer flooding simulations

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Abstract

Chemical-enhanced oil recovery (CEOR) processes are nowadays commonly used by engineers to improve the recovery factor of an oil field. In this paper, we propose to investigate the physical and numerical singularities arising in the numerical simulation of polymer-enhanced oil recovery technique for oil fields. We assume that the polymer is only transported in the water phase or adsorbed on the rock. The polymer reduces the water-phase mobility and can change drastically the behavior of water oil interfaces. Due to its size, the polymer flows faster than water so that an inaccessible pore volume must be added in the model. After a brief description of different models for polymer adsorption, mobility reduction, and inaccessible pore volume, we discuss the mathematical singularities of the obtained system. In the framework of industrial reservoir simulators, we focus on a constant inaccessible pore volume model which may lead to severe mathematical and numerical singularities. We consider an IMPES scheme; we propose approximate Courant-Friedrichs-Levy (CFL) criteria which are required to obtain some numerical stability of the simulation. 1D numerical polymer flooding experiments are computed with a complete reservoir simulator to illustrate the validity of our approximate CFL criteria.

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References

  1. Lake, L.W.: Enhanced Oil Recovery. Prentice Hall (1989)

  2. Green, D. W., Willhite, G. P.: Enhanced Oil Recovery, Vol. 6 of SPE textbook series, Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers (1998)

  3. Sorbie, K. S.: Polymer-Improved Oil Recovery. Springer Science, New York (1991)

    Book  Google Scholar 

  4. Peaceman, D. W.: Fundamentals of Numerical Reservoir Simulation, Vol. 6 of Developments in Petroleum Science. Elsevier Science, Amsterdam (1977)

    Google Scholar 

  5. Delshad, M., Pope, G.A., Sepehrnoori, K.: A compositional simulator for modeling surfactant enhanced aquifer remediation: 1. Formulation. J. Contam. Hydrol. 23(4), 303–327 (1996). doi:10.1016/0169-7722(95)00106-9

    Article  Google Scholar 

  6. Pope, G.A., Nelson, R.C.: A chemical flooding compositional simulator. SPE J. 18(5), 339–354 (1978). SPE-6725-PA. doi:10.2118/6725-PA

    Article  Google Scholar 

  7. Datta-Gupta, A., Pope, G.A., Seperhrnoori, K., Thrasher, R.L.: A symmetric, positive definite formulation of a three-dimensional micellar/polymer simulator. SPE Reserv. Eng. 1(6), 622–632 (1986). SPE-13504-PA. doi:10.2118/13504-PA

    Article  Google Scholar 

  8. Isaacson, E.L., Temple, J.B.: Analysis of a singular hyperbolic system of conservation laws. J. Diff. Eqs. 65(2), 250–268 (1986). doi:10.1016/0022-0396(86)90037-9

    Article  Google Scholar 

  9. Bartelds, G.A., Bruining, J., Molenaar, J.: The modeling of velocity enhancement in polymer flooding. Transp. Porous Media 26(1), 75–88 (1997). doi:10.1023/A:1006563532277

    Article  Google Scholar 

  10. Hilden, S.T., Nilsen, H.M., Raynaud, X.: Study of the well-posedness of models for the inaccessible pore volume in polymer flooding. Transp. Porous Media 114(1), 65–86 (2016). doi:10.1007/s11242-016-0725-8

    Article  Google Scholar 

  11. Saad, N., Pope, G.A., Sepehrnoori, K.: Application of higher-order methods in compositional simulation. SPE Reserv. Eng. 5(4), 623–630 (1990). SPE-18585-PA. doi:10.2118/18585-PA

    Article  Google Scholar 

  12. Liu, J., Delshad, M., Pope, G., Sepehrnoori, K.: Application of higher-order flux-limited methods in compositional simulation. Transp. Porous Media 16(41), 1–29 (1994). doi:10.1007/BF01059774

    Article  Google Scholar 

  13. Braconnier, B., Flauraud, É., Nguyen, Q.L.: Efficient scheme for chemical flooding simulation. Oil Gas Sci. Technol. 69(4), 585–601 (2014). doi:10.2516/ogst/2013189

    Article  Google Scholar 

  14. Trangenstein, J.A., Bell, J.B.: Mathematical structure of the black-oil model for petroleum reservoir simulation. SIAM J. Appl. Math. 49(3), 749–783 (1989). doi:10.1137/0149044

    Article  Google Scholar 

  15. Brooks, R.H., Corey, A.T.: Hydraulic properties of porous media and their relation to drainage design. Trans. ASAE 7(1), 26–28 (1964). doi:10.13031/2013.40684

    Article  Google Scholar 

  16. Corey, A. T.: Mechanics of heterogenous fluids in porous media, Water Resources Publications. Fort Collins, Colorado (1977)

    Google Scholar 

  17. Huggins, M.L.: Solutions of long chain compounds. J. Chem. Phys. 9 (5), 440 (1941). doi:10.1063/1.1750930

    Article  Google Scholar 

  18. Flory, P.J.: Principles of Polymer Chemistry. Cornell University Press, Ithaca (1953)

    Google Scholar 

  19. Yuan, C., Delshad, M., Wheeler, M. F.: Modeling multiphase non-Newtonian polymer flow in IPARS parallel framework. Networks Heter. Med. 5(3), 583–602 (2010)

    Article  Google Scholar 

  20. De Gennes, P.-G.: Scaling Concepts in Polymer Physics. Cornell University Press, Ithaca (1979)

    Google Scholar 

  21. Lin, E.: A study of micellar/polymer flooding using a compositional simulator, Ph.D. thesis, University of Texas at Austin (1981)

  22. Trushenski, S. P.: Micellar flooding: sulfonate-polymer interaction. In: Shah, D. O., Schechter, R. S. (eds.) Improved Oil Recovery by Surfactant and Polymer Flooding, pp 555–575. Academic Press, New York (1977)

    Chapter  Google Scholar 

  23. Dawson, R., Lantz, R.B.: Inaccessible pore volume in polymer flooding. SPE J. 12(5), 448–452 (1972). SPE-3522-PA. doi:10.2118/3522-PA

    Article  Google Scholar 

  24. Liauh, W.C., Duda, J.L., Klaus, E.E.: Investigation of the inaccessible pore volume phenomena AIChE Symp. Series, Vol. 78, Pennsylvania State University, Houston, Texas, 1982, CONF-810417-

  25. Shah, B.N., Lawrence, G., Willhite, P., Green, D.W.: The effect of inaccessible pore volume on the flow of polymer and solvent through porous media SPE Annual Fall Technical Conference and Exhibition, Society of Petroleum Engineers, Houston, Texas, 1978, SPE-7586-MS. doi:10.2118/7586-MS

  26. Lecourtier, J., Chauveteau, G.: Propagation of polymer slugs through porous media SPE Annual Technical Conference and Exhibition, Houston, Texas, 1984, SPE-13034-MS. doi:10.2118/13034-MS

  27. Lotsch, T., Muller, T., Pusch, G.: The effect of inaccessible pore volume on polymer coreflood experiments SPE Oilfield and Geothermal Chemistry Symposium, Society of Petroleum Engineers, Phoenix, Arizona, 1985, SPE-13590-MS. doi:10.2118/13590-MS

  28. Preux, C., McKee, F.: Study and approximation of IMPES stability: the CFL criteria. In: Fort, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds.) Finite Volumes for Complex Applications VI: Problems & Perspectives, Vol. 4 of Springer Proceedings in Mathematics. doi:10.1007/978-3-642-20671-9_75, pp 713–721. Springer, Prague (2011)

    Chapter  Google Scholar 

  29. Keyfitz, B.L., Kranzer, H.C.: A system of non-strictly hyperbolic conservation laws arising in elasticity theory. Arch. Rat. Mech. Anal. 72(3), 219–241 (1980). doi:10.1007/BF00281590

    Article  Google Scholar 

  30. Coats, K.H.: A note on IMPES and some IMPES-based simulation models. SPE J. 5(3), 245–251 (2000). SPE-65092-PA. doi:10.2118/65092-PA

    Article  Google Scholar 

  31. Coats, K.H.: IMPES stability: the CFL limit. SPE J. 8(3), 291–297 (2003). SPE-85956-PA. doi:10.2118/85956-PA

    Article  Google Scholar 

  32. Coats, K.H.: Computer simulation of three-phase flow in reservoirs, Ph.D. thesis, University of Texas at Austin (1968)

  33. Leray, S., Douarche, F., Tabary, R., Peysson, Y., Moreau, P., Preux, C.: Multi-objective assisted inversion of chemical EOR corefloods for improving the predictive capacity of numerical models. J. Petrol. Sci. Eng. 146, 1101–1115 (2016). doi:10.1016/j.petrol.2016.08.015

    Article  Google Scholar 

  34. Buckley, S.E., Leverett, M.C.: Mechanism of fluid displacement in sands. Trans. AIME 146(1), 107–116 (1942). SPE-942107-G. doi:10.2118/942107-G

    Article  Google Scholar 

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Authors and Affiliations

  1. IFP Energies nouvelles, 1 et 4 avenue de Bois-Préau, 92852, Rueil-Malmaison Cedex, France

    Benjamin Braconnier, Christophe Preux, Éric Flauraud & Quang-Huy Tran

  2. Laboratoire de Mathématiques Jean Leray, UMR 6629, Département de Mathématiques, Université de Nantes, 2 rue de la Houssinière, BP 92208 - 44322, Nantes Cedex 3, France

    Christophe Berthon

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  1. Benjamin Braconnier
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  4. Quang-Huy Tran
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  5. Christophe Berthon
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Correspondence to Benjamin Braconnier.

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Braconnier, B., Preux, C., Flauraud, É. et al. An analysis of physical models and numerical schemes for polymer flooding simulations. Comput Geosci 21, 1267–1279 (2017). https://doi.org/10.1007/s10596-017-9637-0

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