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Computational Thermal Sciences: An International Journal

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ISSN Druckformat: 1940-2503

ISSN Online: 1940-2554

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NUMERICAL SIMULATIONS OF THERMO-VISCOUS FINGERING INSTABILITY IN POROUS MEDIA

Volumen 2, Ausgabe 2, 2010, pp. 183-201
DOI: 10.1615/ComputThermalScien.v2.i2.70
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ABSTRAKT

Numerical simulations using a pseudo-spectral method based on the Hartley transform are conducted to examine the viscous fingering instability of miscible flow displacements involving heat transfer between the fluids. The flow geometry consists of a rectilinear homogeneous porous media where the fluids and the media are assumed in thermal equilibrium. The physical model is represented using a continuity equation, Darcy's law, and volume-averaged forms of the convection-diffusion equation for mass and energy balance. The dependence of the fluids viscosities on both temperature and concentration is represented by two dimensionless parameters; the solutal viscosity ratio; βC, and the thermal viscosity ratio; βT. In particular, the study analyzed the effects of varying important parameters such as the Lewis number, the thermal lag coefficient, and the thermal mobility ratio on the dynamics of the flow. The development of new finger structures is analyzed by examining contours of the concentration and characterizing them qualitatively through a spectral analysis of the average concentration and an analysis of the variations of the mixing length and the relative contact area. It is found that diffusion of heat and its redistribution between the fluid and solid phases have a strong effect on the growth of the fingers. Furthermore, close and intricate interactions between the fluid and thermal fronts affect the subsequent development of instability, even when the two fronts are separated, with the thermal front lagging behind the fluid one.

REFERENZEN
  1. Bird, R. B., Stewart, W. E., and Lightfoot, E. N., Transport Phenomena.

  2. Bracewell, R. N., The Fourier Transform and its Applications.

  3. Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A., Spectral Methods in Fluid Dynamic.

  4. Ghesmat, K. and Azaiez, J., Viscous fingering instability in porous media: Effect of anisotropic velocity-dependent dispersion tensor.

  5. Holloway, K. E. and de Bruyn, J., Viscous fingering with a single fluid.

  6. Homsy, G. M., Viscous fingering in porous media.

  7. Islam, M. N. and Azaiez, J., Fully implicit finite difference pseudo-spectral method for simulating high mobility-ratio miscible displacements.

  8. Kong, X., Haghighi, M., and Yortsos, Y. C., Visualization of steam displacement of heavy oils in a Hele-Shaw cell.

  9. Kuang, J. and Maxworthy, T., The effect of thermal diffusion on miscible viscous displacement in a capillary tube.

  10. McCloud, K. V. and Maher, J. V., Experimental perturbations to Saffman-Taylor flow.

  11. Pritchard, D., The instability of thermal and fluid fronts during radial injection in a porous medium.

  12. Saghir, M. Z., Chaalal, O., and Islam, M. R., Numerical and experimental modeling of viscous fingering during liquid-liquid miscible displacement.

  13. Sasaki, K., Akibayashi, S., Yazawa, N., and Kaneko, F., Microscopic visualization with high resolution optical-fiber scope at steam chamber interface on initial stage of SAGD process.

  14. Sheorey, T., Muralidhar, K., and Mukherjee, P. P., Numerical experiments in the simulation of enhanced oil recovery from a porous formation.

  15. Singh, B. and Azaiez, J., Numerical simulation of viscous fingering of shear-thinning fluids.

  16. Tan, C. T. and Homsy, G. M., Simulation of nonlinear viscous fingering in miscible displacement.

REFERENZIERT VON
  1. Sajjadi M., Azaiez J., Dynamics of fluid flow and heat transfer in homogeneous porous media, The Canadian Journal of Chemical Engineering, 91, 4, 2013. Crossref

  2. Sajjadi M., Azaiez J., Scaling and unified characterization of flow instabilities in layered heterogeneous porous media, Physical Review E, 88, 3, 2013. Crossref

  3. Sajjadi Mozhdeh , Azaiez Jalel , Thermo-Viscous Fingering in Heterogeneous Media, All Days, 2012. Crossref

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