Advertisement

Nonequilibrium Effects in Immiscible Two-Phase Flow

  • Yuhang Wang
  • Saman A. AryanaEmail author
Chapter
Part of the Advances in Science, Technology & Innovation book series (ASTI)

Abstract

Two-dimensional, high-resolution, numerical solutions for the classical formulation and two widely accepted nonequilibrium models of multiphase flow through porous media are generated and compared. Flow equations for simultaneous flow of two immiscible phases through porous media are written in a vorticity stream-function form. In the resulting system of equations, the vorticity stream-function equation is solved using a spectral method and the transport equation is discretized in space using a central-upwind scheme. A semi-implicit time-stepper is used to solve the coupled system of equations. The solutions reveal that inclusion of dynamic capillary pressure sharpens the front and lengthens the viscous fingers. The inclusion of nonequilibrium effects in constitutive relations introduces diffusion and smears the otherwise highly resolved viscous fingers in the saturation front.

Keywords

Multiphase flow Nonequilibrium effects High-resolution methods Flow instability 

References

  1. 1.
    Barenblatt, G.I., Patzek, T.W., Silin, D.B.: The mathematical model of nonequilibrium effects in water-oil displacement. SPE J. 8(4), 409–416 (2003)Google Scholar
  2. 2.
    Hassanizadeh, S.M., Gray, W.G.: Thermodynamic basis of capillary pressure in porous media. Water Resour. Res. 29(10), 3389–3405 (1993)CrossRefGoogle Scholar
  3. 3.
    Aryana, S.A., Kovscek, A.R.: Nonequilibrium effects and multiphase flow in porous media. Transp. Porous Media 97(3), 373–394 (2013)CrossRefGoogle Scholar
  4. 4.
    Ren, G., Rafiee, J., Aryana, S.A., Younis, R.M.: A Bayesian model selection analysis of equilibrium and nonequilibrium models for multiphase flow in porous media. Int. J. Multiph. Flow 89, 313–320 (2017)CrossRefGoogle Scholar
  5. 5.
    Canuto, C., Hussaini, M.Y., Quarteroni, A., Thomas Jr., A.: Spectral Methods in Fluid Dynamics. Springer Science & Business Media (2012)Google Scholar
  6. 6.
    Kurganov, A., Tadmor, E.: New high-resolution central schemes for nonlinear conservation laws and convection–diffusion equations. J. Comput. Phys. 160(1), 241–282 (2000)CrossRefGoogle Scholar
  7. 7.
    Kurganov, A., Noelle, S., Petrova, G.: Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. SIAM J. Sci. Comput. 23(3), 707–740 (2001)CrossRefGoogle Scholar
  8. 8.
    Kutz, J.N.: Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data. Oxford University Press (2013)Google Scholar
  9. 9.
    Berg, S., Ott, H.: Stability of CO2–brine immiscible displacement. Int. J. Greenhouse Gas Control 11, 188–203 (2012)CrossRefGoogle Scholar
  10. 10.
    Riaz, A., Tang, G.Q., Tchelepi, H.A., Kovscek, A.R.: Forced imbibition in natural porous media: comparison between experiments and continuum models. Phys. Rev. E 75, 036305 (2007)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of WyomingLaramieUSA

Personalised recommendations