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Stability of a stationary steam-water front in a porous medium

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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.

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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

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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

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  • DOI: https://doi.org/10.1007/BF00617025

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