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Porosity variations in saline media caused by temperature gradients coupled to multiphase flow and dissolution/precipitation

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Abstract

We present a theoretical-numerical investigation of porosity variations induced by temperature gradients in unsaturated saline media. It is known that temperature variations cause humidity variations which lead to liquid flow towards and vapour flow away from the hot source. When this phenomenon occurs in saline media, the liquid is salt saturated brine, so that evaporation causes salt precipitation and an ensuing porosity reduction. Condensation of water causes salt dissolution and porosity increase. This process may be important in the case of heat generating waste because it suggests that selfsealing may take place near the waste. On the other hand, salt mass balance will lead to porosity increases in other zones.

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Abbreviations

b :

body forces vector in equilibrium equation (FL−3)

D :

thermal diffusivity (L2T−1)

D ία :

dispersion tensor (i = h, w for α = l and i = w, a for α = g) (ML−1T−1

D ίm :

molecular diffusion coefficient (i = h, w) (L2T−1)

D lα :

mechanical dispersion tensor α = l, g (L2T−1)

d l , d t :

longitudinal and transversal dispersivities (L)

E α :

internal energy of α-phase per unit mass of α-phase (EM−1)

E ία :

internal energy of i-species in α-phase per unit mass of i-species (EM−1)

f ί :

external mass supply per unit volume of medium (i = h, w, a) (ML−3T−1)

f E :

internal/external energy supply per unit volume of medium (EL−3T−1)

f ws :

internal sink of water in fluid inclusion equation (ML−3T−1)

g:

gravity vector (LT−2)

i :

species index, h salt (halite), w water and a air (superscript)

I :

identity matrix

i ία :

nonadvective mass flux of i-species in α-phase (ML−2T−1)

i c :

nonadvective heat flux (EL−2T−1)

j Eα :

advective energy flux in α-phase w.r.t a fixed reference system (EL−2T−1)

j' Eα :

advective energy flux in α-phase w.r.t. the solid phase (EL−2T−1)

j ία :

total mass flux of ί-species in α-phase w.r.t. a fixed reference system (ML−2T−1)

j' ί α :

total mass flux of ί-species in α-phase w.r.t. the solid phase (ML−2T−1)

k :

intrinsic permeability tensor (L2)

k rα :

α-phase relative permeability (α = l, g) (-)

M a :

molecular mass of air (M) (0.02895 kg/mol)

M w :

molecular mass of water (M) (0.018 kg/mol)

P α :

fluid pressure of α-phase (α = l, g) (FL−2)

P v :

partial pressure of vapour (FL−2)

P a :

partial pressure of air (FL−2)

q α :

volumetric flux of α-phase w.r.t. the solid matrix (α = l, g) (LT−1)

R :

constant of gases (EΘ−1) (8.314 J/mol/K)

S α :

volumetric fraction of pore volume occupied by α-phase (α = l, g) (-)

S e :

\(\left( { = \frac{{S_l - S_{lr} }}{{S_{ls} - S_{lr} }}} \right)\) effective liquid saturation

S lr :

residual liquid saturation

S ls :

maximum liquid saturation

T :

temperature (Θ)

∂ u/∂t :

solid velocity vector (LT−1)

α :

phase index, s solid, l liquid and g gas (subscript)

β α :

thermal expansion coefficient (Θ−1)

θ ία :

(= ω ία ρα) mass of ί-species per unit volume of a-phase (ML−3)

λ α :

thermal conductivity (EΘ−1L−1T−1)

μ α :

dynamic viscosity of a-phase (a = l, g) (FL−2T)

▽:

gradient vector (L−1)

ρ α :

mass of α-phase per unit volume of a-phase (ML−3)

φ :

porosity

σ :

stress tensor (FL−2)

σ :

surface tension of liquid (FL−1)

Τ :

tortuosity

ω ία :

mass fraction of ί-species in a-phase

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Authors and Affiliations

  1. Geotechnical Department, Civil Engineering School, Technical University of Catalunya, Barcelona, Spain

    S. Olivella, J. Carrera, A. Gens & E. E. Alonso

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  1. S. Olivella
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  2. J. Carrera
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  3. A. Gens
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  4. E. E. Alonso
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Olivella, S., Carrera, J., Gens, A. et al. Porosity variations in saline media caused by temperature gradients coupled to multiphase flow and dissolution/precipitation. Transp Porous Med 25, 1–25 (1996). https://doi.org/10.1007/BF00141260

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  • DOI: https://doi.org/10.1007/BF00141260

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