THEORY
Here we follow closely the lucid, complete presentation of the chemicalther-
modynamic theory of frozen porous media presented by Brun et al. (1977). Con-
sider three phases, solid (s), liquid (l), and gas (g), which are in thermal, but not
temperature (K) and p is pressure (Pa)]. Their development begins with two sets of
classic equalities:
1. The GibbsDuhem equations, and
2. The Kelvin equations.
GibbsDuhem equations
For each phase, the GibbsDuhem relation holds:
g
g
0 = SmdT Vmdpg + ∑ xBd B
g
g
B
0 = SmdT Vmdpl + ∑ xBdB
l
l
l
l
(1)
B
0 = SmdT Vmdps + ∑ xBds
s
s
s
B
B
g
l
s
where Sm , Sm , and Sm are the molar entropies (J K1 mol1) of the gas, liquid, and
g
s
l
s
solid phases, respectively; Vm , Vm , and Vm , their molar volumes (m3 mol1); xB ,
g
s
l
l
xB , and xB , the mole fraction of component B in the three phases; and B , B , and
s , the chemical potentials (J mol1) of component B in the three phases.
B
Kelvin equations
The Kelvin equations give the pressure gradients across the gas/solid and liq-
uid/solid interfaces in terms of the differential geometry of these interfaces:
dAs,g
s
m
g
s
sg
p p =γ
(2)
g
dVm
dAsgm
l
,
l
s
ls
p p =γ
(3)
l
dVm
where Assm and As,g (m2 mol1) are the molar areas of the liquid/solid and solid/
l
s
,
m
cial tensions.
Capillary pressures of liquid phases can be estimated by applying these equali-
ties. Below we present a summary of the development: first for systems with pure-
water liquid phases, then for aqueous-electrolyte-solution liquid phases.
Systems with pure liquid-water phases
If the solid, liquid, and vapor phases are pure, then eq 1 can be rewritten:
*g
*g
*g
g
0 = Sm,H
Odp + d H
(4)
OdT Vm,H
2O
2
2
0 = Sm,H2OdT Vm,H2Odpl + d*l 2O
*l
*l
(5)
H
0 = Sm,H2OdT Vm,H2Odps + d*s 2O
*s
*s
(6)
H
where the superscript * indicates a pure phase. By taking the partial derivatives of
eq 2 and 3, dpg and dpl can be related to dps by:
2
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