TY - GEN

T1 - The Efficacy of Thermodynamics in Development of Governing Equations and Constitutive Relations for Saline Solutions in Variably Saturated Porous Media

AU - Burns, E. R.

AU - Dragila, M. I.

AU - Selker, J. S.

AU - Guenther, R. B.

AU - Parlange, J.

AU - Weisbrod, N.

PY - 2004/12/1

Y1 - 2004/12/1

N2 - Relations are presented that describe the behavior of water with high
salt concentrations in variably saturated porous media for isothermal
systems. Equations were derived using classic equilibrium
thermodynamics of closed systems. Resulting corrections for vapor
pressure, liquid pressure, and Darcy coefficients are presented, and an
extension of the relations to non-isothermal systems is proposed. Next,
the governing equations obtained using general process thermodynamics
for continuous systems are presented. A discussion of the usual use of
these equations follows, along with some general observations.
Historically, the principles of Onsager have been employed to develop a
linearly coupled set of forces and fluxes. Except for the reciprocity
relations, which allow the determination of fewer coefficients, little
is gained by this standard approach. A similar set of governing
equations results from simply assuming every flux may be driven by a
gradient in any of the potentials, but this requires estimation of every
coefficient separately. On the other hand, the use of Onsager relations
requires a unique separation of the reversible and irreversible terms in
the energy equation, which is not always a trivial derivation. Either
method guarantees a sufficient number of coefficients requiring
determination that within the experimental uncertainty, it may be
difficult to tell if the physics is really captured, or if there just
exists sufficient freedom of the parameters to fit the data. Results of
recent research indicates that for the case of water movement in the
vicinity of highly concentrated salts, the dilute approximations
extended by use of a more general chemical activity term is sufficient
for modeling the constitutive relations, except in very dry, fine
textured sediments.

AB - Relations are presented that describe the behavior of water with high
salt concentrations in variably saturated porous media for isothermal
systems. Equations were derived using classic equilibrium
thermodynamics of closed systems. Resulting corrections for vapor
pressure, liquid pressure, and Darcy coefficients are presented, and an
extension of the relations to non-isothermal systems is proposed. Next,
the governing equations obtained using general process thermodynamics
for continuous systems are presented. A discussion of the usual use of
these equations follows, along with some general observations.
Historically, the principles of Onsager have been employed to develop a
linearly coupled set of forces and fluxes. Except for the reciprocity
relations, which allow the determination of fewer coefficients, little
is gained by this standard approach. A similar set of governing
equations results from simply assuming every flux may be driven by a
gradient in any of the potentials, but this requires estimation of every
coefficient separately. On the other hand, the use of Onsager relations
requires a unique separation of the reversible and irreversible terms in
the energy equation, which is not always a trivial derivation. Either
method guarantees a sufficient number of coefficients requiring
determination that within the experimental uncertainty, it may be
difficult to tell if the physics is really captured, or if there just
exists sufficient freedom of the parameters to fit the data. Results of
recent research indicates that for the case of water movement in the
vicinity of highly concentrated salts, the dilute approximations
extended by use of a more general chemical activity term is sufficient
for modeling the constitutive relations, except in very dry, fine
textured sediments.

KW - 1866 Soil moisture

KW - 1875 Unsaturated zone

M3 - Conference contribution

VL - 31

BT - American Geophysical Union, Fall Meeting 2004

ER -