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Nonisothermal multiphase flow of brine and gas through saline media

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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.

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Abbreviations

b :

body forces vector in equilibrium equation

C e :

elastic compliance matrix

d :

ratio between volume and surface of the grains

d o :

grain size

D w s :

effective diffusion coefficient for inclusion migration

D iα :

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

E α :

internal energy ofα-phase per unit mass ofα-phase

E iα :

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

f i :

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

f E :

internal/external energy supply per unit volume of medium

f w s :

internal sink of water in fluid inclusion equation

g :

gravity vector

i :

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

i iα :

nonadvective mass flux ofi-species inα-phase

i c :

nonadvective heat flux

j Eα :

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

j ′ Eα :

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

j i α :

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

j ′i α :

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

K α :

permeability tensor (α=l, g)

k :

intrinsic permeability tensor

k rα :

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

M w :

molecular mass of water

P α :

fluid pressure ofα-phase (α=l, g)

q α :

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

R :

constant of gases

S α :

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

T :

temperature

u :

solid velocity vector

v w s :

velocity of brine inclusions in the solid phase

α :

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

\(\dot \varepsilon \) :

strain rate tensor

θ iα :

(=ω iα 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

ω iα :

mass fraction ofi-species inα-phase

References

  • Abriola, L. M. and Pinder, G. F. (1985), A multiphase approach to the modeling of porous media contamination by organic compounds. 1. Equation development,Water Resour. Res. 21(1), 11–18.

    Google Scholar 

  • Bachmat, Y. and Bear, J. (1986), Macroscopic modelling of transport phenomena in porous media. 1: The continuum approach,Transport in Porous Media 1, 213–240.

    Google Scholar 

  • Bear, J. (1979),Dynamics of Fluids in Porous Media, American Elsevier.

  • Bear, J. and Bachmat, Y. (1986), Macroscopic modelling of transport phenomena in porous media. 2: Applications to mass, momentum and energy transport,Transport in Porous Media 1, 241–269.

    Google Scholar 

  • Bear, J. and Bensabat, J. (1989), Advective fluxes in multiphase porous media under nonisothermal conditions,Transport in Porous Media 4, 423–448.

    Google Scholar 

  • Bear, J., Bensabat, J. and Nir, A. (1991), Heat and mass transfer in unsaturated porous media at a hot boundary: I. One-dimensional analytical model,Transport in Porous Media 6, 281–298.

    Google Scholar 

  • Bird, R. B., Stewart, W. E. and Lightfoot, E. N. (1960),Transport Phenomena, John Wiley, New York, 1960.

    Google Scholar 

  • Corapcioglu, M. Y. (1991), Formulation of electro-chemico-osmotic processes in soils,Transport in Porous Media 6, 435–444.

    Google Scholar 

  • Edlefson, N. E. and Anderson, A. B. C. (1943), Thermodynamics of soil moisture,Hilgardia 15(2), 31–298.

    Google Scholar 

  • Engelmann, H. J., Broochs, P. W., HÄnsel, W., and Peters, L. (1989), Dams as sealing systems in rock salt formations — Test dam construction and determination of permeability,Sealing of Radioactive Waste Repositories, Proceedings of an NEAJCEC Workshop, ISBN 92-64-03290-8, 151–162.

  • Faust, C. R. and Mercer, J. W. (1979), Geothermal reservoir simulation: 1. Mathematical models for liquid- and vapour-dominated hydrothermal systems,Water Resour. Res. 15(1), 23–30.

    Google Scholar 

  • van Genuchten, R. (1980), A closed-form equation for predicting the hydraulic conductivity of unsaturated soils,Soil Sci. Soc. Am. J., 892–898.

  • Hassanizadeh, S. M. and Gray, W. G. (1979a), General conservation equations for multiphase systems: 1. Averaging procedure,Adv. Water Resour. 2, 131–144.

    Google Scholar 

  • Hassanizadeh, S. M. and Gray, W. G. (1979b), General conservation equations for multiphase systems: 2. Mass, momenta, energy and entropy equations,Adv. Water Resour. 2, 191–203.

    Google Scholar 

  • Hassanizadeh, S. M. (1986a), Derivation of basic equations of mass transport in porous media, Part 1. Macroscopic balance laws,Adv. Water Resour. 9, 196–206.

    Google Scholar 

  • Hassanizadeh, S. M. (1986b), Derivation of basic equations of mass transport in porous media, Part 2. Generalized Darcy's and Fick's laws,Adv. Water Resour. 9, 207–222.

    Google Scholar 

  • Horvath, A. L. (1985),Aqueous Electrolyte Solutions, Physical Properties, Estimation and Correlation Methods, Ellis Horwood, Chichester.

    Google Scholar 

  • Langer, H. and Offermann, H. (1982), On the solubility of sodium chloride in water,J. Crystal Growth 60, 389–392.

    Google Scholar 

  • Lewis, R. W., Roberts, P. J. and Schrefler, B. A. (1989), Finite element modelling of two-phase heat and fluid flow in deforming porous media,Transport in Porous Media 4, 319–334.

    Google Scholar 

  • Milly, P. C. D. (1982), Moisture and heat transport in hysteretic, inhomogeneous porous media: A matrix head-based formulation and a numerical model,Water Resour. Res. 18(3), 489–498.

    Google Scholar 

  • Olivella, S., Gens, A., Alonso, E. E. and Carrera, J. (1992), Constitutive modelling of porous salt aggregates,Proc. Fourth International Symposium on Numerical Models in Geomechanics — NUMOG-IV/Swansea/UK/24–27 August 1992, A. A. Balkema, Rotterdam, pp. 179–189.

  • Olivella, S., Gens, A., Carrera, J. and Alonso, E. E. (1993), Behaviour of porous salt aggregates. Constitutive and field equations for a coupled deformation, brine, gas and heat transport model,Proc. 3rd Conference on the Mechanical Behaviour of Salt, September 14–16, 1993, Ecole Polytechnique, Palaiseau, France, 255–269

    Google Scholar 

  • Panday, S. and Corapcioglu, M. Y. (1989), Reservoir transport equations by compositional approach,Transport in Porous Media 4, 369–393.

    Google Scholar 

  • Philip, J. R. and de Vries, D. A. (1957), Moisture movement in porous materials under temperature gradients,EOS Trans. AGU 38(2), 222–232.

    Google Scholar 

  • Pinder, G. F. and Abriola, L. M. (1986), On the simulation of nonaqueous phase organic compounds in the subsurface,Water Resour. Res. 22(9), 109S-119S.

    Google Scholar 

  • Pollock, D. W. (1986), Simulation of fluid flow and energy transport processes associated with high-level radioactive waste disposal in unsaturated alluvium,Water Resour. Res. 22(5), 765–775.

    Google Scholar 

  • Pruess, K. (1987),TOUGH User's Guide. Report LBL-20700, NUREG/CR-4640, 80 pp.

  • Ratigan, J. L. (1984), A finite element formulation for brine transport in rock salt,Int. J. Numer. Anal. Meth. Geomech. 8, 225–241.

    Google Scholar 

  • Roedder, E. (1984), The fluids in salt,American Mineralogist 69, 413–439.

    Google Scholar 

  • Spiers, C. J., Schutjens, P. M. T. M., Brzesowsky, R. H., Peach, C. J., Liezenberg, J. L. and Zwart, H. J. (1990), Experimental determination of constitutive parameters governing creep of rock salt by pressure solution, Geological Society Special Publication No. 54,Deformation Mechanisms, Rheology and Tectonics.

  • Sprackling, M. T. (1985),Liquids and Solids, Student Physics Series, King's College, University of London. Eds. Routledge and Kegan-Paul, London.

    Google Scholar 

  • Yagnik, S. K. (1983), Interfacial stability of migrating brine inclusions in alkali halide single crystals supporting a temperature gradient,J. Crystal Growth 62, 612–626.

    Google Scholar 

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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. Nonisothermal multiphase flow of brine and gas through saline media. Transp Porous Med 15, 271–293 (1994). https://doi.org/10.1007/BF00613282

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  • DOI: https://doi.org/10.1007/BF00613282

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