Abstract
The instability of a plane front between two phases of the same fluid (steam and water) in a porous medium is considered. The configuration is taken to be initially stationary with the more dense phase overlying the less dense phase. The frontal region is assumed sharp, so that macroscopic boundary conditions can be utilized. This assumption precludes the existence of dispersion instabilities. The stabilizing influence of phrase transition as well as the implication of different macroscopic pressure boundary conditions on the stability of the front are discussed and illustrated.
Similar content being viewed by others
Abbreviations
- A 12 :
-
surface area between fluids
- C * :
-
macroscopic curvature of front
- C :
-
microscopic curvature
- C 1,C 2 :
-
unknown coefficients of determinant
- c i :
-
heat capacity
- f i :
-
macroscopic constants
- g :
-
acceleration of gravity
- h :
-
upper bound of reservoir
- h * :
-
lower bound of reservoir
- h i :
-
heat enthalpy
- k :
-
wave number
- K ij :
-
general relative permeability
- n :
-
stability index
- P :
-
pressure
- q :
-
darcy velocity
- u, v :
-
velocity
- T :
-
temperature
- α :
-
surface tension coefficient
- α * :
-
effective surface tension coefficient
- Β :
-
parameter estimated by Equation (A4)
- ε i :
-
internal energy
- η(x, t):
-
interface location
- k i :
-
thermal conductivity
- λ 1,λ 2 :
-
unknown coefficients of determinant
- γ i :
-
parameter estimated by Equation (A4)
- ρ i :
-
density
- Μ i :
-
viscosity
- Φ :
-
porosity
- ψ i :
-
velocity potential
- Ω :
-
constant
- 1:
-
gas or steam
- 2:
-
water
- m:
-
medium
References
Tayor, G., 1959, The instability of liquid surfaces when accelerated in a direction perpendicular to their planes I,Proc. Roy. Soc. A. 201, 192.
Saffman, P. G., and Taylor, G., 1958, The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous fluid,Proc. Roy. Soc. A.,245, 312–329.
Saffman, P. G., 1959, Exact solutions for the growth of fingers from a flat surface between two fluids in a porous medium or Hele-Shaw cell,Quart. J. Mech. Appl. Math. 12, 146–150.
Chouke, R. L., van Meurs, P., and van der Pol, C., 1959, The instability of slow immiscible viscous liquid-liquid displacements in permeable media,Trans Amer. Inst. Min. Eng. 216, 188–194.
Aleman, M. A. and Slattery, J. C., 1988, A linear stability analysis for immiscible displacements,Transport in Porous Media 3, 455–472.
Peters, E. J. and Flock, D. L. 1981, The onset of instability during two-phase immiscible displacement in porous media,Soc. Pet. Eng. J. 21, 249–258.
Perkins, T. K. and Johnston, O. C., 1969, A study of immiscible fingering in linear models,Soc. Pet. Eng. J. 9, 39–46.
McLean, J. W. and Saffman, P. G., 1981, The effects of surface tension on the shape of fingers in a Hele-Shaw cell,J. Fluid Mech. 102, 455–469.
Spanos, T. J. T. and de la Cruz, V., 1984, Some stability problems during immiscible displacement in a porous medium,AOSTRA J. Res. 1, 63–80.
de la Cruz, V. and Spanos, T. J. T., 1989, Seismic boundary conditions for porous media,J. Geophys. Res. 94, 3024–3029.
Cyr, T. J., de la Cruz, V. and Spanos, T. J. T., 1988, An analysis of the viability of polymer flooding as an enhanced oil recovery technology,Transport in Porous Media 3, 591–618.
Udey, N. and Spanos, 1993, The equations of miscible flow with negligible molecular diffusion,Transport in Porous Media 10, 1–41.
Udell, K. S., 1983, Heat transfer in porous media heated from above with evaporation, condensation, and capillary effects,J. Heat Transfer ASME,105, 485–492.
Krueger, D. A., 1982, Stability of piston like displacements of water by steam and nitrogen in porous media,Soc. Pet. Eng. J. 625–634.
Miller, C. A., 1975, Stability of moving surfaces in fluid systems with heat and mass transport, III. Stability of displacement fronts in porous media,AIChE J. 21, 474–479.
Schubert, G. and Straus, J. M., 1980, Gravitational stability of water over steam in vapor-dominated geothermal systems,J. Geophys. Res. 85, 6505–6512.
de la Cruz, V., Spanos, T. J. T., and Sharma, R. C., 1985, The stability of a steam-water front in a porous medium,Can. J. Chem. Eng. 63, 735–745.
Ramesh, P. S. and Torrance, K. E., 1990 Stability of boiling in porous media,Int. J. Heat Mass Transfer 33 (9), 1895–1908.
Eastwood, J. E., 1991, Thermomechanics of porous media, PhD Thesis, University of Alberta.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T.,Numerical Recipes, Cambridge University Press, New York, 1986.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Eastwood, J.E., Spanos, T.J.T. Stability of a stationary steam-water front in a porous medium. Transp Porous Med 14, 1–21 (1994). https://doi.org/10.1007/BF00617025
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00617025