1887

Abstract

Summary

The new computational model for multiphase flow in deforming elastic porous media is proposed. The derivation of the model is based on the thermodynamically compatible hyperbolic systems of conservation laws theory. The flow of the mixture of compressible fluids in the elastic medium is supposed to be a continuum, in which the multiphase character of flow is taken into account. This phenomenological approach of continuum mechanics modelling allows us to formulate the system of governing equations in a divergent form, which is advantageous for the mathematical study of the different problems and for the development of advanced numerical methods.

We present a thermodynamically compatible model for the flow of fluids mixture in elastic porous medium. The governing equations comprise balance laws for phase masses, total momentum and total energy supplemented by the equations for relative velocities in divergent form. The high accuracy Runge-Kutta-WENO numerical method for solving equations of the model is presened along the numerical test problem.

The proposed model and developed numerical framework can be used in the wide range of oil recovery problems. Examples are: tracking oil/water interfaces in oil reservoirs, modeling of flows in the well surrounding formation.

Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.20141817
2014-09-08
2024-03-28
Loading full text...

Full text loading...

References

  1. De Groot, S.R. and MazurP.
    [1984] Non-equilibrium thermodynamics. Dover Publications. ISBN 0486647412.
    [Google Scholar]
  2. Dorovsky, V.N., Romenski, E.I., Fedorov, A.I. and Perepechko, Yu.V.
    [2011] Resonance method for measuring the permeability of rocks. Russian Geology and Geophysics, 52(7), 950–961.
    [Google Scholar]
  3. Jeremic, B., Cheng, Z., Taiebat, M. and Dafalias, Y.
    [2008] Numerical simulation of fully saturated porous materials. Int. J. Numer. Anal. Meth. Geomech., 32(13), 1635–1660.
    [Google Scholar]
  4. Godunov, S.K. and Romenskii, E.I.
    [2003] Elements of continuum mechanics and conservation laws. Kluwer Academic/Plenum Publ., NY.
    [Google Scholar]
  5. Khoei, A.R. and Mohammadnejad, T.
    [2011] Numerical modeling of multiphase flow in deforming porous media; A comparison between two- and three-phase models for seismic analysis of earth and rockfill dams. Comput. Geotech., 38(2), 142–166.
    [Google Scholar]
  6. Romenski, E., Belozerov, A. and Peshkov, I.M.
    [2013] Thermodynamically compatible hyperbolic conservative model of compressible multiphase flow: Application to four phase flow. AIP Conference Proceedings, 1558, 123–.
    [Google Scholar]
  7. Romenski, E., Drikakis, D. and Toro, E.
    [2010] Conservative models and numerical methods for compressible two-phase flow. J. Sci. Comput., 42(1), 68–95.
    [Google Scholar]
  8. Romenski, E.
    [2013] Conservative formulation for compressible fluid flow through elastic porous media. Numerical Methods for Hyperbolic Equations, Vázquez-Cendón et al. (eds), Taylor & Francis Group, London, 193–200.
    [Google Scholar]
  9. Shu, C.W.
    [1997] Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. NASA/CR-97-206253, ICASE. report No.97–65.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.20141817
Loading
/content/papers/10.3997/2214-4609.20141817
Loading

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error