Abstract
Two-phase mixtures of hot brine and steam are important in geothermal reservoirs under exploitation. In a simple model, the flows are described by a parabolic equation for the pressure with a derivative coupling to a pair of wave equations for saturation and salt concentration. We show that the wave speed matrix for the hyperbolic part of the coupled system is formally identical to the corresponding matrix in the polymer flood model for oil recovery. For the class ofstrongly diffusive hot brine models, the identification is more than formal, so that the wave phenomena predicted for the polymer flood model will also be observed in geothermal reservoirs.
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Abbreviations
- A,B :
-
coefficient matrices (5)
- c(x,t):
-
salt concentration (primary dependent variable)
- C(p, s, c, q t):
-
wave speed matrix (6)
- f :
-
source term (5)
- g :
-
acceleration due to gravity (constant)
- h b(p, c):
-
brine specific enthalpy
- h v(p):
-
vapour specific enthalpy
- j :
-
conservation flux (1)
- k :
-
absolute permeability (constant)
- k b(s), kv(s):
-
relative permeabilities of the brine and vapour phases
- K :
-
conductivity
- p(x,t):
-
pressure (primary dependent variable)
- q :
-
volume flux (Darcy velocity) (3)
- s(x,t):
-
brine saturation (primary dependent variable)
- t :
-
time (primary independent variable)
- T=T sat(p):
-
saturation temperature
- u b(p, c):
-
brine specific internal energy
- u m ∞ T:
-
rock matrix specific internal energy
- u v(p):
-
vapour specific internal energy
- U(x, t):
-
shock velocity
- x :
-
space (primary independent variable)
- Φ :
-
porosity (constant)
- Μ b(p, c):
-
brine dynamic viscosity
- Μ v(p):
-
vapour dynamic viscosity
- ρ(p, s, c) :
-
conservation density (1)
- ρ b(p, c):
-
brine density
- ρ v(p):
-
vapour density
- b :
-
brine
- m :
-
rock matrix
- t :
-
total
- v :
-
vapour
- S :
-
salt
- M :
-
mass
- E :
-
energy
References
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Young, R. Two-phase brine mixtures in the geothermal context and the polymer flood model. Transp Porous Med 11, 179–185 (1993). https://doi.org/10.1007/BF01059633
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DOI: https://doi.org/10.1007/BF01059633