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.

For each phase, the GibbsDuhem relation holds:

g

g

0 = *S*md*T * *V*md*p*g + ∑ *x*Bd B

g

g

B

0 = *S*md*T * *V*md*p*l + ∑ *x*BdB

l

l

l

l

(1)

B

0 = *S*md*T * *V*md*p*s + ∑ *x*Bds

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

s , the chemical potentials (J mol1) of component B in the three phases.

B

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:

d*A*s,g

s

m

g

s

sg

(2)

g

d*V*m

d*A*sgm

l

,

l

s

ls

(3)

l

d*V*m

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.

If the solid, liquid, and vapor phases are pure, then eq 1 can be rewritten:

*g

*g

*g

g

0 = *S*m,H

Od*p *+ d H

(4)

Od*T * *V*m,H

2O

2

2

0 = *S*m,H2Od*T * *V*m,H2Od*p*l + d*l 2O

*l

*l

(5)

H

0 = *S*m,H2Od*T * *V*m,H2Od*p*s + d*s 2O

*s

*s

(6)

H

where the superscript * indicates a pure phase. By taking the partial derivatives of

eq 2 and 3, d*p*g and d*p*l can be related to d*p*s by:

2