Full Article - Open Access.

Idioma principal


Dias, R.A.C.; Chalhub, D.J.N.M.; Oliveira, T.J.L de; Sphaier, L.A.; Fernandes, P.D.;

Full Article:

Water injection into oil formations has a very wide application in the oil industry. The injection of water has as main objective: to maintain formation pressure and provide the recovery of oil by water displacement. This work compares two different theoretical formulations used in reservoir simulations. One is the saturation differential equation and the other is the mixture theory equation applied to fluid flow in porous media. The saturation differential equation is widely used in reservoir simulations. This equation is found when Darcy’s Law for each phase is applied in the continuity equation for each phase. However, there is another theoretical approach for multiphase flows in porous media. Mixture theory allows a local description of the flow in a porous medium, supported by a thermodynamically consistent theory which generalizes the classical continuum mechanics. This article compares the results obtained by the equation based on the mixture theory with the saturation differential equation. To solve the saturation equation the Generalized Integral Transform Technique (GITT) was employed. The GITT has been successfully employed in various petroleum reservoir simulation problems. The numerical method for the solution of mixture theory was obtained using advanced, commercial, general-purpose CFD code: FLUENT.

Full Article:

Palavras-chave: Integral Transform Technique, Finite Volumes Method, Waterflooding, Porous Media,


DOI: 10.5151/meceng-wccm2012-19588

Referências bibliográficas
  • [1] J. E. Adkins. Phil. Trans. Roy. Soc. London, A255:607, 1963.
  • [2] R. J. Atkin and R. E. Craine. Q. J. Mech. Appl. Math., XXIX:209, 1976.
  • [3] S. E. Buckley and M. C. Leverett. Mechanism of fluid displacement in porous media. Petroleum Technology, pages 107–116, 1942.
  • [4] J. M. Z. Chongxuan Liu, Jim E. Szecsody andW. P. Ball. Use of the generalized integral transform method for solving equations of solute transport in porous media. Advances in Water Resources, 23(5):483–492, 2000.
  • [5] R. M. Cotta. Integral Transforms in Computational Heat and Fluid Flow. CRC Press, Boca Raton, FL, 1993.
  • [6] H. Darcy. Les fountaines publiques de la ville de dijon. Dalmont, Paris, 185
  • [7] J. R. Fanchi. Principles of Applied Reservoir Simulation. Boston, Gulf Professional Publishing, 1nd edition, 2001.
  • [8] A. Fick. Ann-der Phys., 94:56, 1976.
  • [9] A. E. Green and P. M. Naghid. Int. J. Engng. Sci., 3:231, 1965.
  • [10] A. E. Green and P. M. Naghid. Int. J. Engng. Sci., 6:631, 1968.
  • [11] R. A. Greenkorn. Flow Phenomena in Porous Media. Marcel Dekker, New York, 1nd edition, 1983.
  • [12] R. Helmig. Multiphase Flow and Transport Processes in the Subsurface (AContribution to the Modeling of Hydrosystems). Springer, Berlin, Germany, 1nd edition, 1997.
  • [13] T. S. J.S. P´erez Guerrero a. Analytical solution for one-dimensional advection dispersion transport equation with distance dependent coefficients. Journal of Hydrology, 390:57– 65, 2010.
  • [14] W. Lake, L. Enhanced Oil Recovery. Prentice-Hall, New Jersey, 1nd edition, 1989.
  • [15] M. L. Martins-Costa and R. M. Saldanha da Gama. A local model for the heat transfer process in two distinct flow regions. Int. J. Heat and Fluid Flow, 15(6), 1994.
  • [16] D. Nield and A. Bejan. Convection in Porous Media. Springer, New York,, 3nd edition, 2006.
  • [17] D. W. Peaceman. Fundamentals of Numerical Reservoir Simulation. Elsevier, Englewood Cliffs, NJ, 1977.
  • [18] L. S. D. A. R. M. Cotta, H. Luznetq and J. N. N. Quaresma. Integral transforms for natural convection in cavities filled with porous media. Transport Phenomena in Porous Media III, (5):97–119, 2000.
  • [19] R. Sampaio. Arch. Ratl. Mech. Anal., 62:99, 1976.
  • [20] L. A. Sphaier, R. M. Cotta, C. P. Naveira-Cotta, and J. N. N. Quaresma. The UNIT algorithm for solving one-dimensional convection-diffusion problems via integral transforms. International Communications in Heat and Mass Transfer, 38:565–571, 2011.
  • [21] C. Truesdell. Rend. Lincei., 22:33, 1957.
  • [22] C. Truesdell. Rend. Lincei., 22:158, 1957.
  • [23] C. Truesdell. J. Chem. Phys., 37:2337, 1962.
  • [24] C. Truesdell and R. Toupin. The Classical Field Theories. Springer-Verlag, New York, NY, 1960.
Como citar:

Dias, R.A.C.; Chalhub, D.J.N.M.; Oliveira, T.J.L de; Sphaier, L.A.; Fernandes, P.D.; "COMPARISONS BETWEEN MIXTURE THEORY AND DARCY LAW FOR TWO-PHASE FLOW IN POROUS MEDIA USING GITT AND FLUENT SIMULATIONS", p. 3793-3805 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-19588

últimos 30 dias | último ano | desde a publicação