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Transport in Porous Media

, Volume 15, Issue 3, pp 271–293 | Cite as

Nonisothermal multiphase flow of brine and gas through saline media

  • S. Olivella
  • J. Carrera
  • A. Gens
  • E. E. Alonso
Article

Abstract

We propose a general formulation for nonisothermal multiphase flow of brine and gas through saline media. The balance equations include mass balance (three species), equilibrium of stresses and energy balance (total internal energy). Salt, water and air mass balance equations are established. The balance of salt allows the establishment of the equation for porosity evolution due to solid skeleton deformation, dissolution/precipitation of salt and migration of brine inclusions. Water and air mass balance equations are also obtained. Two equations are required for water: total water in the medium and water present in solid phase brine inclusions. The mechanical problem is formulated through the equation of stress equilibrium. Finally, the balance of internal energy is established assuming thermal equilibrium between phases. Some general aspects of the constitutive theory are also presented.

Key words

brine creep deformation gas heat inclusion multiphase porosity salt 

Notation

b

body forces vector in equilibrium equation

Ce

elastic compliance matrix

d

ratio between volume and surface of the grains

do

grain size

Dsw

effective diffusion coefficient for inclusion migration

Dαi

dispersion tensor (i=h, w forα=l andi=w, a forα=g)

Eα

internal energy ofα-phase per unit mass ofα-phase

Eαi

internal energy ofi-species inα-phase per unit mass ofi-species

fi

external mass supply per unit volume of medium (i=h, w, a)

fE

internal/external energy supply per unit volume of medium

fsw

internal sink of water in fluid inclusion equation

g

gravity vector

i

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

iαi

nonadvective mass flux ofi-species inα-phase

ic

nonadvective heat flux

j

advective energy flux inα-phase with respect to a fixed reference system

j

advective energy flux inα-phase with respect to the solid phase

jαi

total mass flux ofi-species inα-phase with respect to a fixed reference system

jα′i

total mass flux ofi-species inα-phase with respect to the solid phase

Kα

permeability tensor (α=l, g)

k

intrinsic permeability tensor

k

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

Mw

molecular mass of water

Pα

fluid pressure ofα-phase (α=l, g)

qα

volumetric flux ofα-phase with respect to the solid matrix (α=l, g)

R

constant of gases

Sα

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

T

temperature

u

solid velocity vector

vsw

velocity of brine inclusions in the solid phase

α

phase index,s solid,l liquid andg gas (subscript)

\(\dot \varepsilon \)

strain rate tensor

θαi

(=ω α i ρα) mass ofi-species per unit volume ofα-phase

μα

dynamic viscosity ofα-phase (α=l, g)

gradient vector

ρα

mass ofα-phase per unit volume ofα-phase

σ, σ′

stress tensor (total and net)

\(\dot \sigma \)

stress rate tensor

Φ

porosity

ωαi

mass fraction ofi-species inα-phase

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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • S. Olivella
    • 1
  • J. Carrera
    • 1
  • A. Gens
    • 1
  • E. E. Alonso
    • 1
  1. 1.Geotechnical Department, Civil Engineering SchoolTechnical University of CatalunyaBarcelonaSpain

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